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Mechanics and additive manufacturing of bio-inspired polymers
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Mechanics and additive manufacturing of bio-inspired polymers
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Mechanics and Additive Manufacturing of Bio-inspired Polymers by Kun-Hao Yu A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (CIVIL ENGINEERING) August 2022 Copyright [2022] Kun-Hao Yu ii Acknowledgements Firstly, I would like to express my deepest gratitude to Professor Qiming Wang for his continuous support throughout my Ph.D. study and his motivation, patience, and immense knowledge. As an advisor, colleague, and friend, his wise guidance allowed me to grow as a better researcher, educator, and person. It would not be possible to achieve my path without you. I would also like to extend my deepest gratitude to my qualifying and defense committee, Professor Erik A Johnson, Roger Georges Ghanem, Vincent W Lee, and Yong Chen, for their valuable advice and guidance in this dissertation. I also wish to express my sincerest thankfulness to all collaborators, Professor Amy E Childress, Chiara Daraio, Guoliang Huang, Lizhi Sun, Nicholas X Fang, Sami F Masri, Yang Yang, Ying Li, and Yong Chen, for the inspiring and enjoyable collaboration. My journey at USC could not be possible without the fellowship supports from USC-Taiwan Fellowship through the University of Southern California and the Taiwan Ministry of Education, and funding agencies from the National Science Foundation and the Air Force Office of Scientific Research. During my journey at USC, I am incredibly grateful to all my colleagues and friends, Dr. An Xin, Di Wang, Haixu Du, Dr. Hasan Al Ba’ba’a, Kyung Hoon Lee, Ketian Li, Dr. Lily Shi, Dr. Phillip Wang, Dr. Siming Chen, Weijian Ding, Yanchu Zhang, Yanhui Jiang, Dr. Yipin Su, Zheming Gao, and Zhangzhengrong Feng, for their help and support. I would also like to express my greatest appreciation to Professor Chung-Chan Hung at National Cheng Kung University for his selfless support in helping and encouraging me to become a researcher. Finally, I gratefully thank my loved grandfather, grandmother, father, mother, sister, and wife for their understanding, encouragement, and endless love at every moment of my Ph.D. study. Without your support, I would be unable to finish my studies. I love you with all my heart. iii Table of Contents Acknowledgements ......................................................................................................................... ii List of Tables .................................................................................................................................. x List of Figures ................................................................................................................................ xi Abstract ......................................................................................................................................... xv Chapter 1: Introduction and Overview ........................................................................................... 1 1.1 Bio-inspired polymers ........................................................................................................... 1 1.2 Challenges in bio-inspired self-healing polymers ................................................................. 1 1.3 Overview of the dissertation ................................................................................................. 2 Chapter 2: Mechanics of Self-healing Polymer Networks Crosslinked by Dynamic Bonds ......... 5 2.1 Objective ............................................................................................................................... 5 2.2 Introduction ........................................................................................................................... 5 2.3 Theoretical models ................................................................................................................ 8 2.3.1 Theory of original DPNs ............................................................................................ 9 2.3.2 Self-healing behavior of fractured DPNs ................................................................. 16 2.4 Results of the theoretical models ........................................................................................ 22 2.4.1 Diffusion-reaction around the interface ................................................................... 22 2.4.2 Stress-strain behaviors of original and self-healed DPNs ........................................ 23 2.4.3 Effect of key parameters on healing behaviors ........................................................ 25 2.5 Comparison with experimental results ................................................................................ 28 2.5.1 DPNs crosslinked by dynamic covalent bonds ........................................................ 28 2.5.2 DPNs crosslinked by hydrogen bonds ..................................................................... 31 2.5.3 DPNs crosslinked by ionic bonds ............................................................................ 32 2.6 Conclusive remarks ............................................................................................................. 35 Chapter 3: Additive Manufacturing of Self-Healing Elastomers ................................................. 37 3.1 Objective ............................................................................................................................. 37 3.2 Introduction ......................................................................................................................... 37 3.3 Materials and methods ........................................................................................................ 39 3.3.1 Materials. .................................................................................................................. 39 3.3.2 Synthesis and characterization of material inks. ...................................................... 39 3.3.3 Additive manufacturing. .......................................................................................... 39 iv 3.3.4 Photocuring depth test. ............................................................................................. 40 3.3.5 Self-healing test. ....................................................................................................... 41 3.3.6 Self-healable actuator. .............................................................................................. 41 3.3.7 Self-healable composite. .......................................................................................... 41 3.3.8 Self-healable electronics. ......................................................................................... 42 3.4 Results ................................................................................................................................. 42 3.4.1 Molecular design of the self-healable photoelastomer ............................................ 42 3.4.2 Characterization of the self-healing property ........................................................... 45 3.4.3 Competition between photocuring and healing ....................................................... 48 3.4.4 Theoretical modeling of the self-healing behavior .................................................. 49 3.5 Applications of additively manufactured self-healing elastomers ...................................... 50 3.5.1 Self-healable 3D soft actuator. ................................................................................. 50 3.5.2 Self-healable structural composite. .......................................................................... 51 3.5.3 Self-healable architected electronics. ....................................................................... 51 3.6 Discussion ........................................................................................................................... 53 Chapter 4: Mechanics of Light-Activated Self-Healing Polymer Networks ................................ 55 4.1 Objective ............................................................................................................................. 55 4.2 Introduction ......................................................................................................................... 55 4.3 Experiments of hydrogels with inorganic photophores ...................................................... 57 4.4 Theoretical model ............................................................................................................... 59 4.4.1 A general theory for light-activated interfacial healing ........................................... 59 4.4.2 Light-activated production of free radicals .............................................................. 60 4.4.3 Radical-assisted chain binding ................................................................................. 62 4.4.4 Model for soft polymers with nanomaterial photophores ........................................ 66 4.4.5 Model for soft polymers with organic photophores ................................................. 70 4.5 Results for light-activated self-healing polymers with inorganic photophores .................. 72 4.5.1 Results for the light propagation within the TiO2 nanocomposite hydrogel ........... 72 4.5.2 Results for the penetration of the ith chain .............................................................. 75 4.5.3 Results for the light-activated self-healing of soft polymers with nanomaterial photophore ........................................................................................................................ 76 4.5.4 Effect of light intensity ............................................................................................ 78 4.5.5 Effect of light wavelength ........................................................................................ 79 4.6 Results for light-activated self-healing polymers with organic photophores ..................... 80 4.6.1 Effect of photoinitiator concentration. ..................................................................... 83 v 4.7 Conclusive remarks ............................................................................................................. 84 Chapter 5: Tough and Self-Healable Nanocomposite Hydrogels for Repeatable Water Treatment ...................................................................................................................................................... 86 5.1 Objective ............................................................................................................................. 86 5.2 Introduction ......................................................................................................................... 86 5.3 Materials and methods ........................................................................................................ 89 5.3.1 Materials ................................................................................................................... 89 5.3.2 Fabrication of nanocomposite hydrogels ................................................................. 90 5.3.3 Mechanical tests of nanocomposite hydrogels ......................................................... 90 5.3.4 Light-triggered heavy metal adsorption ................................................................... 91 5.3.5 Light-triggered degradation of dye molecules ......................................................... 91 5.4 Results ................................................................................................................................. 91 5.4.1 High toughness of the TiO 2 nanocomposite hydrogel ............................................. 91 5.4.2 Light-assisted self-healing ....................................................................................... 92 5.4.3 Light-assisted heavy-metal adsorption ..................................................................... 94 5.4.4 Light-assisted dye degradation ................................................................................. 97 5.5 Conclusive remarks ............................................................................................................. 99 Chapter 6: Mechanics of Self-healing Thermoplastic Elastomers .............................................. 101 6.1 Objective ........................................................................................................................... 101 6.2 Introduction ....................................................................................................................... 101 6.3 Experiments ...................................................................................................................... 104 6.4 Theoretical model ............................................................................................................. 106 6.4.1 Overview of the material system ........................................................................... 106 6.4.2 Constitutive model of the virgin thermoplastic elastomer ..................................... 106 6.4.3 Interfacial Self-healing model ................................................................................ 114 6.4.4 Summary of the model calculation ........................................................................ 117 6.5 Theoretical results ............................................................................................................. 118 6.5.1 Stress-strain of the virgin thermoplastic elastomer ................................................ 119 6.5.2 Effect of phase fraction on the stress-strain of the virgin material ........................ 120 6.5.3 Stress-strain of the healed thermoplastic elastomer ............................................... 121 6.5.4 Effect of average chain length of soft rubbery phase ............................................. 122 6.6 Comparison with our own experimental results ............................................................... 124 6.7 Comparison with others’ experimental results ................................................................. 126 vi 6.7.1 Disulfide bonds ...................................................................................................... 127 6.7.2 𝜋− 𝜋 interaction ................................................................................................... 127 6.8 Conclusive remarks ........................................................................................................... 128 Chapter 7: Healable, Memorizable, and Transformable Lattice Structures Made of Stiff Polymers .................................................................................................................................................... 130 7.1 Objective ........................................................................................................................... 130 7.2 Introduction ....................................................................................................................... 130 7.3 Materials and methods ...................................................................................................... 132 7.3.1 Materials ................................................................................................................. 132 7.3.2 Preparation of experimental polymer inks ............................................................. 133 7.3.3 Additive manufacturing ......................................................................................... 133 7.3.4 Self-healing characterization .................................................................................. 134 7.3.5 Shape-memory characterization ............................................................................. 134 7.3.6 Manual-contact-assisted healing of octet lattices ................................................... 135 7.3.7 Shape-memory-assisted healing of lattice structures ............................................. 135 7.3.8 Stiffness transformation of honeycomb lattices ..................................................... 136 7.3.9 Vibration transformation of triangle lattices .......................................................... 136 7.3.10 Acoustic transformation of lattice structures ....................................................... 137 7.3.11 Preparation of control 1 and control 2 polymer inks ........................................... 137 7.3.12 Vibration band simulations .................................................................................. 138 7.3.13 Acoustic transmittance simulations ..................................................................... 138 7.4 Results ............................................................................................................................... 139 7.4.1 Design principle for the transformable lattice structures ....................................... 139 7.4.2 Characterization of shape memory and fracture healing ........................................ 142 7.4.3 Manual-contact-assisted healing of lattice structures ............................................ 145 7.4.4 Shape-memory-assisted healing of lattice fractures ............................................... 148 7.4.5 Lattice transformation via fracture-memory-healing cycles .................................. 151 7.5 Discussion ......................................................................................................................... 155 Chapter 8: Photosynthesis Assisted Remodeling of Three-Dimensional Printed Structures ..... 157 8.1 Objective ........................................................................................................................... 157 8.2 Introduction ....................................................................................................................... 157 8.3 Materials and methods ...................................................................................................... 158 8.3.1 Materials ................................................................................................................. 158 vii 8.3.2 Extraction of chloroplasts ...................................................................................... 159 8.3.3 Preparation of polymer inks with and without free NCO groups .......................... 159 8.3.4 Preparation of polymer inks with chloroplasts ...................................................... 160 8.3.5 3D-printing process ................................................................................................ 160 8.3.6 Photosynthesis process in different conditions ...................................................... 161 8.3.7 Characterization of strengthening effect ................................................................ 161 8.3.8 Verification of glucose production from the embedded chloroplasts .................... 162 8.3.9 Characterization of polymer strengthened by glucose ........................................... 162 8.3.10 Effects of chloroplast concentration and illumination time ................................. 162 8.3.11 Freezing chloroplasts with a chilling temperature ............................................... 163 8.3.12 Cleavage of glucose crosslinkers in the strengthened polymer ........................... 163 8.3.13 Local strengthening with an “S” shape ................................................................ 163 8.3.14 Local strengthening with circles .......................................................................... 164 8.3.15 Homogeneous and graded lattice structures ......................................................... 164 8.3.16 3D-printing and strengthening of tree-like structures .......................................... 165 8.3.17 3D-printing and strengthening of Popeye-like structures .................................... 165 8.3.18 Effect of pre-stretch on Photosynthesis-assisted strengthening ........................... 165 8.3.19 Photosynthesis-assisted strengthening under a non-uniform pre-stress distribution. ......................................................................................................................................... 166 8.3.20 Characterization of Photosynthesis-assisted healing ........................................... 166 8.3.21 Photosynthesis-assisted healing of 3D-printed propeller ..................................... 166 8.4 Results ............................................................................................................................... 167 8.4.1 Mechanism of photosynthesis-assisted strengthening ........................................... 167 8.4.2 Photosynthesis-assisted strengthening with patterned light ................................... 174 8.4.3 Photosynthesis-assisted strengthening regulated by pre-loads .............................. 176 8.4.4 Photosynthesis-assisted healing ............................................................................. 178 8.5 Conclusive remarks ........................................................................................................... 181 Chapter 9: Mechanics of Photosynthesis Assisted Polymer Strengthening ............................... 182 9.1 Objective ........................................................................................................................... 182 9.2 Introduction ....................................................................................................................... 182 9.3 Experimental ..................................................................................................................... 185 9.4 Theoretical model ............................................................................................................. 188 9.4.1 Part 1: Glucose production and exportation ........................................................... 189 9.4.2 Part 2: Polymer strengthening by additional crosslinking ..................................... 194 viii 9.5 Results ............................................................................................................................... 201 9.5.1 Results of Part 1 theory .................................................................................................. 202 9.5.2 Results of Part 2 theory .......................................................................................... 203 9.5.3 Results of the integrated theory ............................................................................. 206 9.6 Conclusive remarks ........................................................................................................... 211 Chapter 10: Constructive adaptation of 3D-printable polymers in response to the typically destructive aquatic environment ................................................................................................. 214 10.1 Objective ......................................................................................................................... 214 10.2 Introduction ..................................................................................................................... 214 10.3 Materials and methods .................................................................................................... 217 10.3.1 Materials ............................................................................................................... 217 10.3.2 Synthesis of polymers .......................................................................................... 217 10.3.3 3D printing process .............................................................................................. 217 10.3.4 Characterization of water-induced strengthening ................................................ 218 10.3.5 Localized water-induced strengthening ............................................................... 219 10.3.6 Characterization of water-induced healing and bonding ..................................... 219 10.3.7 Constructive training of robotic arms .................................................................. 220 10.3.8 Strengthening and healing of robotic fish fins ..................................................... 220 10.3.9 Healable packaging polymer for flexible circuits ................................................ 221 10.4 Results ............................................................................................................................. 221 10.4.1 The overall mechanism of constructive adaptation in the aquatic environment .. 221 10.4.2 Water-induced bulk strengthening ....................................................................... 222 10.4.3 Water-induced interfacial healing and bonding ................................................... 225 10.4.4 Constructive training of robotic arms in the aquatic environment ....................... 227 10.4.5 Strengthening and healing of robotic fish fin in the aquatic environment ........... 229 10.4.6 Healable packaging polymers for flexible electronics ......................................... 230 10.5 Conclusive remarks ......................................................................................................... 233 Chapter 11: Conclusions and Outlook ........................................................................................ 234 Appendices .................................................................................................................................. 238 A. Supplementary Information ............................................................................................... 238 SI Tables ......................................................................................................................... 238 SI Figures ........................................................................................................................ 240 ix B. Supplemental Methods ....................................................................................................... 288 B.1 Analytical modeling of disulfide-bond enabled self-healing ................................... 288 B.2 Mathematical model of polymer strengthening by additional crosslinking ............. 300 B.3 Supplies of water and carbon dioxide ...................................................................... 309 References ................................................................................................................................... 312 x List of Tables Table 1. Research status of self-healing soft polymers with dynamic bonds. .............................................. 7 Table 2. Model parameters used in this study. ........................................................................................... 30 Table 3. Definition and value of the employed parameters. ....................................................................... 73 Table 4. Model parameters used in this study. ......................................................................................... 123 Table 5. Definition, value, and estimation source of the employed parameters. ...................................... 213 xi List of Figures Figure 1. Overview of the dissertation ......................................................................................................... 4 Figure 2. Schematics to show the process of a typical self-healing experiment. ......................................... 8 Figure 3. Schematics to illustrate an interpenetrating network model. ...................................................... 10 Figure 4. Schematic and energy landscape of the association-dissociation kinetics. ................................. 12 Figure 5. Examples of chain dynamics behaviors. ..................................................................................... 15 Figure 6. Schematics of the eight-chain network model before and after the cutting process and the diffusion behavior of the polymer chain. .................................................................................................... 18 Figure 7. Healed chain behaviors. .............................................................................................................. 23 Figure 8 Study of stress-strain behaviors. ................................................................................................. 24 Figure 9. Effect of chain length distribution on the healing behaviors. ..................................................... 25 Figure 10. Effect of chain mobility on the healing behaviors. ................................................................... 26 Figure 11. Effect of bond dynamics on the healing behaviors. .................................................................. 27 Figure 12. Modeling of diarylbibenzofuranone self-healing behaviors. .................................................... 29 Figure 13. Modeling of olefin metathesis enabled self-healing. ................................................................ 30 Figure 14. Modeling of DPNs crosslinked by hydrogen bonds. ................................................................ 32 Figure 15. Modeling of DPNs crosslinked by ionic bonds. ....................................................................... 34 Figure 16. Additive Manufacturing of Self-healing elastomers. ................................................................ 45 Figure 17. Characterization of the self-healing property. .......................................................................... 47 Figure 18. Competition between the photocuring and self-healing ........................................................... 49 Figure 19. Applications of additively manufactured self-healing elastomers. ........................................... 53 Figure 20. Experiments of hydrogels with inorganic photophores TiO2 nanocomposite .......................... 59 Figure 21. Two possible pathways for the photoinitiated binding process between an open distal group on a polymer chain and a binding site. ............................................................................................................. 60 Figure 22. Schematics to show the experimental procedure. ..................................................................... 62 xii Figure 23. Schematics to show the polymer chain behaviors around the healing interface. ...................... 66 Figure 24. Schematics of the nanocomposite hydrogel .............................................................................. 67 Figure 25. Schematic of interpenetration network model. ......................................................................... 72 Figure 26. Photoinitiation within the TiO2 nanocomposite hydrogel. ....................................................... 75 Figure 27. The effective concentration of the linked ith chain within the healed region as a function of normalized UV illumination time. .............................................................................................................. 76 Figure 28. Results for the light-activated self-healing of soft polymers with nanomaterial photophore. .. 78 Figure 29. Effect of the light intensity on the self-healing behavior of the TiO2 nanocomposite hydrogel. ..................................................................................................................................................................... 79 Figure 30. Effect of the UV wavelength on the self-healing behaviors of the TiO2 nanocomposite hydrogel. ...................................................................................................................................................... 80 Figure 31. Schematic of the healing process of the thiuram disulfide (TDS) diol. .................................... 81 Figure 32. Results for light-activated self-healing polymers with organic photophores. .......................... 82 Figure 33. Effect of photoinitiator concentration on the self-healing behavior of the polymer with organic photophores. ................................................................................................................................................ 83 Figure 34. Comparison of experimental and theoretical results. ................................................................ 84 Figure 35. Tough and Self-Healable Nanocomposite Hydrogels ............................................................... 89 Figure 36. Results of light-assisted self-healing. ....................................................................................... 94 Figure 37. Results of light-assisted heavy-metal adsorption. ..................................................................... 96 Figure 38. Results of light-assisted dye degradation. ................................................................................. 99 Figure 39. Schematics of healing process ................................................................................................ 104 Figure 40. Experimental results of self-healing thermoplastic elastomer. ............................................... 105 Figure 41. Schematics of the constitutive model ..................................................................................... 107 Figure 42. Proposed network model of the thermoplastic elastomer. ...................................................... 111 Figure 43. Deformation of the viscoelastic-plastic element in element C and D. .................................... 112 Figure 44. Schematics of interfacial self-healing model .......................................................................... 114 xiii Figure 45. Summary of the model calculation ......................................................................................... 118 Figure 46. Stress-strain of the virgin thermoplastic elastomer ................................................................. 120 Figure 47. Effect of the phase fraction on the stress-strain of the virgin material ................................... 121 Figure 48. Stress-strain of the healed thermoplastic elastomer ................................................................ 122 Figure 49. Effect of average chain length of soft rubbery phase ............................................................. 122 Figure 50. Effect of chain mobility .......................................................................................................... 123 Figure 51. Experimental and theoretical results ....................................................................................... 125 Figure 52. Experimental and theoretical results ....................................................................................... 126 Figure 53. Theoretical results of self-healing based on disulfide bonds .................................................. 127 Figure 54. Theoretical results of self-healing based on 𝜋− 𝜋 interaction .............................................. 128 Figure 55. Design principle for transformable lattice structures enabled by fracture and shape-memory- assisted healing. ......................................................................................................................................... 141 Figure 56. Characterization of the shape-memory and self-healing properties. ...................................... 145 Figure 57. Manual-contact-assisted healing of lattice structures. ............................................................ 147 Figure 58. Shape-memory-assisted healing of lattice fractures ............................................................... 150 Figure 59. Lattice transformation enabled by fracture-memory-healing cycles. ..................................... 155 Figure 60. Concept of the photosynthesis-assisted remodeling of 3D-printed structures. ....................... 169 Figure 61. Mechanism of photosynthesis-assisted strengthening ............................................................ 173 Figure 62. Photosynthesis-assisted strengthening with patterned light .................................................... 175 Figure 63. Photosynthesis-assisted strengthening regulated by pre-loads ............................................... 178 Figure 64. Photosynthesis-assisted healing .............................................................................................. 180 Figure 65. Schematics and properties of the photosynthesis-assisted remodeling ................................... 185 Figure 66. Experimental results of photosynthesis-assisted remodeling ................................................. 188 Figure 67. Schematics of glucose production and exportation ................................................................ 189 Figure 68. Light propagation in the materials matrix ............................................................................... 192 Figure 69. Schematics to show the formation of additional crosslinks .................................................... 197 xiv Figure 70. Theoretical results of the production and exportation of glucose ........................................... 203 Figure 71. Theoretical results for various normalized additional crosslink density 𝑛𝑎𝑛0. ..................... 204 Figure 72. Relationships between the step number m and additional crosslink density .......................... 205 Figure 73. Theoretical results for method 2 with m = 3 and 𝑛𝑎𝑛0=2.5. .............................................. 206 Figure 74. FTIR spectra and results of exported glucose concentration .................................................. 208 Figure 75. Effect of the illumination period ............................................................................................. 209 Figure 76. Effect of the chloroplast concentration ................................................................................... 210 Figure 77. Effect of light intensity ........................................................................................................... 211 Figure 78. The overall mechanism of constructive adaptation in the aquatic environment ..................... 216 Figure 79. Water-induced bulk strengthening. ......................................................................................... 224 Figure 80. Water-induced interfacial healing and bonding. ..................................................................... 226 Figure 81. Constructive training of robotic arms in the aquatic environment ......................................... 228 Figure 82. Strengthening and healing of robotic fish fins ........................................................................ 230 Figure 83. Healable packaging polymers for flexible electronics ............................................................ 232 xv Abstract Living organisms are continuous sources of inspiration for engineering materials and structures. However, synthetic materials are typically different from living creatures because the latter consist of living cells to support their metabolisms, such as self-healing, response to stimuli, remodeling, and reproduction. Bio- inspired self-healing materials have been developed to mimic natural living materials to show the spectacular capability of repairing fractures or damages and restoring mechanical strengths. However, existing self-healing polymers still face two central challenges in their development: missing the fundamental understanding of self-healing mechanics and deficiency in 3D shaping. This dissertation aims to provide a comprehensive theoretical understanding of bio-inspired self-healing polymers and propose novel polymer design strategies to address the challenges. This dissertation starts by presenting a general analytical model to understand the interfacial self-healing behaviors of dynamic polymer networks. Based on the theoretical understanding, a self-healable elastomer polymer ink is molecularly designed to enable stereolithography-based additive manufacturing with rapid and full self-healing. Guided by the theoretical and experimental methods, four examples of novel bio-inspired polymer systems are proposed to provide comprehensive scientific advances to solve different engineering problems. In the first example, we propose a theoretical framework to understand the light-activated interfacial self-healing of soft polymers with light-responsive photophores. We introduce a tough and self-healable nanocomposite hydrogel that can be activated by ultraviolet (UV) light to efficiently adsorb heavy metal ions and degrade dye molecules in wastewater. In the second example, we propose a model to understand self-healable thermoplastic elastomers' constitutive and healing behaviors with both dynamic bonds and semi-crystalline phases. We present a class of transformable lattice structures enabled by fracture and shape-memory-assisted healing. In the third example, we harness photosynthesis in chloroplasts embedded in a synthetic polymer matrix to remodel 3D-printed structures and demonstrate matrix strengthening and crack healing. We propose a theoretical framework to model the self- strengthening behaviors of polymers assisted by the photosynthesis process. In the last example, we xvi report a class of 3D-printable synthetic polymers that constructively strengthen their bulk and interfacial mechanical properties in response to the typically destructive aquatic environment. In the end, concluding remarks and an outlook of future work are provided to summarize the dissertation. 1 Chapter 1: Introduction and Overview 1.1 Bio-inspired polymers Nature has developed well-adapted materials and structures over millions of years of evolution. Humans have applied nature’s wisdom to solve design challenges in various engineering applications, for example, underwater vehicles 1,2 , self-cleaning surfaces 3,4 , climbing tools 5,6 , and wind turbine blades 7,8 . However, the mechanical properties of engineering structures continuously weaken during service life because of material fatigue or degradation. By contrast, living organisms can heal and strengthen their mechanical properties within challenging environments. These intrinsic differences between synthetic and natural materials pose a significant challenge to developing sustainable engineering applications. Thanks to the recent advances in material synthesis, bio-inspired polymers that mimic biological systems provide promising opportunities to bridge the gap between synthetic material systems and living organisms 9-11 . Inspired by natural living materials that can autonomously self-heal wounds, scientists have developed bio-inspired self-healing polymers capable of repairing fractures or damages at the microscopic scale and restoring mechanical strength at the macroscopic scale. Self-healing polymers are among the most promising candidates to propose sustainable development solutions with their exceptional properties. Thanks to their healing capability, self-healing polymers have enabled a wide range of applications, such as flexible electronics 12-14 , energy transducers 15,16 , soft robotics 17,18 , lithium batteries 19 , water membranes 20 , and biomedical devices 21 . 1.2 Challenges in bio-inspired self-healing polymers Despite the great success in syntheses and applications of self-healing polymers, existing self-healing polymers are still facing two critical challenges. The first challenge is the theoretical modeling of the interfacial self-healing 11 . In the 1980s, scaling models were proposed for the interpenetration of polymer melts 22,23 . After entering the 21 st century, molecular dynamics simulations were employed to understand the healing behaviors of polymers 24,25 . Although bulk healing 26,27 and high-temperature welding 28 have 2 been modeled in recent years, how to analytically model the interfacial healing is still elusive. The missing of this theoretical understanding would significantly drag down the innovation of self-healing polymers to achieve optimal self-healing performance. The second challenge is that 3D-shaping methods for self-healing polymers are limited. Several promising applications of self-healing polymers demand complex 2D/3D architectures, such as soft robotics 29 , structural composites 30,31 , architected electronics 32 , and biomedical devices 33 . However, the architecture demand for self-healing polymers has not been sufficiently fulfilled because existing 3D methods of shaping self-healing polymers are limited to molding 34,35 and direct-writing 36-38 . In this dissertation, I address the above two challenges by proposing theoretical models to explain the interfacial self-healing behavior of different self-healing polymers and molecularly designing novel bio-inspired self-healing polymers for additive manufacturing to benefit a broad range of engineering applications. 1.3 Overview of the dissertation This dissertation starts with presenting a general analytical model to understand the interfacial self- healing behaviors of dynamic polymer networks (DPNs) in Chapter 2 (Fig. 1). We develop polymer- network based analytical theories that can mechanistically model the constitutive behaviors and interfacial self-healing behaviors of DPNs. The theoretically predicted healing behaviors can consistently match the documented experimental results of DPNs with various dynamic bonds. In Chapter 3, a strategy for photopolymerization-based additive manufacturing of self-healing elastomer structures with free-form architectures is proposed (Fig. 1). The strategy relies on a molecularly designed photoelastomer ink with both thiol and disulfide groups, where the former facilitates a thiol-ene photopolymerization during the additive manufacturing process, and the latter enables a disulfide metathesis reaction during the self-healing process. The rapid additive manufacturing and full healing of the photoelastomer shows potential application in 3D soft actuators, multiphase composites, and architected electronics. 3 In Chapter 4, a theoretical framework is presented to understand the light-activated interfacial self-healing of soft polymers with light-responsive photophores (Fig. 1). The theory considers that the light propagation through the material matrix triggers the production of free radicals that facilitate the interfacial self-healing process. The theory is applied to understand two types of soft polymers with inorganic and organic photophores, respectively. In Chapter 5, a tough and self-healable nanocomposite hydrogel is designed for repeatable water treatment (Fig. 1). The self-healing behavior is enabled by the UV-assisted rebinding of the reversible bonds between the polymer chains and nanoparticle surfaces. The UV-induced free radicals on the nanoparticle can facilitate the binding of heavy metal ions and repeated degradation of dye molecules. In Chapter 6, a theoretical framework is presented to understand the constitutive and healing behaviors of self-healable thermoplastic elastomers with both dynamic bonds and semi-crystalline phases. The theory is applied to explain our own experiments on self-healable thermoplastic elastomers polyurethane and the documented experiments on self-healable thermoplastic elastomers with disulfide bonds and π-π interactions. In Chapter 7, a class of transformable lattice structures enabled by fracture- and shape-memory- assisted healing is proposed (Fig. 1). The lattice structures are additively manufactured with a molecularly designed thermoplastic photopolymer capable of both fracture healing and shape memory. By harnessing the coupling of fracture and shape-memory-assisted healing, we demonstrate reversible configuration transformations of lattice structures to enable switching among property states of different stiffnesses, vibration transmittances, and acoustic absorptions. In Chapter 8, a class of 3D-printable polymers is presented that can be remodeled by the photosynthesis of embedded chloroplasts, to enable matrix-strengthening and crack-healing (Fig. 1). The mechanism relies on a 3D printable polymer that allows for an additional cross-linking reaction with photosynthesis-produced glucose in the material bulk or on the interface. This work provides a unique platform for remodeling engineering materials via the communication between synthetic polymers and natural photosynthesis processes. 4 In Chapter 9, a theoretical framework is developed to model the self-strengthening behaviors of polymers assisted by the photosynthesis process (Fig. 1). The glucose production and exportation of the embedded chloroplasts is modeled with a general photosynthesis theory. A polymer strengthening network model with glucose molecules as additional crosslinkers is presented. The theory can consistently explain the effects of the illumination period, the concentration of embedded chloroplasts, and the light intensity on the stiffness strengthening. In Chapter 10, a class of 3D-printable synthetic polymers is proposed that constructively strengthen their bulk and interfacial mechanical properties in response to the typically destructive aquatic environment (Fig. 1). The water can constructively enhance the polymer’s bulk mechanical properties such as stiffness, tensile strength, and fracture toughness by factors of 746-790%, and the interfacial bonding by a factor of 1000%. In Chapter 11, concluding remarks and an outlook of future work are provided to summarize the dissertation. Figure 1. Overview of the dissertation 5 Chapter 2: Mechanics of Self-healing Polymer Networks Crosslinked by Dynamic Bonds 2.1 Objective Dynamic polymer networks (DPNs) crosslinked by dynamic bonds have received intensive attention because of their special crack-healing capability. Diverse DPNs have been synthesized using a number of dynamic bonds, including dynamic covalent bond, hydrogen bond, ionic bond, metal-ligand coordination, hydrophobic interaction, and others. Despite the promising success in the polymer synthesis, the fundamental understanding of their self-healing mechanics is still at the very beginning. Especially, a general analytical model to understand the interfacial self-healing behaviors of DPNs has not been established. Here, we develop polymer-network based analytical theories that can mechanistically model the constitutive behaviors and interfacial self-healing behaviors of DPNs. We consider that the DPN is composed of interpenetrating networks crosslinked by dynamic bonds. The network chains follow inhomogeneous chain-length distributions and the dynamic bonds obey a force-dependent chemical kinetics. During the self-healing process, we consider the polymer chains diffuse across the interface to reform the dynamic bonds, being modeled by a diffusion-reaction theory. The theories can predict the stress-stretch behaviors of original and self-healed DPNs, as well as the healing strength in a function of healing time. We show that the theoretically predicted healing behaviors can consistently match the documented experimental results of DPNs with various dynamic bonds, including dynamic covalent bonds (diarylbibenzofuranone and olefin metathesis), hydrogen bonds, and ionic bonds. We expect our model to be a powerful tool for the self-healing community to invent, design, understand, and optimize self-healing DPNs with various dynamic bonds. 2.2 Introduction Self-healing polymers have been revolutionizing the originally man-made engineering society through bringing in the autonomous intelligence that widely exists in Nature. Self-healing polymers have been 6 applied to a wide range of engineering applications, including flexible electronics 39 , energy storage 40 , biomaterials 33 , and robotics 34 . Motivated by these applications, the synthesis of self-healing polymers has received tremendous success during the past years 9,11,41-47 . The self-healing polymers usually fall into two categories. The first category is called “extrinsic self-healing” that harnesses encapsulates of curing agents that can be released upon fractures 48-52 . These curing agents can help glue the fractured interfaces, thus restoring the mechanical property of the polymer. The second category is so-called “intrinsic self- healing” which harnesses dynamic bonds that can autonomously reform after fracture or dissociation. The dynamic bonds (Table 1) include dynamic covalent bonds 53-57 , hydrogen bonds 58-63 , ionic bonds 64-70 , metal-ligand coordinations 40,71-75 , host-guest interactions 76,77 , hydrophobic interactions 78,79 , and π-π stacking 80 . Despite the great success in synthesis and applications of self-healing polymers, the fundamental understanding and theoretical modeling have been left behind (Table 1) 11,23,26,27 . Scaling models have been proposed for the interpenetration of polymer melts 22,23,81 . In more recent years, molecular dynamics simulations have been employed to capture the healing properties 24,25,82,83 . However, how to construct an analytical theory for modeling the physical process of the polymer networks crosslinked by various dynamic bonds is still elusive. Yu et al. reported an analytical theory to model the interfacial welding of a polymer under relatively high temperatures 28 ; however, the welding is different from interfacial self- healing in that self-healing behaviors usually occur at relatively low temperatures. In addition, Wang et al. proposed a diffusion-governed self-healing mechanics theory to model the interfacial self-healing behaviors of nanocomposite hydrogels 84 ; however, the model is specifically designed for self-healing networks crosslinked by nanoparticles 64,65,85-97 . The understanding of general self-healing networks crosslinked by general dynamic bonds remains elusive. The missing of this theoretical understanding would significantly drag down the innovation of self-healing polymers to achieve their optimal self- healing performance. 7 Table 1. Research status of self-healing soft polymers with dynamic bonds. Mechanism Representative reference Experiment Simulation Analytical model Dynamic covalent bond 53-57 Yes No This study Hydrogen bond 58-63 Yes No This study Ionic bond 64-70 Yes No This study Metal-ligand coordination 40,71-75 Yes No No Host-guest interaction 76,77 Yes No No Hydrophobic association 78,79 Yes No No π-π stacking 80 Yes No No Nanoparticle 64,65,85,87,90,92,94,96,97 Yes 25,98 84 Here, we consider general polymer networks crosslinked by dynamic bonds, named as dynamic polymer networks (DPNs). We model a typical healing experiment of a DPN polymer in Fig. 2. A DPN polymer with dynamic bonds in a rod sample-shape is first cut/broken into two parts, and then immediately brought into contact for a certain period of healing time. The self-healed sample is then uniaxially stretched until the sample fracture. The key process of this healing experiment is the interpenetration and bond-reformation of polymer chains with dynamic bonds around the healing interface. Here, we develop polymer-network based analytical theories that can mechanistically model the constitutive behaviors and interfacial self-healing behaviors of DPNs. We consider that the DPN is composed of interpenetrating networks crosslinked by dynamic bonds. The network chains follow inhomogeneous chain length-distributions and the dynamic bonds obey a force-dependent chemical kinetics. During the self-healing process, we consider the polymer chains diffuse across the interface to reform the dynamic bonds, which is modeled using a diffusion-reaction theory. The theories can predict the stress-stretch behaviors of original and self-healed DPNs. We show that the theoretically predicted healing behaviors can consistently match the documented experimental results of DPNs with various dynamic bonds, including dynamic covalent bonds (diarylbibenzofuranone and olefin metathesis), hydrogen bonds, and ionic bonds. We expect our model to become a powerful tool for the self-healing community to invent, design, understand, and optimize self-healing DPNs with various dynamic bonds. 8 Figure 2. Schematics to show the process of a typical self-healing experiment. An original sample is first cut/broken into two parts and then brought into contact for a healing time. Subsequently, the sample is stretched to measure the healing performance. The plan of this study is as follows. In section 2.3, we construct the theoretical frameworks for the constitutive behaviors of the original DPNs, and the interfacial self-healing behaviors of the self- healed DPNs. In section 2.4, we present the theoretical results of the models and discuss the effect of chain-length distribution, bond dynamics, and chain mobility on the theoretical results. Section 2.5 focuses on three representative dynamic bonds including covalent dynamic bonds, hydrogen bond, and ionic bonds to discuss how the theoretical framßework can be applied to explain the self-healing behaviors of these DPNs. The conclusive remarks are presented in section 2.6. 2.3 Theoretical models We will introduce theoretical models to first consider the constitutive behaviors of original DPNs and then the interfacial self-healing behaviors of fractured DPNs. 9 2.3.1 Theory of original DPNs 2.3.1.1 Interpenetrating network model We assume that the polymer is composed of m types of networks interpenetrating in the material bulk space (Fig. 3) 99 . The ith network is composed of the ith polymer chains with Kuhn segment number. The length of the ith chain at the freely joint state is determined by the Kuhn segment number as (2-1) where b is the Kuhn Segment length. Researchers usually denote the “chain length” as 100 . Without loss of generality, the Kuhn segment number follows an order . We denote the number of ith chain per unit volume of material as . Therefore, the total chain number per unit volume of material is (2-2) The chain number follows a statistical distribution as (2-3) The summation of the statistical distribution function is a unit, i.e., . This chain-length distribution is usually unknown if without a careful experimental examination. Although researchers usually accept that chain length is non-uniform but should follow a chain-length distribution as shown in Eq. 2-3 101 , the most prevailing model for the rubber elasticity still considers the uniform chain length, such as three-chain model, four-chain model, and eight-chain model 100,102,103 . The consideration of non- uniform chain-length to model the elasticity behaviors of rubber-like materials was recently carried out by Wang et al. 99 . Because of the limited experimental technique to characterize the chain length distribution to date, the selection of chain-length distribution is still a little ambiguous. Wang et al. tested a number of chain-length distribution functions including uniform, Weibull, normal, and log-normal, and found that the log-normal distribution can best match the material’s mechanical and mechanochemical behaviors 99 . In this study, we will simply employ the log-normal chain-length distribution (more in sections 2.4 and 2.5), while other distributions may also work for our model. i n i n b n r i i = 0 i n m n n n £ £ ..... 2 1 i N å = = m i i N N 1 ( ) N N n P i i i = 1 1 = å = m i i P 10 For the ith chain, if the end-to-end distance at the deformed state is , the chain stretch is (2-4) The free energy of the deformed ith chain can be written as (2-5) where is the Boltzmann constant, is the temperature in Kelvin, and is the inverse Langevin function. Considering the chain as an entropic spring, the force within the deformed ith chain can be written as (2-6) Figure 3. Schematics to illustrate an interpenetrating network model. m types of networks interpenetrate in the material bulk space. The ith network is composed of the ith polymer chains with Kuhn segment number 𝒏 𝒊 (𝟏≤𝒊≤𝒎). Each type of polymer chain self-organizes into eight-chain structures. To link the relationship between the macroscopic deformation at the material level and the microscopic deformation at the polymer chain level, we consider an interpenetrating model as shown in Fig. 3 99 . We assume the ith chains assemble themselves into regular eight-chain structures. We assume i r 0 i i i r r = L ÷ ÷ ø ö ç ç è æ + = i i i i B i i T k n w b b b b sinh ln tanh B k T ( ) i i i n L L = -1 b ( ) 1 - L i B i i i b T k r w f b = ¶ ¶ = 11 the material follows an affined deformation model 100,103 , so that the eight-chain structures deform by three principal stretches ( ) under the macroscopic deformation ( ) at the material level. Therefore, the stretch of each ith chain is (2-7) At the undeformed state, the number of ith chain per unit material volume is . However, as the material is deformed, the active ith chain is decreasing because the chain force promotes the dissociation of the dynamic bonds. We assume at the current deformed state, the number of active ith chain per unit material volume is . Since every ith chain undergoes the same stretch , the total free energy of the material per unit volume is (2-8) where and is given in Eq. 2-7. Note that we ignore the chain entanglement effect in this interpenetration model and the following self-healing model; the entanglement contribution to hyperelastic materials can be found in other works, such as 104-107 . If the material is incompressible and uniaxially stretched with three principal stretches ( ), the nominal stress along direction can be written as (2-9) 2.3.1.2 Association-dissociation kinetics of dynamic bonds Next, we consider the association-dissociation kinetics of dynamic bonds (Fig. 4). We model the bond association and dissociation as a reversible chemical reaction 108,109 . The forward reaction rate (from associated state to dissociated state) is and reverse reaction rate is . For simplicity, we assume that only two ends of a chain have ending groups for the dynamic bond 24 . If two end groups are associated, 3 2 1 , , l l l 3 2 1 , , l l l 3 2 3 2 2 2 1 l l l + + = L i i N a i N i L å = ÷ ÷ ø ö ç ç è æ + = m i i i i i B i a i T k n N W 1 sinh ln tanh b b b b ( ) i i i n L L = -1 b i L 2 / 1 3 2 1 , - = = = l l l l l 1 l ( ) å = - - - - ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ + + - = m i i i a i B n L n N T k s 1 1 2 1 1 2 2 1 3 2 6 3 l l l l l l f i k r i k 12 we consider this chain as “active”; otherwise, the chain is “inactive”. A chemical reaction shown in Fig. 4a averagely involves one polymer chain; that is, the chemical reaction represents the transition between an active chain and an inactive chain. Here we denote the active ith chain per unit volume is and the inactive ith chain per unit volume is . The chemical kinetics can be written as (2-10) Since the total number of ith chain per unit volume defined as , the chemical kinetics can be rewritten as (2-11) Figure 4. Schematic and energy landscape of the association-dissociation kinetics. (a) Schematic to show the association-dissociation kinetics of the dynamic bond on the ith chain. We consider the reaction from associated state to dissociated state as the forward reaction of the ith chain with reaction rate 𝑘 " # (1≤𝑖 ≤𝑚), and corresponding reaction from the dissociated state to associated state as the reverse reaction with reaction rate 𝑘 " $ . (bc) Potential energy landscape of the reverse reaction of the dynamic bond on the ith chain with chain force (b) 𝑓 " =0 and (c) ) 𝑓 " ≠0. “A” stands for the associated state, “D” stands for the dissociated state, and “T” stands for the transition state. a i N d i N d i r i a i f i a i N k N k dt dN + - = d i a i i N N N + = ( ) i r i a i r i f i a i N k N k k dt dN + + - = 13 At the as-fabricated undeformed state, the reaction rates are and , respectively. As the material is fabricated as an integrated solid, we simply assume the association reaction is much stronger than the dissociation reaction at the fabricated state, i.e., . Therefore, most of the ith chains are at the associated state, as the equilibrium value of at the undeformed state is (2-12) At the deformed state, the ith chain is deformed with stretch . Since the bond strength of the dynamic bonds is much weaker than those of the permanent bonds such as covalent bonds, the chain force would significantly alter the bonding reaction 108,109 . Specifically, the chain force tends to pull the bond open to the dissociated state. This point has been well characterized by Bell model for the ligand-receptor bonding for the cell adhesion behaviors, as well as for biopolymers 110 . We here adopt the Bell-like model and consider the energy landscape between the associated state and dissociated state as shown in Fig. 4b 99 . We consider an energy barrier exists between the associated state (denoted as “A”) and dissociated state (“D”) through a transition state (“T”). At the undeformed state of the ith chain, the energy barrier for A D transition is and the energy barrier for D A transition is . Under the deformed state of the ith chain, the chain force lowers down the energy barrier of A D transition to and increases the energy barrier for D A transition to , where is the distance along the energy landscape coordinate (Fig. 4c). Since the occurrence of the chemical reaction requires the overcoming of the energy barriers, the higher energy barrier is corresponding to the lower likelihood of the reaction. According to the Bell model, the reaction rates are governed by the energy barrier through exponential functions as 110,111 . (2-13a) (2-13b) 0 f i f i k k = 0 r i r i k k = 0 0 r i f i k k << a i N i i f i r i r i a i N N k k k N » + = 0 0 0 i L ® f G D ® r G D i f ® x f G i f D - D ® x f G i r D + D x D ÷ ÷ ø ö ç ç è æ D = ÷ ÷ ø ö ç ç è æ D - D - = T k x f k T k x f G A k B i f i B i f f i exp exp 0 ÷ ÷ ø ö ç ç è æ D - = ÷ ÷ ø ö ç ç è æ D + D - = T k x f k T k x f G B k B i r i B i r r i exp exp 0 14 Where A and B are constants and is treated as a fitting parameter for a given material. We first consider the initially-undeformed material is suddenly loaded with a deformation state ( ) at t = 0 and then deformation remains constant. The reaction rates are time independent. Therefore, the active ith chain number per unit material volume can be calculated as (2-14) In Eq. 2-14, the force in the ith chain is constant. Therefore, we can rewrite Eq. 2-14 as (2-15) Over a period of loading time, the active ith chain number per unit volume in Eq. 2-15 decreases from to a plateau with a value (Fig. 5a). The required timescale is the characteristic time scale of the chemical reaction. If the material is loaded with increasing stretch ( ), the chemical reaction rates are both time-dependent. In solving the chemical kinetics, we have to consider the time-dependent behavior of the reaction rates and solve the equation numerically. In a more common case, we apply the load with a very small loading rate, so that the deformation of the material is usually assumed as quasi- static. It means that in every small increment of the load, the chemical reaction already reaches its equilibrium state with an equilibrium active ith chain number . Under this condition, the active ith chain number per unit material volume is expressed as x D 2 / 1 3 2 1 , - = = = l l l l l ú ú ú ú ú ú û ù ê ê ê ê ê ê ë é + ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ ÷ ÷ ø ö ç ç è æ D - + ÷ ÷ ø ö ç ç è æ D - ÷ ÷ ø ö ç ç è æ D - ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ ÷ ÷ ø ö ç ç è æ D - + ÷ ÷ ø ö ç ç è æ D - = ò ò ò i t B i r i B i f i i B i r i t B i r i B i f i a i N d d T k x f k T k x f k N T k x f k d T k x f k T k x f k N 0 0 0 0 0 0 0 0 exp exp exp exp exp exp exp t V t t i f ÷ ÷ ø ö ç ç è æ D - + ÷ ÷ ø ö ç ç è æ D ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ ÷ ÷ ø ö ç ç è æ D - + ÷ ÷ ø ö ç ç è æ D - ÷ ÷ ø ö ç ç è æ D - + ÷ ÷ ø ö ç ç è æ D - = T k x f k T k x f k t T k x f k T k x f k T k x f k T k x f k N N B i r i B i f i B i r i B i f i B i f i B i r i i a i exp exp exp exp exp exp exp 0 0 0 0 0 0 a i N i N ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ D - + ÷ ÷ ø ö ç ç è æ D ÷ ÷ ø ö ç ç è æ D - T k x f k T k x f k T k x f k N B i r i B i f i B i r i i exp exp exp 0 0 0 2 / 1 3 2 1 , - = = = l l l l l a i N 15 (2-16) with the chain force as expressed in Eq. 2-6. As shown in Fig. 5b, decreases from to near-zero at various speeds for various chain lengths, because different chain lengths are corresponding to different chain forces. Once is solved, it can be plugged into Eq. 2-9 to obtain the stress-stretch behaviors of the DPNs. As shown from Eq. 2-16, the density of active ith chain should decrease as the chain force increases. This molecular picture is different from the dynamic polymers with bond exchange reactions, for which the density of associated bonds is assumed as constant during the network evolution 28 . Figure 5. Examples of chain dynamics behaviors. (a) The active ith chain number in functions of the loading time of various constant uniaxial stretch. (b) The active ith chain number of various chain length 𝑛 " in functions of the quasi-statically increasing uniaxial stretch. The used parameters can be found in Table 2. 2.3.1.4 Additional consideration In addition to the above association-dissociation kinetics, we also consider two supplementary points. The first one is the network alteration. During the mechanical loading, a portion of dissociated short chains may reorganize to become active long chains 112,113 . To capture this effect, we follow the network alteration theory to model the number of active chains to be an exponential function of the chain stretch as ÷ ÷ ø ö ç ç è æ D - + ÷ ÷ ø ö ç ç è æ D ÷ ÷ ø ö ç ç è æ D - = T k x f k T k x f k T k x f k N N B i r i B i f i B i r i i a i exp exp exp 0 0 0 i f a i N i N a i N i L 16 (2-17) where is the chain alteration parameter. Similar network alteration model has been employed to model the chain reorganization for the Mullin’s effect of rubber 112,113 , double-network hydrogels 114 , and nanocomposite hydrogels 115 . It has been shown that the network alteration is a unique network damage mechanism that facilitates the stiffening effect of the stress-stretch curve 112,113,115 . Since the effect of network alteration on the stress-strain behaviors of polymer networks has been clearly demonstrated in the existing literature 115 , we would not discuss in details about their effects in this study, and just harness this network alteration effect to better capture the stress-stretch curve shapes of the original DPNs. The second point is about the full dissociation when the chain length is longer than the length limit of the chain. The fully extended length of the ith chain is with a stretch as . If the stretch of the ith chain is larger than , the dynamic bond will be fully dissociated. This can be expressed as , if (2-18) 2.3.2 Self-healing behavior of fractured DPNs We consider a DPN polymer sample shown in Fig. 2. We cut the sample into two parts and then immediately contact back. After a certain period of healing time t, the sample is uniaxially stretched until breaking into two parts again. If the healing is not fully, the breaking point will be at the healing interface; however, if the healing is close to 100%, the breaking point should be distributed stochastically through the whole sample. Here, we consider the self-healed sample is composed of two segments (Fig. 2): Around the healing interface, the polymer chain would diffuse across the interface to form new networks through forming new dynamic bonds. We call this region as “self-healed segment”. Away from the self- healed segment, the polymer networks are intact, and we call this region as “virgin segment”. ( ) [ ] 1 exp - L = i i a i N N a a b n i ( ) i i i n b n b n = i n 0 = a i N i i n ³ L 17 2.3.2.1 Behavior of the self-healed segment As we assume in section 2.3.1, the ith chains form network following eight-chain structures (Fig. 6a). For simplicity of analysis, we assume the cutting position is located at a quarter part of the eight- chain cube, namely the center position between a corner and the center of the eight-chain cube (Fig. 6a). The cutting process forces the polymer chains to be dissociated from the dynamic bond around the corner or center positions. This assumption is based on the Lake-Thomas theory that assumes that the chain force is transferred through every Kuhn segment on the chain, and under the same chain force, the dynamic bonds with much weaker strengths are expected to break sooner than the permanent bonds 116 . Since we immediately contact the material back, we assume the ending groups of the dynamic bonds are still located around the cutting interface, yet without enough time to migrate into the material matrix (Fig. 6b) 84 . Driven by weak interactions between ending groups of the dynamic bonds, the ending groups on the interface will diffuse across the interface to penetrate into the matrix of the other part of the material to form new dynamic bonds. Specifically in Fig. 6b, the ending groups of the part A will penetrate into part B towards the center position of the cube, and the ending groups of part B will penetrate into Part A towards the corner positions of the cube. These interpenetration behaviors can be simplified as a 1D model shown in Fig. 6c. As shown in Fig. 6c, an open ending group around the interface penetrates into the other part of the material to find another open ending group to form a dynamic bond. Once the dynamic bond reforms, the initially “inactive” chain becomes “active”. This behavior can be understood as two processes: chain diffusion and ending group reaction. 18 Figure 6. Schematics of the eight-chain network model before and after the cutting process and the diffusion behavior of the polymer chain. (a, b) Schematics of the eight-chain network model before and after the cutting process. The cutting is assumed to be located in a quarter position of the cube. (c) A schematic to show the diffusion behavior of the ith polymer chain across the interface. To model the chain diffusion, we consider a reptation-like model shown in Fig. 6c 100,117-119 . We assume the polymer chain diffuses along its contour tube analogous to the motion of a snake. The tube diameter is assumed as much smaller than the chain length. The motion of the polymer chain is enabled by extending out small segments called “minor chains”. The curvilinear motion of the polymer chain is characterized by the Rouse friction model with the curvilinear diffusion coefficient of the ith chain written as (2-19) where is the Rose friction coefficient per unit Kuhn segment. In the original reptation model, the contour length of the primitive chain is considered as , where a is a step length of the primitive chain 117,120 . The step length a is an unknown parameter that depends on the statistical nature of the network and is of the order of the mesh side of the network. Conceptually, we may assume a=b, then the contour length of the primitive chain will be approximated as . x i B i n T k D = x a b n i 2 b n i 19 We note that the chain motion follows a curvilinear path; therefore, we construct two coordinate systems s and y, where s denotes the curvilinear path along the minor chains and y denotes the linear path from the interface to the other open ending group. When the ith chain moves distance along the curvilinear path, it is corresponding to distance along y coordinate. Here we assume the selection of the curvilinear path is fully stochastic following the Gaussian statistics 121-123 . Therefore, the conversion of the distances in two coordinate systems is expressed as (2-20) According to the eight-chain cube assumption, the distance between the corner and the center within the ith network cube at its freely joint state is (2-21) The distance between the ending group around the interface and the other ending group in the matrix is . According to Eq. 2-21, the positions and are corresponding to and , respectively. If we only consider the polymer chain diffusion, the diffusion of the ith chain can be modeled with the following diffusion equation along the curvilinear coordinate s, (2-22) where is the inactive ith chain number per unit length (with unit area) along the coordinate s ( ) at time t. However, the chain behavior is more complicated than just diffusion, because during the diffusion the ending group would encounter another ending group to undergo a chemical reaction to form a new dynamic bond. Although the chemical reaction may only occur around the ending group within the material matrix (relatively immobile ending group at ), the reaction forms dynamic bonds to transit an inactive chain into an active chain, and this reaction would reduce the amount of the inactive ending groups and further drive the motion of the other inactive ending groups. Therefore, the chain diffusion and ending group reaction actually are strongly coupled. Therefore, we consider an i s i y b s y i i = b n L i i » 2 i L 0 = y 2 i L y= 0 = s b L s i 4 2 = ( ) ( ) 2 2 , , s s t C D t s t C d i i d i ¶ ¶ = ¶ ¶ ( ) s t C d i , b L s i 4 0 2 £ £ b L s i 4 2 = 20 effective diffusion-reaction model to consider the effective behaviors of the chain and the ending group as 124 (2-23) (2-24) where is the active ith chain number per unit length (with unit area) along the coordinate s ( ) at time t. As the polymer chain is freely joint during the diffusion process, we here use the chemical reaction rates and . In the initial state of the self-healing, all mobile open-ending groups of the ith chains are located around the healing interface. Therefore, the initial condition of the diffusion-reaction model is (2-25) (2-26) where . For a self-healing polymer that is capable of forming a stable solid form and enabling relatively short healing time, the basic requirement is . This requirement means that the association reaction is stronger than the dissociate reaction. Otherwise, the polymer is unstable under external perturbations. Here, we further focus our attention on polymers with good healing capability, so that the polymers can easily self-heal under relatively mild conditions. This requirement further implies that should be much larger than , i.e., . Under this condition, Eqs. 2-23-24 can be reduced as (2-27) At the same time, around the location , all open ending groups form dynamic bonds. This leads to the vanishing of inactive chains around the location , written as ( ) ( ) ( ) t s t C s s t C D t s t C a i d i i d i ¶ ¶ - ¶ ¶ = ¶ ¶ , , , 2 2 ( ) ( ) ( ) s t C k s t C k t s t C a i f i d i r i a i , , , 0 0 - = ¶ ¶ ( ) s t C a i , b L s i 4 0 2 £ £ 0 f i k 0 r i k ( ) ( ) s N s t C i d i d = = , 0 ( ) 0 , 0 = = s t C a i ( ) 1 = ò ¥ ¥ - ds s d 0 0 r i f i k k < 0 r i k 0 f i k 0 0 f i r i k k >> ( ) ( ) ( ) s t C k s s t C D t s t C d i r i d i i d i , , , 0 2 2 - ¶ ¶ = ¶ ¶ b L s i 4 2 = b L s i 4 2 = 21 (2-28) Along with above initial and boundary conditions, the reaction-diffusion equation (Eq. 2-27) can be solved analytically or numerically. Once in the diffusion-reaction model (Eq. 2-27) is solved, we can further obtain the active ith chain number per unit volume of the self-healing segment at healing time t, written as (2-29) where is for the self-healed segment at the undeformed state ( ), and the superscript “h” denotes “healed”. At the deformed state, the active ith chain number in the self-healed segment decreases with the increasing stretch. If we consider a quasistatic load with principal stretches ( ), the active ith chain number per unit volume of the self-healing segment can be calculated as (2-30) with the chain force expressed as (2-31) Therefore, the free energy per unit volume of the self-healed segment can be written as (2-32) where and is given by Eq. 2-30. The nominal stress along direction can be written as ( ) 0 4 , 2 = = b L s t C i d i ( ) s t C d i , ( ) ( ) ò - = b L i d i i i h i i ds N s t C L b N t N 4 0 2 2 , 4 1 ( ) t N h i 1 3 2 1 = = = l l l ( ) 2 / 1 3 2 1 , - = = = h h l l l l l ( ) ( ) ÷ ÷ ø ö ç ç è æ D - + ÷ ÷ ø ö ç ç è æ D ÷ ÷ ø ö ç ç è æ D - = T k x f k T k x f k T k x f k t N t N B i r i B i f i B i r i h i ah i exp exp exp 0 0 0 ( ) ( ) ÷ ÷ ÷ ø ö ç ç ç è æ + = - - i h h B i n L b T k f 3 2 1 2 1 l l ( ) å = ÷ ÷ ø ö ç ç è æ + = m i h i h i h i h i B i ah i h T k n t N W 1 sinh ln tanh b b b b ( ) ( ) [ ] ÷ ø ö ç è æ + = - - i h h h i n L 3 2 1 2 1 l l b ( ) t N ah i 1 l 22 (2-33) where t is the healing time and is the uniaxial stretch in the self-healed segment. 2.3.2.2 Behavior of the self-healed sample We consider a self-healed sample (length ) with a self-healed segment (length , ) and two virgin segments (Fig. 2). Under a uniaxial stretch, the lengths of the whole sample and the self-healed segment become and , respectively. The stretch of the self-healed segment is . The stretch of the virgin segment is approximately equal to the stretch of the whole sample because . We assume the initial cross-sections of the virgin segment and the self-healed segment are the same; then, the uniaxial nominal stresses in the self-healed segment and the virgin segment should be equal, written as (2-34) where is referred to Eq. 2-33, and is referred to Eq. 2-9. From Eq. 2-34, we can determine the stress-stretch behaviors of the self-healed sample for various healing time t. 2.4 Results of the theoretical models We first discuss results of the diffusion-reaction model for the interpenetration of polymer chains, and then predict the stress-stretch behaviors of original DPNs and self-healing DPNs. We further predict the healing strength in a function of the healing time, and discuss how chain distribution, chain mobility, and bond reaction dynamics affect the healing behavior. 2.4.1 Diffusion-reaction around the interface Using the Danckwert’s method, we can solve in Eq. 2-27 as 124 (2-35) ( ) ( ) ( ) ( ) ( ) ( ) ( ) å = - - - - ú ú ú û ù ê ê ê ë é ÷ ÷ ÷ ø ö ç ç ç è æ + + - = m i i h h i ah i h h B h h h h n L n t N T k t s 1 1 2 1 1 2 2 1 3 2 6 3 , l l l l l l l h l H h H H H h << h h h h h h H h = l l ( ) ( ) h h H H h h H h - - » = l ( ) ( ) l l 1 1 s s h h = ( ) h h s l 1 ( ) l 1 s ( ) s t C d i , ( ) ( ) ( ) ) exp( , ) exp( , , 0 0 0 0 t k s t C d k s C k s t C r i d i t r i d i r i d i - + - = ò t t t 23 (2-36) Through Eq. 2-29, we can obtain the healed ith chain number in a function of the healing time t. As shown in Fig. 7a, we plot the normalized healed ith chain number in functions of normalized healing time for various normalized reverse reaction rate . The initially zero normalized healed ith chain number gradually increases until the plateau 1. Here, we define the time for 90% healing as the equilibrium diffusion-reaction time . We find that decreases as increasing reverse reaction rate. It is because higher reverse reaction rate would drive the movement of the polymer chain to be faster, thus enabling a smaller . Figure 7. Healed chain behaviors. (a) The normalized healed ith chain number in functions of normalized time for various normalized reverse reaction rate . (b) The normalized equilibrium time in a function of the normalized reverse reaction rate. 2.4.2 Stress-strain behaviors of original and self-healed DPNs In this section, we discuss examples of stress-stretch behaviors of original and self-healed DPNs. For simplicity, we only consider a log-normal chain length distribution as 99 (2-37) where and are the mean of and standard deviation of , respectively. As an example, we plot a chain length distribution shown in Fig. 8a. As discussed in section 2.3, the application of the stretching ( ) ( ) ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ - - - ÷ ÷ ø ö ç ç è æ - = t D b L s t D s t D N s t C i i i i i d i 4 2 exp 4 exp 4 2 , 2 2 2 p ( ) t N h i ( ) i h i N t N 4 2 16 i i L t D b t = ( ) ( ) t D b L k k i i r i r i 2 4 0 0 16 = e t e t e t 4 2 16 i i L t D b t = ( ) ( ) t D b L k k i i r i r i 2 4 0 0 16 = e t ( ) ( ) ú ú û ù ê ê ë é - - = 2 2 2 ln ln exp 2 1 d p d a i i i i n n n n P a n d i n i n ln 24 force would destabilize the association-dissociation kinetics of the dynamic bonds and decrease the number of active chains. As the stretch increases, the corresponding stress first increases. As the decreased active chain number reaches a certain level, the stress reaches a peak point and then begins to decrease (Fig. 8b). Stress at the peak point is corresponding to the strength of the DPN . As the self-healed sample, we first calculate the healed ith chain number in the self-healed segment, and then obtain the self-healed stress-strain behaviors from Eq. 2-33. Using Eq. 2-34, we subsequently determine the stress-stretch behavior of the self-healed sample that is composed of a self- healed segment and two virgin segments (Fig. 8c). We plot the example stress-stretch behaviors of the self-healed samples for various healing time in Fig. 8c. We define a parameter called healing strength ratio , where is the strength of the self-healed sample under uniaxial stretch. The healing strength ratio increases with increasing healing time t until the plateau 100% (Fig. 8d). We further define the healing time corresponding to 90% healing strength ratio as the equilibrium healing time . Figure 8. Study of stress-strain behaviors. (a) Active ith chain number distribution evolution under various uniaxial stretches. (b) The predicted stress-stretch behaviors of the original sample under quasi-statically increasing uniaxial stretches. (c) Predicted stress-stretch curves of original and self-healed samples under quasi-statically increasing max s ( ) t N h i max max s s h = h h s max h eq t 25 uniaxial stretches. (d) The predicted healing strength ratio in a function of healing time. The healing time corresponding to 90% healing strength ratio is defined as the equilibrium healing time 𝑡 % & . The used parameters can be found in Table 2. 2.4.3 Effect of key parameters on healing behaviors Once the calculation methods for the stress-stretch behaviors of the original and self-healed DPNs are established, we further discuss the effects of some key factors on the healing behaviors in this section. These factors include the chain length, the chain mobility, and the bond dynamics. Figure 9. Effect of chain length distribution on the healing behaviors. (a) The chain length distributions for various average chain length . (b) The predicted stress-stretch curves of the original sample under quasi-statically increasing uniaxial stretches. (c) The predicted healing strength ratios in functions of healing time. (d) The predicted equilibrium healing time in a function of average chain length . The used parameters are the same as those used in Fig. 8 except . 2.4.3.1 Effect of chain length We consider the chain length within the polymer matrix follows a certain log-normal distribution. The probability of the chain length distributes over a wide range with the highest probability at the average chain length . As the average chain length changes, the chain length distribution shifts (Fig. 9a). With increasing average chain length , the original DPN becomes more stretchable (Fig. 9b). At the a n eq t a n a n a n a n a n 26 same time, according to Eq. 2-19, the effective diffusion coefficient decreases as the average chain length increases. With the same bond kinetics, the healing process of the DPN should become slower. As shown in Figs. 9cd, the theory predicts that the equilibrium healing time of the DPN increases with increasing average chain length . 2.4.3.2 Effect of chain mobility The chain mobility is represented by the Rouse friction coefficient . When the chain is less mobile within the matrix, the Rouse friction coefficient becomes larger. Rouse friction coefficient may not affect the stress-stretch behaviors of the original DPNs. However, according to Eq. 2-19, the effective diffusion coefficient of the polymer chains decreases as the Rouse friction coefficient increases, and subsequently, the healing process becomes slower. As shown in Figs. 10ab, the equilibrium healing time of the DPN increases with increasing Rouse friction coefficient . Figure 10. Effect of chain mobility on the healing behaviors. (a) The predicted healing strength ratios in functions of healing time for various Rouse friction coefficients . (b) The predicted equilibrium healing time in a function of Rouse friction coefficients. The used parameters are the same as those used in Fig. 8 except Rouse friction coefficients . 2.4.3.3 Effect of bond dynamics The association-dissociation bond dynamics is represented by the forward and reverse reaction rates of the ith chain and , respectively. As we consider the forward reaction rate is much smaller than the reverse reaction rate, we fix forward reaction rate as and vary the reverse a n x x x x x x eq t x 0 f i k 0 r i k 1 7 0 10 2 - - ´ = s k f i 27 reaction rate to examine its effect on the healing behavior (Fig. 11). With increasing reverse reaction rate (reverse reaction is from dissociated state to the associated state), the associated state is less likely to be destabilized by the chain force; therefore, the strength and stretchability of the original DPNs increase (Fig. 11a). During the self-healing process, the higher reverse reaction rate promotes the re- formation of the dynamic bonds, thus speeding the healing process. Therefore, with increasing reverse reaction rate , the equilibrium healing time of the DPNs decreases (Fig. 11bc). It is noted that during the self-healing process, two processes coexist: chain diffusion and association-dissociation bond dynamics. As increases to a sufficiently large value, the bond dynamics timescale is much smaller than the chain diffusion timescale. Under this condition, the self-healing timescale is mainly governed by the chain diffusion, and the change of the reverse reaction rate may not affect the self-healing time scale anymore. As shown in Fig. 11c, when , the equilibrium healing time only changes slightly with increasing reverse reaction rate . Figure 11. Effect of bond dynamics on the healing behaviors. 0 r i k 0 r i k 0 r i k 0 r i k 1 4 0 10 3 - - ´ > s k r i 0 r i k 28 (a) The predicted stress-stretch curves of the original sample under quasi-statically increasing uniaxial stretches. (b) The predicted healing strength ratios in functions of healing time. (c) The predicted equilibrium healing time 𝑡 %& in a function of reverse reaction rates 𝑘 " $' . The used parameters are the same as those used in Fig. 8 except reverse reaction rates 𝑘 " $' . 2.5 Comparison with experimental results In section 2.4, we present general results of the theoretical models of the original and self-healed DPNs. In this section, we will compare the theoretical results with the experimental results. We show our model is very generic and can be applied to understanding a number of DPNs with a variety of dynamic bonds, including dynamic covalent bonds, hydrogen bonds, and ionic bonds. 2.5.1 DPNs crosslinked by dynamic covalent bonds We show our model can be used to explain the self-healing polymers with dynamic covalent bonds 53-57 . The first example is a self-healing polymeric gel crosslinked by dynamic covalent bond Diarylbibenzofuranone (DABBF) (Fig. 12a) 56 . DABBF is a dimer of arylbenzofuranone (ABF) that can be reversibly transformed to two radical species by cleaving the DABBF tolerate oxygen under a sufficiently large chain force. When these two radicals contact back, it can form DABBF again at room temperature. DABBF can crosslink the toluene-2,4-diisocyanate-terminated poly(propylene glycol) (PPG) through a polyaddition reaction with the presence of a catalyst di-n-butyltin dilaurate. This polymeric gel exhibits more than 90% strength healing for 6 h at room temperature. The corresponding experimental results are shown in Figs. 12bc. Using our model described in section 2.2, we can choose adequate model parameters to consistently match the experimentally measured stress-stretch behaviors of the original and self-healed samples (Fig. 12b, parameters in Table 2). In addition, the theoretically calculated healing ratio-time relationship also shows a good agreement with the experimentally measured results (Fig. 12c). It is noted that we only consider the stretching free energy of the polymer network but neglect the solvent- induced missing free energy in Eqs. 2-8 and 2-32. It is because the time scale of solvent diffusion within the gel matrix (e.g., 30 min) is usually much larger than the experimental testing time scale (e.g., 3 min); 29 then the mixing free energy of the gel can be assumed as a constant during the mechanical testing process 84,115 . Figure 12. Modeling of diarylbibenzofuranone self-healing behaviors. (a) Chemical structure and reactions of diarylbibenzofuranone (DABBF) 56 . The experimentally measured and theoretically predicted (b) stress-stretch curves of the original and self-healed samples, and (c) healing strength ratios in a function of the healing time. The graph in (a) and the experimental data in (bc) are reproduced from reference 56 with permission. The used parameters can be found in Table 2. Our model can also be used to explain the self-healing behaviors of DPNs crosslinked by other dynamic covalent bonds, such as reversible C-C double bonds enabled by the olefin metathesis reaction 57 . Olefin metathesis is an organic reaction that enables the redistribution of alkenes (or olefins) by the scission and regeneration of C-C double bonds. Lu and Guan reported a polymer with polybutadiene networks crosslinked by Ru-catalyzed olefin metathesis (Fig. 13a) 57 . The demonstrated polymers show efficient self-repairing capability, with more than 90% healing within 1 h or shorter depending on the concentration of the Ru catalyst. As shown in Fig. 13b, our model with adequate model parameters can nicely capture the stress-stretch behaviors of the original and self-healed polymer samples (parameters in 30 Table 2). The theoretically calculated healing ratio-time curve can also consistently match the experimentally measured results (Fig. 13c). Figure 13. Modeling of olefin metathesis enabled self-healing. (a) Olefin metathesis enabled reversible reaction 57 . The experimentally measured and theoretically predicted (b) stress-stretch curves of the original and self-healed samples, and (c) healing strength ratios in a function of the healing time. The graph in (a) and the experimental data in (bc) are reproduced from reference 57 with permission. The used parameters can be found in Table 2. Table 2. Model parameters used in this study. The chain dynamics parameters and Rouse friction coefficients are within the reasonable order compared with limited experimental or simulation results in the references 122,125,126 . Parameter Definition Fig. 5 Fig. 8 Fig. 12 Fig. 13 Fig. 14 Fig. 15 strong Fig. 15 weak (s -1 ) Forward reaction rate 2x10 -7 2x10 -7 2x10 -7 2x10 -7 2x10 -7 2x10 -7 2x10 -7 (s -1 ) Reverse reaction rate 2x10 -5 4x10 -4 4x10 -4 4x10 -4 4x10 -5 4x10 -5 8x10 -6 (m) Distance along the energy landscape coordinate 4x10 -9 3.8x10 -9 3.8x10 -9 4x10 -9 9.4x10 -10 9x10 -10 4x10 -9 b (m) Kuhn segment length 5.2x10 -10 5.2x10 -10 5.2x10 -10 5.2x10 -10 5.2x10 -10 5.2x10 -10 Minimum chain length NA 50 50 20 20 700 Maximum chain length NA 1500 1500 200 160 3500 Average chain length NA 690 690 71 64 1600 Chain length distribution width NA 0.2 0.2 0.2 0.2 0.2 Chain alteration parameter NA 0 0 0 0.9 0.05 0.3 0 f i k 0 r i k x D 1 n m n a n d a 31 (N/m) Rouse friction coefficient NA 2.3x10 -4 2.3x10 -4 2x10 -3 1x10 -2 1.5x10 -4 2.5.2 DPNs crosslinked by hydrogen bonds Hydrogen bonds stem from the electrostatic attraction between hydrogen (H) atom and a highly electronegative atom such as nitrogen (N), oxygen (O), or fluorine (F). These hydrogen bonds can be easily dissociated under external forces, and reform when two groups contact again. Hydrogen bonds have been employed to crosslink polymer networks to enable efficient self-healing capability 58-63 . For example, Cordier et al. reported a self-healing rubber that harnessed the hydrogen bonds between carboxylic-acid ends and amide groups in amidoethyl imidazolidone, di(amido ethyl) urea, and diamido tetraethyl triurea (Fig. 14a) 60 . This rubber exhibited an outstanding stretchability up to more than 500% strain and impressive self-healing capability with nearly 90% strength healing within 3 h. With our theory models, we can theoretically capture the stress-stretch behaviors of the original and self-healed rubber samples under the uniaxial stretch (Fig. 14b). The theoretically calculated healing ratio-time relationship can also roughly match the experimentally measured results (Fig. 14c). Within the rubber matrix, carboxylic-acid ends can form multiple hydrogen bonds with the amide groups in the polymer chains. When one hydrogen bond is dissociated under stretch, the polymer chain may not become inactive immediately, but form a longer active chain within the matrix 112,113 . Therefore, in modeling this hydrogen-enabled self-healing DPN, we introduce the effect of the chain alteration described in section 2.2 with the chain alteration parameter . The chain alteration effect facilitates to display the stiffening shape of the stress-stretch curve in the large stretch range. More discussions regarding the effect of chain alteration parameters on the stress-stretch behaviors can be found in references 114,115 . x 9 . 0 = a 32 Figure 14. Modeling of DPNs crosslinked by hydrogen bonds. (a) Schematic of a hydrogen bond crosslinked polymer network 60 . The experimentally measured and theoretically predicted (b) stress-stretch curves of the original and self-healed samples, and (c) healing strength ratios in a function of the healing time. The graph in (a) and the experimental data in (bc) are reproduced from reference 60 with permission. The used parameters can be found in Table 2. 2.5.3 DPNs crosslinked by ionic bonds An ionic bond is a type of chemical bond that involves the electrostatic attraction between the oppositely charged ions. Compared to covalent bonds, ionic bonds are relatively weak so that they can easily be dissociated under external perturbations, and can also reversibly be associated again when the condition is permitted 64-70 . Ionic bonds have been employed to fabricate soft polymers for a long time 42 ; however, traditional soft polymers crosslinked by a single type of ionic bonds are usually weak and brittle, such as alginate hydrogels 68 . To enable tough hydrogels, Sun and Suo et al. reported a double- network hydrogel with ionic networks and covalent networks; however, the reported hydrogels cannot fully self-heal their mechanical strength because of the presence of the permanent covalent networks 68 . Later, Sun and Gong et al. reported a hydrogel with two types of ionic bonds, one stronger and the other 33 weaker (Fig. 15a) 67 . Because only reversible ionic bonds exist in the hydrogel matrix, the hydrogels exhibit outstanding self-healing capability with over 95% strength healing within 24 h 67,70 . To model this DPN with two types of ionic bonds 67,70 , we divide the polymer chains into two portions: chains with strong ionic bonds and chains with weak ionic bonds. Both chains follow the similar chain-length distribution. The total chain number can thus be written as (2-38) where and are chain numbers for the polymer chains crosslinked by strong ionic bonds and weak ionic bonds, respectively; and is the portion ratio of the chains with strong ionic bonds. We plot an example of chain-length distributions with in Fig. 15b. Two portions of chains share the same Rouse friction coefficient, but feature different bond-dynamics parameters and chain alteration parameters (Table 2). The DPN portion with weak ionic bonds can be easily dissociated and become inactive; therefore, the peak point of the stress-stretch curve of the weak DPN sets in at a very small stretch (Fig. 15c). However, the DPN portion with strong ionic bonds remains resilient over a large range of stretch and exhibit a stiffening region at the large-stretch region (Fig. 15c). As a summation, the stress-stretch curve of the total DPN exhibits multiple regions over the whole stretch range (Fig. 15c): In the small stretch region, the whole DPN exhibits a relatively large tangent modulus and then rapidly softens due to the dissociation of the weak DPN; thereafter, the DPN exhibits a stiffening region to primarily display the behavior of the strong DPN until reaching the peak point. Our theoretically calculated stress-stretch behavior of the original DPN can consistently match the experimentally measured results (Fig. 15d). It is particularly noted that only strong DPN portion cannot capture the stress-stretch behaviors at the small stretch region (e.g., stretch=1-8). In modeling the self-healing, we consider the strong and weak DPNs follow different healing time scale with different bond dynamic kinetics parameters. Overall, the theoretically predicted stress- strain behaviors of the self-healed hydrogel sample can consistently match the experimentally measured results (Fig. 15d). The theoretically calculated healing ratio-time curve can also roughly match with the ( ) å å = = - + = + = m i i m i i w s N N N N N 1 1 1 f f s N w N f % 50 = f 34 experiments (Fig. 15e). The discrepancy probably comes from the complexity of the real polymer networks that cannot be fully modeled by our simplified interpenetrating network model. Figure 15. Modeling of DPNs crosslinked by ionic bonds. (a) Schematic of a polymer network crosslinked by strong and weak ionic bonds 67 . (b) Chain-length distributions of all chains, chains crosslinked by strong ionic bonds, and weak ionic bonds, respectively. (c) Predicted stress-stretch behaviors of the networks with strong ionic bonds, weak ionic bonds, and all bonds. The experimentally measured and theoretically predicted (d) stress-stretch curves of the original and self-healed samples, and (e) healing strength ratios in a function of the healing time. The graph in (a) is reproduced from reference 67 with permission. The experimental data in (bc) are reproduced from reference 70 with permission. The used parameters can be found in Table 2. 35 2.6 Conclusive remarks In summary, we report a theoretical framework that can analytically model the constitutive behaviors and interfacial self-healing behaviors of DPNs crosslinked by a variety of dynamic bonds, including dynamic covalent bonds, hydrogen bonds, and ionic bonds. We consider that the DPN is composed of interpenetrating networks crosslinked by dynamic bonds. The network chains follow inhomogeneous chain-length distributions and the dynamic bonds obey a force-dependent chemical kinetics. During the self-healing process, we consider the polymer chains diffuse across the interface to reform the dynamic bonds, being captured by a diffusion-reaction model. The theories can predict the stress-stretch behaviors of original and self-healed DPNs, as well as the corresponding healing strength over the healing time. We show that the theoretically predicted healing behaviors can consistently match the documented experimental results of DPNs with various dynamic bonds, including dynamic covalent bonds (diarylbibenzofuranone and olefin metathesis), hydrogen bonds, and ionic bonds. We expect that our model can be further extended to explain the self-healing behaviors of DPNs with a wide range of dynamic bonds 9,11,41-47 . Despite the shown salient capability of the current model system, it may also leave a number of open questions. These open questions may forecast a number of future research possibilities. First, the choice of the bond dynamics parameters and Rouse friction coefficient is primarily determined by the exhibited macroscopic experimental results (Table 2 parameters for Figs. 12~15). These parameters are within the reasonable order compared with limited experimental or simulation results in the references 122,125,126 . The requirement of these physical parameters poses an urgent demand for the atomic dynamics simulations or experiments to determine these parameters. Second, the model system presents an opportunity to model DPNs with very complex network geometries 127-129 . For example, Wang and Bao et al. reported a metal-ligand coordination crosslinked soft polymer that exhibits ultrahigh stretchability and efficient self-healing 40 . The metal-ligand coordination crosslinked polymer chains are sequentially released and stretched out under the chain force. This self- 36 healing polymer cannot be modeled by the current theory system in this study; however, involving the consideration of the special sequential-releasing network behaviors may forecast the future possibility. Third, the current theory system only models the simple geometry of the uniaxial bar stretching. Modeling the self-healing behaviors of more complex geometries to guide the future self-healing practice may demand a sophisticated finite element simulation method; however, such a mature finite-element method to fully model the self-healing mechanics of DPNs is still unavailable 130 . Fourth, the current theory employs the simplest interpenetration network model with an assumption that polymer chains within a network feature the same chain length and different networks interpenetrate into each other 99 . The assumption would lead to a subsequent assumption that the association-dissociation bond dynamics only occur among chains with the same chain length. These restrictions can be relaxed by considering the connection of chains with dissimilar chain lengths 131 . If so, the same chain force will induce imbalance stretches to different chains within a network, and diffusion time-scales for these different chains are also different. A more sophisticated statistical averaging model should be considered to address these issues. 37 Chapter 3: Additive Manufacturing of Self-Healing Elastomers 3.1 Objective Nature excels in both self-healing and 3D shaping; for example, self-healable human organs feature functional geometries and microstructures. However, tailoring man-made self-healing materials into complex structures faces substantial challenges. Here, we report a paradigm of photopolymerization- based additive manufacturing of self-healable elastomer structures with free-form architectures. The paradigm relies on a molecularly designed photoelastomer ink with both thiol and disulfide groups, where the former facilitates a thiol-ene photopolymerization during the additive manufacturing process and the latter enables a disulfide metathesis reaction during the self-healing process. We find that the competition between the thiol and disulfide groups governs the photocuring rate and self-healing efficiency of the photoelastomer. The self-healing behavior of the photoelastomer is understood with a theoretical model that agrees well with the experimental results. With projection micro-stereolithography systems, we demonstrate rapid additive manufacturing of single- and multi-material self-healable structures for 3D soft actuators, multiphase composites, and architected electronics. Compatible with various photopolymerization-based additive manufacturing systems, the photoelastomer is expected to open promising avenues for fabricating structures where free-form architectures and efficient self-healing are both desirable. 3.2 Introduction Natural living materials such as animal organs can autonomously self-heal wounds. Inspired by natural living materials, scientists have developed synthetic self-healing polymers capable of repairing fractures or damages at the microscopic scale and restoring mechanical strengths at the macroscopic scale 9,11,48 . The healing capability usually relies on extrinsic curing-agent encapsulates released upon fractures 51,52 , or intrinsic dynamic bonds such as dynamic covalent bonds 53,55 and physical bonds 58,60,61,64,67,71,79,132 that autonomously reform after fracture-induced dissociations. Thanks to their healing capability, these 38 polymers have enabled a wide range of applications, such as flexible electronics 35,39,133 , energy transducers 132,134 , soft robotics 29,34 , lithium batteries 40 , water membranes 135 , and biomedical devices 33 . Despite the success in syntheses and applications, the existing self-healing polymers are still facing a critical bottleneck — deficiency in 3D shaping. This bottleneck makes the synthetic self-healing polymers different from the living materials (such as human organs) that usually feature functional geometries and microstructures. Besides, a number of promising applications of self-healing polymers demand complex 2D/3D architectures, such as soft robotics 29,136 , structural composites 30,31 , and architected electronics 32 . However, the architecture demand of self-healing polymers has not been sufficiently fulfilled, as the existing 3D shaping methods of self-healing polymers only include molding 35 and direct-writing 36-38,137 , which are either time-consuming or limited in forming complex 3D architectures 138,139 . Here we report a strategy for photopolymerization-based additive manufacturing (AM) of self- healing elastomer structures with free-form architectures. The strategy relies on a molecularly designed photoelastomer ink with both thiol and disulfide groups, where the former facilitates a thiol-ene photopolymerization during the AM process, and the latter enables a disulfide metathesis reaction during the self-healing process. Using projection microstereolithography systems, we demonstrate rapid AM of single- and multi-material elastomer structures in various 3D complex geometries within a short time (e.g., 0.6 mm ×15 mm × 15 mm/min=13.5 mm 3 /min). These structures can rapidly heal the fractures and restore their initial structural integrity and mechanical strengths by 100%. We find that the competition between the thiol and disulfide groups governs the photocuring rate and self-healing efficiency of the photoelastomer. The self-healing behavior of the photoelastomer is understood with a theoretical model that agrees well with the experimental results. To demonstrate potential applications of the 3D-printable self-healing elastomers, we show self-healable 3D soft actuator that can lift a weight ten times of its own weight, a nacre-like stiff-soft composite that restores the toughness by over 90% after a fracture, and a self-healable force sensor with both dielectric and conductive phases. Equipped with the capability of rapid photopolymerization that is compatible with various AM systems such as stereolithography 140,141 , self-propagation photopolymer waveguide 142,143 , two-photon lithography 144,145 , and PolyJet printing 146 , the 39 new self-healing photoelastomer system is expected to open promising avenues for fabricating structures where free-form architecture and efficient self-healing are both desirable 29,147 3.3 Materials and methods 3.3.1 Materials. Vinyl-terminated polydimethylsiloxanes (V-PDMS, molar mass 6,000-20,000 g/mol) and [4-6% (mercaptopropyl)methylsiloxane]-dimethylsiloxane (MMDS) were purchased from Gelest. Iodobenzene diacetate (IBDA), toluene, tributylphosphine (TBP), 1,6-hexanediol diacrylate (HDDA), phenylbis(2,4,6- trimethylbenzoyl)phosphine oxide (photoinitiator), Sudan I (photoabsorber), ethanol were purchased from Sigma-Aldrich. The chemicals were used as purchased without further purifications. Carbon grease was purchased from GM chemicals. 3.3.2 Synthesis and characterization of material inks. To prepare the experiment elastomer ink, 0.5 g of IBDA was first mixed with 5 mL toluene under the nitrogen environment with the magnetic stirring for 6 h. Then, 1 g MMDS was oxidized by adding different amounts of IBDA solution (0g, 0.35g, 0.7g, 1g, and 1.2g) for 1 min. Subsequently, 1.95 g of V-PDMS, 1 wt% photoinitiator, and 0.1 wt% photoabsorber were added and mixed for another 1 min. The 0.1wt% of TBP was then added and mixed for another 1 min. To prepare the control elastomer ink, 1 g MMDS, 1.95 g of V-PDMS, 1wt% photoinitiator, and 0.1wt% photoabsorber were mixed for 5 min. The Raman spectroscopy measurements were performed using a Horiba Raman Infrared Microscope with an acquisition time of 1 min. The spectra of the material inks from 200 to 1800 cm -1 were collected using a laser excitation wavelength of 532 nm. 3.3.3 Additive manufacturing. The single- and multi-material stereolithography systems were described elsewhere 140,141 . To fabricate multi-material structures (Fig. S15), we first divided the computer-aided-design (CAD) model of a biphase composite into two models with respective phases. Each phase model was then sliced into an image 40 sequence with a prescribed spacing along the vertical direction. Then two image sequences were alternatively integrated into one image sequence. The images were sequentially projected onto a resin bath that is filled with a material ink. The ink capped with a motor-controlled printing stage was exposed to the image light (405 nm) and solidified to form a layer structure bonded to the printing stage. As the printing stage was lifted up, the wheel was rotated to deliver the ethanol beneath the printing stage. With the printing stage lowered down into the ethanol, the printed structure was washed, and the ethanol residue was subsequently absorbed by the cotton pad. Then, another material ink was delivered beneath the stage by the rotational wheel. By lowering the stage by a prescribed height and illuminating another image, a second material layer could be printed on the existing structures. By repeating these processes, we printed multimaterial structures. To fabricate single-material structures (Fig. 16b), we just simplified the process by using one image sequence and removing the intermediate cleaning process. It is noted that traditional stereolithography system with acrylic-based resins has an oxygen-rich layer to quench the photopolymerization close to the printing window 148 , and this oxygen-rich layer can facilitate the manufacturing process by reducing the adhesion between the printed part and the window 148 . However, the thiol-ene photopolymerization system cannot be quenched by the oxygen 149 . To enable easy separation between the solidified part and window, we employ a Teflon membrane with a low surface tension (~20 mN/m) to enable low separation forces. In addition, all fabricated samples were heated for 2 h at 60°C to remove the residual toluene and ethanol, and then post-cured in a UV chamber for additional 1 h (same wavelength as the AM system) to ensure the samples to be fully polymerized. 3.3.4 Photocuring depth test. A 10mm x 10mm square image was illuminated on the printing window with different photoexposure time for the experiment elastomers with various IBDA concentrations (Fig. 18b). The thicknesses of the photocured parts were measured at the cross-sections by an optical microscope (Nikon ECLIPSE LV100ND). 41 3.3.5 Self-healing test. The dog-bone-shaped samples (thickness 4 mm) were first additively manufactured. Then, the samples were cut into two pieces with a blade and brought into contact with an additional force (~0.5N) on two sides to ensure good contact. The samples were then put on a hot plate under 60°C for various healing time. Both the original and healed samples were clamped by two rigid plates in a tensile testing machine (Instron, Model 5942) to be uniaxially stretched until ruptures with a low strain rate 0.06 s -1 . The microscopic images of the damaged and healed interfaces were taken with the optical microscope (Nikon ECLIPSE LV100ND). 3.3.6 Self-healable actuator. The 3D actuator was first designed and additively manufactured. A 10-g weight was hanged at the bottom of the actuator which was connected to a syringe pump (Fig. S14). When the syringe pump was moved, the weight was lifted up. A camera was used to image the distance change of the weight. Then, we cut the actuator in half with a blade and contacted back to heal for 2 h at 60°C. Once healed, the actuator was used to lift up the 10-g weight again for multiple cycles. 3.3.7 Self-healable composite. The experiment composites (width 10 mm, length 15 mm, and thickness 1 mm) with stiff phase HDDA and soft phase self-healing elastomer were first additively manufactured. Then a small notch was made at the center edge of the samples. The notched samples were clamped and stretched in the Instron tensile tester with a low strain rate 0.06 s -1 . The first group of control samples included pure HDDAs and self-healing elastomers of the same size as the experiment composites. The second group of control samples included composite samples with stiff phase HDDA and soft phase non-self-healing elastomer (also the same size as the experiment composites). These two groups of control samples underwent the similar tensile tests as the experiment composites. 42 3.3.8 Self-healable electronics. The self-healable conductive elastomer ink was synthesized by adding 50 wt% carbon grease into the self- healing elastomer ink. The self-healable conductive elastomer samples were fabricated using the single- material stereolithography system (Fig. 16b). The USC Trojan pad (width 10 mm, length 10 mm, and thickness 1 mm) with dielectric phase self-healing elastomer and conductive phase conductive elastomer was fabricated using the multimaterial stereolithography system (Fig. S15). The resistance was measured with a source meter (Keithley 2400). The voltage (10V AC) for lightening the LED was provided by the source meter. The force sensor was fabricated by laminating the Trojan pad between of two same-size self- healable elastomer pads. The compressive force was applied and measured by the Instron machine with two compression plastic plates. 3.4 Results 3.4.1 Molecular design of the self-healable photoelastomer The molecular design of the self-healing elastomer with integrated features of photopolymerization and self-healing is based on the coexistence of thiol (R-S-H) and disulfide (R-S-S-R’) groups (Fig. 16a). The photopolymerization is achieved by harnessing the high-rate and high-yield thiol-ene crosslinking reaction that thiol groups (R-S-H) and alkene groups (H 2-C=C-HR’) react to form alkyl sulfides (R-S-C-C-H 2R’) under the photo-induced radical initiation (Fig. 16ab) 149 . The efficient self-healing is achieved by harnessing dynamic disulfide bonds that undergo disulfide metathesis reactions (assisted by a catalyst tributylphosphine) to bridge the fractured interface (Fig. 16c) 150 . To introduce the disulfide groups in the polymer network, we partially oxidize the thiol groups using a highly-efficient oxidant, iodobenzene diacetate (IBDA) (Fig. 16a) 151,152 . After the partial oxidation, the thiol and disulfide groups coexist in the material ink to form thiol-disulfide oligomers. After the photopolymerization, the dynamic disulfide bonds will be covalently integrated within the crosslinker regions (Fig. 16a). To prove the concept, we employ [4-6% (Mercaptopropyl)methylsiloxane]-Dimethylsiloxane copolymer (MMDS, Fig. S1a) and vinyl-terminated polydimethylsiloxane (V-PDMS, Fig. S1b) to provide 43 the thiol groups and alkene groups, respectively 153,154 . Both chemicals have relatively low viscosities (below 200 cSt) that are suitable for the stereolithography process. V-PDMS with relatively high molar mass (6,000-20,000 g/mol) constitutes the polymer backbone, enabling the high flexibility and stretchability of the elastomer. The material ink is used in a projection microstereolithography system to enable rapid prototyping of various 2D/3D elastomer structures, including a logo of the University of Southern California (Fig. 16d), a circular cone (Fig. 16e), a pyramid (Fig. 16f), a cup (Fig. 16g), and an Octet truss lattice (Fig. 16h). The manufacturing process is rapid with a speed of ~25 μm/s for each layer and around 5-60 min for each structure shown in Fig. 16d-h. The manufacturing resolution can reach as low as 13.5 μm (Fig. S2). The elastomer not only can be 3D printed to nearly any 3D architectures but also can self-heal fatal fractures. As a simple demonstration in Fig. 16i, we fabricate a delicately-patterned shoe pad that can be flexibly twisted by 540 degrees. We then cut the pad into two parts and contact back to heal for 2 h at 60 o C. After the healing process, the sample can sustain the 540-degree twist again. 44 45 Figure 16. Additive Manufacturing of Self-healing elastomers. (a) Molecular design of the self-healing elastomer. MMDS with thiol groups was first oxidized with the IBDA to form a thiol-disulfide oligomer. The oligomer then undergoes a photo-initiated thiol-ene reaction with the V-PDMS with alkene groups to form a solid elastomer. The elastomer embeds dynamic disulfide bonds within the crosslinker region. (b) Stereolithography-based additive manufacturing process. An image sequence sliced from a computer-aided-design (CAD) model is sequentially projected onto a resin bath to form a layer-by-layer structure. (c) Schematics to show the disulfide-bond enabled self-healing process. The fractured interface can be healed through a disulfide metathesis reaction. (d-h) The manufactured samples: (d) a logo of the University of Southern California, (e) a circular cone, (f) a Pyramid lattice unit, (g) a cup, and (h) an Octet truss lattice. (i) Self-healing of a shoe pad sample. The fabricated shoe pad can sustain a 540-degree twist. Once cut, the shoe pad is brought into contact to heal for 2 h at 60°C. Then, the healed shoe pad can sustain the 540-degree twist again. The scale bars in (d-i) represent 4 mm. 3.4.2 Characterization of the self-healing property Next, we characterize the self-healing property of the synthesized photoelastomer (Fig. 17). We design two types of photoelastomers: experiment elastomers with IBDA-enabled disulfide bonds (Fig. 16a) and control elastomers without the disulfide bonds (the molecular structure in Fig. S3). Both elastomer inks can be 3D printed into dog-bone-shaped samples (Fig. 17a). Then we cut the samples into two parts and bring into contact for various healing time (0-270 min) at 60°C. Subsequently, the samples are uniaxially stretched until ruptures. We can verify the self-healing property of the experiment elastomer from three aspects. First, the existence of the disulfide bond in the experiment elastomer is verified by Raman spectroscopy measurements that show a new peak with a band ~520 cm -1 (Fig. S4). This new band is consistent with the Raman band in the reported disulfide-bond-enabled self-healing polymers (500-550 cm - 1 ) 155,156 . Second, microscopic images show that the crack gap of the fractured experiment elastomer is nicely bridged after 2-h healing at 60°C (Figs. 17bc). Third, we find that the tensile strengths of the experiment elastomers gradually increase with increasing healing time until a plateau around 100% of the original strength after 60 min (Fig. 17d). However, the tensile strengths of the control elastomers reach a plateau only 40% of the original strength after 60 min at 60°C (Figs. 17ef). It shows that the dynamic disulfide bonds play a central role in healing the fractured interface to restore 100% strength. Without the disulfide- bond enabled interfacial bridging, the interfacial bonding of the control elastomer possibly stems from the 46 non-crosslinking chain entanglement around the fracture interface 23 ; however, this chain entanglement effect cannot lead to 100% interfacial self-healing. For the experiment elastomer, we can further carry out self-healing tests for more than 10 cycles, and corresponding healing strength ratios (tensile strength of the healed sample over that of the original sample) remain 90-100% (Figs. 17g and S5a). It is also noted that due to the solvent-free character, the elastomer samples do not show any visible volume shrinkage during the 10-cycle healing process (each 2 h at 60 °C) (Fig. S5b). This character enables the self-healing elastomer to be intrinsically different from the reported directly-written self-healing hydrogels 36,37,137 . In addition, we find that the mechanical property of the experiment elastomer remains almost unchanged after being immersed in the water for 24 h (Fig. S6), which makes it dramatically different from the moisture-sensitive self-healing elastomers with hydrogen bonds 39,60 . Although the experiment elastomer displays relatively low Young’s modulus (~17.4 kPa), the frequency sweep test shows that its loss moduli (500-600 Pa) for frequency 0.1-1 Hz are much lower than their storage moduli (Young’s moduli) (Fig. S7a). It shows that the elastic character of the experiment elastomer dominates over the viscous character. Besides, we further test the storage-loss moduli of the experiment elastomer over a large range of temperature (25-165°C), and we find that the elastomer remains stable and the elastic character dominates over the viscous character below 165 °C (Fig. S7b). Moreover, this low-viscous feature can also verified by the cyclic tensile tests which show low hysteresis over 3 sequential loading-unloading cycles (Fig. S8ab). 47 Figure 17. Characterization of the self-healing property. (a) Self-healing process of a dog-bone-shaped elastomer sample. A dog-bone-shaped sample is first cut with a blade and brought into contact to heal for 2 h at 60°C. The healed sample is then uniaxially stretched. The scale bar represents 5 mm. (b-c) The optical microscope images of the (b) damaged and (c) healed interfaces. The scale bars in (b-c) represents 50 μm. (d) Nominal stress-strain curves of the original and self-healed experiment elastomers for various healing time. The nominal stress is calculated as the force over the initial cross-section area of the sample neck. (e) Nominal stress-strain curves of the original and self-healed control elastomers for various healing time. (f) Healing strength ratios of experiment and control elastomers as functions of the healing time at 60°C. The healing strength ratio is defined as healing strength of the self-healed sample over that of the original sample. The theoretically predicted relationship between the healing strength ratio and the healing time of the experiment elastomer agrees well with the experimental results. (g) Healing strength ratios of experiment elastomers for 10-cycle healing tests (each 2 h at 60°C). 48 3.4.3 Competition between photocuring and healing The IBDA-enabled partial oxidation is an approach to regulate the photocuring and self-healing properties. Since the total concentration of thiol groups ( ) is initially provided, the concentrations of thiol ( ) and disulfide groups ( ) in the material ink are conserved ( if we assume the ink volume is approximately unchanged). The amount of the thiol group affects the photocuring rate, and the amount of the disulfide group influences the healing performance; therefore, the photocuring rate and the healing efficiency are expected to be under competition. This point can be first verified by the Raman spectroscopy measurements: The Raman peak associated with the disulfide bond becomes stronger as the IBDA concentration increases (Fig. 18a), indicating that disulfide bond concentration increases as more oxidant IBDA is applied. To further verify the competition, we carry out the photocuring experiments to measure the relationship between the curing depth and photoexposure time for various IBDA concentrations (Fig. 18b). We find that the curing depth H is approximately in a linear relationship with the photoexposure time t, written as , where is the curing coefficient (μm/s) and is the threshold time for the curing depth growth. The curing coefficient k represents the photocuring rate during the AM process. The curing coefficient k decreases with increasing IBDA concentrations (η=0-3 wt%) because more IBDAs transform more thiol groups to disulfide groups (Figs. 18b). At the same time, we find that the healing strength ratios of the cured elastomers within 2 h healing time (at 60 °C) increase as the IBDA concentration increases within η=0-2.6 wt% (Fig. 18c). It confirms that the properties of photocuring and self-healing are indeed under competition, and judicious selection of the partial oxidant IBDA concentration is required to enable both rapid photocuring and rapid self-healing. We further find that as the IBDA concentration is larger than η 0=2.6 wt%, the healing strength ratio reaches a plateau at 100%. To enable both rapid curing and rapid self-healing (>90% within 2h at 60 °C), we choose the IBDA concentration η=2.2-2.8 wt% to carry out the oxidation experiments. If the IBDA concentration is out of this range, rapid photocuring and rapid healing cannot be achieved simultaneously. 0 T c T c d c 0 2 T d T c c c » + ( ) 0 t t k H - » k 0 t 49 Figure 18. Competition between the photocuring and self-healing (a) Raman spectra of the elastomer ink with various IBDA concentrations η (wt%). The band around 520 cm-1 is corresponding to the disulfide bond. (b) Photocuring depth of the photoelastomer ink as a function of the photoexposure time for various IBDA concentrations. The slope is defined as the photocuring coefficient k (μm/s). (c) Nominal stress-strain curves of the original and self-healed elastomers (2-h healing at 60°C) for various IBDA concentrations. (d) The photocuring coefficients and healing strength ratios (2-h healing at 60°C) of the photoelastomer as functions of the applied IBDA concentration. The shadow region with IBDA concentration η=2.2-2.8 wt% is corresponding to rapid photocuring and rapid healing. 3.4.4 Theoretical modeling of the self-healing behavior To theoretically understand the self-healing behavior of photoelastomers, we develop a polymer-network- based model that is an extension of a model we recently developed for self-healing hydrogels crosslinked by nanoparticles 84 (model details in Appendix B and Figs. S13). The theory employs a bell-like model to analyze the stretching-induced dissociation of the dynamic disulfide bonds during the tensile loading process 110 , and a diffusion-reaction model to capture the chain interpenetration and re-crosslinking during the self-healing process 100,117,124 . Using this theoretical model, we can consistently explain the experimentally measured stress-strain behaviors of the original and self-healed samples (Fig. S13). The predicted healing strength ratios also agree well with the experiments (Fig. 17f). To further verify the theory, we carry out the self-healing experiments at various temperatures (40-60 o C). The experiments show 50 that the higher temperature leads to the more rapid healing process. Our theory can also consistently explain the experimentally measured relationships between the healing strength ratios and healing time under various temperatures (Fig. S13c). It is worth noting that the temperature plays a key role during the self- healing process. As it has been identified from the theoretical model, the self-healing capability of the designed photoelastomer is governed by the polymer chain diffusion and disulfide group-enabled reaction across the fractured interface. The higher temperature enables, the more rapid diffusion of polymer chains across the fractured interface. Besides, according to Bell’s theory 110 , raising the temperature will increase the vibrational excitation of sulfide atoms and favor the reformation of disulfide bonds during the self- healing process. Both of these aspects have been well captured in our theoretical model. We expect that this theoretical framework can be further extended to understand self-healing soft polymers with various dynamic bonds, including dynamic covalent bonds 53,55 , hydrogen bonds 58,60,61 , metal-ligand coordination 71,132 , and ionic interactions 64,67 . 3.5 Applications of additively manufactured self-healing elastomers 3.5.1 Self-healable 3D soft actuator. To demonstrate the potential applications, we first present a self-healable 3D soft actuator (Fig. 19a-c). The actuator is composed of a series of circular cones that can be shrunk inward to enable a contraction when a negative pressure is applied (Fig. 19a, the experimental setup in Fig. S14). When a negative pressure 30 kPa is applied, the actuator (~1 g) can lift up a 10-g weight (around 10 times of its own weight) by a distance of 6 mm. Then, we cut the actuator into two parts and bring them into contact to heal for 2 h at 60°C. Once the actuator is self-healed, it can lift the 10-g weight by 6 mm again (Fig. 19ab). The pressure-distance curve of the healed sample is very close to that of the original one (Fig. 19c). This lifting efficiency (lifting weight per self-weight) is comparable with those of the existing contraction actuators that are fabricated with molding or assembly methods 134,157 . Comparing with the soft actuators fabricated using traditional molding method 34,136 , the stereolithography-enabled fabrication of the self-healable soft actuator requires less time and material consumption. Comparing with the AM-enabled soft actuators composed of non- 51 healable materials 158,159 , this soft actuator harnesses the self-healing elastomers to enable 100% healing after fatal fractures. 3.5.2 Self-healable structural composite. Natural structural materials, such as nacres and teeth, feature outstanding toughness, primarily due to their multiphase composition that both stiff and soft phases are arranged in complex architectures 30,31 . These structural composites motivate tremendous efforts in creating tough synthetic composites with multiple phases 30,31 ; however, these natural and synthetic composites are generally not self-healable. Here we demonstrate AM of a healable nacre-like composite composed of a non-healable stiff plastic phase and a healable soft elastomer phase (Fig. 19d, the multi-material stereolithography system is shown in Fig. S15). During the photopolymerization enabled AM process, a thiol-acrylate reaction is triggered to enable a relatively strong interfacial bonding between two phases (Fig. S16a) 160 . Under a tensile load, the crack in the composite sample (with a small crack notch) propagates through the soft phase in a wavy pattern, inducing a higher toughness than the parent materials (Figs. 19e and S16b). Since the crack propagates through the soft phase, we bring the two fractured parts back to heal for 2 h at 60°C. After the healing process, the sample can sustain the tensile load again, with the toughness is around 90% of that of the original composite (Fig. 19de). As a control experiment, we manufacture a stiff-soft composite with non- healable soft elastomers which only show 14.5% of the original toughness in the second load (Figs. 19e and S16c). 3.5.3 Self-healable architected electronics. The self-healing photoelastomer is dielectric; to enable electronic conductivity, we dope carbon-blacks into the elastomer ink (Fig. 19f). We additively manufacture a flexible composite pad with a dielectric elastomer phase and a conductive elastomer phase with a contour path of the USC Trojan. We show that the sample is conductive along the Trojan path to lighten up an LED, and also can be bent by a large angle (~120°). Since both phases in the composite pad are self-healable, we then bring two parts back to heal the interface for 4 h at 60°C. The healed pad becomes conductive again and can be used to lighten up the LED. We find 52 that the resistance of healed sample only changes by 9% (Fig. 19g). The composite pad can be used as a self-healable force sensor, as the resistance of the conductive pathway decreases with increasing the compressive force (Fig. 19h). It is probably because that the effective spacing between carbon black particles within the conductor becomes smaller when the compressive force is applied 39 . The relationship between the relative resistance and the applied force can be used as a sensing signal to inversely predict the applied force. When we cut the structure and heal back for 4 h at 60°C, we obtain a self-healed force sensor with the resistance-force curve close to that of the original force sensor (Fig. 19h). 53 Figure 19. Applications of additively manufactured self-healing elastomers. (a-c) Self-healable 3D soft actuator. (a) Negative pressure actuation can enable the additively manufactured elastomer actuator to lift up a 10-g weight by 6 mm. The inset shows the CAD model of the elastomer actuator. The actuator is then cut in half and brought into contact to heal for 2 h at 60°C. The self-healed actuator can be actuated again by the negative pressure to lift up the 10-g weight by 6 mm. The scale bar represents 5 mm. (b) The cyclic lifting distance of the 10-g weight as a function of time of the original and self-healed actuators. (c) The relationships between the negative pressure values and the lifting distances of the original and self-healed actuators. (d-e) Self-healable structural composite. (d) A notched stiff-soft composite is first uniaxially stretched until a rupture, and then brought into contact to heal for 2 h at 60°C. The healed composite is then uniaxially stretched again until a rupture. The scale bar represents 3 mm. (e) The toughnesses of the original and healed experiment composites, single materials (pure plastic and pure elastomer), and the original and healed control composites. The toughness is defined as the enveloped area of the uniaxial nominal stress-strain curves until the rupture per unit sample area. (f-h) Self-healable architected electronics. (f) A flexible Trojan pad with a self-healable elastomer phase and a self-healable conductor phase can lighten up an LED. Once cut and healed after 4 h at 60°C, the self-healed Trojan pad can sustain bending and lighten up the LED again. The scale bar represents 4 mm. (g) The Resistance of the conductive path of the Trojan path before and after the self-healing. (h) The relationships between the normalized resistances and the applied force of the original and self-healed force sensors. The normalized resistance is calculated as the resistance normalized by the resistance for the force-free state. The inset shows the working paradigm of the force sensor. 3.6 Discussion In summary, we present a molecularly-designed photoelastomer ink that can enable stereolithography- based AM of elastomers with rapid and full self-healing. The dual functions of photopolymerization and self-healing are achieved by molecularly balancing the thiol and disulfide groups in the material ink. As a model self-healing photoelastomer, the material system with adequate modifications should be easily translatable to other photopolymerization-based AM systems, such as self-propagation photopolymer waveguide 142,143 , two-photon lithography 144,145,161 , and PolyJet printing 146 . The AM of self-healing elastomers with various tailored 3D architectures is expected to open various application possibilities, not limited to the demonstrated 3D soft actuators (Fig. 19a-c), structural composites (Fig. 19de), and flexible electronics (Fig. 19f-h), also including artificial organs, biomedical implants, and bionic sensors and robotics 29,136,147,162,163 . In addition, in nature, the disulfide bond is a reversible cross-link that provides tunable stability to folded structures of proteins with specific mechanical functions, such as molecular sensing, switching, and signaling 164,165 . The AM of biomimetic materials with dynamic disulfide bonds may open possibilities for materials with protein-like functions. Moreover, as a model system to incorporate desirable material properties (i.e., self-healing) into the existing AM system, the molecular design strategy 54 may be extended to various other salient properties such as stimulus actuation 146,166 and mechanochromism 167 . To that end, the presented strategy may motivate molecular designs of various unprecedented material inks for the emerging AM systems to enable rapid prototyping of 3D structures that cannot be fabricated with traditional shaping methods 143,168-170 . 55 Chapter 4: Mechanics of Light-Activated Self-Healing Polymer Networks 4.1 Objective Optically healable polymers represent an interesting stimuli-responsive self-healing material as the healing process can be controlled on-demand and remotely. The fundamental mechanism of the light- activated interfacial self-healing process has not been theoretically understood. Here, we present a theoretical framework to understand the light-activated interfacial self-healing of soft polymers with light- responsive photophores. We consider that the light propagation through the material matrix triggers the production of free radicals that facilitate the interfacial self-healing process. The self-healing process is considered as a coupled behavior that polymer chains diffuse across the interface and re-form the dynamic bonds assisted by the free radicals. We theoretically relate the light property to the interfacial self-healing strength of the polymers. We predict that the interfacial self-healing strength of the polymer increases with the light illumination time until reaching a plateau. We theoretically explain the effects of the light intensity, light wavelength, and photoinitiator concentration on the self-healing performance. We then apply the theory to two types of soft polymers with inorganic and organic photophores, respectively. The experimentally measured stress–strain behaviors of the original and self-healed samples can be consistently explained by the theory. The experimentally measured relationships between the healing strength and the healing time also agree well with the theoretical results. 4.2 Introduction The self-healing polymers capable of self-repairing fractures or damages have shown great potential in a number of applications, such as flexible electronics 39 , energy storage 40 , biomaterials 33 , and robotics 34 . These self-healing polymers, either relying on encapsulates of curing agents 48-52 , or various dynamic bonds 40,53-55,58-62,64-68,71-73,84,171-176 , can usually activate the interfacial bridging mechanism under an adequate condition when the fractured interfaces are brought into contact. Among these self-healing polymers, the 56 ones with self-healing behaviors responsive to the remote stimuli are especially interesting, because the remote stimuli can usually be delivered locally to achieve on-demand self-healing performance. Optically healable polymer is a type of stimuli-responsive self-healing polymer that harnesses the external visible or ultraviolet (UV) light to activate the self-healing reaction around the fracture interface 177-190 . Within the optically self-healable polymers, a special photo-responsive chemical group called “photophore” is incorporated within the polymer network. When two fractured interfaces are brought into contact under the exposure of light with an adequate wavelength, the light-triggered free radicals will activate the photophore to facilitate the polymer-chain rebinding to bridge the fractured interface. The photophores can usually be divided into two types: organic photophores and inorganic photophores. The organic photophores include special photo-responsive organic chemical groups 177,181-186,188 . The inorganic photophores include metal-organic frameworks 187 and nanoparticles or nanosheets 189,190 . These optically healable polymers with diverse photophores provide a representative paradigm of stimuli-controlled self- healing and offer great potential for a wide range of on-demand healing applications 179,180 . Despite the great potential, the theoretical modeling of the underlining self-healing mechanism of the light-activated self-healing is not available. Though mechanics models for the constitutive behaviors of light-activated polymers have been proposed 191-194 , how to model the light-activated interfacial self-healing behavior remains elusive. For example, how the light activates the photophores during the self-healing process remains unknown. How the light-triggered free radicals activate the polymer chain evolution around the healing interface remains unclear. And how the light properties including intensity and wavelength affect the self-healing performance is also ambiguous. If theoretical models for the light- activated interfacial self-healing are successfully established, the future design and optimization of these materials will be significantly facilitated. The theory may also be extended to model the self-healing behaviors of polymers under various other stimuli, such as heat, pH value, and electromagnetic fields 9,23,43,44,48,195 . Here, we establish a theoretical framework to model the light-activated interfacial self-healing of light-responsive polymer networks. We consider that light-triggered free radicals around the healing 57 interface can facilitate the interpenetration of the polymer chain to bridge the fracture interface. We consider two groups of coupled diffusion-reaction systems around the healing interface: one for the light-activated production of free radicals, and the other for the polymer chain diffusion and distal-group binding kinetics. We apply the theoretical framework to two types of soft polymers with inorganic nanoparticle photophores and organic photophores, respectively. We predict that the healed interfacial strengths for both polymers increase with light-illumination-associated healing time until reaching plateaus. We also elucidate the effects of the light intensity, the light wavelength, and the photoinitiator concentration on the self-healing performance. The theoretical calculations can consistently agree with the experimental results of light- activated self-healing of soft polymers with inorganic and organic photophores, respectively. The plan of this part is as follows: In section 4.3, we introduce the experimental procedure and results of optically healable TiO 2 nanocomposite hydrogels. In section 4.4, we construct the theoretical frameworks of light-activated production of free radicals and radical-assisted polymer-chain interpenetration across the healing interface. We then apply the theories to soft polymers with inorganic nanoparticle photophores and organic photophores, respectively. Subsequently, in section 4.5 and 4.6, we present the theoretical results of light-activated self-healing of soft polymers with respective inorganic and organic photophores. The theoretical results are compared with the corresponding experimental measurements. The conclusive remarks are presented in section 4.7. 4.3 Experiments of hydrogels with inorganic photophores We will study the light-activated self-healable polymer networks with nanoparticle and organic photophores. The experiments of light-activated self-healable polymer networks with organic photophores are shown in 186 . We introduce the experiments of light-activated self-healable polymer networks with representative TiO 2 particle photophores in this section. We hope the study can be extended to explain other light-activated self-healable polymer networks with various particle photophores. TiO 2 nanoparticles dispersion (Anatase, 15 wt%, 5-15 nm, crosslinker) was purchased from US Research Nanomaterials. Acrylamide (AAm, monomer), N,N-Dimethylacrylamide (DMAA, monomer), 58 potassium peroxodisulfate (KPS, photoinitiator), and N,N,N′,N′-Tetramethylethylenediamine (TEMED, accelerator) were purchased from Sigma-Aldrich (United States). All chemicals were used as received without further purification. The 10g TiO 2 solution was first bubbled with nitrogen for 30 min to remove the oxygen dissolved in the solution. Then, the solution was mixed with 0.039g (0.009 mol) AAm and 2.079g (0.021 mol) DMAA under the magnetic stirring for 30 min at 20℃. The mixed solution was cooled down to 0℃ in an iced water bath. 0.1 wt% KPS and 8𝜇𝐿 TEMED were then added in with another 30 min stirring. The obtained solution was poured into a glass tube (diameter 11mm and length 50mm) or a glass mold (150mm x 75mm x 3mm) with the cover up to avoid contact with the oxygen. To facilitate the in-situ free-radical polymerization, the hydrogel was put in a UV chamber (UVP CL-1000 Ultraviolet Crosslinker) with light intensity 37 W/𝑚 ( (Five 8 Watt light bulbs with 254 nm wave length) for 30 min (Fig. 20a). Note that The TiO 2 nanoparticles and the polymer chains are bonded through dynamic bonds, such as hydrogen bonds (between -OH on the particle surface and -NH 2 group on polymer chains) 189,196 , or ionic bonds (between K + groups from redox initiator KPS and anionic groups of the polymer chains) 44,85,90,197 . For the characterization of the self-healing behavior, cylindrical hydrogel samples (diameter 11mm, length 10 mm) were cut into two pieces with a blade and then were brought into contact with the additional force for 30 s on two sides to ensure the cut surfaces have good enough contact during the healing process (Figs. 20b-d). The samples were then put into UV chamber with different light intensities (7.4 W/𝑚 ( , 22.2 W/𝑚 ( and 37 W/𝑚 ( ) and controlled moisture using wet study to avoid the swelling and de-swelling behavior of the samples. The self-healed samples were then stretched uniaxially until ruptures using the same testing system (Instron, Model 5942) with strain rate 0.06 s -1 at 20 °C (Fig. 20e). We found that the original hydrogel ruptured at a strain around 4.3 (Fig. 20f). The corresponding nominal stress was denoted as the uniaxial strength. As the healing time increased, the uniaxial strength increased until a plateau of the original uniaxial strength (Fig. 20g). However, the uniaxial strength of the contacted samples without the illumination of the UV light only showed a slight increase, and could not reach the original strength even 59 when the healing time is 6-7 h. Besides, we found that the healing process of the TiO 2 nanocomposite hydrogels becomes more rapid as the UV light intensity increases (Fig. 20g). Figure 20. Experiments of hydrogels with inorganic photophores TiO ( nanocomposite (a) A schematic to show the polymer chain network of the TiO ( nanocomposite hydrogel and the related light-triggered production of free radicals. (b-e) A typical self-healing experiment of TiO 2 nanocomposite hydrogel. A hydrogel sample is first cut into two parts and then immediately brought into contact with the UV illumination. After a period of healing time, the sample can be stretched again. (f) Nominal stress- strain behaviors for the original and healed hydrogel samples. (g) Healing strength ratio of self-healed samples as functions of healing time for various UV intensities. The healing strength ratio is calculated as the nominal strength of the self-healed sample normalized by the nominal strength of the original sample. 4.4 Theoretical model 4.4.1 A general theory for light-activated interfacial healing With the presence of photoinitiators in the polymer matrix, the light can trigger the production of free radicals (Fig. 21). The basic process is shown in Fig. 21. The free radicals will assist the binding of the open distal groups on a polymer chain to become an active binding site (RM● shown in Fig. 21), thus to 60 bridge the fractured interface. In soft polymers with nanomaterial photophores, the active binding site is on the nanomaterial surface. In soft polymers with organic photophore, the active binding site is the open distal group on a polymer chain within the counterpart matrix. In section 4.4, we will model the light-activated production of free radicals; we will then model the radical-assisted chain rebinding. In the subsequent sections, we will apply the general model for light-activated interfacial healing to soft polymers with nanomaterial photophores and organic photophores, respectively. Figure 21. Two possible pathways for the photoinitiated binding process between an open distal group on a polymer chain and a binding site. (a) Pathway 1: The photoinitiator (PI) is first decomposed into free radicals (R·). A radical binds with the open distal group to form a distal radical (RM·). The distal radical reacts with the binding site and then is terminated by another radical. (b) Pathway 2: The photoinitiator (PI) is first decomposed into free radicals (R·). A radical transfers to the open distal group to form a distal radical (M·). The distal radical reacts with the binding site and then is terminated by another radical. 4.4.2 Light-activated production of free radicals When light with an initial light intensity 𝐼 ' is illuminated on a polymer material, the light will be attenuated through the material matrix. The light propagation can be modeled by the Beer-Lambert law 191-193 , )*(x,.) )0 =−𝐴(x,𝑡)𝐼(x,𝑡) (4-1) where 𝐼(x,𝑡) is the light intensity at position x=(𝑥,𝑦,𝑧) 1 and time t, the light propagation direction is along the z-axis (Fig. 22), and 𝐴(x,𝑡) is the absorption coefficient of the material. The light-sensitive R n R n 61 polymers contain photoinitiators that absorb light to produce free radicals (Fig. 22). Within the nanocomposite polymers, nanomaterials such as TiO 2 usually serve as the photoinitiator; while in other light-sensitive polymers, organic photoinitiators are employed. In both cases, the absorption coefficient can be estimated as 𝐴(x,𝑡) ≈𝛼 2 𝐶 * (x,𝑡)+𝐴 34. (4-2) where 𝐶 * (x,𝑡) is the concentration of the photoinitiator, 𝛼 2 is the molar absorptivity of the photoinitiator, and 𝐴 34. is the absorption coefficient of the material matrix. For the nanocomposite polymers, 𝐶 * (x,𝑡) is the concentration of the photosensitive nanomaterial such as TiO 2 nanoparticles. With the local light intensity 𝐼(x,𝑡), free radicals are produced from the photoinitiator. The governing equation of the concentration of the free radical 𝐶 5 (x,𝑡) can be written as 191-194,198-200 )6 ! (x,.) ). =𝑛 5 𝛼 ( 𝐶 * (x,𝑡)𝐼(x,𝑡)+𝐷 5 ∇ ( 𝐶 5 (x,𝑡)−𝑘 . [𝐶 5 (x,𝑡)] ( (4-3) where 𝛼 ( is the light absorption coefficient for the radical production, 𝑛 5 is the number of radicals produced per photoinitiator, 𝐷 5 is the diffusivity of the radical, 𝑘 . is the termination rate of the radical. Here, we assume the combination of two radicals will result in a termination of the radicals; therefore, the termination term involves a square term [𝐶 5 (x,𝑡)] ( . Note that for the organic photoinitiator, one photoinitiator is usually decomposed into two radicals, and thus 𝑛 5 =2 (Fig. 21). However, for a nanomaterial photoinitiator such as TiO 2, 𝑛 5 is an unknown large number that varies for nanoparticles with different activities 115,201 . Along with the production of radicals, the photoinitiator concentration of the nanocomposite may not change, i.e., 𝐶 * (x,𝑡)=𝜂 , where 𝜂 is the nanomaterial volume concentration. However, the concentration of the organic photoinitiator may change with a governing equation written as 191-193 )6 " (x,.) ). =−𝛼 ( 𝐶 * (x,𝑡)𝐼(x,𝑡)+𝐷 * ∇ ( 𝐶 * (x,𝑡) (4-4) where 𝐷 * is the diffusivity of the organic photoinitiator. Given an initial light intensity and material geometry (Fig. 22), we can calculate the concentration distribution of the radical within the material matrix from Eqs. 4-1 to 4-4. The theoretical results are presented in section 4.5. 62 Figure 22. Schematics to show the experimental procedure. The global Cartesian coordinate system is constructed on the healing interface. The light illumination direction is along the z-axis. 4.4.3 Radical-assisted chain binding The sample is first cut into two parts, and then immediately brought into contact to heal the interface with the illumination of a UV light (Fig. 23). During the cutting process, the dynamic bonds that crosslink the polymer chains will be dissociated by the large force induced by the cutting (Figs. 23ab). We assume one distal group of the chain is dissociated from a binding site that is within the matrix, and then this distal group will be pulled out of the matrix to the fracture interface. Since the healing experiment is carried out immediately after the cutting, we assume the open distal group on the chain will still be around the interface at the very beginning of the healing process (Figs. 23bc), primarily because the migration of the chain and its distal group takes substantial time. During the healing process, the polymer chain with the open distal group will gradually diffuse cross the interface to find the binding site to reform the dynamic bond. Once the dynamic bond is reformed (or re-associated), the polymer chain becomes linked and can sustain loading forces. We assume the original polymer networks crosslinked by the dynamic bonds consist of m types of chains with Kuhn segment number n 1, n 2, …. and n m, respectively. Each Kuhn segment has a length b. The specific polymer network architecture will be discussed in section 4.4. Here, we only focus on the ith chain with Kuhn segment number n i, where 1≤𝑖 ≤𝑚. The number of ith chain per unit volume of material is 𝑁 " . 63 The re-binding process of the ith chain involves the chain diffusion and distal group reaction. We first model the binding between the open distal group and the binding site as a chemical reaction. This chemical reaction involves multiple small processes shown as two representative pathways in Figs. 21ab. In the first pathway (Fig. 21a), the free radical binds on the open distal group on the ith chain to become a distal radial. Then, the distal radical binds on the binding site. Finally, the radical will be terminated by combining with another free radical. Effectively, the reaction involves two radicals, an open distal group on the ith chain, and a binding site. In the second pathway (Fig. 21b), the photoinitiator (PI) is first decomposed into free radicals (R·). A radical transfers to the open distal group to form a distal radical (M·). The distal radical reacts with the binding site and then is terminated by another radical. This re-binding process turns an open ith chain into a linked ith chain. We denote 𝐶 " 7 (𝑠,𝑡) as the open ith chain number per unit length along the curvilinear coordinate s (0≤𝑠 ≤𝐿 " ( /4𝑏) at time t (Fig. 23c), and 𝐶 " 4 (𝑠,𝑡) as the corresponding linked quantity. We further denote the reaction from the open chain to the linked chain as the forward reaction and the else as the reverse reaction. The reaction kinetics can be written as )6 # $ (8,.) ). =𝑘 " #' 𝐶 " 7 (𝑠,𝑡)−𝑘 " $' 𝐶 " 4 (𝑠,𝑡) (4-5) where 𝑘 " #' is the forward reaction rate and 𝑘 " $' is the reverse reaction rate. We further assume that the self- healing capability of the studied polymer is relatively strong; that is to say, the association reaction rate 𝑘 " #' is much larger than the dissociation reaction rate 𝑘 " $' . Therefore, Eq. 5 can be reduced to )6 # $ (8,.) ). ≈𝑘 " #' 𝐶 " 7 (𝑠,𝑡) (4-6) As shown in Figs. 23ab, the presence of free radicals significantly facilitates the re-association process of the ith chain. The forward reaction rate can be approximated as 𝑘 " #' =𝑘 2 [𝐶 5 (x,𝑡)] ( (4-7) where 𝑘 2 is a positive coefficient and the square term is because of the presence of two radicals per reaction (Figs. 23ab). R n 64 The radical-assisted binding will facilitate the chain diffusion to cross the healing interface. The chain diffusion can be modeled by following a snake reptation model proposed by De Gennes 100,117-119 . The basic idea is that the polymer chain is constrained by the polymer matrix so it can only reptate along a primitive tube 120 . The primitive tube length is 𝐿 9 , so the original chain is divided into 𝑛 " segment with each segment length 𝑏 9 = : % ; # (4-8) At each small time step, the chain is considered to jump by a step length 𝑏 9 in a random-walk fashion. In the original reptation model, the tube length is considered as smaller than the contour length of the ith chain, i.e., 𝐿 9 ≤𝑛 " 𝑏; because the chain may coil around the reptation tube. Subsequently, the jump step 𝑏 9 is considered as an unknown parameter. Here, we make a bold assumption that the contour length of the ith chain is approximately equal to the reptation tube length; therefore, the jump step length 𝑏 9 ≈𝑏 (4-9) The motion of the polymer chain is enabled by extending out small segments called “minor chains” (Fig. 23c). The curvilinear motion of the polymer chain is characterized by the Rouse friction model with the curvilinear diffusivity of the ith chain expressed as 𝐷 " = < & 1 ; # = (4-10) where 𝜉 is the Rose friction coefficient per unit Kuhn segment, 𝑘 > is the Boltzmann constant, and 𝑇 is the temperature in Kelvin. As shown in Fig. 23c, we assume the end-to-end distance of the ith chain is L i. Without loss of generality, we assume the cutting position is located in the middle of the chain; thus, the distance between the healing interface and the binding site is L i/2. This assumption is just for the sake of analysis simplicity; other location may also work but may involve more complicated statistic averaging algorithm. As shown in Fig. 23c, the distal group will diffuse cross the normal distance L i/2 following a curvilinear pathway. To facilitate the analysis, we construct two coordinate systems: s denotes the curvilinear path along the minor chains, and u denotes the linear path from the interface to the binding site. When the ith chain 65 moves 𝑠 " distance along the curvilinear path, it is corresponding to 𝑢 " distance along u coordinate. Here we assume the selection of the curvilinear path is stochastic in a random-walk fashion 121-123 . Therefore, the conversion of the distances in two coordinate systems is expressed as 117,120 𝑢 " =W𝑠 " 𝑏 9 ≈W𝑠 " 𝑏 (4-11) According to Eq. 4-11, the 𝐿 " /2 in the y coordinate is corresponding to 𝐿 " ( /4𝑏 in the s coordinate. The chain diffusion and the association reaction are strongly coupled, as the binding reaction may greatly facilitate the diffusion process; therefore, we couple the chain diffusion and binding reaction within the region 0≤𝑠 ≤𝐿 " ( /4𝑏 using an effective diffusion-reaction equation as )6 # ' (8,.) ). =𝐷 " ) ( 6 # ' (8,.) )8 ( − )6 # $ ). (4-12) Coupled with Eqs. 4-6 and 4-7, Eq. 4-12 can be rewritten as )6 # ' (8,.) ). =𝐷 " ) ( 6 # ' (8,.) )8 ( −𝑘 2 [𝐶 5 (x,𝑡)] ( 𝐶 " 7 (𝑠,𝑡) (4-13) It can be shown from Eq. 4-13 that the light-triggered production of radicals can facilitate the binding reaction and thus promote the chain diffusion. At the beginning of the healing process, all mobile open distal groups of the ith chain are located around the healing interface, which can be expressed as 𝐶 " 7 (𝑠,𝑡 =0)=𝑁 " 𝛿(𝑠) (4-14) 𝐶 " 4 (𝑠,𝑡 =0)=0 (4-15) where ∫ 𝛿(𝑠) ? @? =1. Besides, we assume the association reaction rate is much larger than the dissociated reaction rate; subsequently, we can make a bold assumption that all open distal groups form dynamic bonds around the binding site location 𝑠 =𝐿 " ( /4𝑏, which is expressed as 𝐶 " 7 Z𝑠 =𝐿 " ( /4𝑏,𝑡[ ≈0 (4-16) From Eqs. 4-13 to 4-16, we can solve the concentration distributions 𝐶 " 7 (𝑠,𝑡) within the curvilinear coordinate. To convert these to the effective concentration of linked ith chain within the region 0≤𝑢 ≤ 𝐿 " /2, we write 66 A # ) (.) A # =1− BC : # ( ∫ 6 # ' (8,.) A # 𝑑𝑠 : # ( /BC ' (4-17) where 𝑁 " E (𝑡) is the average ith chain number per unit volume of the region 0≤𝑢 ≤𝐿 " /2 at the undeformed state (𝜆 2 =𝜆 ( =𝜆 F =1), and the superscript “h” denotes “healed”. Figure 23. Schematics to show the polymer chain behaviors around the healing interface. (a) At the original state, a polymer chain is bond by two binding sites across the cutting interface. (b) The cutting forces the detachment between the polymer chain and one binding site. Since we immediately contact two fractured parts, we assume the distal group of the polymer chain is still around the interface. (c) During the healing process, the distal group migrates into the counterpart to find and bind the binding site under the activation of the UV light. 4.4.4 Model for soft polymers with nanomaterial photophores In this section, we apply the general theory of the light-activated interfacial self-healing to soft polymers with nanomaterial photophores such as TiO 2 nanoparticles 190 . The nanomaterials serve as multifunctional crosslinkers that are able to bridge a large number of polymer chains (Figs. 20 and 23ab). These polymer chains may not have the same chain length but follow an inhomogeneous chain length distribution (Fig. 24c). Following our previous study on nanocomposite hydrogels, we assume the nanomaterial crosslinkers self-organize into body-centered cubes through the whole material matrix (Fig. 24a). Like the eight-chain model, the center nanocrosslinker and a corner nanocrosslinker bridge m types of chains with chain lengths number n 1, n 2, …. and n m. The distance between the center nanocrosslinker and the corner nanocrosslinker 67 𝐿 " can be estimated from the volume concentration of the nanocrosslinker 𝜂. A cube in Fig. 24a with a volume 8𝐿 " F /3√3 averagely involve two nanocrosslinkers; therefore, 𝐿 " ≈ √F HBI * (4-18) We denote the ith chain number between a center nanocrosslinker and a corner nanocrosslinker as 𝑁 " ∗ . As we assume the chain number of the ith chain per unit volume as 𝑁 " , we have 𝑁 " = KA # ∗ , *√* : # * = F√FA # ∗ : # * (4-19) We thus calculate 𝑁 " ∗ as 𝑁 " ∗ = A # BI (4-20) The chain length distribution of these m types of chains can be written as 𝑃 " (𝑛 " ) = A # ∑ A # . #/0 (4-21) For simplicity, we only consider a log-normal chain length distribution as 99 𝑃 " (𝑛 " )= 2 ; # M√(N 𝑒𝑥𝑝d− (OP; # @OP; $ ) ( (M ( e (4-22) where 𝑛 4 and 𝛿 are the mean of 𝑛 " and standard deviation of ln𝑛 " , respectively. Figure 24. Schematics of the nanocomposite hydrogel 68 (a) A network model for the nanocomposite hydrogel. (b) A number of polymer chains with inhomogeneous chain lengths are bridged between a particle pair. (c) A schematic to show the chain- length distribution of the polymer chains between a particle pair. (d) Schematics of the network model during the cutting and healing process. The cutting is assumed to be located in a quarter position of the cube. For the ith chain, the freely-joint end-to-end distance is W𝑛 " 𝑏. The presence of nanocrosslinker makes the initial end-to-end distance as 𝐿 " . As the ith chain is deformed with the end-to-end distance 𝑟 " , the chain stretch is calculated as Λ " = $ # H; # C (4-23) The free energy of the deformed ith chain can be written as 𝑤 " =𝑛 " 𝑘 > 𝑇k Q # tanh Q # +ln Q # sinh Q # l (4-24) where 𝛽 " =𝐿 @2 ZΛ " /W𝑛 " [ and 𝐿 @2 ( ) is the inverse Langevin function. The force within the deformed ith chain can be written as 𝑓 " = )Y # )$ # = < & 1 C 𝛽 " (4-25) We consider an affined deformation model with the assumption that the bond-centered cube deforms by three principal stretches (𝜆 2 ,𝜆 ( ,𝜆 F ) under the macroscopic deformation (𝜆 2 ,𝜆 ( ,𝜆 F ) at the material level. Therefore, the stretch of each ith chain is Λ " = n Z 0 ( [Z ( ( [Z * ( F : # H; # C (4-26) For the original material, the initial number of ith chain per unit material volume is 𝑁 " . This ith chain density will decrease to 𝑁 " 4 as the material deforms because the chain force will motivate the dissociation of the dynamic bond between the chain the nanocrosslinker. Following Eq. 4-5, we write the binding reaction kinetics as 7A # $ 7. =𝑘 " # 𝑁 " 7 +𝑘 " $ 𝑁 " 4 (4-27) where 𝑘 " # and 𝑘 " $ are forward and reverse reaction rates at the deformed state, respectively. Following the Bell’s model 110 , we can write the chain-force-dependent reaction rates as 69 𝑘 " # =𝑘 " #' expk− # # \] < & 1 l 4-(28a) 𝑘 " $ =𝑘 " $' expk # # \] < & 1 l (4-28b) where Δ𝑥 is the distance along the energy landscape coordinate. If the loading is applied quasistatically, the linked ith chain volume density can be calculated as 𝑁 " 4 = A # < # 12 exp`@ 1 # 34 5 & 6 a < # 72 exp` 1 # 34 5 & 6 a[< # 12 exp`@ 1 # 34 5 & 6 a (4-29) As shown in Eq. 4-29, 𝑁 " 4 decreases as the chain force of the ith chain increases. With Eqs. 4-24 and 4-29, we can express the strain energy per unit material volume as 𝑊 =∑ 𝑁 " 4 𝑛 " 𝑘 > 𝑇k Q # tanh Q # +ln Q # sinh Q # l 3 "b2 (4-30) where 𝛽 " =𝐿 @2 ZΛ " /W𝑛 " [ and Λ " is given in Eq. 4-26. If the material is incompressible and uniaxially stretched with three principal stretches (𝜆 2 =𝜆,𝜆 ( =𝜆 F =𝜆 @2/( ), the nominal stress along 𝜆 2 direction can be written as 𝑠 2 = (Z@Z 8( )< & 1 √FZ ( [cZ 80 ∑ t𝑁 " 4 : # C 𝐿 @2 un Z ( [(Z 80 F : # ; # C vw 3 "b2 (4-31) As the stretch increases, the chain forces on the short chains are larger than those on the long chains; the short chains will be first detached from the nanoparticles and then the long chains (Fig. 24c). When the stretch is sufficiently large, the majority of chains are detached from the nanoparticles, and the corresponding stress would decrease with the increasing stretch. Therefore, the stress-stretch behavior of the original material features a maximal stress that is defined as the tensile strength of the material. In the healing experiment, we first use a sharp blade to cut through the hydrogel bar (Fig. 22 and 24d). For simplicity of analysis, we assume the cutting position is located in the middle of polymer chains between particle pairs as shown in Fig. 24d 84,174 . This echoes the assumption in section 4.4 that the cutting location is in the middle of two binding sites shown in Fig. 23b. At the cutting tip, the blade highly deforms the polymer chains until the chains are detached from the particles. Since the chain strength is much larger than the chain-particle bonding strength, we assume that the polymer chains can only be detached from the 70 particle surfaces without breaking in the middle of the chains 115 . At the detachment point, the chain may be detached from either particle, with the other end being still attached to the other particle. We assume that each particle of a particle-pair still attach half portion of polymer chains after cutting (Fig. 24d). Then two parts are immediately brought into contact with the polymer chains interpenetrate into each other to rebind on the particles. For the self-healing sample that is composed of two original segments and a small self-healed segment (Fig. 22c). Within the self-healed segment, the strain energy per unit material volume is 𝑊 =∑ 𝑁 " 4E 𝑛 " 𝑘 > 𝑇k Q # tanh Q # +ln Q # sinh Q # l 3 "b2 (4-32) 𝑁 " 4E = A # ) < # 12 exp`@ 1 # 34 5 & 6 a < # 72 exp` 1 # 34 5 & 6 a[< # 12 exp`@ 1 # 34 5 & 6 a (4-33) where 𝑁 " E is given by Eq. 4-17. If the material is uniaxially stretched by 𝜆 E , the corresponding nominal stress is 𝑠 2 E = (Z ) @Z ) 8( )< & 1 d FZ ) ( [cZ ) 80 ∑ t𝑁 " 4E : # C 𝐿 @2 u n Z ) ( [(Z ) 80 F : # ; # C vw 3 "b2 (4-34) If the self-healed sample is uniaxially stretched (like Fig. 20e), the nominal stresses in the original material segment and the self-healed segment should be equal, i.e., 𝑠 2 E =𝑠 2 . Based on the above theoretical framework, we can calculate the stress-strain behaviors of the self-healed sample and the corresponding healing strength for various healing time (results in section 4.5). 4.4.5 Model for soft polymers with organic photophores In this section, we apply the general theory of the light-activated interfacial self-healing to soft polymers with organic photophores. Unlike the soft polymers crosslinked by multifunctional nanomaterials, the organic crosslinker cannot bridge a large number of polymer chains. To consider the inhomogeneous chain length distribution, we employ an interpenetration network model that assumes the polymer is composed of m types of networks interpenetrating in the material bulk (Fig. 25a) 99 . In each network, the chain length 71 is the same, denoted as n 1, n 2, …. and n m. In the undeformed state, all chains are freely-joint; therefore, the end-to-end distance of the ith chain is 𝐿 " =W𝑛 " 𝑏 (4-35) With the chain number of the ith chain per unit volume as 𝑁 " , we can also express the chain length distribution as Eq. 4-21. With the affined deformation model, the stretch of the ith chain is different from Eq. 4-26, but should be Λ " = n Z 0 ( [Z ( ( [Z * ( F (4-36) With the strain energy density expressions of the original material similar to Eq. 30, we can write the uniaxial nominal stresses of the original material as 𝑠 2 = (Z@Z 8( )< & 1 √FZ ( [cZ 80 ∑ t𝑁 " 4 W𝑛 " 𝐿 @2 un Z ( [(Z 80 F; # vw 3 "b2 (4-37) Then, following the similar microscopic picture as self-healing of the nanocomposite hydrogels shown in Fig. 24d, we can model the behavior of the self-healed segment of the soft polymers with organic photophores in Fig. 25b. The corresponding uniaxial nominal stress of the self-healed segment can be written as 𝑠 2 E = (Z ) @Z ) 8( )< & 1 d FZ ) ( [cZ ) 80 ∑ t𝑁 " 4E W𝑛 " 𝐿 @2 u n Z ) ( [(Z ) 80 F; # vw 3 "b2 (4-38) Going through the calculation process shown in section 4.4, we can calculate the stress-strain behaviors of the self-healed samples and the corresponding healing strength for various healing time (results in section 4.6). 72 Figure 25. Schematic of interpenetration network model. (a) An interpenetration network model for the light-activated self-healing polymers with organic lightophores. (d) Schematics of the ith network model during the cutting and healing process. The cutting is assumed to be located in a quarter position of the cube. 4.5 Results for light-activated self-healing polymers with inorganic photophores In this section, we will first take the photo-healable TiO 2 nanocomposite hydrogel as an example to illustrate how to relate the light property to the interfacial self-healing performance. We will also examine the effects of light intensity and light wavelength on the self-healing performance. The theoretical results will be compared with the experimental ones. All used parameters are presented in Table 3. 4.5.1 Results for the light propagation within the TiO2 nanocomposite hydrogel As shown in Figs. 20b-e, the TiO 2 nanocomposite hydrogel is partially opaque; therefore, the absorption coefficient of the material matrix is much larger than the absorption induced by the photoinitiator, i.e., 𝛼 2 𝐶 * (x,𝑡)≪𝐴 34. . We thus solve the light intensity distribution as (Fig. 22c) 𝐼(𝑧)≈𝐼 ' expd−𝐴 34. kW𝑟 ( −𝑦 ( +𝑧le (4-39) 73 where 𝐼 ' is the initial light intensity and r is the radius of the cross-section area. The light intensity distribution in the cross-section region is shown in Fig. 26a. The corresponding light intensity along the central line is plotted in Fig. 26b. This light intensity distribution will not change during the whole light- activation process. As for the TiO 2 nanocomposite hydrogel, the photoinitiator is the TiO 2 nanoparticle whose concentration does not change during the whole light-activation process; thus, we have 𝐶 * =𝜂 in Eq. 4-3. Solving Eq. 4-3 leads to the concentration distributions of the free radical in the cross-section region (Fig. 26c). With increasing illumination time, more and more free radicals are produced on the cross-section region (Fig. 26d). Note that the concentration distribution of the free radical is inhomogeneous over the cross-section area: more radicals are produced at the locations closer to the light incident surface. It means that the healing percentage will vary across the interface. To simplify the problem, we average the radical concentration across the interface as 𝐶 5 yyy (𝑡) (Fig. 26) and consider an effectively homogeneous self-healing across the interface in section 4.5. Table 3. Definition and value of the employed parameters. The initial light intensity for Figs. 26-30 are directly extracted from experiments. The initial light intensity for Figs. 32-34 is estimated by 𝑃/(4𝜋𝐿 ( ), where the power 𝑃 =14𝑤 and L=20cm is the distance between the lamp and the sample 186 . The absorption coefficient of the material matrix of partially opaque TiO2 hydrogel follows the one of the optically thick polymer discussed in 192,198 , and the absorption coefficient of the material matrix of clear polymers in 186 follows the one of the optically thin polymer discussed in 192,198 . The number of radicals produced per TiO 2 nanoparticle photoinitiator in Figs. 26-30 is estimated as in the same order of the active binding sites 𝑁 8".% on the nanoparticle surfaces. As 𝑁 8".% =4𝑟 ( 𝜅/𝑏 ( , where b is the Kuhn segment length, r is the particle radius, and 𝜅 is the particle activity parameter 115,201 . Following 115 , we estimate 𝜅 is in the order of 0.01; then, we roughly estimate the binding site number is in the order of 10 3 . Therefore, we estimate the number of radicals produced per TiO 2 nanoparticle photoinitiator in Figs. 26-30 as 1000. Forward and reverse reaction rates are estimated from the ones for the dynamic covalent bonding kinetics in 174 . 𝑛 4 is a fitting parameter used to match the stress-strain behaviors of original polymer networks. Δ𝑥 is another fitting parameter used to match the tensile strength of original polymer networks 84,115,174 . The rouse friction coefficient is the third fitting parameter to match the healing time-scale 84,174 . Parameter Definition Figs. 26- 28 Fig. 29 Fig. 30 Figs. 32 & 34 Fig. 33 Estimation source 𝐼 9 (W m -2 ) Initial light intensity 37 7.4-37 37 27.9 27.9 Experimental data 𝛼 : (m 3 mol -1 s -1 ) Molar absorptivity of the photoinitiator N/A N/A N/A 0.1 0.1 192,198 𝐴 ;<= (m -1 ) absorption coefficient of the material matrix 120 120 120 10 10 192,198 74 𝛼 > (m 2 W -1 s -1 ) Light absorption coefficient for the radical production 2.65x10 -5 2.65x10 -5 2.65x10 -5 & 1.25x10 -5 3.51 x10 -8 3.51 x10 -8 192,194,198 𝑛 ? number of radicals produced per photoinitiator 1000 1000 1000 2 2 115,201 𝐷 ? (m 2 s -1 ) diffusivity of the radical 1x10 -10 1x10 -10 1x10 -10 1x10 -10 1x10 -10 192,198 𝑘 = (s -1 mol -1 m 3 ) termination rate of the radical 0.1 0.1 0.1 0.1 0.1 192,198 𝐷 @ (m 2 s -1 ) diffusivity of organic photoinitiator N/A N/A N/A 1x10 -10 1x10 -10 192,198 𝜂 (mol m -3 ) volume concentration of nanocrosslinker 2.33x10 -3 2.33x10 -3 2.33x10 -3 N/A N/A Experimental data 𝐶 @9 (mol m -3 ) Initial photoinitiator concentration 0.5 0.01-1 Experimental data 𝑘 : (s -1 mol -2 m 6 ) Coefficient for the forward reaction rate 0.5 0.5 0.5 5 5 84,174 𝑘 A B9 (s -1 ) Reverse reaction rate 2x10 -6 2x10 -6 2x10 -6 2x10 -6 2x10 -6 84,174 Δ𝑥(m) Distance along the energy landscape coordinate 4x10 -9 4x10 -9 4x10 -9 5.1x10 -9 5.1x10 -9 Fitting parameter b (m) Kuhn segment length 5.2x10 -10 5.2x10 -10 5.2x10 -10 5.2x10 -10 5.2x10 -10 84,174 𝑛 : Minimum chain length 300 300 300 100 100 Chosen based on 𝑛 < 𝑛 ; Maximum chain length 1500 1500 1500 800 800 Chosen based on 𝑛 < 𝑛 < Average chain length 576 576 576 400 400 Fitting parameter 𝛿 Chain length distribution width 0.15 0.15 0.15 0.2 0.2 84,115,174 𝜉(N/m) Rouse friction coefficient 5x10 -8 5x10 -8 5x10 -8 5x10 -5 5x10 -5 Fitting parameter h h h 75 Figure 26. Photoinitiation within the TiO2 nanocomposite hydrogel. (a) The light intensity distribution on the healing interface. (b) The light intensity distribution along the depth z. (c) The radical concentration distribution on the healing interface at illumination time t=500s. (d) The radical concentration C R as functions of the depth z for various light illumination time t. (e) The average radical concentration on the healing interface as a function of light illumination time t. 4.5.2 Results for the penetration of the ith chain Once the average radical concentration in the cross-section area is calculated, we can employ Eqs. 4-13 and 4-17 and related boundary and initial conditions (Eqs. 4-14 to 4-16) to calculate the average ith chain number density 𝑁 " E within the self-healed region (Fig. 27). Note that the radical concentration 𝐶 5 (x,𝑡) will be replaced by the time-dependent average radical concentration in the cross-section area 𝐶 5 yyy (𝑡). As seen from Fig. 27, the average ith chain density 𝑁 " E (𝑡) increases from zero to reach a plateau 𝑁 " as the time is long enough. The time scale to reach the plateau depends on the Rouse diffusivity of the ith chain 𝐷 " and the free radical concentration 𝐶 5 yyy (𝑡). 76 Figure 27. The effective concentration of the linked ith chain within the healed region as a function of normalized UV illumination time. 4.5.3 Results for the light-activated self-healing of soft polymers with nanomaterial photophore The self-healed sample has three segments: two segments with original materials and one small self-healed segment with the re-formed linked chains (see inset of Fig. 28a). Once the healed linked ith chain density within the self-healing region is calculated, we can employ the interpenetration network model shown in section 4.4 to calculate the stress-strain behaviors of the original and the self-healed segments, respectively (Fig. 28a). Note that the stress-strain curve of the original material features a maximum that is considered as the tensile strength of the material (Fig. 28a). For an original hydrogel sample, as the nominal stress gradually increases with the stretch, the polymer chains are gradually detached from the nanoparticles (Fig. 24c). Once most of the polymer chains are detached, the nominal stress begins to decrease. At the critical point (denoted by the red cross on the blue line in Fig. 28a), the hydrogel sample breaks into two parts, and the red cross indicates the tensile strength of the hydrogel. In the following, we will employ the tensile strength as the indicator for the interfacial healing. The major reason is that the measurement of the interfacial strength in experiments is relatively easy and most of the researchers in the self-healing community use the tensile strength in their experiments 9,11,23,41,48,195 . The results of interfacial strength are reliable when the sample number is large enough to eliminate the effects of small defects. In the experiments, we always use multiple samples (up to 10 samples for each case) to validate the accuracy of the measurement. 77 We assume undeformed and deformed lengths of the self-healed segment are 𝐻 E and ℎ E , respectively, and the corresponding undeformed and deformed lengths of the sample are 𝐻 and ℎ , respectively. The stretch of the original segment is calculated as E@E ) e @e ) ≈ E e (4-40) because ℎ ≫ℎ E and 𝐻 ≫𝐻 E ; therefore, the stretch of the self-healed sample is approximately the same as the stretch of the original segment. As nominal stresses in the original segment and the self-healed segment should be equal (𝑠 2 E =𝑠 2 ), we can predict that the stress-strain curve of the self-healed sample follows the trace of the stress-strain curve of the original sample, only with a lower maximal nominal stress (indicated as the red cross in Fig. 28b). This can be validated by the experimentally measured stress-strain behaviors of the self-healed sample (Fig. 28c). Collecting the maximal nominal stress (named as healing strength) corresponding to each healing time, we can predict the relationship between the healing strength as a function of the healing time (Fig. 28d). To present the results, we usually normalize the healing strength with the uniaxial strength of the original material and calculate as healing strength ratio (Fig. 28d). We find the healing strength ratio increases with increasing the healing time and reaches a plateau when the healing time is long enough. To indicate the healing speed, we denote the equilibrium healing time as the time corresponding to 90% healing strength ratio. We find that the theoretically calculated relationship between the healing strength ratio can roughly match with the experimental results of the light-activated self-healing of the TiO 2 nanocomposite hydrogels (Fig. 28d). The discrepancy exists in the short healing time range because the theoretical model does not take the immediate adhesion into account. More discussions about this limitation can be found in the conclusive remarks. 78 Figure 28. Results for the light-activated self-healing of soft polymers with nanomaterial photophore. (a) The nominal stresses of the original and self-healed segments as functions of uniaxial strains of these segments. (b) The nominal stresses of the original and self-healed samples as functions of uniaxial strains of these samples. (c) The comparisons between the experimentally measured and theoretically calculated nominal stress-strain behaviors of the original and self-healed nanocomposite hydrogel samples. (d) The experimentally measured and theoretically calculated healing strength ratios of the nanocomposite hydrogel as functions of the healing time. 4.5.4 Effect of light intensity To illustrate the capability of our theoretical model, we then study the effect of light intensity on the self- healing performance of the TiO 2 nanocomposite hydrogels (Fig. 29). With the higher initial UV light intensity I 0, the average radical concentration on the healing interface reaches the higher plateau within a shorter light illumination time (Fig. 29a). According to Eq. 4-13, the higher concentration of radicals will promote the binding reactions between the distal groups and binding sites, and thus accelerate the healing process. Therefore, the predicted healing strength ratios reach the plateau within a shorter healing time for the higher light intensity cases (Figs. 29b and 20f). In addition, we show that the theoretically calculated healing strength ratio and equilibrium healing time can consistently match with the corresponding experimental results (Fig. 29c). 79 Figure 29. Effect of the light intensity on the self-healing behavior of the TiO2 nanocomposite hydrogel. (a) The average radical concentrations on the healing interface for various initial UV light intensities as functions of the UV illumination time. (b) The experimentally measured and theoretically calculated healing strength ratios of the TiO 2 nanocomposite hydrogels for various UV intensities as functions of healing time. (c) The experimentally measured and theoretically calculated equilibrium healing time as functions of the UV light intensity. 4.5.5 Effect of light wavelength To further illustrate the capability of the theoretical model, we study the effect of UV wavelength on the self-healing performance of the TiO 2 nanocomposite hydrogels (Fig. 30). The activities of TiO 2 nanoparticles vary for different wavelengths of the incident light. The absorption intensities of the employed TiO 2 nanoparticle for various incident light wavelength is shown in Fig. 30a 202 . The absorption coefficient 𝛼 ( in Eq. 3 is expected to be proportional to the absorption intensity of the TiO 2 nanoparticle. From Fig. 30a, we can estimate that 𝛼 ( Fcf /𝛼 ( (fB ≈2.12, where 𝛼 ( Fcf and 𝛼 ( (fB are the absorption coefficient of the TiO 2 nanoparticle for UV lights with wavelengths 365 nm and 254 nm, respectively. Based on the theoretical calculation for 254 nm UV light, we can predict the relationship between the healing strength ratio and the healing time for 365 nm UV light (Fig. 30b). The theoretical results match consistently with the experimentally measured ones. 80 Figure 30. Effect of the UV wavelength on the self-healing behaviors of the TiO2 nanocomposite hydrogel. (a) The absorption spectrum of the TiO 2 nanoparticles. The curve is reproduced from reference 202 with permission. (b) The healing strength ratio of the TiO2 nanocomposite hydrogel under UV light 254 nm and 365 nm as functions of the healing time. 4.6 Results for light-activated self-healing polymers with organic photophores In this section, we show that the theory can also be used to explain the light-activated self-healing of soft polymers with organic photophores. The effect of photoinitiator concentration on the self-healing performance is examined. The theoretical calculations of the self-healing performance of the soft polymers with organic photophores are compared with the experimentally measured results. Here, we consider a light-activated healable polymer system in 186 (Fig. 31). The thiuram disulfide (TDS) unit can undergo a light-induced homolytic cleavage reaction to produce free radicals 185,186,203 . This TDS unit can be within a crosslinked polymer network or the TDS diol. The TDS diol comes from the unreacted TDS diol during the polymer synthesis. Since the mobility of the TDS unit within the crosslinked polymer network is very limited, the mobile TDS diols are anticipated to contribute the majority mobile free radicals during the light-activated self-healing process. Therefore, we believe that the TDS diol serves as the major photoinitiator. Under light actuation, the TDS diol is decomposed into two free TDS radicals (Fig. 31a). Then, the TDS radicals transfer across the interface to re-bridge the fractured interface (Fig. 31b) 185,186,203 . 81 Figure 31. Schematic of the healing process of the thiuram disulfide (TDS) diol. (a) The light-induced homolytic cleavage reaction of the thiuram disulfide (TDS) diol to produce free radicals. (b) Reaction process around the healing interface of the light-activated healable polymers with thiuram disulfide (TDS) moieties. The TDS radicals transfer across the interface to rebridge the fractured interface. For the TiO 2 nanocomposite hydrogel, TiO 2 nanoparticles serve as the photoinitiator, and its concentration does not change during the light-activation process. However, for the soft polymers with organic photophores, the concentration of the initial organic photoinitiator will decrease during the light illumination process. The photoinitiators will be decomposed into free radicals to activate the self-healing process. As for a sample in a circular bar shape, three fields are coupled within the circular healing interface: the light intensity (Eq. 4-1), the photoinitiator concentration (Eq. 4-3), and radical concentration (Eq. 4-4). We employ the numerical software COMSOL with its general PDE function to solve the coupled fields. As shown in Figs. 32ab, the light intensity decreases from the incident surface to the rear surface. Higher light intensity consumes more photoinitiators to produce more radicals; therefore, the photoinitiator concentration is lower at the incident surface (Fig. 32cd), while the radical concentration is higher at the incident surface (Figs. 32ef). As the light illumination time increases, the overall photoinitiator concentration decreases but the radical concentration increases. Similar to the TiO 2 nanocomposite 82 hydrogel, we consider an effectively homogenous self-healing over the healing interface. We thus calculate the average radical concentration as a function of the illumination time (Fig. 32g). We find that the average radical concentration first increases with the increasing illumination time and then reaches a plateau. This plateau is because of the saturation of radical production. Then, with the average radical concentration, we follow the model shown in section 4.3 to calculate the relationship between the healing strength ratio and the healing time for the soft polymer with organic photophores (Fig. 32h). Figure 32. Results for light-activated self-healing polymers with organic photophores. (a) The light intensity distribution on the healing interface. (b) The light intensity distribution along the depth z on the healing interface. (c) The photoinitiator concentration distribution on the healing interface at t=8h. (d) The photoinitiator concentration C I as functions of the depth z for various light illumination time t. (e) The radical concentration distribution on the healing interface at t=8h. (f) The radical concentration C R as functions of the depth z for various light illumination time t. (g) The average radical concentration on the healing interface as a function of light illumination time t. (h) The healing strength ratio as a function of healing time of the polymer with organic photophores. 83 4.6.1 Effect of photoinitiator concentration. With the above method, we can predict the effect of the initial photoinitiator concentration 𝐶 *' on the self- healing behavior of the soft polymer with organic photophores (Fig. 33). Higher photoinitiator concentration induces the higher average radical concentration on the healing interface. And higher radical concentration leads to the faster healing process of the material (Figs. 33ab). Therefore, the equilibrium healing time decreases with increasing initial photoinitiator concentration (Fig. 33b). Besides, we find that the changing rate of the equilibrium healing time is decreasing with increasing photoinitiator concentration. It is because the radical production is close to the saturation state when the photoinitiator concentration is high, and the equilibrium healing time change is less insensitive than that when the photoinitiator concentration is low. Figure 33. Effect of photoinitiator concentration on the self-healing behavior of the polymer with organic photophores. (a) The healing strength ratios for various initial photoinitiator concentrations as functions of the healing time. (b) The equilibrium healing time as a function of the initial photoinitiator concentration. To verify the theoretical model, we compare the theoretical results with the experimentally measured results for a polymer with organic photophores thiuram disulfide moieties 186 . This polymer can self-heal the interfacial strength by around 100% with the illumination of visible light for 24 h (Fig. 33a). Using the developed theory in section 4.4, we can plot the uniaxial nominal stress-strain behaviors for the original and self-healed polymer samples, which agree well with the experimentally measured results. The theoretically calculated relationship between the healing strength ratio and the healing time also match the experimental results. Note that the theoretical calculations for Fig. 34 follow the method discussed around Fig. 32. The cross-section shape of the sample here is rectangular (2 mm x 1 mm). As we actually 84 homogenize the chemical concentrations across the interface, the cross-section shape has little influence on the healing strength. To be consistent, we still roughly approximate the cross-section as a circle (radius 0.8 mm) for the case in Fig. 34. We predict that the equilibrium healing time with 90% healing strength is around 6 h, while this specific number is usually challenging to determine in the experiment without carefully screening over the whole hour range. Figure 34. Comparison of experimental and theoretical results. (a) The experimentally measured nominal stress-strain behaviors of the original and self-healed polymers with organic photophores. (b) The comparisons between the experimentally measured and theoretically calculated nominal stress-strain behaviors of the original and self-healed polymers with organic photophores. (c) The experimentally measured and theoretically calculated healing strength ratios as functions of the healing time. The results in (a-c) are reproduced from 186 with permission 4.7 Conclusive remarks In summary, we present a theoretical framework to understand the light-activated interfacial self-healing of soft polymers with both inorganic and organic photophores. We consider that the light within the material matrix triggers the production of free radicals that further facilitate the interfacial self-healing process. The self-healing process is considered as a coupled phenomenon that polymer chains diffuse across the interface and re-form the dynamic bonds assisted by the free radicals. We theoretically relate the light property and the interfacial self-healing strength of the polymers. We predict that the interfacial self-healing strength of the polymer increases with the light illumination time until reaching a plateau. We study the effects of the light intensity, light wavelength, and photoinitiator concentration on the self-healing performance. We apply the theory to two types of soft polymers with inorganic and organic photophores, respectively. The experimentally measured stress-strain behaviors of the original and self-healed samples can be consistently explained by the theory. The theoretically calculated relationships between the healing strength and the 85 healing time can also agree well with the experiments. Though mechanics models for the constitutive behaviors of light-activated polymers have been proposed 191-194 , to the best of our knowledge, this study presents the first network-based theory for the light-activated self-healing mechanics. The major contribution of the current work is a theoretical framework to integrate the light-triggered free radical production and the interfacial polymer chain evolution. Despite the contribution to the mechanics field, this theoretical framework also leaves several open questions. First, we have not considered the immediate interfacial adhesion in this theoretical framework. As shown in Figs. 28-30 and 33, the immediate adhesion may lead to around 20-35% of interfacial strength. The immediate adhesion process has a time scale much shorter than the healing process. However, this study considers that only the re-binding of the open chains can sustain the load, and the immediate adhesion of the fractured interface is considered to be around zero. We conservatively think that it may not be fully correct if we simply add the immediate adhesion strength and healing strength as they dominate at different time-scales. Second, we only consider the light-assistance on the self-healing performance is because the light-produced radicals facilitate the binding process. In the experiments without special treatment, the temperature of the material matrix increases slightly during the light illumination process. This temperature increase may also accelerate the chain diffusion and chain re-binding. To mitigate this issue, in our experiments of TiO 2 nanocomposite hydrogels, we maintain the material temperature within a thermal incubator with a constant temperature 25°C. In the future, more careful experiments should be carried out to characterize the material temperature change during the self-healing process, because the temperature is an important factor to affect the self-healing speed. Third, the study may be further extended to explain light-assisted self-healing processes that have not covered in this study. For example, Weder, et al. reported optically healable plastics 179,187,188 . Though the current study focuses on the deformable soft polymer networks, adding the plastic deformation mechanism may further extend the theory to optically healable plastics. 86 Chapter 5: Tough and Self-Healable Nanocomposite Hydrogels for Repeatable Water Treatment 5.1 Objective Nanomaterials with ultrahigh specific surface areas are promising adsorbents for water-pollutants such as dyes and heavy metal ions. However, an ongoing challenge is that the dispersed nanomaterials can easily flow into the water stream and induce secondary pollution. To address this challenge, we employed nanomaterials to bridge hydrogel networks to form a nanocomposite hydrogel as an alternative water- pollutant adsorbent. While most of the existing hydrogels that are used to treat wastewater are weak and non-healable, we present a tough TiO ( nanocomposite hydrogel that can be activated by ultraviolet (UV) light to demonstrate highly efficient self-healing, heavy metal adsorption, and repeatable dye degradation. The high toughness of the nanocomposite hydrogel is induced by the sequential detachment of polymer chains from the nanoparticle crosslinkers to dissipate the stored strain energy within the polymer network. The self-healing behavior is enabled by the UV-assisted rebinding of the reversible bonds between the polymer chains and nanoparticle surfaces. Also, the UV-induced free radicals on the TiO ( nanoparticle can facilitate the binding of heavy metal ions and repeated degradation of dye molecules. We expect this self-healable, photo-responsive, tough hydrogel to open various avenues for resilient and reusable wastewater treatment materials. 5.2 Introduction Wastewater with high concentrations of heavy metal ions or dye molecules has been a ubiquitous problem for environmental sustainability and human health 204-208 . Dye molecules or heavy metal ions may transit to highly toxic products in the drinking water system, causing allergy, dermatitis, skin irritations, or even provoking cancer and mutation in humans 209-216 . Besides, the dyes in the water reduce the light penetration and preclude the photosynthesis of underwater green grasses, thus degrading the underwater plant system and destroying the ecological metabolism 209-216 . Therefore, wastewater must be carefully 87 treated before discharging to the environment. Various methods have been used to treat wastewater, such as adsorption, electrochemical treatment, chemical precipitation, ion exchange, extraction, and filtration 208,217 . Among these methods, adsorption method is considered as one of the most appreciated technology because the adsorption process is effective, convenient, energy-efficient, and inexpensive 206,218,219 . Nanomaterials with ultrahigh specific surface areas are one of the most promising water-pollutant adsorbents 220-223 . However, a long-lasting challenge is that the dispersed nanomaterials can easily flow into the water stream to induce the secondary pollution 224-226 . To address this challenge, we here propose to integrate nanomaterials into the porous hydrogel matrix to form a nanocomposite hydrogel as an alternative water-pollutant adsorber 227,228 . The high porosity promotes the solute diffusion within the hydrogel matrix. The nanomaterial binding agents within the hydrogel matrix can have special interactions with the water pollutants to thus adsorb or degrade those pollutants. Compared to the adsorption directly using the nanoparticles, the hydrogel can provide a protecting matrix that constrains the nanomaterials from entering the water stream to induce the secondary pollution. Considering the low- cost and ease of the fabrication, the hydrogels are also expected to be excellent adsorbent materials for future large-scale industry applications 229 . Despite the great potential, most of existing hydrogels that can be used to embed the nanomaterial agents are weak and brittle. These hydrogels are easy to break and not able to self-heal 227,228 . In addition, hydrogels with special chemical groups are responsive to external stimuli (such as temperature, light, magnetoelectric field, or PH value) to show click intelligence 230,231 . Harnessing external stimuli to enable click responses of the hydrogel-enabled wastewater treatment is desirable, but still limited 232-234 . In this paper, we present a tough and self-healable nanocomposite hydrogel that can be activated by the ultraviolet (UV) light to efficiently adsorb heavy metal ions and degrade dye molecules in the wastewater. This nanocomposite hydrogel is composed of polymer networks bridged TiO 2 nanoparticles 196,235 . These TiO 2 nanoparticles have three functions (Fig. 35a): (1) as crosslinkers to bridge polymer chains into three-dimensional networks which in turn constrain the relative positions of these 88 nanoparticles within the matrix 196,235 , (2) as binding agents to interact with the water pollutants such as heavy metal ions and dye molecules, and (3) as photocatalysts to generate free radicals under the UV exposure. Unlike the usual organic crosslinkers that usually only attach several polymer chains, the TiO 2 nanoparticle crosslinkers are able to attach a large number of polymer chains (e.g., more than 100) with inhomogeneous chain lengths. When the material is under stretch, the polymer chains would be sequentially detached from the nanoparticle surfaces, thus sequentially dissipating a large amount of strain energy and enabling high fracture energy of the material. In addition, the detached polymer chains are able to attach to the particle surface again, thus enabling the polymer to be self-healable after fractures. Furthermore, we show that the photo-induced production of free radicals from the TiO 2 nanoparticles can efficiently facilitate the heavy metal adsorption and dye molecule degradation. We expect this self-healable photo-responsive hydrogel to open various possible avenues for resilient and reusable wastewater treatment materials. 89 Figure 35. Tough and Self-Healable Nanocomposite Hydrogels (a) A schematic to show the polymer chain network of the TiO 2 nanocomposite hydrogel and the related light-triggered catalyzing mechanism of the TiO 2 nanoparticles. (b) Stretching of a TiO 2 nanocomposite hydrogel sample with a small crack. The stretch, 𝛌, represented the length of the deformed sample divided by the length of the undeformed sample. (c) Stress-strain behaviors of notched and unnotched samples for a pure-shear test to measure the fracture energy of the TiO 2 nanocomposite hydrogel. (d) The fracture energy of the TiO 2 nanocomposite hydrogel and a hydrogel with BIS as the crosslinker. 5.3 Materials and methods 5.3.1 Materials TiO 2 nanoparticles dispersion (Anatase, 15 wt %, 5–15 nm) was purchased from US Research Nanomaterials (Houston, TX, USA). Acrylamide (AAm, 99%), N,N-Dimethylacrylamide (DMAA, 99%), N,N-methylenebisacrylamide (BIS, 99%), potassium peroxodisulfate (KPS, 99%), N,N,N′,N′- Tetramethylethylenediamine (TEMED, 99%) and Copper(II) perchlorate hexahydrate (Cu(ClO B ) ( ∙ 6H ( O) were purchased from Sigma-Aldrich (Atlanta, GA, USA). Reactive blue 4 (dye content 40 wt %) 90 was purchased from Alfa Aesar (Tewksbury, MA, USA). All chemicals were used as received without further purification. 5.3.2 Fabrication of nanocomposite hydrogels The 10 g TiO 2 solution was first bubbled with nitrogen for 30 min to remove the oxygen dissolved in the solution. Then, the solution was mixed with 0.039 g (0.009 mol) AAm and 2.079 g (0.021 mol) DMAA under magnetic stirring for 30 min at 20 °C. The mixed solution was cooled down to 0 °C in an ice water bath. 0.1 wt %. KPS and 8 µL TEMED were then added with another 30 min stirring. The obtained solution was poured into a glass tube (diameter 11 mm and length 50 mm) or a glass mold (150 mm × 75 mm × 3 mm) with the cover up to avoid contact with the oxygen. To facilitate the in situ free-radical polymerization, the hydrogel was put in a UV chamber (UVP CL-1000 Ultraviolet Crosslinker, Upland, CA, USA)) with light intensity 37 W/m ( (five 8-Watt light bulbs with 254 nm wave length) for 30 min. 5.3.3 Mechanical tests of nanocomposite hydrogels The fracture toughness of the nanocomposite hydrogel was measured using a pure shear test following [ 236 ]. Two identical samples were chosen to carry out the experiments: one hydrogel sample was clamped by rigid plates on an Instron machine (INSTRON, Model 5942, Norwood, MA, USA) with testing domain dimensions of 10 mm × 75 mm × 3 mm; the other sample had the same testing dimensions but with a 30 mm notch in the middle of the sample. Both samples were stretched using a strain rate of 0.06 s −1 until rupture. The entire testing time was within 5 min which was much less than the gel de-swelling and healing equilibrium timescale. For the characterization of the self-healing behavior, cylindrical hydrogel samples (diameter 11 mm, length 10 mm) were cut into two pieces with a blade and then were brought into contact with the additional force for 30 s on two sides to ensure the cut surfaces had good contact during the healing process. The samples were then put into a UV chamber with different light intensities (7.4 W/m ( , 22.2 W/m ( and 37 W/m ( ) and controlled moisture using wet paper to avoid the swelling and de-swelling behavior of the samples. The self-healed samples were then stretched uniaxially until rupture using the same testing system (Instron, Model 5942) with strain rate 0.06 s −1 at 20 °C. 91 5.3.4 Light-triggered heavy metal adsorption A cylindrical hydrogel (diameter: 11 mm, length: 10 mm) was immersed in a 150 mL beaker containing a 75 mL Cu 2+ solution (10 @F mol/L). NaOH solution (1 mol/L) and HClO 4 solution (1 mol/L) a are used to adjust the PH value of the solution to be around 7 237 . The beaker was put in the UV chamber with various light intensities (7.4 W/m ( , 22.2 W/m ( and 37 W/m ( ). The concentration of the treated solution was then determined through the solution color assisted by an image processing software Image J (version 1.51). Control experiments were carried out for the same heavy metal solution under the same UV light exposure but without the nanocomposite hydrogel. 5.3.5 Light-triggered degradation of dye molecules A cylindrical hydrogel (diameter 11 mm, length 10 mm) was immersed in a 15 mL vial with stopper containing 10 mL blue active dye solutions (0.02 wt %). The bottle was then put in the UV chamber with various light intensities (14.8 W/m ( , 22.2 W/m ( and 37 W/m ( ). The hydrogel was removed from the glass bottle to measure the swelling behavior. The dye concentration of the remaining solution was determined by the solution color using Image J. Control experiments were carried out for the same dye solution under the same UV light exposure but without the nanocomposite hydrogel. 5.4 Results 5.4.1 High toughness of the TiO2 nanocomposite hydrogel The nanocomposite hydrogels were prepared using TiO 2 nanoparticles as inorganic crosslinkers. After the in situ free-radical polymerization, the gel was formed as a water-mediated three-dimensional network with a schematic shown in Fig. 35a. The TiO 2 nanoparticles and the polymer chains are bonded through reversible bonds, such as hydrogen bonds (between -OH on the particle surface and -NH 2 group on polymer chains) 238 , or ionic bonds (between K + groups from redox initiator KPS and anionic groups of the polymer chains) 197 . Unlike the organic crosslinkers which usually attach only a few polymer chains on one crosslinker, the inorganic crosslinker nanoparticles allow a large number of polymer chains to be 92 attached to the surface of crosslinkers 196,197 . These attached polymer chains do not have the same chain lengths but follow a wide chain-length distribution 84,115 . Under stretching, the short polymer chains are first detached from the particles to release the stored energy in the chains, while the long polymer chains are still attached on the nanoparticle surface to maintain the elasticity of the chain network (Fig. 35b). Therefore, under increasing stretch, the polymer chains will be sequentially detached from the nanoparticles to dissipate a large amount of the strain energy. This energy dissipation capability leads to an ultrahigh fracture toughness in the nanocomposite hydrogel. As shown in Fig. 35b, the hydrogel sample is stretched with a 10 mm notch in the middle of the sample. When the sample was stretched to 12 times its initial length, the crack in the sample is still blunted without propagating through the sample. To quantitatively measure the fracture energy of the nanocomposite hydrogel, the pure-shear method was employed to test the stress-strain behavior of a notched sample and unnotched sample (Fig. 35c) 236,239 . The stress-strain behavior of the notched sample was used to determine the critical strain of the crack propagation, and the area of the stress-strain curve of the unnotched sample under this critical strain is defined as the fracture energy 239 . The fabricated TiO 2 nanocomposite hydrogels have average fracture energy 8233 J m −2 , which is over 15 times higher than that of the hydrogel with the same polymer chains but organic crosslinkers N,N-methylenebisacrylamide (BIS) (Fig. 35d). Besides, the fracture energy of the fabricated TiO 2 nanocomposite hydrogel is comparable to the highest fracture energy of the state-of-the- art tough hydrogels (the pink region in Fig. 35d) 67,236 . 5.4.2 Light-assisted self-healing The TiO 2 hydrogels exhibit not only high toughness but also extraordinary self-healing capability (Fig. 36a). A TiO 2 hydrogel bar was first cut into two pieces, and then brought back into contact with exposure to UV light for a period of time. Then, the healed sample is stretched until it ruptured. As shown in Fig. 36b, the healing strength of the hydrogel increases with an increase in the healing time. When the healing time is long enough, the healing strength reaches a plateau, almost 100% of the strength of the original 93 sample (Fig. 36c). However, the strength of the healed sample without the UV exposure is much smaller, less than 50% the strength of the original sample at the plateau (Fig. 36c). The light-triggered self-healing of the TiO 2 hydrogels can be qualitatively understood as follows (Fig. 36a). During the cutting process, the polymer chains around the cutting interface are detached from the particle surface. When two hydrogel parts are brought into contact, the polymer chains with free distal groups diffuse across the interface to find the nanoparticle binding sites to reform the bonding between the polymer chains and the particle binding sites. Effectively, the process can be understood as a coupling of chain diffusion and binding reaction around the interface 84 . Under the UV exposure (wavelength <384 nm, the photons with energy greater than the bandgap of the TiO 2), electrons are promoted from the valence band to the conduction band leaving holes in the valence band 240-243 . The photoinduced holes migrate to the particle surface to react with H 2O to produce hydroxyl radicals ( ) (Fig. 36a). At the same time, the conduction band electrons reduce O 2 to form superoxide radicals ( ) (Fig. 36a). Like the free-radical polymerization process during the hydrogel fabrication, these free radicals can facilitate the rebinding reaction between the polymer chain distal groups and the particle binding sites (Fig. 36a). The acceleration of the rebinding reaction can further promote the chain diffusion across the interface. Therefore, the exposure of UV light as expected, can greatly accelerate the self-healing process (Fig. 36c). To quantitatively verify this mechanism, various light intensities (from 0 to 37 W/m 2 ) were carried out for the light-assisted self-healing experiments (Figs. 36cd). According to the mechanism, higher light intensity induces higher concentration of free radicals, thus leading to faster self-healing process. In the experiment, the healing ratio of the hydrogel without UV exposure was found to only reach around 50% at a healing time of 350 min, while the healing ratio of the hydrogel with a small UV exposure (7.4 W/m 2 ) reached more than 95% (Fig. 36c). Here, the equilibrium healing time is denoted as corresponding to the healing ratio (uniaxial strength of the healed hydrogel over that of the original OH • 2 O -• 94 hydrogel) reaching 90%. Furthermore, the equilibrium healing time was observed to monotonically decrease as the UV light intensity increased from 7.4 to 37 W/m 2 (Fig. 36d). Figure 36. Results of light-assisted self-healing. (a) Experimental images and polymer-network schematics to show the self-healing experiment. (b) Stress-strain behaviors of the original TiO2 hydrogel sample and self-healed samples for various healing time. The nominal stress is defined as the tensile force over the original cross-section area. (c) The normalized strength of TiO2 hydrogel samples as functions of healing time under UV exposure with various light intensities. and denote the strength of the self-healed sample and original samples, respectively. (d) Equilibrium healing time of TiO2 hydrogel samples as a function of the light intensity. The equilibrium healing time is defined as the healing time corresponding to the normalized healing strength around 90%. 5.4.3 Light-assisted heavy-metal adsorption We next studied the light-assisted adsorption of the heavy metal ions with the TiO 2 nanocomposite hydrogels. The heavy metal adsorption on the TiO 2 surface in a solution with a pH around 7 is conceptually understood as follows 237 . The hydroxo complexes among the 10 @F mol/L Cu (II) aqueous solution depend on the pH of the solution. For example, Cu ([ ,Cu(OH) [ and Cu(OH) ( are the main complexes at pH around 7. During surface hydrolysis reactions, the hydrous oxide groups of the TiO 2 95 nanoparticles form O–Cu bonds that yield a series of surface Cu(II) complexes such as TiO–Cu + , TiO– CuOH + and TiO–Cu(OH) 2 species (Fig. 37a). Besides, the negative surface charges generated by the dissociation reactions at pH 7, similar to the binding between the polymer chain and particle binding site, the formation of the O–Cu bonds can be promoted by the UV induced free radicals (i.e., and ). Therefore, a higher concentration of free radicals would also induce better performance of the heavy metal adsorption of the TiO 2 nanocomposite hydrogels. Here, the TiO 2 nanocomposite hydrogel samples were immersed in a water solution with heavy metal ions and then the solution was exposed to UV light. The heavy metal ions in the water solution diffuse into the hydrogel matrix and bind on the nanoparticle surface, undergoing a diffusion-binding process. The free radicals accelerate the binding of the metal ions and thus further promote the diffusion of the ions from the solution into the hydrogel matrix. After a period of UV exposure, the hydrogel sample was removed to measure the concentration of the heavy metal ions in the water solution. As shown in Fig. 37b, the color intensity of the heavy metal solution decreases as the UV time increases. After UV exposure (37 W/m 2 ) for 120 min, the solution color is very close to that of pure DI water (Fig. 37b). To quantify the adsorption performance, the heavy metal concentration of the treated water was measured as a function of the UV exposure time (Fig. 37c). The measured relative concentration decreased as the UV exposure time increased and reached a plateau when the time was long enough. To verify the experimental results, the control experiments were carried out with the same UV exposure intensity (37 W/m 2 ) but without the presence of TiO 2 nanocomposite hydrogels. The concentration of heavy metal ions was found to remain almost constant over around 3 h of testing time (Fig. 37c). Furthermore, various UV intensities were used in the experiments and we found that the adsorption process was significantly accelerated by increasing the UV intensity (Figs. 37cd). To study the effect of the ions on the property change in the nanocomposite hydrogels, we measured the mechanical and self-healing properties of the hydrogel after the heavy metal ion experiments. Specifically, after the hydrogel was immersed in the heavy metal solution for 2 h under UV 2 O -• OH • 96 illumination, the swollen gel was taken out from the beaker with a volumetric swelling ratio of around 167%. Then, the swollen gel was de-swelled to the same weight and volume as the original gel under a slightly elevated temperature of 40 °C. Compared to the original gel, the obtained gel featured a similar small-strain Young’s modulus, and 81% large-strain shear modulus, 43% higher stretchability, and similar tensile strength (Fig. S17). Besides, the obtained gel featured around 88% healing ratio after 2 h healing while the original gel featured around 97% (Fig. 36 and S17). Qualitatively, the ionic pollutants may induce minor effects on the mechanical and self-healing properties of the TiO 2 nanocomposite hydrogels. These minor effects may be because the ionic pollutants slightly alter the chemical equilibrium of the bonding dynamics between the polymer chain and the TiO 2 nanoparticles. Figure 37. Results of light-assisted heavy-metal adsorption. (a) Schematics to show the mechanism of the light-assisted adsorption of copper ions (Cu 2+ ) on the TiO 2 nanoparticle surface. (b) Image sequences of the treated Cu 2+ solution after the UV light-assisted adsorption for various adsorption times. (c) The relative concentrations of Cu 2+ as functions of UV exposure time for various UV light intensities. and denote the concentrations of Cu 2+ in the treated and original solutions, respectively. (d) The equilibrium adsorption time as a function of the light intensity. The equilibrium adsorption time is defined as the UV exposure time corresponding to the relative concentration around 10%. C 0 C 0 C C 97 5.4.4 Light-assisted dye degradation The TiO 2 nanocomposite hydrogels not only adsorb heavy metal ions but also adsorb and degrade dye molecules (Fig. 38). The mechanism can be understood as follows. With redox initiators potassium peroxodisulfate (KPS) doped on the TiO 2 nanoparticles, the TiO 2 nanoparticles are (weakly) positively charged with cations (K + ). The dye molecule blue active carries a net negative charge due to the sulphonate (SO 3 − ) groups at the end 197 . When the TiO 2 nanocomposite hydrogel is immersed in the dye solution, the negatively charged dye molecules migrate into the hydrogel matrix and form weak ionic binding with the positively charged TiO 2 nanoparticles. At the same time, free radicals (i.e., and ) are produced on the TiO 2 nanoparticle surfaces under the UV exposure. These radicals have strong reactions with the dye molecules to decompose the dye into small colorless molecules (H 2O, CO 2, and others) (Fig. 38a) 244-247 . The produced radicals decompose the adsorbed dye molecules bound on the nanoparticle surface, and also diffuse through the gel matrix to decompose the freely moving dye molecules. To test this mechanism, the dye degradation experiments were carried out by immersing the hydrogel samples into a dye solution (0.02 wt% dye) under UV exposure. The initially dark blue color gradually became lighter and lighter, and finally becomes colorless like the DI water (Fig. 38b). Quantitatively, the measured dye concentration decreased with increasing the UV exposure time, and eventually reached a plateau close to 0 (Fig. 38c). However, the dye concentration in the control experiment with the same UV exposure intensity but without the presence of hydrogel sample remained almost constant over 40 h (Fig. 38c). As the UV light intensity increased, the degradation process became more rapid (Fig. 38d). Another outstanding property of using nanocomposite hydrogel to enable dye degradation is that the hydrogel can be used for multiple cycles without lowering the degradation efficiency. Because the binding and degradation agents TiO 2 nanoparticles are fixed within a hydrogel matrix, the amount of TiO 2 nanoparticles does not decrease during the degradation process. Besides, after degradation for sufficient 2 O -• OH • 98 time, the amount of dye within the hydrogel matrix decreases to nearly zero; therefore, the efficiency of the second-time degradation is not compromised by the dye adsorption. This is different from the adsorption of heavy metal ions demonstrated in Fig. 37: the adsorbed heavy metal ions did not disappear, and the additional adsorption capability of the TiO 2 gel decreased with the adsorption process. As shown in Fig. 38e, a hydrogel sample was first immersed in the dye solution with 8 h UV exposure; the corresponding dye concentration decreased until it reached a plateau with increasing UV exposure time. Then, the swollen hydrogel sample was taken out to de-swell it to the original size for 60 h at 25 ℃ After that, the hydrogel sample could be used to degrade a dye solution with the same concentration for a second and third time. The corresponding degradation efficiency was almost the same as that of the first cycle (Fig. 38e). It should be noted that the UV-induced radicals may degrade bonds between the polymers and nanoparticles during the dye degradation process. However, due to the reversible character of the bonds, these bonds can reform autonomously. Therefore, the mechanical properties of the used hydrogels in the de-swollen state are not compromised (Fig. 38e). 99 Figure 38. Results of light-assisted dye degradation. (a) Schematics to show the mechanism of light-assisted dye degradation. (b) Image sequences of the treated dye solution after the UV light-assisted degradation for various UV exposure time. (c) The relative concentrations of the dye molecule as functions of UV exposure time for various UV light intensities. and denote the concentrations of the dye molecule in the treated and original solutions, respectively. (d) The equilibrium degradation time as a function of the light intensity. The equilibrium time is defined as the UV exposure time corresponding to the relative concentration around 10%. (e) The relative dye concentration and the swelling volume ratio of the hydrogel sample as functions of the processing time. 5.5 Conclusive remarks In summary, we present a tough TiO 2 nanocomposite hydrogel that can be activated by UV light to demonstrate highly efficient self-healing, heavy-metal adsorption, and dye degradation. Our strategy for the treatment of wastewater harnesses the ultrahigh specific surface area of nanoparticles while C 0 C 0 C C 100 demonstrating a novel framework to preclude the negative side effects of the commonly employed nanomaterial-assisted water treatment. Also, external controls with UV light would provide further flexibility in this water treatment strategy. Furthermore, the high toughness and crack-healing capability of the hydrogel matrix offer great robustness of the adsorbent materials. We expect this strategy of stimuli-assisted water treatment with resilient hydrogel materials could be extended to various applications beyond wastewater treatment, such as resilient and pollutant-free artificial organs, tissue dressings 248 , contact lenses, soft-material glues 249,250 , and hydrogel electronics 251 . 101 Chapter 6: Mechanics of Self-healing Thermoplastic Elastomers 6.1 Objective Self-healing polymers crosslinked by dynamic bonds have shown great potential in various engineering applications ranging from electronics to robotics. Due to the intrinsic weakness of dynamic bonds, most of the existing self-healing polymers have relatively weak mechanical strengths. To address this drawback, it is proposed to incorporate crystalline domains within the polymer matrix during the synthesis to make tough and strong self- healing thermoplastic elastomers with semi-crystalline phases. Despite the success in the polymer synthesis, the theoretical understanding of self-healing thermoplastic elastomers remains elusive. In this paper, we develop a theoretical framework to model the constitutive and healing behaviors of self-healable thermoplastic elastomers with both dynamic bonds and semi- crystalline phases. We model the virgin thermoplastic elastomer by using a spring-dash model that couples the soft rubbery phase and the stiff crystalline phase. The rubbery polymer network is formed by layering the body-centered unit cubes that link polymer chains via dynamic bonds. Then, the healing is considered as a coupling of polymer chain diffusion and dynamic-bond binding, leading to an effective diffusion-reaction model. Based on the theoretical framework, we can model the stress-strain behavior of the virgin and healed polymers and theoretically explain the relationship between the healing strength and the healing time. The model can consistently explain our own experiments on self-healable thermoplastic elastomers polyurethane and the documented experiments on self-healable thermoplastic elastomers with disulfide bonds and π- π interactions. 6.2 Introduction Self-healing polymers with dynamic bonds have been used in a broad range of engineering applications, such as flexible electronics 39 , energy storage 40 , biomaterials 33 , and robotics 34 . The healing mechanism primarily relies on the reversible nature of dynamic bonds, i.e., reforming when the fractured materials are contacted. The dynamic bonds include dynamic covalent bonds 53-57 , hydrogen bonds 58-63 , ionic bonds 64- 102 70 , metal-ligand coordinations 40,72-75,252 , host-guest interactions 76,77 , hydrophobic interactions 78,79 , and π-π interactions 80 . An evident drawback of most of the existing self-healing polymers enabled by dynamic bonds (primarily elastomers and hydrogels) is that their mechanical strengths are typically much weaker than polymers with permanent covalent bonds, because the strength of a dynamic bond is typically much weaker than that of a permanent covalent bond 61 . To address this drawback, it is proposed to incorporate crystalline domains within the polymer matrix to make tough and strong self-healing thermoplastic elastomers with semi-crystalline phases 55,61,155,156,253-256 . These tough self-healing polymers overcome the low-stiffness- drawback of existing soft self-healing elastomers or hydrogels. Despite the synthesis success, the theoretical understanding of the mechanics of self-healing thermoplastic elastomers has been left behind. The theoretical understanding should include two parts: (1) the modeling of the constitutive behaviors and (2) the modeling of the self-healing behaviors. In the first part, though the constitutive behaviors of the thermoplastic elastomers with permanent covalent bonds have been modeled 257-263 , it remains elusive how to understand the constitutive behaviors of the self-healing thermoplastic elastomers with dynamic bonds that can be dissociated by the applied force. In the second part, though we have recently proposed several models to understand the self-healing of self-healable soft polymers in the amorphous state 84,115,174,264,265 , it remains elusive how to model the coupling of dynamic bonds, amorphous phase, and crystalline phase within the semi-crystalline polymer network. Here, we propose a theoretical framework to model the constitutive and self-healing behaviors of self-healable thermoplastic elastomers with both dynamic bonds and crystalline phases. A typical healing experiment is shown in Fig. 39. A thermoplastic elastomer is first cut/broken into two parts, and then immediately brought into contact at a given temperature for a certain period of healing time. The healed sample is then uniaxially stretched until the sample rupture. The tensile stress-strain behavior of the virgin sample will be first modeled by considering both the coupling of the rubbery phase and the crystalline phase and the force-induced dissociation of the dynamic bonds. Then, a diffusion-reaction model will be considered to model the interfacial healing process. Finally, considering the healed sample as a composite 103 with two virgin segments and a small healing segment, we model the stress-strain behavior of the healed sample and then theoretically explain the relationship between the healing strength and the healing time. Effects of the crystallinity fraction, the chain length of the rubbery phase and the chain mobility on the stress-strain or healing behaviors will be studied. The theoretically model can consistently explain our own experiments on self-healable thermoplastic elastomers polyurethane with dynamic disulfide bonds. The model can also consistently explain others’ experimental results on self-healable thermoplastic elastomers with disulfide bonds and π-π interactions. The plan of the paper is as follows: Section 6.3 introduces our experiments on self-healable polyurethanes. In section 6.4, we present the theoretical model system by considering first the constitutive model of the virgin polymer with dynamic bonds, then the interfacial healing process, and finally the stress- strain behavior of the healed polymer. In section 6.5, we show the theoretical results for both the virgin and healed polymer. Effects of the crystallinity fraction, the chain length of the rubbery phase and the chain mobility on the stress-strain or healing behaviors will be studied. In section 6.6, we will compare our experimental results on the self-healable polyurethanes with the theoretically calculated results. In section 6.7, we will use the theoretical model to further explain others’ experimental data of self-healable thermoplastic elastomers. The conclusive remarks will be presented in section 6.8. 104 Figure 39. Schematics of healing process (a) Schematics to show the healing process. (b) Schematics to show the molecular structures around the healing interface during the healing process. 6.3 Experiments The self-healing thermoplastic elastomers were prepared by preheating 0.00829 mole Polytetramethylene ether glycol (PTMEG, molar mass 250, 1000, and 1810 g/mol) at 90°C and bubbled with nitrogen for 1 h to remove water and oxygen. 7.369 g isophorone diisocyanate (IPDI), 5 g dimethylacetamide (DMAc) and 0.15 g dibutyltin dilaurate (DBTDL) were mixed with the preheated PTMEG at 70°C under magnetic stirring for 1 h. Then, a solution with 20 g DMAc and 2.557 g 2-Hydroxyethyl disulfide (HEDS) was added drop-wisely to the mixture with magnetic stirring for another 1 h. To complete the synthesis, 2.147 g 2- Hydroxyethyl methacrylate (HEMA) was mixed with the mixture at 40°C for 1 h. During the synthesis process, nitrogen was bubbled in the solution to prevent the reaction between the mixture and the oxygen. The obtained solution was put in a vacuum chamber for 12 hours to evaporate 90% of solvent and then mixed with 1 w.t% tributylphosphine (TBP, catalyst), 1 w.t% phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide (photoinitiator) and 0.01~ 0.02 w.t% Sudan I (photoabsorber) for 2 h. The solution was then used for the projection-based additive manufacturing process to print the thermoplastic elastomer samples. Prepared samples were post-cured for one hour in a UV chamber to enable the full photopolymerization of the material and were heated for 12 h at 40°C to remove the residual solvent inside the material matrix. Note that all chemicals were purchased from Sigma-Aldrich, USA and were commercially available without further purification. The prepared strip samples (length 20 mm, width 5 mm, and thickness 1 mm) were first cut into two pieces with a sharp blade and then contact back immediately with clamped on two ends to ensure good contact during the healing process (Fig. 40a). The samples were then healed under 80°C for various healing time. Note that the glass transition temperatures for polymers with PTMEG 250, 1000, and 1810 g/mol are 65-71°C, 39°C, and below 25°C, respectively (Fig. S18). At 80°C, all these polymers are in the rubbery state during the healing. The optical microscope (Nikon ECLIPSE LV100ND) was used to monitor the 105 healed surface. The microscopic images show that the fractured interface can be nicely healed during the healing process (Fig. 40b). The healed strip sample can sustain a weight of 50g that is 200 times its own weight (0.25g) (Fig. 40a). The mechanical behavior of both virgin and healed samples was tested using Instron (Model 5942) to uniaxially stretch the samples with a strain rate of 0.06 s-1 until ruptures (Fig. 40c). The tensile stress corresponding to the rupture is considered as the tensile strength of the polymer. The tensile strengths of the self-healed samples for various healing time were normalized by the tensile strength of the virgin sample are calculated as the healing strength ratios, which were then plotted as a function of the healing time (Fig. 40d). On the contrary, the control polymers without disulfide bonds (PTMEG 250 g/mol) could not bond together after the healing experiments at 80°C for 18 h (Fig. S18). Figure 40. Experimental results of self-healing thermoplastic elastomer. (a) Image sequence to show a self-healing process of a strip polymer sample. The healed sample (0.5 g) can sustain a weight of 200 g. (b) Microscope images to show the fractured and healed interfaces. (c) Tensile stress-strain curves of virgin and healed polymers with various healing time. (d) Healing strength ratios of the healed polymers in functions of the healing time. The healing strength ratio is defined as the tensile strength of the healed polymer normalized by the tensile strength of the virgin polymer. The shadow areas in d indicate the healing time corresponding to 90% healing strength ratio. Scale bars in a represent 4 mm. Scale bars in b represent 300 µm. 106 6.4 Theoretical model 6.4.1 Overview of the material system The overall process is shown in Fig. 39a and the molecular structure is modeled as Fig. 39b. We consider that the thermoplastic elastomer is composed of both soft rubbery phase with amorphous polymer chains and stiff crystalline phase with folded polymer segments (Fig. 39b). Effectively, the stiff crystalline phase resembles nanoparticles and each of them bridges a number of polymer chains. Literally, the dynamic bonds can be located within the rubbery phase or crystalline phase. For the sake of analysis simplicity, we here assume that dynamic bonds are only located around the interface between the rubbery phase and the crystalline phase. This assumption can reveal the key physics of the problem, and at the same time significantly reduce the complexity of the problem. Under a sufficiently large force (such as stretching to deform globally and cutting to deform a spot locally), the dynamic bonds between the amorphous chains and the crystalline domain will be forced to broken. When a dynamic bond is broken, it becomes two open distal groups attaching on respective parts. When a sufficiently amount of dynamic bonds are broken, a crack will emerge, or the polymer will be fractured into two pieces. When two fractured pieces are brought into contact with an adequate temperature condition, we assume that the dissociated polymer chain with open distal group will diffuse into the other matrix to find another open distal group to reform the dynamic bond. 6.4.2 Constitutive model of the virgin thermoplastic elastomer Following Boyce, Parks, and other authors 257-261 , we employ a spring-dash model to analyze the large- deformation of the thermoplastic elastomer (Fig. 41). The thermoplastic elastomer consists of two phases (Fig. 41ab): The soft rubbery phase is modeled as nonlinear springs (A and B) and the stiff crystalline phase is modeled as an elastic spring (C) in series with a plastic dash pot (D). To consider the connection between the rubbery phase and the crystalline phase, we consider a general dash-spring model (Fig. 41b). In the model, the rubbery phase is divided into two parts: part A is in series with the crystalline phase C-D, and 107 part B is in parallel with the element A-C-D. The volume fraction of the crystalline phase (CD) within the thermoplastic elastomer matrix is P CD, and the volume fraction of element A within the rubbery phase is 𝜂 g . The overall deformation gradient of the thermoplastic elastomer can be expressed as 𝑭=𝑭 > =𝑭 g 𝑭 6h (6-1) where 𝑭 g , 𝑭 > , and 𝑭 6h are the deformation gradients of elements A, B, and C-D, respectively. According to the schematic layout, the deformation gradient 𝑭 6h can be decomposed into two parts as 𝑭 6h =𝑭 6 𝑭 h (6-2) where 𝑭 6 and 𝑭 h are the deformation gradient of the spring element C and the dash pot element D, respectively. Accordingly, the overall Cauchy stress of the thermoplastic elastomer can be written as 𝑻=𝑻 > +𝑻 g =𝑻 > +𝑻 6h (6-3) where 𝑻 g , 𝑻 > , and 𝑻 6h are the Cauchy stresses of elements A, B, and C-D, respectively. Due to the in-series configuration, the Cauchy stress of element A and element C-D should be equal, namely, 𝑻 g =𝑻 6h =𝑻 6 =𝑻 h (6-4) where 𝑻 6 and 𝑻 h are the Cauchy stresses of the spring element C and the dash element D, respectively. Figure 41. Schematics of the constitutive model F T 108 (a) Schematics to show the molecular structure of thermoplastic elastomer. (b) Schematics to show the proposed spring-dash model for the thermoplastic elastomer. A and B are nonlinear springs that present for the soft rubbery phase. C is an elastic spring present for the stiff crystalline phase in series with a plastic dash pot D. 6.4.2.1 Rubbery polymer network Following the essential idea of polymer-network theories 100,101,103 , we assume the rubbery polymer network is constructed by layering unit cubes to span over the whole volume (unit cube shown in Fig. 42a). In each unit cube, crystals are located at the corners and centers in a body-centered fashion (Fig. 42a). The corner and center crystals form a crystal pair, and polymer chains with inhomogeneous lengths attach between the crystal pair with dynamic bonds (Fig. 42a). Between a crystal pair, we assume that N polymer chains are attached (Fig. 42b), each polymer chain made of freely-jointed Kuhn segments with each segment length b 100,101,103 . We assume that the polymer chains can be classified into m types, each with the same Kuhn number. We denote the Kuhn number (chain length) of the ith type polymer chain as , and the number of ith type chains as N i, where 1≤𝑖 ≤𝑚 and 𝑛 2 ≤𝑛 ( ≤...𝑛 " ...≤𝑛 3 . The ith chain number follows a statistical distribution written as (Fig. 42c) 𝑃 " (𝑛 " )= A # ∑ A # . #/0 = A # A (6-5) where 𝑁 =∑ 𝑁 " 3 "b2 is the total chain number. We here consider a log-normal distribution function as 99 𝑃 " (𝑛 " ) = 2 ; # M√(N 𝑒𝑥𝑝d− (i;; # @j) ( (M ( e (6-6) where 𝜓 and 𝛿 are the mean and standard deviation of , respectively. denotes logarithm of the average chain length, and indicates the chain distribution width. We then consider the deformation of a single chain, the ith chain. In the freely-joint state, the average end-to-end distance of the ith chain is 𝑟 " ' = W𝑛 " 𝑏 (6-7) Under deformation, the end-to-end distance of the ith chain becomes 𝑟 " , and the stretch of the ith chain can be expressed as i n i n ln y d 109 𝛬 " = $ # $ # 2 (6-8) We approximate the end-to-end distance of ith chain at the fabricated state as the distance between a crystal pair L, written as, 𝑟 " ' =𝐿 (6-9) The distance between a crystal pair L can be estimated by using the volume fraction of the crystalline phase P CD. The volume fraction of the crystalline phase is estimated as 𝑃 6h =k KN7 * F l k (:[(7 √F l F (6-10) where d is the average diameter of the crystalline phase. Using Eq. 6-10, the crystal pair distance L is calculated as 𝐿 =tk √FN k CD l 2/F −1w𝑑 (6-11) At the deformed state, the rubbery phase has a deformation gradient 𝑭 g or 𝑭 > . We assume that the deformation of the body-centered cube follows the affined deformation assumption 100,102,103 . Therefore, the distance of the crystal pair at the deformed state becomes 𝑟 " =𝐿n * 0 F (6-12) where the strain invariant 𝐼 2 is 𝐼 2 =𝑡𝑟𝑎𝑐𝑒k𝑭 g 𝑭 g 1 l or 𝑡𝑟𝑎𝑐𝑒k𝑭 > 𝑭 > 1 l (6-13) The stretch of the ith chain can be calculated as 𝛬 " = $ # H; # C =n * 0 F : H; # C (6-14) The chain force on the ith chain at the current state is 𝑓 " = < & 1 C 𝛤 @2 k $ # ; # C l = < & 1 C 𝛤 @2 un * 0 F : ; # C v (6-15) where 𝛤 @2 ( ) is the inverse Langevin function, and the Langevin function can be written as 𝛤(𝑥)= 𝑐𝑜𝑡ℎ𝑥−1 𝑥 ⁄ . 𝑘 > is Boltzmann constant and T is the absolute temperature in Kelvin. 110 For the original material, the initial number of ith chain per unit material volume is 𝑁 " . This ith chain density will decrease to 𝑁 " 4 as the material deforms because the chain force will motivate the dissociation of the dynamic bond between the chain and the crystal. To model the binding kinetics of the dynamic bond, we denote the reaction from the dissociated state to the associated state as the forward reaction, and otherwise as the reverse reaction. We further denote the associated ith chain number per unit volume as and the dissociated ith chain number per unit volume as 𝑁 " 7 . The binding reaction kinetics can be written as 7A # $ 7. =𝑘 " # 𝑁 " 7 +𝑘 " $ 𝑁 " 4 (6-16) where 𝑘 " # and 𝑘 " $ are forward and reverse reaction rates at the deformed state, respectively. Following the Bell’s model, we can write the chain-force-dependent reaction rates as 110,111,174,264,265 𝑘 " # =𝑘 " #' expk− # # \] < & 1 l (6-17) 𝑘 " $ =𝑘 " $' expk # # \] < & 1 l (6-18) If the loading is applied quasi-statically, the active ith chain volume density 𝑁 " 4 can be calculated as a function of the applied chain force, 𝑁 " 4 = A # < # 12 exp`@ 1 # 34 5 & 6 a < # 72 exp` 1 # 34 5 & 6 a[< # 12 exp`@ 1 # 34 5 & 6 a (6-19) As shown in Fig. 42, one cubic element averagely involves 2 crystals and 8 crystal pairs. The crystal number per unit volume can be estimated as 𝜂 9 = Fk CD BN7 * (6-20) The number of crystal pairs per unit volume is 4𝜂 9 . Therefore, the free energy density of stretching the polymer network of the deformed original-polymer can be expressed as 𝑊 5 = Fk CD N7 * ∑ k𝑛 " 𝑘 > 𝑇d Q # .4;ℎQ # +𝑙𝑛k Q # 8";ℎQ # le𝑁 " 4 l 3 "b2 (6-21) where 𝛽 " =𝛤 @2 Z𝛬 " W𝑛 " ⁄ [ =𝛤 @2 ZW𝐼 2 3 ⁄ 𝐿 (𝑛 " 𝑏) ⁄ [. a i N 111 Figure 42. Proposed network model of the thermoplastic elastomer. (a) The polymer consists of layered unit cubes. (b) Crystals are located at the corners and centers in a body-centered fashion. (c) Between a crystal pair, polymer chains with inhomogeneous lengths are attached to the crystal surfaces via dynamic bonds. 6.4.2.2 Visco-elasto-plastic element The viscoelastic-plastic element is composed of an elastic spring element C and a viscoplastic dash pot element D. The deformation of the two elements can be simply decomposed into two steps: first the plastic flow (element D) and the elastic deformation (element C) (Fig. 43). As the plastic flow is incompressible, we have 𝐽 h =𝑑𝑒𝑡(𝑭 h )=1 (6-22) Therefore, we have 𝐽 6h =𝑑𝑒𝑡(𝑭 6 ) (6-23) The Cauchy stress of C-D element can be calculated as 257-261 𝑻 6h = 2 7%.l𝑭 C n 𝑹 6 𝑴 6 𝑹 6 (6-24) where 𝑹 6 is the rotation tensor that can be obtained through the polar decomposition of the deformation gradient, obtained from 𝑭 6 =𝑹 6 𝑼 6 (6-25) where 𝑼 6 is the elastic stretch tensor. The Mandel stress 𝑴 6 is given by 257-261 𝑴 6 = o C l2[p C n 𝑙𝑛𝑼 6 + o C Fl2@(p C n − o C Fl2[p C n 𝑡𝑟(𝑙𝑛𝑼 6 )𝑰 (6-26) 112 where 𝐸 6 and 𝜈 6 are Young’s modulus and Poisson’s ratio of element C, respectively; and is the identity tensor. The evolution of the plastic flow is given by 𝑭 ̇ h =𝑫 h 𝑭 h (6-27) where the flow rule is 𝑫 h = 2 ( p D q̄ 𝑴 7 h (6-28) where 𝑴 7 h =𝑴 6 −𝑡𝑟(𝑴 6 )𝑰 3 ⁄ is the deviator of 𝑴 6 , and the equivalent plastic shear strain rate 𝜈 h is modeled as 257,260,261,266 𝜈 h =𝜈 ' 𝑒𝑥𝑝d− st E < & 1 k1− q̄ u le (6-29) And the equivalent shear stress is 𝜏̄ =n 2 ( 𝑴 7 h ⋅̇𝑴 7 h (6-30) The evolution of the deformation resistance is modeled as 𝑌 ̇ = ℎ(𝑌 84. −𝑌)𝜈 h (6-31) where 𝑌 84. is a saturation level of the deformation resistance. Figure 43. Deformation of the viscoelastic-plastic element in element C and D. 6.4.2.3 Stress-strain under uniaxial stretch We assume the rubbery phases are nearly incompressible with the deformation as I Y 113 𝑑𝑒𝑡(𝑭)=𝑑𝑒𝑡(𝑭 > )≈1 (6-32) when the material is under a large-strain uniaxial tension with stretch 𝜆 2 =𝜆, the total deformation gradient can be written as 𝑭=¢ 𝜆 𝜆 @2 ( ⁄ 𝜆 @2 ( ⁄ £ (6-33) At a given uniaxial stretch 𝜆, we assume the deformation of the element A as 𝑭 g =¤ 𝜆 g 𝜆 g @2 ( ⁄ 𝜆 g @2 ( ⁄ ¥ (6-34) The deformation gradient of element C-D is 𝑭 6h =¤ 𝜆𝜆 g @2 𝜆 @2 ( ⁄ 𝜆 g 2 ( ⁄ 𝜆 @2 ( ⁄ 𝜆 g 2 ( ⁄ ¥ (6-35) At a given 𝑭, 𝑭 g can be determined by using 𝑻 g =𝑻 6h , where 𝑻 6h is calculated by section 6.4.2.2 using the deformation gradient 𝑭 6h . When the element B is under a uniaxial tension with 𝑭 > =𝑭, the Cauchy stress along the stretching direction can be calculated as 𝑇 2 > (𝜆 > ) = Fk CD N7 * 𝑘 > 𝑇 : C k𝜆 > ( −𝜆 > @2 l ∑ ¦ A # $ Q # & dF* 0 & § 3 "b2 (6-36) where 𝐼 2 > =𝑡𝑟k𝑭 > 𝑭 > 1 l and 𝛽 2 > =𝛤 @2 k𝐿 (𝑛 " 𝑏) ⁄ W𝐼 2 > 3 ⁄ l . Combining the Cauchy stress 𝑻 > , we can obtain the overall Cauchy stress as 𝑻=𝑻 > +𝑻 g =𝑻 > +𝑻 6h (6-37) which can be written as a function of the deformation gradient 𝑭. It is expected that the stresses should first increase and then decrease with increasing strains, with a peak point in the middle. In the strain- controlled tensile testing experiment, the peak point is corresponding to a breaking, and the corresponding stress is the tensile strength. 114 6.4.3 Interfacial Self-healing model The sample is first cut into two parts, and then immediately brought into contact to heal the interface (Fig. 44a). During the cutting process, the dynamic bonds that crosslink the polymer chains in the rubbery elements A and B will be dissociated by the large force induced by the cutting (Fig. 44b). We assume one distal group of the chain is dissociated from a binding site that is within the matrix, and then this distal group will be pulled out of the matrix to the fracture interface. Since the healing experiment is carried out immediately after the cutting, we assume the open distal group on the chain will still be located around the interface at the very beginning of the healing process, primarily because the migration of the chain and its distal group takes substantial time. During the healing process, the polymer chain with the open distal group will gradually diffuse cross the interface to find the binding site to reform the dynamic bond. Once the dynamic bond is reformed (or re-associated), the polymer chain becomes active and can sustain loading forces. Figure 44. Schematics of interfacial self-healing model (a) Schematics to show the molecular structures during the healing process. (b) Schematics to show the dissociation and re-association of spring elements during the cutting and healing process, respectively. (c) A schematic to show the diffusion of the ith polymer chain across the interface. 115 6.4.3.1 Healing process of the ith chain The re-binding process of the ith chain involves the chain diffusion and distal group reaction (Fig. 44c). The radical-assisted binding will facilitate the chain diffusion to cross the healing interface. Therefore, these two processes are strongly coupled. The chain diffusion can be modeled by following a snake reptation model proposed by De Gennes 100,117-119 . The basic idea is that the polymer chain is constrained by the polymer matrix so it can only reptate along a primitive tube 120 . The primitive tube length is 𝐿 9 , so the original chain is divided into 𝑛 " segment with each segment length 𝑏 9 = : % ; # (6-38) At each small time step, the chain is considered to jump by a step length 𝑏 9 in a random-walk fashion. In the original reptation model, the tube length is considered as smaller than the contour length of the ith chain, i.e., 𝐿 9 ≤𝑛 " 𝑏; because the chain may coil around the reptation tube. Subsequently, the jump step 𝑏 9 is considered as an unknown parameter. Here, we make a bold assumption that the contour length of the ith chain is approximately equal to the reptation tube length; therefore, the jump step length 𝑏 9 ≈𝑏 (6-39) The motion of the polymer chain is enabled by extending out small segments called “minor chains” (Fig. 44c). The curvilinear motion of the polymer chain is characterized by the Rouse friction model with the curvilinear diffusivity of the ith chain expressed as 𝐷 " = < & 1 ; # = (6-40) where 𝜉 is the Rouse friction coefficient per unit Kuhn segment, 𝑘 > is the Boltzmann constant, and 𝑇 is the temperature in Kelvin. As shown in Fig. 44c, we assume the end-to-end distance of the ith chain is L. Without loss of generality, we assume the cutting position is located in the middle of the chain; thus, the distance between the healing interface and the binding site is L/2. This assumption is just for the sake of analysis simplicity; other location may also work but may involve more complicated statistic averaging algorithm. As shown 116 in Fig. 44c, the distal group will diffuse cross the normal distance L/2 following a curvilinear pathway. To facilitate the analysis, we construct two coordinate systems: s denotes the curvilinear path along the minor chains, and y denotes the linear path from the interface to the binding site. When the ith chain moves 𝑠 " distance along the curvilinear path, it is corresponding to 𝑦 " distance along y coordinate. Here we assume the selection of the curvilinear path is stochastic in a random-walk fashion 121-123 . Therefore, the conversion of the distances in two coordinate systems is expressed as 117,120 𝑦 " =W𝑠 " 𝑏 9 ≈W𝑠 " 𝑏 (6-41) According to Eq. 6-41, L/2 in the y coordinate is corresponding to 𝐿 ( /4𝑏 in the s coordinate. The chain diffusion and the association reaction are strongly coupled. We couple the chain diffusion and binding reaction within the region 0≤𝑠 ≤𝐿 " ( /4𝑏 using an effective diffusion-reaction equation as )6 # ' (8,.) ). =𝐷 " ) ( 6 # ' (8,.) )8 ( − )6 # $ ). (6-42a) )6 # $ (8,.) ). =𝑘 " #' 𝐶 " 7 (𝑠,𝑡)−𝑘 " $' 𝐶 " 4 (𝑠,𝑡) (6-42b) where 𝐶 " 7 (𝑠,𝑡) is the inactive ith chain number per unit length along the curvilinear coordinate s (0≤𝑠 ≤ 𝐿 ( /4𝑏) at time t (Fig. 44c), and 𝐶 " 4 (𝑠,𝑡) is the corresponding active quantity. 𝑘 " #' and 𝑘 " $' are the forward and the reverse reaction rates at the force-free state, respectively. At the beginning of the healing process, all mobile open distal groups of the ith chain are located around the healing interface, which can be expressed as 𝐶 " 7 (𝑠,𝑡 =0)=𝑁 " 𝛿(𝑠) (6-43) 𝐶 " 4 (𝑠,𝑡 =0)=0 (6-44) where ∫ 𝛿(𝑠) ? @? =1. From Eqs. 6-42 to 6-44, we can solve the concentration distributions 𝐶 " 7 (𝑠,𝑡) within the curvilinear coordinate. To convert these to the effective concentration of active ith chain within the region 0≤𝑦 ≤ 𝐿/2, we write 117 A # ) (.) A # =1− BC : ( ∫ 6 # ' (8,.) A # 𝑑𝑠 : ( /BC ' (6-45) where 𝑁 " E (𝑡) is the average ith chain number per unit volume of the region 0≤𝑦 ≤𝐿/2 at the undeformed state, and the superscript “h” denotes “healed”. 6.4.4 Summary of the model calculation The healed sample has three segments: one self-healed segment and two original segments (Fig. 39a). The stress-strain behavior of the original segment can be calculated using the scheme shown in Fig. 45a. The stress-strain behavior of the self-healed sample is calculated as follows (Fig. 45b). Under a uniaxial stretch, we consider the deformation gradients of the self-healed segment and the original segments are 𝑭 8ℎ Z𝜆 8ℎ [ and 𝑭 w (𝜆 w ), respectively. As the volume of the self-healed segment is so small, we approximate the overall stretch of the sample 𝜆 E as 𝜆 ℎ =𝜆 w (6-46) For the self-healed segment with the deformation gradient 𝑭 xℎ , the deformation gradient of element B as 𝑭 >ℎ . Under uniaxial stretch 𝜆 >ℎ , the Cauchy stress of the element B 𝑇 2 >ℎ Z𝜆 >ℎ [ = Fk CD N7 * 𝑘 > 𝑇 : C k𝜆 >ℎ ( −𝜆 >ℎ @2 l ∑ ¦ A # ℎ$ Q # &ℎ dF* 0 &ℎ § 3 "b2 (6-47) where 𝐼 2 >ℎ =𝑡𝑟k𝑭 >ℎ 𝑭 >ℎ 1 l and 𝛽 2 >ℎ =𝛤 @2 u𝐿 (𝑛 " 𝑏) ⁄ n𝐼 2 >ℎ 3 ⁄ v. At a given 𝑭 xℎ , we will employ 𝑻 >ℎ = 𝑻 g +𝑻 6h to determine 𝑭 >ℎ . Then the overall stress-strain behavior of the healed segment can be determined. Along the stretching direction, we consider that the Cauchy stress of the self-healed segment and the original segment should be equal, written as 𝑇 2 >ℎ Z𝜆 >ℎ [ =𝑇 2 > (𝜆 >w ) (6-48) 118 where 𝑇 2 >ℎ Z𝜆 >ℎ [is given by Eq. 6-47 and 𝑇 2 > (𝜆 >w )is given by Eq. 6-36; and 𝜆 >w is determined using 𝜆 w and Eq. 6-3. From the above equations, we can eventually calculate the overall stress-strain behavior of the self-healed sample (Fig. 45b). When the temperature increases from the room temperature to the healing temperature (e.g., 80°C), the crystalline phase will undergo a phase transition to transfer to the rubbery phase. However, we do not need to consider the phase transition in our modeling system. It is because of the following reasons: (1) We only test the stress-strain behavior of polymers at room temperature, that is, virgin polymers at room temperature and healed polymer at room temperature. The crystalline phase would transfer to the rubbery phase at 80°C, but will transfer back to the crystalline phase at room temperature. (2) We here assume that only the rubbery phase is fractured before healing (Fig. 44b). Then, during the healing process, only the polymer chains within the rubbery phase interpenetrate into the other matrix. Figure 45. Summary of the model calculation (a) A scheme for calculating the stress-strain behavior of the original polymer. (b) A scheme for calculating the stress-strain behavior of the self-healed polymer sample. 6.5 Theoretical results In this section, we will present the theoretical results calculated from the model presented in section 6.4. We will first show the stress-strain behavior of the virgin thermoplastic elastomer and study the effect of the phase fraction on the stress-strain behavior of the virgin material. Then, we will study the stress-strain 119 behavior of the healed material and examine the effects of chain length and chain mobility on the self- healing behavior. 6.5.1 Stress-strain of the virgin thermoplastic elastomer We consider the chain length of the soft phase follows a log-normal distribution (Fig. 46a). When the soft phase is loaded, the stress response will first increase to resist the deformation. As the strain increases, the polymer chain is dissociated due to the dissociation of the dynamic bonds. When the strain is sufficiently large, most of the polymer chains are dissociated and the stress response begins to decrease. Therefore, the stress-strain curve first increases and then decreases, featuring a critical maximal point (Fig. 46b). For the stiff phase, we model it using a linear combination of an elastic element C and a viscoplastic dash pot element D. When the strain is small (<0.1), it shows an elastic behavior with a modulus much larger than the soft phase (Fig. 46b). As the strain increases, the stress gradually reaches a plateau with the plastic yielding. Overall, the stress-strain of the self-healable thermoplastic elastomer is presented in Fig. 46c. In the small-strain range (<0.1), the material behaves like an elastic solid. Afterwards, the material undergoes a strain-hardening range with increasing stress as the strain increases. This strain-hardening range is due to the increasing stress of the soft rubbery phase during the plastic yielding of the stiff crystalline phase. When the soft phase reaches the critical maximal point, the overall material also reaches a critical maximal point, which is corresponding to the material rupture under the tensile load. It shows that the material rupture is primarily governed by the failure in the soft phase which is related to the dissociation of the dynamic bonds. This critical maximal stress of the material is the tensile strength of the material. Compared to the existing theoretical model for the thermoplastic elastomers 257-261 , this theoretical model has a special capability in predicting the tensile strength of the material. 120 Figure 46. Stress-strain of the virgin thermoplastic elastomer (a) Probability Pi in a function of chain length n for the soft phase. (b) The stress-strain behaviors of the soft phase and stiff phase. (c) The overall stress-strain behavior of the thermoplastic elastomer. The used parameters can be found in Table 4 6.5.2 Effect of phase fraction on the stress-strain of the virgin material There are two phases within the material matrix: the soft rubbery phase and the stiff crystalline phase. The soft rubbery phase is divided into two parts: element A that is in a series of the crystalline phase CD and element B that is in parallel to elements ACD. First, we maintain the phase fraction between elements A and B and vary the phase fraction of CD to examine the effect of the crystalline phase fraction on the overall stress-strain behavior. As shown in Fig. 47a, as the crystalline phase volume fraction increases, the yielding stress increases accordingly. However, the elastic modulus, strain-hardening shape, and the critical failure strain only change slightly (or even negligibly). It is because that the plateau stress of the crystalline phase increases as the crystalline phase volume fraction increases; however, the stress-strain shape of the soft rubbery phase does not change. The elastic modulus of the material is primarily governed by the stiffness of the stiff crystalline phase; the strain-hardening shape and failure strain are primarily governed by the soft rubbery phase. When the yielding stress increases but the strain-hardening shape does not change, the tensile strength of the material increases. Then, we maintain the crystalline volume fraction and vary the volume fraction of element A within the rubbery phase (Fig. 47b). We denote the fraction of element A within the rubbery phase as 𝜂 g ; then, the volume fraction of element A within the material matrix is calculated as 𝜂 g (1−𝑃 6h ). As the element A fraction increases, the strain-hardening range becomes less steep. When 𝜂 g =1, the stress reaches CD P A h 121 a plateau, resembling the stress-strain behavior of the element CD. The behavior shown in Fig. 47b is because that the strain-hardening shape is primarily governed by the behavior of element B which is in a parallel to elements ACD. As the element A fraction increase, the fraction of element B decreases. When 𝜂 g =1, the model is reduced to only elements ACD, displaying a behavior similar to that of element CD. Figure 47. Effect of the phase fraction on the stress-strain of the virgin material (a) The theoretically-calculated stress-strain curves of the virgin samples for various crystalline phase volume fraction 𝑃 6h . (b) The predicted stress-strain curves of the virgin samples for various volume fraction of element A within the rubbery phase (𝜂 g ). The used parameters can be found in Table 4. 6.5.3 Stress-strain of the healed thermoplastic elastomer The stress-strain curves of the healed thermoplastic elastomer sample are shown in Fig. 48a. We find that the stress-strain curves of the healed samples follow the path of that of the virgin sample, just featuring lower critical maximal stress points. These critical points are corresponding to the tensile strengths of the healed samples. As the healing time increases, the tensile strengths of the healed sample increases. We denote the healing strength ratio as the tensile strength of the healed sample normalized by that of the virgin sample. We find that the healing strength ratio increases with the increasing time and then reaches a plateau around 100% when the healing time is sufficiently long (Fig. 48b). We define the healing time corresponding to the healing strength ratio of 90% as the equilibrium healing time. 122 Figure 48. Stress-strain of the healed thermoplastic elastomer (a) Theoretically-calculated stress-strain curves of the virgin and self-healed thermoplastic elastomer samples under uniaxial tensile strains. (b) Theoretically-calculated healing strength ratio in a function of healing time. The used parameters can be found in Table 4. 6.5.4 Effect of average chain length of soft rubbery phase We use a log-normal distribution to capture the chain-length distribution of the rubbery phase (Fig. 49a). As the average chain length increases, the material becomes more stretchable in the rubbery phase; therefore, the failure strain increases, and the corresponding tensile strength increases (Fig. 49b). At the same time, the chain diffusivity 𝐷 " decreases with the increasing chain length (Eq. 6-40); and the equilibrium healing time to reach 90% healing increases with the increasing chain length. Figure 49. Effect of average chain length of soft rubbery phase (a) The chain length distributions for various average chain lengths. (b) The predicted stress-strain curves of virgin samples under uniaxial tensile strains. (c) Theoretically-calculated healing strength ratios in functions of healing time. The used parameters can be found in Table 4. 6.5.5 Effect of chain mobility Similarly, if we increase the mobility of the polymer chain alone, the stress-strain behavior of the thermoplastic elastomer does not change, but the healing process requires a shorter time. As shown in Fig. 50ab, the required equilibrium healing time increases with the increasing Rouse friction coefficient . Because the diffusivity of the polymer chain is in a reverse function of the Rouse friction coefficient , expressed in Eq. 6-40. a n x x 123 Figure 50. Effect of chain mobility (a) Theoretically-calculated healing strength ratios in functions of healing time for various Rouse friction coefficients 𝝃. (b) The predicted equilibrium healing time in a function of the Rouse friction coefficient. The used parameters can be found in Table 4. Table 4. Model parameters used in this study. The chain dynamics parameters and Rouse friction coefficients are within the reasonable order compared with limited experimental or simulation results in the references 122,125,126 . The parameters for the rubbery phase and the parameter for the self-healing behavior are estimated based on our previous papers 84,99,115,174,264,265 . The parameters for the crystalline phase are estimated based on the reported study for the thermoplastic elastomers 257-261 . The parameters for the volume fractions of the soft rubbery and stiff crystalline phases are obtained based on curve fitting. Parameter Definition Fig 46,48,51 Fig 47 Fig 49 Fig 50 Fig 52 PU250 Fig 52 PU 1810 Fig 53 Fig 54 Estimation source Parameters for rubbery phase 𝑘 A F9 (s -1 ) Forward reaction rate 2x10 -7 2x10 -7 2x10 -7 2x10 -7 2x10 -7 2x10 -7 2x10 -7 2x10 -7 84,99,115,174,2 64,265 𝑘 A B9 (s -1 ) Reverse reaction rate 4x10 -4 4x10 -4 4x10 -4 4x10 -4 4x10 -4 4x10 -4 4x10 -4 3x10 -4 𝛥𝑥 (m) Distance along the energy landscape coordinate 1.4x10 -9 1.4x10 -9 1.4x10 - 9 1.4x10 -9 1.4x10 -9 1.4x10 -9 4x10 -9 4x10 -9 b (m) Kuhn segment length 5.2x10 - 10 5.2x10 - 10 5.2x10 - 10 5.2x10 - 10 5.2x10 - 10 5.2x10 - 10 5.2x10 - 10 5.2x10 - 10 𝑛 : Minimum chain length 50 50 50 50 13 50 200 200 𝑛 ; Maximum chain length 200 200 200 200 200 300 1500 2000 𝑛 < Average chain length 77 77 55-77 77 19 96 665 1160 𝛿 Chain length distribution width 0.05 0.05 0.05 0.05 0.1 0.1 0.1 0.15 Parameters for crystalline phase 𝐸 G (MPa) Young’s modulus of element C 170 170 170 170 1088 74.8 34 4.76 257-261 𝛾 G Poisson’s ratio of element C 0.48 0.48 0.48 0.48 0.48 0.48 0.48 0.48 𝑌 9 (MPa) Initial resistance 6.82 6.82 6.82 6.82 43.6 3 1.36 0.19 𝑌 H<= (MPa) Saturated resistance 10.22 10.22 10.22 10.22 65.4 4.5 2 0.29 ℎ Hardening modulus 3 3 3 3 3 3 3 3 124 𝛥𝐺 I (𝑘 J 𝑇) ⁄ Activation energy for plastic deformation 100 100 100 100 100 100 100 100 𝜈 9 Reference plastic shear rate 0.001 0.001 0.001 0.001 0.001 0.001 0.001 0.001 Composition parameters 𝑝 GK Volume fraction of crystalline phase 0.35 0.2-0.5 0.35 0.35 0.5 0.3 0.35 0.35 Estimated from Fig. S19 𝜂 L Volume fraction of element A in rubbery phase 0.98 0.94-1 0.98 0.98 0.8 0.99 0.992 0.993 Fittting for stress- strain curve Parameter for self- healing 𝜉 (N/m) Rouse friction coefficient 4x10 -1 4x10 -1 4x10 -1 4x10 -2 - 4x10 -1 13 2.6x10 -1 6.4x10 -4 5.9x10 -5 Fitting for healing time 6.6 Comparison with our own experimental results After presenting the general characteristics of the theoretically predicted stress-strain behaviors of the virgin and healed thermoplastic elastomers, we compare the theoretical calculations with the experimental results. We first compare the theoretical results with our own experimental results (Fig. 51). The employed parameters and their estimation sources are shown in Table 4. Briefly, the parameters for the rubbery phase and the parameter for the self-healing behavior are estimated based on our previous papers 84,99,115,174,264,265 . The parameters for the crystalline phase are estimated based on the reported study for the thermoplastic elastomers 257-261 . The volume fraction of the stiff crystalline phase (i.e., crystallinity) is estimated using the differential scanning calorimetry thermographs 267-269 (Fig. S19). The compositions of the soft rubbery phases A and B are obtained based on curve fitting. We first take a self-healable thermoplastic elastomer with the molar mass of the chain extender PTEMG 1000 g/mol for an example. As shown in Fig. 51a, the theoretically calculated stress-strain behaviors of the virgin and healed thermoplastic elastomers can agree with the experimental counterparts. Likewise, the theoretically calculated healing strength ratio can also consistently match the experimentally measured results (Fig. 51b). 125 Figure 51. Experimental and theoretical results The experimentally-measured and theoretically-calculated (a) stress-strain curves of the original and self- healed samples, and (b) healing strength ratios in a function of the healing time. The used parameters for the theoretical model can be found in Table 4. Then, we vary the molar mass of the chain extender PTEMG from 250 to 1810 g/mol, and the corresponding stress-strain behaviors of the virgin and healed materials are shown in Fig. 52a-c. As the molar mass of the chain extender increases, the volume fraction of the soft rubbery phase increase and gradually dominate the mechanical behavior of the polymer (Fig. 52d-f). In the experiment, the yielding strength and tensile strength of virgin materials decrease as the volume fraction of the rubbery phase increases. This behavior can be theoretically understood based on our model with the effect of phase fraction explained in Section 4. Our theory can quantitively capture the elastic range, strain hardening and tensile strength of different phase fraction polymers. Also, as the healing time increases, tensile strengths of the healed samples increase until reaching a plateau. The healing strength ratios with various healing time of polymers with different phase compositions can also quantitively capture by our self-healing model (Fig. 52g-i). It is also noted that as the rubbery phase volume fraction increases, the equilibrium healing time increases from 6-15h. This phenomenon can be explained as follows: The healing process is primarily governed by the coupling of diffusion of polymer chains and reforming of dynamic disulfide bonds around the healing interface. Base on the Eq. 6-40, as the molar mass of the chain extender increases (corresponding to chain length increasing), the diffusivity decreases, and the required healing time is expected to be longer. 126 Figure 52. Experimental and theoretical results (a-c) Tensile stress-strain curves of the virgin and healed polymers with various healing time. The polymers in a-c have various PTMEG molar masses from 250 to 1810 g/mol, respectively. The experimentally-measured and theoretically-calculated (d-f) stress-strain curves of the original and self- healed samples, and (g-i) healing strength ratios in functions of the healing time. The polymers in d-f and g-i have various PTMEG molar masses corresponding to a-c, respectively. The used parameters for the theoretical model can be found in Table 4. 6.7 Comparison with others’ experimental results In section 6.6, we compare our experimental results on the self-healable polyurethanes with the theoretically calculated results. To further demonstrate the versatility of the present model, we show our model may be applied to understand a number of thermoplastic polymers with variety of dynamic bonds, including disulfide bonds 155,156,270 , urea bonds 271 and hydrogen bonds 61 . In this section, we will compare the theoretical results with several other’s reported experimental results 254 272 127 6.7.1 Disulfide bonds The first example is a self-healing polyurethane based on disulfide bonds from 4-4-aminophenyl disulfide 254 . The disulfide bond is a type of dynamic covalent bond that can trigger the dynamic exchange under elevated temperature. The disulfide bonds were treated as chain-extender introduced in polyurethane prepolymer and exhibited 93.43% healing efficient after being healed for 24 h at 80c. The corresponding experimental results are shown in Fig. 53a. Using the presented model, we can use adequate model parameters to consistently explain the experimental stress-strain behavior of original and healed samples (Fig. 53b, parameters in Table 4). In addition, the theoretically calculated healing strength ratio–healing time relationship has a good agreement with the referenced experimental results (Fig. 53c). Figure 53. Theoretical results of self-healing based on disulfide bonds (a) The experimentally-measured stress-strain curves of the original and self-healed samples. The experimentally-measured and theoretically-calculated (b) stress-strain curves of the original and self- healed samples, and (c) healing strength ratios in a function of the healing time. The experimental data in a-c are reproduced from reference 254 with permission. The used parameters for the theoretical model can be found in Table 4. 6.7.2 𝜋− 𝜋 interaction The second example is a self-healing polymer that crosslinked by Pt···Pt and π-π interactions between polydimethysiloxane (PDMS) and platinum (II) complex (Fig. 54a) 272 . The dynamic and reversible association-disassociation process of Pt···Pt and π-π stacking interactions allow the polymer to realize the self-healing property. The excellent mobility of PDMS chins allows the polymer to heal at room temperature. The healed sample shows the tensile modulus, strength and stretchability can reach more than 90% of those of the original sample after 12 h at room temperature. The corresponding experimental results are shown in Fig. 54b. With adequate parameters, our theoretical model can consistently capture the 128 experimental stress-strain behaviors of the original and healed samples (Fig. 54c). In addition, the healing strength ratios with different healing time from the experiment roughly agree with theoretically calculated results (Fig. 54d). Note that the polymers shown in 272 have backbone PDMS chains, but their mechanical behaviors do not necessarily resemble that of the commonly used elastomer PDMS. Actually, the PDMS shown in 272 showed an elastoplastic stress-strain curve: a small-strain linear elastic range followed by a strain-hardening region (Fig. 54b). Figure 54. Theoretical results of self-healing based on 𝜋− 𝜋 interaction (a) The photograph and proposed structure of the PDMS-Pt film (b) The experimentally-measured stress- strain curves of the original and self-healed samples. The experimentally-measured and theoretically- calculated (c) stress-strain curves of the original and self-healed samples, and (d) healing strength ratios in a function of the healing time. The graph in a and the experimental data in b-d are reproduced from reference 272 with permission. The used parameters for the theoretical model can be found in Table 4. 6.8 Conclusive remarks In summary, we report a theoretical framework that can explain the constitutive and self-healing behaviors of self-healable thermoplastic elastomers with both dynamic bonds and crystalline phases. We consider the 129 virgin thermoplastic elastomer by employing a general spring-dash model that couples the soft rubbery phase and the stiff crystalline phase. The rubbery polymer network is formed by layering the body-centered unit cubes that link polymer chains via dynamic bonds. During the self-healing process, we use a diffusion- reaction model to model the interfacial healing process. The theoretical framework can explain the stress- strain behaviors of original and self-healed thermoplastic elastomers, as well as the corresponding healing strengths over the healing time. We show that the theoretical framework can nicely explain our own experiments on self-healable thermoplastic elastomers polyurethane with dynamic disulfide bonds and the documented results of thermoplastic materials with disulfide bonds and pi-pi interactions. We expect that our model can be further extended to explain the self-healing behaviors of thermoplastic polymer with a wide range of dynamic bonds 61,155,156,270,271 . Note that as an initial attempt to model the self-healing thermoplastic elastomers, we here only focus on the quasistatic loading condition. Actually, the loading rate can affect two aspects of the material behavior: First, the loading rate affects the mechanical behavior of the plastic element D (reference plastic shear rate 𝜈 ' ). Second, the loading rate also affects the binding kinetics of the dynamic disulfide bonds. We would leave the effect of the loading rate on the mechanical properties of the virgin and healed self-healing thermoplastic elastomers to future research. In addition, we do not consider the train-induced crystalline change in our material system. The typical strain-induced crystallinity change is considered in natural rubbers in which the strain can enable the increase of the crystallinity 273-277 . However, for the polyurethane system, most of the modeling works on polyurethanes have not considered the strain-induced crystallinity change 257-261 . 130 Chapter 7: Healable, Memorizable, and Transformable Lattice Structures Made of Stiff Polymers 7.1 Objective Emerging transformable lattice structures provide promising paradigms to reversibly switch lattice configurations, thereby enabling their properties to be tuned on demand. The existing transformation mechanisms are limited to nonfracture deformation, such as origami, instability, shape memory, and liquid crystallinity. In this study, we present a class of transformable lattice structures enabled by fracture and shape-memory-assisted healing. The lattice structures are additively manufactured with a molecularly designed photopolymer capable of both fracture healing and shape memory. We show that 3D-architected lattice structures with various volume fractions can heal fractures and fully restore stiffness and strength over two to ten healing cycles. In addition, coupled with the shape-memory effect, the lattice structures can recover fracture-associated distortion and then heal fracture interfaces, thereby enabling healing of lattice wing damages, mode-I fractures, dent-induced crashes, and foreign-object impacts. Moreover, by harnessing the coupling of fracture and shape-memory-assisted healing, we demonstrate reversible configuration transformations of lattice structures to enable switching among property states of different stiffnesses, vibration transmittances, and acoustic absorptions. These healable, memorizable, and transformable lattice structures may find broad applications in next-generation aircraft panels, automobile frames, body armor, impact mitigators, vibration dampers, and acoustic modulators. 7.2 Introduction Precisely architected lattice structures with extraordinary properties, including low density, high specific stiffness, high specific strength, and high energy absorption, have been used in a broad range of engineering applications, such as aerospace panels, impact absorbers, acoustic modulators, thermal exchangers, battery electrodes, and biomedical scaffolds 278-286 . A key limitation in most existing lattice structures is that their properties and functions may not be modulated once fabricated. A promising direction in the field is 131 designing transformable lattice structures whose configurations can be reversibly switched to enable tunable properties 287,288 . Existing transformation mechanisms primarily rely on nonfracture deformation, such as origami 289-291 , instability 292-294 , shape-memory 146,295,296 , and liquid crystallinity 297 . Fractures have rarely been harnessed to transform lattice structures because fractures have long been considered a failure mode that compromises the structural integrity and properties; furthermore, healing fractures is also typically challenging for 3D-architected lattice structures. However, fractures and the corresponding healing, if successfully realized to transform lattice structures, would greatly benefit a broad range of engineering applications in two aspects. First, damage to lattice structures may be intelligently managed and recovered: examples include lightweight panel structures that may recover from foreign-object-impact- induced damage, body armor that may self-repair damage induced by bullets or other shrapnel on the battlefield, lattice dampers that may regain damping properties after healing overload crashes, and biomedical scaffolds that may imitate self-healable bones. Second, fracture healing can be a new tool to intelligently tune the lattice connectivity, thereby reversibly switching the static or dynamic properties of lattice structures. Despite the great potential, the realization of fracture healing in lattice structures is still challenging, primarily due to two technical barriers. First, innovating materials feasible for manufacturing self-healable lattice structures is challenging. Taking photopolymerization-based additive manufacturing (e.g., stereolithography 141,298 , polyjet 146,299 , self-propagation photopolymer waveguides 142,143 , and two-photon lithography 144,145 ) as an example, the required material should be both photocurable and self-healable; this kind of material remains largely unexplored. Although Yu et al. recently invented photocurable and self- healable elastomers 300 , the stiffnesses of these materials are relatively low (10-50 kPa), making them unsuitable for the application of force-sustaining lattice structures. In addition, although high-strength self- healable polyurethane has been reported recently 268,301 , how to molecularly tailor high-strength self-healable polyurethane to enable photocuring for additive manufacturing remains largely elusive. Second, healing of lattice structures requires precise contact or alignment of fracture interfaces, whereas damage to lattice structures is typically associated with shape change around fracture locations. The fractures cannot be 132 healed properly without the contact of fracture interfaces. Existing healing experiments of self-healing bulk materials typically rely on manual contact of fracture interfaces 9,47,48,238 ; however, manual contact is challenging for deep cracks or complex lattice architectures. Consequently, the development of transformable lattice structures that can heal fractures is still an outstanding engineering challenge. In this study, we present a class of transformable lattice structures enabled by fracture and shape- memory-assisted healing. The lattice structures are additively manufactured via a projection stereolithography system (Fig. S20) with a polymer ink that features acrylate groups for photocuring and disulfide groups for fracture healing. The printed solid features a Young’s modulus as high as 500 MPa, similar to that of a typical Teflon (200-600 MPa) 302 . We show that 3D-architected lattice structures with various volume fractions can heal critical fractures and fully restore stiffness and strength over 2-10 healing cycles. In addition, coupled with the shape-memory effect, damaged lattice structures can first recover fracture-associated shape changes to align and then heal the fracture interfaces, thereby enabling healing of lattice wing damages, mode-I fractures, dent-induced crashes, and foreign-object-impact-induced damages. Moreover, by harnessing the coupling of fracture and shape-memory-assisted healing, we demonstrate reversible configuration transformations of lattice structures to enable switching among property states of different stiffnesses, vibration transmittances, and acoustic absorptions. Equipped with coupled features, including additive manufacturing, fracture healing, and shape memory, our lattice structures may open promising avenues for smart lightweight structures that can reversibly transform architectures and recover damage through fracture-memory-healing cycles. These healable, memorizable, and transformable lattice structures may find broad applications in next-generation aircraft panels, automobile frames, body armor, impact mitigators, vibration dampers, and acoustic modulators 278-286 . 7.3 Materials and methods 7.3.1 Materials Polytetramethylene ether glycol (PTMEG, molar masses of 250, 1000, and 1810 g/mol), isophorone diisocyanate (IPDI), dimethylacetamide (DMAc), dibutyltin dilaurate (DBTDL), 2-hydroxyethyl disulfide 133 (HEDS), 1,4 butanediol (BDO), 2-hydroxyethyl methacrylate (HEMA), tributylphosphine (TBP), phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide (photoinitiator), and Sudan I (photoabsorber) were purchased from Sigma-Aldrich and used without further purification. 7.3.2 Preparation of experimental polymer inks First, 0.00829 mole of PTMEG was preheated at 90 °C and bubbled with nitrogen for 1 h to remove oxygen and water. After lowering the temperature to 70 °C, the preheated PTMEG was mixed with 7.369 g IPDI, 5 g DMac and 0.15 g DBTDL by magnetic stirring for 1 h. Then, a solution with 2.557 g HEDS in 20 g DMac was added dropwise to the mixture by magnetic stirring for another 1 h. After cooling the mixture to 40 °C, 2.147 g HEMA was added, and then the mixture was subjected to one more hour of magnetic stirring to complete the reaction. During the whole process, nitrogen was bubbled into the solution. The obtained solution was then placed in a vacuum chamber for 12 h to evaporate the solvent. To allow additive manufacturing of the polymer ink, the solution was mixed with 1 wt % photoinitiator, 0.01~0.02 wt % photoabsorber, and 0.1 wt % TBP and then stirred for 2 h. To monitor each reaction step during the ink synthesis, we employed a Spectrum Two FT-IR Spectrometer (PerkinElmer, USA) to carry out Fourier- transform infrared spectroscopy (FTIR) analyses (Fig. S22). All the samples were scanned in the range of 450 to 4000 cm -1 at a resolution of 0.5 cm -1 . 7.3.3 Additive manufacturing The projection-based stereolithography system used to manufacture all the samples presented in this study was described elsewhere 141,300 . We first designed 3D structures in computer-aided design (CAD) software; the models were output as STL files. Each STL file was then sliced into image sequences with a designated spacing in the vertical direction. The images were sequentially projected with 405 nm wavelength light onto the resin bath, which was filled with a synthesized polymer ink. A motor-controlled printing stage was mounted onto the resin bath with a prescribed liquid height. The light-exposed resin was solidified and bonded onto the printing stage. As the printing stage was lifted, the fresh resin refluxed beneath the printing stage. By lowering the printing stage to a prescribed height and illuminating the resin with another slice 134 image, a second layer was printed and bonded onto the first layer. These processes were repeated to form a 3D-architected structure. Note that a Teflon membrane with a low surface tension (~20 mN/m) was employed to reduce the separation force between the solidified part and the printing window. Fabricated samples were post-cured for 1 h in a UV chamber to enable the full photopolymerization of the material, and then the samples were heated for 12 h at 40 °C to remove the residual solvent within the material matrix. 7.3.4 Self-healing characterization Strip samples (length of 20 mm, width of 5 mm, and thickness of 1 mm) were prepared following the method mentioned in the additive manufacturing section. Samples were first cut into two pieces with a sharp blade and then immediately placed in contact, during which the two ends were clamped to ensure good contact during the healing process. The samples were then placed on a hot plate at 80 °C for various healing times. Both the original and the healed samples were uniaxially stretched until rupture with a strain rate of 0.06 s -1 with a tensile tester (Instron, Model 5942). Microscopic pictures of the healed surfaces were taken using an optical microscope (Nikon ECLIPSE LV100ND). Raman spectroscopy analyses of the experimental and control samples were carried out using a Horiba Raman infrared microscope with a laser excitation wavelength of 785 nm in the range of 400 to 1500 cm -1 . 7.3.5 Shape-memory characterization The shape-memory behavior in Fig. 56 was characterized with the thermomechanical cyclic test programmed in a dynamic mechanical analyzer (DMA 850, TA instrument) using the controlled-force mode. The sample was preheated to an equilibration temperature of 80 °C, and then a static force was applied to the sample. The force was continuously held until the temperature cooled to 35 °C. Then, the force was released at a rate of 0.5 N/min to an initial preload of 0.001 N. Finally, the sample was heated back to 80 °C again. To measure the glass transition temperature, the samples were tested with the oscillation temperature ramp program in a dynamic mechanical analyzer (DMA 850, TA instrument) and heated in the range of 20 °C to 160 °C at a rate of 5°/min. The glass transition temperature was determined using the obtained storage modulus curve as introduced in the literature 303 . To verify the existence of 135 crystalline domains, samples with various molar masses of PTMEG (250, 1000, and 1810 g/mol) were tested using differential scanning calorimetry (DSC-8000, PerkinElmer). A 5 mg sample was placed in the alumina plate and heated in the range of 30 °C to 160 °C at a rate of 10°/min under the flow of ultrahigh purity nitrogen. An empty alumina plate was placed in the other chamber as a reference. 7.3.6 Manual-contact-assisted healing of octet lattices The abovementioned additive manufacturing process was used to fabricated 1×1×4 octet trusses with different densities (ρ/ρ 0 = 13.1%, 23.4%, 37.9%, and 53%). The printed structures were first subjected to a 3PB test until fracture (Instron, Model 5942). The damaged samples were brought into contact at 80 °C and then healed for 6 h at 80 °C. The healed structures were subjected to another 3PB test until fracture. Then, the sample was healed and broken again until completing ten healing cycles. 7.3.7 Shape-memory-assisted healing of lattice structures Octet lattice structures with different shapes were fabricated using the abovementioned additive manufacturing process. The unit cell size is approximately 2 mm × 2 mm × 2 mm. The lattices in Figs. 58a- d feature 2×4×8 unit cells. The lattices in Fig. 58h-i feature 2×9×9 unit cells. For the mode-I fracture example in Fig. 58a, we employed an electric cutter (WORX WX081L) to cut the lattice structure in half at the center of the sample width, bent the sample to open the crack to ~3.6 mm at 80 °C, and froze the bending deformation by cooling to room temperature. The damaged lattice, with both shape change and material fracture, was heated to 80 °C on a hot plate to allow the crack width to close within 1 min. The corresponding shape-memory temperature cycle is shown in Fig. 56b. The temperature of 80 °C was maintained for an additional 6 h to enable the fracture-fracture healing. The load-displacement curves of the original (Fig. 58a(i)), shaped-recovered but fractured (Fig. 58a(iv)), and fracture-healed lattices (Fig. 58a(v)) in the 3PB tests were obtained by the Instron mechanical tester. For the denting example in Fig. 58d, a steel rod (diameter 8 mm) was employed to dent the lattice at 60 °C until the internal beams were fractured. The experimental procedures for the shape recovery and fracture healing at 80 °C were the same as those of the mode-I fracture example in Fig. 58a. The corresponding shape-memory temperature cycle 136 is shown in Fig. S36. Denting tests were used to measure the load-displacement curves of the original (Fig. 58d(i)), shape-recovered but fractured (Fig. 58d(iv)), and fracture-healed lattices (Fig. 58d(v)) in the center region. In Fig. 58i, a rod with a spherical end (50 g) was dropped from a height of 1 m onto the sample at 60 °C. The experimental procedures for the shape recovery and fracture healing at 80 °C were the same as those of the mode-I fracture example in Fig. 58a. The corresponding shape-memory temperature cycle is shown in Fig. S36. An impact-mitigation test was performed by dropping a 50 g rod from a height of 5 cm onto a rigid plastic substrate. An accelerometer (352C22, PCB Piezotronics, USA) was attached beneath the substrate to measure the reaction acceleration during the impact. The signal was collected with an oscilloscope (TBS 1052B-EDU, Tektronix) when no, virgin, damaged and healed lattices were placed on the substrate. 7.3.8 Stiffness transformation of honeycomb lattices Honeycomb lattice structures were first fabricated using the abovementioned additive manufacturing process. A sharp blade was used to cut the selected vertical beams, which were then deactivated by bending at 80 °C; then, the shape was frozen by cooling to room temperature. The programmed lattice structures were heated to 80 °C for 6 h to allow shape recovery and self-healing of the deactivated beams. The stiffnesses of the original and programmed structures (with deactivated beams) were measured using compression tests in the Instron mechanical tester (strain rate = 0.06 s -1 ). 7.3.9 Vibration transformation of triangle lattices Triangle lattice structures were first fabricated using the abovementioned additive manufacturing process. The structures were placed on the top of a vibration generator (2185.00, Frederiksen) that was powered by a function generator (PI-8127, PASCO). Two accelerometers (352C22, PCB Piezotronics, USA) were attached on the bottom and top of the structures. Both accelerometers were connected to a signal conditioner (482C05, PCB Piezotronics) to display the signal on an oscilloscope (TBS 1052B-EDU, Tektronix). The vibration transmittances of the lattice structures were measured as |𝑃 . /𝑃 C |, where 𝑃 . and 𝑃 C are the acceleration amplitudes of the top and bottom accelerometers, respectively. To transform a triangular lattice 137 into a Kagome lattice, the horizontal beams were cut with a sharp blade and deactivated by bending at 80 °C and cooling to room temperature. To transform the Kagome lattice back into a triangular lattice, the Kagome structure was heated to 80 °C for 6 h to allow shape recovery and fracture healing. 7.3.10 Acoustic transformation of lattice structures Lattice plates with small islands were designed and fabricated using the abovementioned additive manufacturing process. Three lattice plates were aligned and spaced 2 cm apart in a rectangular acrylate chamber (length of 30 cm, height of 5 cm and width of 5 cm, McMaster Carr). A loudspeaker (OT19NC00- 04, Tymphany) connected to a function generator (PI-8127, PASCO) was placed at one end of the chamber to provide an acoustic signal. At the other end of the chamber, a microphone (378B02 with 426E01, PCB Piezotronics, USA) was used to collect the acoustic signal. The collected acoustic signal was processed by a signal conditioner (482C05, PCB Piezotronics) and displayed on a digital oscilloscope (TBS 1052B-EDU, Tektronix). The acoustic transmittance was measured as |𝑃 Y /𝑃 Yw |, where 𝑃 Y and 𝑃 Yw were the measured acoustic pressures from the microphone with and without lattice structures, respectively. To program the lattice structures, one thin beam in each frame was cut with a sharp blade and deactivated by bending at 80 °C and cooling to room temperature. To restore the structures, the programmed structures were heated to 80 °C for 6 h to allow shape recovery and fracture healing. 7.3.11 Preparation of control 1 and control 2 polymer inks The control 1 polymer ink without disulfide bonds (shape-memorizable but not self-healable) was prepared with the same steps as mentioned in the preparation of experimental polymer inks except that the HEDS was replaced by BDO. BDO had a similar chemical structure as HEDS but without disulfide bonds. The control 2 polymer ink without crystalline domain (self-healable but not shape-memorizable) was prepared based on the reported work 300 . 138 7.3.12 Vibration band simulations Numerical simulations of vibration band structures of triangle and Kagome lattices were implemented with the solid mechanics module in COMSOL Multiphysics v5.3a. Figures S38a and S38e illustrated the periodic units used in the simulation. Material parameters included Young’s modulus (500 MPa), Poisson’s ratio (0.33), and density (1000 kg/m 3 ). Irreducible Brillouin zones of triangle and Kagome lattices are shown in Figs. S38b and S38f, respectively 304 . Triangle meshes were employed to discretize the models, and the mesh numbers of the triangle and Kagome units are 482 and 480, respectively. The mesh accuracy was ascertained through a mesh refinement study. 7.3.13 Acoustic transmittance simulations Acoustic transmittance simulations were implemented in COMSOL Multiphysics v5.3a. Figures S42ab illustrated model set-ups used in the simulations. Two phases, polymer and air, were simulated with the solid mechanics and acoustic modules, respectively. The material parameters of the polymer included Young’s modulus (500 MPa), Poisson’s ratio (0.33), and density (1000 kg/m 3 ). Considering the periodicity of the lattice structures, symmetric boundary condition was applied in the lateral direction. Perfectly matching layers were employed to ensure the open boundary along the acoustic transport direction. The simulation was validated by benchmark calculations and the mesh accuracy was ascertained through a mesh refinement study. 139 7.4 Results 7.4.1 Design principle for the transformable lattice structures The design principle for transformable lattice structures enabled by fracture and shape-memory-assisted healing is motivated by limitations in existing lattice structures featuring either shape-memory (Figs. 55a- c) 146,295,296 or self-healing (Figs. 55d-f) 300 . On the one hand, when an external intervention forces a lattice structure to undergo both a fracture and a shape change around the fracture location, a shape-memorizable lattice structure (typically made of a semi-crystalline polymer) may recover the shape change in a thermal cycle, whereas the fracture interface cannot be healed properly (Fig. 55a-c) 146,295,296 . On the other hand, a fracture-healable lattice structure may heal the fracture interface by reversibly forming dynamic bonds (e.g., disulfide bonds 300 ), whereas the damage-associated shape change cannot be recovered properly (Figs. 55d- f). Therefore, both types of lattice structures may not fully recover the structural integrity or function. Herein, we propose a class of lattice structures made of polymers featuring both shape memory and fracture healing (Figs. 55g-i). In a typical working cycle, a damaged lattice structure with both shape change and material fracture undergoes a shape-recovery process to align the fracture interfaces and then a fracture- healing process to fully repair the fracture interfaces (Fig. 55g). In this way, the damaged lattice structures are expected to fully recover the initial structural integrity and function and even enable multiple damage- recovery cycles. The polymers employed to fabricate the proposed lattice structures are designed based on urethane linkages (-NH-CO-O-) formed from a reaction between isocyanate groups (-NCO) and hydroxyl groups (- OH) (Figs. 55j(i), S21 and S22) 305,306 . The backbone of the polymer network is constructed by an aromatic diisocyanate (isophorone diisocyanate) and a diol (polytetramethylene ether glycol, PTMEG) via urethane linkages. To enable self-healing properties, we covalently incorporate dynamic disulfide bonds into the network by linking a diol-terminated disulfide (HO~S-S~OH) (Fig. 55j(i), S21 and S22) 155,253 . The self- healing properties primarily rely on disulfide metathesis reactions (assisted by a catalyst tributylphosphine) to bridge the fracture interface (Fig. S23a) 150,300 . In addition, to enable photocuring properties for 140 stereolithography-based additive manufacturing, we incorporated a hydroxyl-ended acrylate group (CH 2=CHCOO~OH) (Fig. 55j(i), S21 and S22) 305 . The acrylate groups can undergo a photo-radical- assisted addition reaction to solidify the polymer (Fig. S23b). Thus, the polymer ink for stereolithography is made of disulfide-linked urethane-acrylate oligomers (Figs. 55j(ii-iii)). After photopolymerization, the solid polymer embeds not only dynamic disulfide bonds but also crystalline domains formed through the intermolecular interactions of the polymer chains (Fig. 55j(vi)) 306 . The existence of disulfide bonds within the polymer is verified by Raman spectroscopy measurements, which show a new peak with a band at ~520 cm -1 (Fig. S24) that was not observed in the control polymer (control 1) without disulfide bonds (Fig. S25). This new band is consistent with the Raman band in the reported disulfide-bond-enabled self-healing polymers (500-550 cm -1 ) 155,156,300 . The existence of the crystalline domain within the polymer is verified by a new endothermic peak at ~130 °C (Fig. S26) that was not observed in the control self-healing polymer (control 2) without crystalline domains 300 . This endothermic peak is consistent with those in reported semi- crystalline polyurethanes 306 . Using a stereolithography system, we can fabricate lattice structures with complex architectures and geometries and produce the coupled properties of shape memory and fracture healing (Figs. 55j(iv-vi)). The manufacturing process is relatively rapid with a speed of ~25 µm/s for each layer and a total construction time of approximately 1.5 h for the lattice wing structure shown in Fig. 55j(v) (Fig. S20). As a quick demonstration of a transformable lattice wing in Fig. 55k, the lattice wing is first damaged with both a material fracture and a dent. After heating to 80 °C for 1 min, the dent can be recovered through a shape-memory process, thereby aligning the initially distorted fracture interface. By maintaining the temperature at 80 °C for another 6 h, the fracture interface can be nicely healed to resume the structural function of the lattice wing. The fracture healing is verified by the magnified pictures and microscope images around the healing interface (inset images in Fig. 55k and Fig. S27). 141 Figure 55. Design principle for transformable lattice structures enabled by fracture and shape-memory- assisted healing. 142 (a) Schematics of the working principle of a shape-memorizable lattice wing structure. (b) Schematic of the molecular structure of a shape-memorizable semi-crystalline polymer. (c) Schematics of the shape- memory working cycle of a shape-memorizable polymer. (d) Schematics of the working principle of a fracture-healable lattice wing structure. (e) Schematic of the molecular structure of a fracture-healable polymer with dynamic disulfide bonds. (f) Schematics of the fracture-healing working cycle of a fracture- healable polymer. (g) Schematics of the working principle of the proposed lattice wing structure with the coupled properties of shape memory and fracture healing. (h) Schematic of the molecular structure of the proposed polymer with both crystalline domains and dynamic disulfide bonds. (i) Schematics of the working cycle of the proposed polymer. (j) Schematics and samples to show the additive manufacturing of a lattice wing: (i) key monomers including 2-hydroxyethyl methacrylate (HEMA) to provide acrylate groups, isophorone diisocyanate (IPDI) to provide isocyanate groups, hydroxyethyl disulfide (HEDS) to provide disulfide groups, and polytetramethylene ether glycol (PTMEG) to provide hydroxyl groups; (ii) chemical formula of the polymer ink with disulfide-linked urethane-acrylate oligomers; (iii) schematic of the polymer ink with disulfide-linked urethane-acrylate oligomers; (iv) schematic of the stereolithography system; (v) lattice wing sample; and (vi) schematic of the molecular structure of the proposed polymer. (k) Sample image sequence showing the fracture-memory-healing cycle of a lattice wing. The inset images show the magnified views of the fracture location. The scale bars in j(v) and k represent 4 mm. 7.4.2 Characterization of shape memory and fracture healing Next, we characterize the shape-memory properties of the synthesized polymers. To qualitatively show the shape-memory properties, we first program a twist on a strip sample (with a PTMEG molar mass of 250 g/mol) at 80 °C and then fix the twist by cooling to room temperature. As the temperature increases again to 80 °C, the twisted sample returns to the initially flat shape within 1 min (Fig. 56a). The selection of 80 °C as the recovery temperature is because the glass transition temperature of the polymer is approximately 65-71 °C (Fig. S28). To quantify the shape-memory properties, we measure the tensile stress-strain behaviors of polymer samples with PTMEG of various molar masses within a thermal cycle (see Materials and methods). As the molar mass of PTMEG increases, the polymer becomes more flexible with a decreasing glass transition temperature (from above 65-71 °C for 250 g/mol PTMEG to below 25 °C for 1810 g/mol PTMEG, Fig. S28). We find that polymers with different glass transition temperatures exhibit different shape-memory cycles (Figs. 56b-d). A typical shape-memory cycle consists of four segments (Figs. 56b-d): (1) Loading: a polymer sample is uniaxially stretched to a prescribed strain 𝜀 i at 80 °C. (2) Cooling: the strain slightly changes to 𝜀 9 after cooling to 35 °C under the maintained load. (3) Unloading: the applied load is relaxed at 35 °C with the strain decreasing to 𝜀 y . (4) Recovering: the temperature increases again to 80 °C with the strain further decreasing to 𝜀 $ . To quantify the shape-memory properties, 143 we define shape-fixity and shape-recovery ratios as 𝑅 # =𝜀 y 𝑚𝑎𝑥(𝜀 i ,𝜀 9 ) ⁄ and 𝑅 $ =1−𝜀 $ 𝜀 y ⁄ , respectively 146,295,296,306 . With decreasing glass transition temperature, although the shape-recovery ratio 𝑅 $ remains at 98-100%, the shape-fixity ratio 𝑅 # drastically decreases from 98% for 250 g/mol PTMEG to ~1% for 1810 g/mol PTMEG (Figs. 56e-g). Hence, the polymer with the lower PTMEG molar mass exhibits better shape-memory properties for a thermal cycle within 35-80 °C 306 . In addition to the shape-memory properties, the synthesized polymers with disulfide bonds also exhibit self-healing properties. To qualitatively show this phenomenon, we first cut a strip sample into two parts and then brought these parts into contact at 80 °C for 6 h (Fig. 56h). The microscopic images show that the fracture interface can be nicely healed (Fig. 56i). The healed strip sample can sustain a weight of 50 g, which is 400 times its own weight (0.125 g) (Fig. 56h). In contrast, the control polymers (control 1) without disulfide bonds cannot heal the fracture interface after more than 18 h under the same healing conditions (Figs. S25 and S29). To quantify the self-healing properties of disulfide-containing polymers, we carry out uniaxial tensile tests on the virgin polymer strips and healed samples for various healing periods at 80 °C (Figs. 56j-l). The Young’s modulus of the virgin polymer with a PTMEG molar mass of 250 g/mol is approximately 500 MPa (Fig. S30), which is within the modulus range of a typical Teflon (200-600 MPa) 302 . As the healing time increases, the tensile strength of the healed sample increases until reaching a plateau, which is the tensile strength of the virgin sample. We take the healing time corresponding to 90% of the healing strength ratio (tensile strength of the healed sample normalized by that of the original sample) as the equilibrium healing time. We find that the equilibrium healing time increases from 6 h to 15 h as the PTMEG molar mass increases from 250 to 1810 g/mol (Figs. 56m-o). This trend can be understood as follows: at 80 °C, which is above the glass transition temperature (Fig. S28), the polymer transforms to a rubbery state. The healing process is primarily governed by the coupling of diffusion of polymer chains and the reforming of dynamic disulfide bonds around the healing interface 84,174,264 . The Rouse diffusivity of a polymer chain is 𝐷 =𝑘 > 𝑇 (𝑛𝜉) ⁄ , where n is the Kuhn segment number (understood as the chain length) of the amorphous polymer chain with the disulfide bond, 𝜉 is the 144 Rouse friction coefficient, 𝑘 > is the Boltzmann constant, and T is the temperature 100,119 . As the chain length increases (corresponding to increasing PTMEG molar mass), the diffusivity decreases, and the required healing time is expected to be longer. Based on the characterization of the shape-memory and self-healing properties, we conclude that to obtain desirable shape-memory and efficient self-healing properties, we should design a polymer with a small PTMEG molar mass. Herein, we selected a polymer with a PTMEG molar mass of 250 g/mol, which features excellent shape-memory properties for a thermal cycle within 35-80 °C and more than 90% healing within 6 h at 80 °C. 145 Figure 56. Characterization of the shape-memory and self-healing properties. (a) Image sequence showing the shape-memory process of a strip polymer sample. (b-d) Stress-strain- temperature behaviors of synthesized polymers with various PTMEG molar masses within a shape- memory cycle. (e-g) Shape-fixity ratios Rf of synthesized polymers corresponding to b-d. (h) Image sequence showing the self-healing process of a strip polymer sample. The healed sample (0.125 g) can sustain a weight of 50 g. (i) Microscope images showing fractured and healed interfaces. (j-l) Tensile stress-strain curves of virgin polymers and polymers subjected to various numbers of healing cycles. The polymers in j-l have various PTMEG molar masses corresponding to b-d. (m-o) Healing strength ratios of healed polymers as a function of healing time. The healing strength ratio is defined as the tensile strength of the healed polymer normalized by the tensile strength of the virgin polymer. The shadow areas in m-o indicate the healing time corresponding to a healing strength ratio of 90%. The scale bars in a and h represent 4 mm, whereas the scale bars in i represent 300 µm. 7.4.3 Manual-contact-assisted healing of lattice structures Next, we study the healing behavior of the lattice structures (Fig. 57). We first fabricate 1×1×4 octet trusses with relative densities 𝜌 𝜌 ' ⁄ from 13.1% to 53% (𝜌 is the effective lattice density and 𝜌 ' is the material density, Fig. 57a(i)) and use a three-point-bending (3PB) load to fracture the lattices (Figs. 57a(ii-iii) and S31). The effective Young’s modulus (3.2-10.8 MPa) and flexural strength (0.7-3.1 MPa) of the octet trusses with various relative densities can be obtained from the 3PB tests (Figs. 57b-e, S31 and S32). We find that the effective Young’s modulus 𝐸 and flexural strength 𝑆 of the octet trusses are approximately linear functions of their relative densities (Figs. 57f-g), which can be expressed as o o 2 ≈0.055k z z 2 l (7-1) x x 2 ≈0.318k z z 2 l (7-2) where 𝐸 ' and 𝑆 ' are the Young’s modulus and flexural strength (tensile strength) of the parent polymer with a PTMEG molar weight of 250 g/mol, respectively. 𝐸 ' and 𝑆 ' can be obtained from Fig. 56j. These linear relationships (Eqs. 7-1 to 7-2) are consistent with the reported theoretical prediction for the stretching-dominant octet truss 307 . Two fractured parts of the lattice structures are then brought into contact and placed in a glass container to maintain the contact (Fig. S33). After 6 h at 80 °C, the fracture interfaces are self-repaired through disulfide-enabled interfacial healing (Figs. 57a(iv) and S23a), which is verified by microscopic images of the fracture interface (Figs. 57a(v-vi)). The healed lattice can sustain a weight of 70 g, which is 146 approximately 400 times its own weight (0.174 g) (Fig. 57a(vii)). Then, the healed lattice can be fractured by the 3PB load again, and the resulting fracture location is different from that of the first fracture (Fig. 57a(viii)). We find that the effective Young’s moduli and flexural strength of the healed octet lattices (first- healed lattices) can reach above 90% of those of the virgin lattices (Figs. 57b-g and Fig. S32). In addition, the fractured first-healed lattices were healed again after 6 h at 80 °C (Fig. 57a(ix)). The linear relationships in Eqs. 7-1 to 7-2 are still valid for both the first-healed and second-healed lattices (Figs. 57f-g). In this way, the octet lattice with relative densities 𝜌 𝜌 ' ⁄ =13.1% can be repeatedly fractured and healed over 10 cycles (Fig. S34). The effective moduli and strengths of the healed lattice structures fluctuate within 85%- 105% of those of the virgin lattice but do not show evident degradation trends over 10 healing cycles. To the best of our knowledge, this is the first demonstration of full healing of the moduli and strengths of 3D- architected lattice structures over multiple healing cycles. 147 Figure 57. Manual-contact-assisted healing of lattice structures. (a) The healing process of an octet lattice over two healing cycles: (i) virgin octet lattice, (ii) octet lattice under a three-point-bending (3PB) load, (iii) fractured octet lattice, (iv) healed octet lattice after the first healing cycle (6 h at 80 °C), (v) microscope image showing the fracture interface, (vi) microscope image showing the healed interface, (vii) a mass of 70 g placed on the healed lattice, (viii) the healed lattice fractured again, and (ix) healed octet lattice after the second healing cycle (6 h at 80 °C). The scale bars in a(i-iv) and a(vii-ix) represent 4 mm, whereas the scale bars in a(v-vi) represent 300 µm. (b-e) Computer- aided design models and load-displacement curves of virgin, first-healed, and second-healed octet lattices 148 of various relative densities (ρ/ρ0=13.1%, 23.4%, 37.9%, and 53%) in 3PB tests. (f) The effective Young’s moduli of virgin, first-healed, and second-healed octet lattices as functions of the relative density. (g) The effective flexural strength values of the virgin, first-healed, and second-healed octet lattices as functions of the relative density. The error bars represent the standard deviations in 3-5 samples. 7.4.4 Shape-memory-assisted healing of lattice fractures Fractures in lattice structures are typically associated with geometrical distortions of fracture surfaces. Without using manual contact, we show that the shape-memory effect of the lattice structure can assist the distorted interface in returning to the initial geometry, through which the fracture interfaces can be aligned and contacted. This process enables the subsequent interfacial fracture healing to be realized. Note that the self-alignment of the fracture interface through the shape-memory properties can work for complex geometries and deep cracks within the matrix, which are typically challenging for manual contact. In the first example, a lattice structure is fractured in mode I (Fig. 58a). In the damaged state (Fig. 58a(ii)), the fracture surfaces are separated by a frozen crack width d. If the fracture surfaces do not contact each other, the fracture cannot be healed. We first increase the temperature to 80 °C to trigger a shape-memory process, which enables the crack open distance to gradually decrease to zero within 1 min (Figs. 58a(ii-iv), 58b and S35). Note that the fracture interface has not been healed in this stage. Then, we maintained the temperature of 80 °C for 6 h until the fracture interface was fully healed (Fig. 58a(v)). The healing is verified by microscope images of the fracture interface of a beam before and after the healing process (Figs. 58a(vi- vii)). To further verify the fracture healing, we apply a 3PB load to the healed interface (Fig. 58c). We find that the maximal 3PB load of the healed lattice (Fig. 58a(v)) is greater than 90% of that of the virgin lattice (Fig. 58c), whereas the maximal 3PB load of the shape-recovered lattice with an unhealed fracture (Fig. 58a(iv)) is only 20% of that of the virgin lattice (Fig. 58c). In the second example, a circular indenter is loaded onto a lattice structure to induce a geometrical dent with a certain depth h (Figs. 58d(i-iii)). The magnified picture shows microfractures within the internal beams (Fig. 58d(iii)). Harnessing the shape-memory effect at 80 °C, the dent depth can be recovered in 1.5 min, thereby enabling the alignment of the fracture surfaces of the internal beams (Figs. 58d(iv), 58e and 149 S36). Subsequently, additional healing for 6 h at 80 °C can further repair the interfacial microcracks in the beams. The healing is verified by microscope images of the fracture interface of a beam before and after the healing process (Figs. 58d(vi-vii)). To further verify the fracture healing, we use the indenter to test the structural stiffness and find that the stiffness of the healed lattice (Fig. 58d(v)) is approximately equal to that of the virgin lattice, whereas the stiffness of the lattice with the recovered shape but unhealed fractures (Fig. 58d(iv)) is only ~17% of that of the virgin lattice (Fig. 58f). In the third example, we demonstrate that the transformable lattice can be programmed to intelligently recover impact-induced damage (Figs. 58g-h). If the impact force is relatively small and only induces a dent in the lattice structure, the dent can be removed through a shape-memory process (Fig. S37). If the impact force is relatively large and induces a punch-through hole with spike fractures (Figs. 58g, 57h(i-ii), and 57i(i-ii)), the restoration should rely on the coupling of shape recovery and fracture healing. Aside from some small detached debris, the initial shape is first recovered through a shape-memory process at 80 °C for 1.5 min (Figs. 58h(ii-v), 58i(ii-v), and S36). Then, the fracture interfaces of the shape-recovered parts are fully healed through a fracture-healing process at 80 °C for 6 h (Figs. 58h(v-vi) and 58i(v-vi)). Fracture healing is verified by microscopic images before and after the healing process (Figs. 58i(vii-viii)). To demonstrate the advantage of the damage restoration of the lattice structure, we investigate the impact- mitigation behavior of the virgin (Fig. 58i(i)), damaged (Fig. 58i(ii)), and fracture-healed lattices (Fig. 58i(vi)) using the experimental setup shown in Fig. 58j. We employ a weight (50 g) dropped from a height of 5 cm to impact the lattice structures and measure the reaction force beneath the lattice structures (Fig. 58k). We find that the reaction force beneath the virgin lattice is only 16.2% (reaction force ratio) of that without a lattice structure (Fig. 58l). When the lattice is damaged, the reaction force ratio drastically increases to 94% (Fig. 58l). However, when the lattice is healed, the reaction force ratio decreases again to 16.6% (Fig. 58l). 150 Figure 58. Shape-memory-assisted healing of lattice fractures 151 (a) Shape-memory-assisted healing of a mode-I fracture in an octet lattice: (i) virgin lattice, (ii) damaged lattice with a frozen mode-I fracture, (iii) shape-recovering lattice, (iv) shape-recovered lattice with fracture interfaces, (v) healed lattice with recovered shape and healed fracture, (vi) microscope image of a fractured lattice beam, and (vii) microscope image of a healed lattice beam. (b) Crack width as a function of time during the shape-memory and fracture-healing processes. (c) Load-displacement curves of the virgin, shape-recovered with fracture interfaces, and fracture-healed lattices in 3PB tests; the inset shows the 3PB test setup. (d) Shape-memory-assisted healing of a dented octet lattice: (i) virgin lattice, (ii) lattice deformed by an indenter, (iii) damaged lattice, (iv) shape-recovered lattice with fractured beams, (v) healed lattice with recovered shape and healed fracture, (vi) microscope image of a fractured lattice beam, and (vii) microscope image of a healed lattice beam. (e) Dent depth as a function of time during the shape-memory and fracture-healing processes. (f) Load-displacement curves of the virgin, shape- recovered with fracture interfaces, and fracture-healed lattices in the denting tests; the inset shows the denting test setup. (g) Schematic showing the impact-induced damage of an octet lattice structure. (h) Schematic sequence and (i) experimental image sequence of shape-memory-assisted healing of the impact-induced damage of an octet lattice: (i) virgin lattice, (ii) impact-induced damaged lattice, (iii-iv) shape-recovering lattice, (v) shape-recovered lattice with fracture interfaces, (vi) fracture-healed lattice, (vii) microscope image of a fractured lattice beam, and (viii) microscope image of a healed lattice beam. (j) Experimental setup for testing the reaction forces of impacts on lattice structures, in which the impact is applied by a dropping weight (50 g) from a height of 5 cm. (k) The impact reaction forces in the cases with (i) no lattice, (ii) virgin lattice, (iii) damaged lattice, and (iv) fracture-healed lattice. (l) The normalized maximal reaction forces of the virgin lattice, the damaged lattice, and the fracture-healed lattice. The normalized maximal reaction forces are calculated as the maximal reaction force of each case normalized by the maximal reaction force of the no-lattice case. The error bars represent standard deviations from 5-10 tests. The scale bars in a(i), d(i), and i(i) represent 4 mm, whereas the scale bars in a(vi-vii), d(vi-vii), and i(vii-viii) represent 200 µm. 7.4.5 Lattice transformation via fracture-memory-healing cycles Next, we show that harnessing fracture-memory-healing cycles can enable on-demand transformation of lattice configurations and subsequently lead to intelligent switching of static or dynamic mechanical properties of lattice structures (Fig. 59). Take a honeycomb lattice as the first example: the stiffness primarily comes from the contribution of the force-sustaining vertical beams (Figs. 59a(i) and 59b(i)). After deactivating 5 vertical beams via fracture and bending (Figs. 59a(ii) and 59b(ii)), the lattice exhibits a stiffness of 0.96 MPa, which is 22% lower than that of the virgin lattice (1.2 MPa) (Figs. 59cd). Then, the deactivated beams can be fully healed through a memory-healing process (Figs. 59a(iii) and 59b(iii)), thereby recovering 100% of the stiffness of the virgin lattice (Fig. 59d). The lattice can be further transformed to a state with 10 beams deactivated by cutting and bending, which is associated with a 59% stiffness reduction (Figs. 59a(iv), 59b(iv), and 59e). Then, the lattice can be restored to return the stiffness to 1.1 MPa, which is 92% of the stiffness of the virgin lattice (Fig. 59e). 152 In the second example, we show that the fracture-memory-healing cycle can enable lattice transformation and subsequent reversible switching of vibration transmittance of lattice structures. A triangle lattice can be transformed to a Kagome lattice if the horizontal beams are deactivated via fracture and bending (Figs. 59f(i-iii)). According to reported numerical simulations 304 , the triangle lattice displays a band gap in transmitting in-plane elastic waves within a structure-dependent frequency regime, whereas the Kagome lattice does not display any band gap (simulations in Fig. S38). Motivated by the numerical simulations (Fig. S38), we experimentally measure the in-plane vibration transmittance using the setup shown in Fig. 59g (Fig. S39). We find that the triangle lattice exhibits a relatively low vibration transmittance (<0.2) within 32.2-33.2 kHz, whereas the transformed Kagome lattice presents a relatively high vibration transmittance (>0.8) within the same frequency regime (Fig. 59h). After heating the programmed Kagome lattice for ~6 h at 80 °C, the lattice transforms back to the triangle lattice through a coupled process of shape memory and fracture healing (Figs. 59f(iii-iv)). The healing of fracture interfaces can be verified by a magnified picture (Fig. 59f(v)). Once back to the triangle lattice, the vibration transmittances within 32.2- 33.2 kHz shift to low values (<0.2) again (Fig. 59h). As an alternative way to present the results, the normalized wave amplitudes of the lattice at three states at 32.75 kHz are shown in Fig. 59i: the programmed Kagome lattice shows a large increase in the wave amplitude and then returns to a small amplitude after restoration to the triangle lattice. Note that the restoration of vibration transmittance requires the integration of shape recovery and fracture healing, whereas only shape recovery cannot restore the vibration transmittance property (Fig. S40). In the third example, we show that the structural transformation enabled by the fracture-memory- healing cycle can also switch the acoustic absorption of the lattice structures (Figs. 59j-m). The key idea here is to reversibly switch local resonators within a lattice structure. The virgin lattice consists of 16 local resonators in which a rectangular island is connected to the structural frame through two thin beams (resonator A, Figs. 59j(i-ii)) 308 . After deactivating one thin beam via fracture and bending, the island and another thin beam constitute another local resonator (resonator B, Fig. 59j(iii)). The resonances of resonators A and B can be triggered by external acoustic waves with different frequencies because of the 153 difference in the resonator structures. The local resonance within the structure can then trap the incoming acoustic wave and significantly lower the acoustic transmittance. To demonstrate the concept, we measure the acoustic transmittances of the virgin and transformed lattice structures using the setup shown in Fig. 58k (Fig. S41). We find that the virgin lattice with resonator A (Fig. 59j(ii)) shows a relatively low acoustic transmittance within a frequency of 610-670 Hz; however, the transformed lattice with resonator B (Fig. 59j(iii)) exhibits a dramatic decrease in the acoustic transmittance within a frequency of 280-320 Hz (Fig. 59l). These two frequency regimes represent the resonance frequencies of resonator A and resonator B, respectively. The experimental measurements are roughly verified by numerical simulations of the acoustic transmittance of the virgin and transformed lattices (Fig. S42). Then, the transformed lattice structure can transform back to the virgin shape via a memory-healing process (Fig. 59j(iv)). The fracture healing is verified by a magnified picture of the fracture interface (Fig. 59j(v)). After shape recovery and fracture healing, the corresponding acoustic transmittance returns to that of the virgin lattice (Fig. 59l). Overall, at 300 Hz, the transmitted acoustic amplitude can be represented by a high-low-high cycle corresponding to the virgin-programmed-restored cycle of the structure geometry, whereas at 620 Hz, the transmitted acoustic amplitude can be represented by a low-high-low cycle (Fig. 59m). 154 155 Figure 59. Lattice transformation enabled by fracture-memory-healing cycles. (a-b) Schematics and samples of honeycomb lattices in structural transformation processes: (i) virgin lattice, (ii) lattice with 5 vertical beams deactivated, (iii) lattice with 5 deactivated beams restored via shape memory and fracture healing, (iv) lattice with 10 vertical beams deactivated, and (v) lattice with 10 deactivated beams restored via shape memory and fracture healing. Note that the insets in b show the top view of honeycomb lattices. (c) Schematics showing the compression test of a honeycomb lattice. (d) Compressive stress-strain curves of the virgin lattice, lattice with 5 beams deactivated, and lattice with 5 deactivated beams restored. (e) Compressive stress-strain curves of the virgin lattice, lattice with 10 beams deactivated, and 10 lattice with deactivated beams restored. (f) Transformation between a triangle lattice and a Kagome lattice: (i) 3D view of a virgin triangle lattice, (ii) 2D view of the virgin triangle lattice, (iii) programmed Kagome lattice by cutting and bending the horizontal beams of the triangle lattice, (iv) restored triangle lattice, and (v) a magnified image to show the healed interface. Note that the insets show representative cells of the triangle and Kagome lattices. (g) Experimental setup for testing the vibration transmittances of lattice structures. (h) Measured vibration transmittances of the virgin triangle lattice, programmed Kagome lattice, and restored triangle lattice as functions of the vibration frequency. (i) Normalized vibration amplitudes of the virgin triangle lattice, programmed Kagome lattice, and restored triangle lattice at 32.75 kHz. (j) Transformation between a lattice with resonator A and a lattice with resonator B: (i) 3D view of an array of virgin lattices with resonator A, (ii) 2D view of the virgin lattice with resonator A, (iii) programmed lattice with resonator B, (iv) restored lattice with resonator A, and (v) a magnified image to show the healed interface. Note that the insets show unit cells of resonators A and B. (k) Experimental setup for testing the acoustic transmittances of lattice structures. (l) Measured acoustic transmittances of the virgin, programmed, and restored lattices as functions of the acoustic frequency. (m) Normalized acoustic amplitudes of the virgin, programmed, and restored lattices at 300 Hz and 620 Hz. 7.5 Discussion Note that the fractures in Fig. 47 and Figs. 58 and 59 are different. The 3PB-induced fractures in Fig. 57 occur at room temperature; thus, manual contact is required to assist the alignment of the fracture interfaces. However, the fractures and their associated shape change around the fracture locations in Figs. 58 and 59 are programmed at elevated temperatures (80 °C for Figs. 58a-c and 59 and 60 °C for Figs. 58d-l). Elevated temperatures are required to enable the shape-memory process to align the fracture interfaces via externally controlled thermal stimuli rather than manual contact. This elevated-temperature requirement is widely adopted for shape-memory polymers and structures 146,295,296 . From a practical perspective, the shape- memory-assisted healing of the lattice fracture in Fig. 58 can be realized by judiciously heating the lattice structure when damage or fracture is expected. Fortunately, the polymer with a PTMEG molar mass of 250 g/mol does not become too soft at 60-80 °C but still exhibits a Young’s modulus as high as 140-390 MPa (Fig. S28a), which is stiffer than most 3D-printable photopolymers (modulus <100 MPa) 309 . 156 In summary, we present a class of transformable lattice structures enabled by fracture and shape- memory-assisted healing. The presented lattice structures can heal lattice fractures through manual contact or memory-healing processes. The fracture-memory-healing cycle can further enable reversible transformations of lattice configurations, shifting properties among states of different stiffnesses, vibration transmittances, and acoustic absorptions. We expect that self-healable lattice structures can promote the future exploration of next-generation healable and reusable lightweight materials 300 within blank Ashby material property space 278-286 . In addition, the shape-memory-assisted healing of lattice structures revolutionizes the state-of-the-art healing paradigms that primarily rely on manual contacts to align fracture interfaces. This paradigm may greatly facilitate the healing of undetected cracks or cracks deep within a structure without external tethered intervention, thereby potentially enabling broad applications in next- generation aircraft panels, automobile frames, body armor, impact mitigators, vibration dampers, and acoustic modulators 278-286 . Furthermore, the existing transformable structures primarily harness the nonfracture geometrical change of smart materials 146,295,296,310-312 ; the structural transformations enabled by the fracture-memory-healing cycles open a unique avenue by adding a fracture-healing tool, probably enabling previously impossible modulation of functionalities. 157 Chapter 8: Photosynthesis Assisted Remodeling of Three-Dimensional Printed Structures 8.1 Objective The mechanical properties of engineering structures continuously weaken during service life because of material fatigue or degradation. By contrast, living organisms are able to strengthen their mechanical properties by regenerating parts of their structures. For example, plants strengthen their cell structures by transforming photosynthesis-produced glucose into stiff polysaccharides. In this work, we realize hybrid materials that use photosynthesis of embedded chloroplasts to remodel their microstructures. These materials can be used to three-dimensionally (3D)-print functional structures, which are endowed with matrix-strengthening and crack healing when exposed to white light. The mechanism relies on a 3D printable polymer that allows for an additional cross-linking reaction with photosynthesis-produced glucose in the material bulk or on the interface. The remodeling behavior can be suspended by freezing chloroplasts, regulated by mechanical preloads, and reversed by environmental cues. This work opens the door for the design of hybrid synthetic-living materials, for applications such as smart composites, lightweight structures, and soft robotics. 8.2 Introduction Plants can grow and form complex, hierarchical structures that are challenging to reproduce with traditional engineering practices 313 . Plant cells use photosynthesis to produce glucose, which is delivered to selected locations, such as trunks and crotches. Glucose, in turn, is used to form stiff polysaccharides (e.g., cellulose, chitosan, and chitin), which remodel and strengthen the plant structures locally (Fig. 60A) 314,315 . For example, the stiffness of a young stem is typically in the order of kilopascal, while the stiffness of a mature trunk can reach as high as several gigapascals 316 . Mechanical loads are found to augment the strengthening of the plant structure through mechanotransduction pathways 317 . In recent years, the availability of 3D printing technologies has driven the fabrication of engineering structures that attempt to 158 mimic the complexity of the plants’ architectures 161,286,318-320 . However, how to mimic the plants’ ability to remodel their components and strengthen mechanical properties remains elusive. Synthetic structures, on the contrary, typically weaken during service life because of materials fatigue or degradation. Developing hybrid, 3D-printable materials that exploit living photosynthesis processes to remodel their structures would be a major leap forward in engineering materials that mimic natural systems. However, establishing a communication channel between the synthetic 3D-printable materials and the natural photosynthesis process is challenging. Here, we present a class of 3D-printable polymers that can be remodeled by the photosynthesis of embedded chloroplasts, to enable matrix-strengthening and crack-healing. With local light exposure, the polymers harness photosynthesis-produced glucose to facilitate an additional crosslinking reaction, forming a stiff region with “artificial polysaccharides” (Fig. 60B). The region with additional crosslinks features enhanced Young’s modulus, tensile strength, and fracture toughness by factors of 300-620%, compared to the region without the additional crosslinks. Such photosynthesis-assisted strengthening can be suspended by freezing living chloroplasts, regulated by external mechanical pre-loads, and reversed by cleaving glucose crosslinkers with environmental cues. We also show that the photosynthesis-assisted strengthening can be applied to 3D-printed structures through patterned light and patterned loads. In addition, the photosynthesis can equip the 3D-printed structures with a healing capability via glucose- enabled interfacial crosslinking. The paradigm in this work provides a unique platform for remodeling engineering materials via the communication between synthetic polymers and natural photosynthesis processes. 8.3 Materials and methods 8.3.1 Materials Poly(tetrahydrofuran) (PolyTHF, average molar mass 650 g/mol), isophorone diisocyanate (IPDI), dimethylacetamide (DMAc), 2-Hydroxyethyl methacrylate (HEMA), dibutyltin dilaurate (DBTDL), 1,6- hexanediol diacrylate (HDDA), 𝛼-D-Glucose, phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide 159 (photoinitiator), Sudan I (photoabsorber), HEPES buffer solution, Poly (ethylene glycol), Potassium phosphate tribasic (K 3PO 4), Magnesium chloride (MgCl 2), Sodium hydroxide (NaOH), Percoll (pH 8.5- 9.5), and periodic acid (HIO 4) were purchased from Sigma-Aldrich and used without further purification. Baby spinach leaves (Spinacia oleracea L.) were purchased from Trader Joe's. 8.3.2 Extraction of chloroplasts The HEPES buffer solution was prepared by mixing HEPES buffer (30×10 @F M, pH 5.0-6.0), poly(ethylene glycol) (𝑀𝑤.8000,10% (𝑤/𝑣)), 𝑀 { 𝐶𝑙 ( (2.5×10 @F 𝑀), 𝐾 F 𝑃𝑂 B (0.5×10 @F 𝑀), and DI Water. The HEPES buffer solution was then magnetically stirred for 3 h. NaOH solution was added to adjust the pH value to be around 7.6. The HEPES buffer solution was then stored in the fridge at 4°C for 3 h before use. Then, the fresh baby spinach leaves (Spinacia oleracea L.) were washed with DI water and then dried to remove the surface water. Next, the middle veins of the leaves were removed to obtain 65 g leaf meat from about 100 g of fresh leaves. Then, the leaf meat was ground with 100 ml HEPES buffer solution in the pre-chilled kitchen blender for about 2 minutes until the mixture became homogeneous. The mixture was centrifuged with 4000 RPM for 15 min at 4 °C (Eppendorf 5804R). Then, the supernatant was removed, and the chloroplast pellet was re-suspended in the HEPES buffer solution. After adding the suspended mixture on the top of 5 mL of 40% Percoll in two pre-chilled tubes, we centrifuged the mixture at 3636 RPM for 8 min at 4 °C. Later, we removed the supernatant and kept the pellet. Next, we washed the pellet by adding 10 mL HEPES buffer solution and piped it out twice to remove Percoll. Before using the extracted chloroplast, we put the tubes upside down in the fridge for 1 h to get rid of the remained water or buffer solution from the chloroplast pellet. 8.3.3 Preparation of polymer inks with and without free NCO groups To fabricate polymer inks with free NCO groups (Fig. S43), we preheated 0.01 mole of PolyTHF at 100℃ and exposed to Nitrogen environment for 1 h to remove moisture and oxygen. 0.02 mole of IPDI, 10 wt% of DMAc and 1 wt% of DBTDL were mixed with the preheated PolyTHF at 70℃ and stirred 160 with a magnetic stir bar for 1 h. After reducing the temperature to 40℃, 0.01 mole of HEMA was added and mixed for 1 h to complete the synthesis. To fabricate polymer inks without free NCO groups (Fig. S54), we used a similar procedure as that of the polymer ink with free NCO groups except for 0.02 mole of HEMA in the last step. For the additive manufacturing, 2 wt% of photoinitiator (phenylbis(2,4,6- trimethylbenzoyl)phosphine oxide) was mixed with the polymer inks and stored in a dark amber glass bottle until use. 8.3.4 Preparation of polymer inks with chloroplasts Extracted chloroplasts of various weight percent from 0 wt% to 7 wt% were gently mixed with the prepared polymer inks (with or without free NCO groups) using a magnetic stir bar for 30 min at 5℃ in a dark environment to prevent the degradation of chloroplasts (Fig. S44). 8.3.5 3D-printing process A similar printing technique was described elsewhere (Fig. S45) 141,321 . A computer-aided design (CAD) model was designed and converted into an STL file, which was then sliced into an image sequence. The sliced images were then used to print the 3D structure with a bottom-up stereolithography (SLA) printer. An image-patterned light with a wavelength of 405 nm was projected from the bottom to a resin bath that was filled with a synthesized polymer ink. A motor-controlled printing stage was mounted onto the resin bath with a prescribed liquid height. The light-exposed resin was solidified and bonded onto the printing stage. As the printing stage was lifted, the fresh resin refluxed beneath the printing stage. By lowering the printing stage at prescribed height and illuminating the resin with another slice image, a second layer was printed and bonded onto the first layer. These processes were repeated to form a 3D-architected structure. A Teflon membrane with low surface tension (~20 mN/m) was employed to reduce the separation force between the solidified part and the printing window. 161 8.3.6 Photosynthesis process in different conditions The 3D-printed solid samples were placed in a white-light chamber (CL-1000 Ultraviolet Crosslinker with five UVP 34-0056-01 bulbs, light intensity 69.3 𝑊/𝑚 ( ) with different exposure conditions. For the experimental group and control 2 group in Figs. 61A and 61C, the samples went through 4-h illumination of white light followed by 4-h darkness in the chamber. For the control 1 group in Fig. 61B, the samples went through 8-h darkness in the chamber. For the samples with chloroplasts of various weight concentrations (0-7 wt%, Figs. 61I), they went through 4-h light illumination and 4-h darkness. For the samples with various light-illumination periods (Figs. 61J), they went through periods of light illumination and darkness of the same length. For example, the 15-minutes group went through 15-minute light illumination and 15-minute darkness. 8.3.7 Characterization of strengthening effect Dumbbell-like samples were fabricated with the aforementioned 3D-printing process (length 5 mm, width 2 mm, and thickness 2 mm shown in Fig. S51A). After the respective photosynthesis or non- photosynthesis processes described above, the samples were placed in a dark chamber (40℃) for 12 h to evaporate the residual solvent. Then, the samples were uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 using a mechanical tester (Instron, model 5942). Spectrum TWO FT-IR Spectrometer (PerkinElmer, USA) was used for the FT-IR analyses before and after the respective photosynthesis or non-photosynthesis processes with the scanning range of 450 to 4000 𝑐𝑚 @2 at a resolution of 0.5 𝑐𝑚 @2 . The fracture energies of the polymers after different photosynthesis conditions were measured by using pure-shear fracture tests 322,323 . Unnotched and notched samples (length 𝑎 ' =40𝑚𝑚, thickness 𝑏 ' = 1𝑚𝑚 and distance between two clamps 𝐿 ' =5𝑚𝑚) were employed (Figs. S51B, S53). The notched sample was prepared by using a razor blade to cut a 20-mm notch in the middle left region. Both samples were uniaxially stretched with a strain rate of 0.05 𝑠 @2 until rupture. A camera was used to record the critical distance (denoted as 𝐿 9 ) between the clamps when the crack starts propagating on the notched sample. The fracture energy was calculated as 𝑈(𝐿 9 ) (𝑎 ' 𝑏 ' ) ⁄ , where 𝑈(𝐿 9 ) is the work done by the applied 162 force before the critical distance, illustrated as the area beneath the force-distance curve in the unnotched test (Fig. S53). 8.3.8 Verification of glucose production from the embedded chloroplasts The prepared polymer ink without free NCO groups (Fig. S54) was gently mixed with 5wt% of extracted chloroplasts with a magnetic stir bar for 30 min at 5℃ in a dark environment to prevent the degradation of chloroplasts. The mixture was 3D-printed into dumbbell-like samples. The prepared samples were placed in a white-light chamber (light intensity 69.3 𝑊/𝑚 ( ) for two different conditions, including 4-h light illumination and 4-h darkness, and 8-h darkness. The FTIR analyses were conducted to monitor the transmittance corresponding to the OH groups in the polymer samples at the as-fabricated state, after 4-h light and 4-h darkness, and after 8-h darkness (Figs. S55AB). After removing the residual solvent in a dark chamber (40℃) for 12 h, the samples were then uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 (Fig. S55D). 8.3.9 Characterization of polymer strengthened by glucose 𝛼-D-glucose was first mixed with polymer ink with free NCO groups to make different glucose concentrations (0 M-0.389 M). The mixture was 3D-printed into dumbbell-like samples. The FTIR analyses were conducted to monitor the transmittance corresponding to the NCO groups in the polymer samples with different glucose concentrations. After removing the residual solvent in a dark chamber (40℃) for 12 h, the samples were then uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 . 8.3.10 Effects of chloroplast concentration and illumination time The fabricated polymer samples with free NCO groups and chloroplasts of various weight concentrations (0-7wt%) were uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 after 4-h light illumination and 4-h darkness. The fabricated polymer samples with free NCO groups and 5 wt% chloroplasts after undergoing various light illumination periods (0-6 h) and the respective darkness periods (same length of the illumination period), were also uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 . The 163 Young’s modulus and tensile strength of each sample were calculated from the obtained tensile stress- strain curve. 8.3.11 Freezing chloroplasts with a chilling temperature The fabricated polymer samples with free NCO groups and 5 wt% chloroplasts were first sealed in a petri dish and then immersed in an ice bath. The samples with the temperature of 0-4℃ underwent 2-h light illumination and 2-h darkness. These samples were divided into two parts. Some processed samples were uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 . For other processed samples, the temperature was first raised to room temperature (25℃); and then these samples underwent another 2-h light illumination and 2-h darkness, followed by being uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 . 8.3.12 Cleavage of glucose crosslinkers in the strengthened polymer The strengthened polymer samples were immersed in a 2 M periodic acid solution (2 moles of periodic acid and 1 L of DMAc) for 6 h. The samples were swollen by around 220% and then de-swollen by evaporating the residual solvent in a dark chamber (40℃) for 12 h. For the control group, the strengthened samples were immersed in the DMAc solvent for 6 h and then de-swollen by evaporating the solvent in a dark chamber (40℃) for 12 h. Both sets of samples were then uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 . 8.3.13 Local strengthening with an “S” shape Plate samples (with free NCO groups and 5 wt% embedded chloroplasts) with a size of 14mm × 10mm × 2mm were fabricated by the aforementioned 3D-printing system (Fig. 62B). The samples were then placed in an amber container, covered with a mask with an “S” shape, and put in the white-light chamber for 4-h illumination and 4-h darkness. Young’s modulus distribution over the sample surface was measured by using a round-flat end cylinder indenter with radius R=0.5 mm loaded on the Instron mechanical tester to indent the sample by applying force F to certain indentation depth 𝛿. The Young’s 164 modulus of each location was calculated as 𝐸 =𝐹(1−𝜐 ( ) (2𝑅𝛿) ⁄ , where 𝜐 =0.48 is the Poisson’s ratio of material (Fig. S68). The Young’s modulus distribution map was plot using MATLAB (Fig. 62C). 8.3.14 Local strengthening with circles Plate samples (with free NCO groups and 5 wt% embedded chloroplasts) with sizes of 20 mm × 20 mm × 2 mm (for Fig. 62E) and 56 mm × 20 mm × 2 mm (for Fig. 62H) were fabricated by the aforementioned 3D-printing system. The 20 mm × 20 mm × 2 mm sample was locally strengthened with a circular-shaped mask (circle diameter = 3 mm) next to a 3-mm edge notch. The 56 mm × 20 mm × 2 mm sample was locally strengthened with 18 circular patterns (circle diameter = 1mm) with a certain path next to an edge notch. Both samples were then clamped at the left two corners for the tearing test with the Instron mechanical tester. 8.3.15 Homogeneous and graded lattice structures Lattice structures (with free NCO groups and 5 wt% embedded chloroplasts) with various units (2 × 2 × 1 for Fig. S69 and 10 × 4 × 1 for Fig. 62J) were fabricated by the aforementioned 3D-printing system. For the structures with homogeneous light, the printed samples were placed in the white-light chamber with 2-h illumination on the front side and 2-h illumination on the back side, followed with 4 h darkness. For the structure with the darkness condition, the printed samples were placed in the dark chamber for 8 h. For the structures treated with a graded light, a transparent cover was attached with different layers of vinyl-coated white tape and covered on top of the printed sample (Fig. S70). The entire setup was then placed in the white-light chamber to induce a graded light intensity varies from 0 to 69.3 𝑊/𝑚 ( on the long edge direction of the sample for each unit distance (2 mm). The samples were placed in the graded light chamber with 2-h illumination on the front side and 2-h illumination on the back side, followed with 4 h darkness. The 2 × 2 × 1 lattice structures with different conditions were tested under a compressive load along the longitudinal direction (gradient direction) with a strain rate of 0.05 𝑠 @2 using the Instron 165 mechanical tester (Fig. S69). The Young’s modulus of each unit of the 10 × 4 × 1 lattice structures was tested lattice by the indentation test. The Young’s modulus can be calculated as 𝐸 =𝐹(1−𝜐 ( ) (2𝑅𝛿) ⁄ , where F is the applied load, 𝜐 =0.48 is the effective Poisson’s ratio, R is the radius of a round-flat end cylinder indenter (R=1 mm), and 𝛿 is the indentation depth. The energy absorption behaviors of the 10 × 4 × 1 lattices were characterized by impact loading tests with a relatively large strain rate of 10 𝑚𝑚/𝑠. The absorbed energy was calculated by the area underneath the load-displacement curves (Fig. 62L). 8.3.16 3D-printing and strengthening of tree-like structures The tree-like structures were fabricated by the aforementioned 3D printing system using the polymer ink with free NCO groups and 5 wt% embedded chloroplast. The printed tree-like structures were then placed in a white-light chamber with 2-h light illumination (light intensity 69.3 𝑊/𝑚 ( ) and 2-h darkness. To characterize the load sustaining capability of the tree-like structures in different states, we hang a 1-g metal ring on one tree branch at the unstrengthened state (with 4-h darkness) and after photosynthesis process (2-h illumination and 2-h darkness). 8.3.17 3D-printing and strengthening of Popeye-like structures The Popeye-like structures (height 23 mm, width 15 mm, and depth 5 mm) were fabricated by the aforementioned 3D printing system using the polymer ink with free NCO groups and 5 wt% embedded chloroplast. The printed Popeye-like structures were then placed in a white-light chamber with 2-h light illumination (light intensity 69.3 𝑊/𝑚 ( ) and 2-h darkness. To characterize the weight sustaining capability of the Popeye-like structures in different states, we loaded a 200-g weight (two weights of 100 g each) on a glass slide that was placed on the strengthened or unstrengthened Popeye-like structures. 8.3.18 Effect of pre-stretch on Photosynthesis-assisted strengthening The fabricated polymer samples with free NCO groups and 5 wt% chloroplasts were first uniaxially pre- stretched with various stretches (𝜆 =1−1.3) and undergone 4-h light illumination and 4-h darkness. 166 Then, the processed samples were then cut into smaller samples with a dumbbell-like shape, which were uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 . The FTIR analyses were conducted to monitor the transmittance corresponding to the NCO groups in the polymer samples with different pre- stretches. 8.3.19 Photosynthesis-assisted strengthening under a non-uniform pre-stress distribution. Plate sample (with free NCO groups and 5 wt% embedded chloroplasts) with a size of 12 mm × 8 mm × 2 mm was fabricated by the aforementioned 3D-printing system. A foot-like 3D structure with non- uniform surface was also 3D-printed with a rigid polymer ink (HDDA). The foot-like structure was compressed on the sample plate by deforming 1 mm in depth. The deformation-induced a non-uniform stress-distribution on the sample plate. With the deformation, the plate illuminated by white light (light intensity 69.3 𝑊/𝑚 ( ) from the bottom for 4 h, followed by 4-h darkness. Young’s modulus distribution over the sample surface was measured by using a round-flat end cylinder indenter with radius R=0.5 mm loaded on the Instron mechanical tester (Fig. S68). 8.3.20 Characterization of Photosynthesis-assisted healing 3D printed dumbbell-shaped samples with free NCO groups and 5wt% embedded chloroplasts were first cut into two parts with a razor blade, and the fractured surfaces were brought into contact immediately. The samples were then placed in a white-light chamber with light illuminating time various from 1 h to 8 h, followed by the darkness with the same respective period. For the control, 3D printed dumbbell-shaped samples with free NCO groups but without embedded chloroplasts were used. Both healed and control samples were uniaxially stretched to rupture with the same strain rate (0.05 𝑠 @2 ). An optical microscope (Nikon Eclipse LV100ND) was used to image the healing region (Fig. 64B). 8.3.21 Photosynthesis-assisted healing of 3D-printed propeller The 3D-printed propellers were fabricated by the aforementioned 3D printing system. The experiment propellers were fabricated using polymer inks with free NCO groups and 5wt% embedded chloroplasts. 167 4-mm damages were introduced on each sector of the printed propellers with a razor blade. The fractured surfaces were aligned into contact immediately and then placed in a white-light chamber with 4-h light illumination and 4-h darkness. Two healed propellers were assembled onto a remotely controlled boat to provide the pushing force to move forward in a pound (Fig. 64F). The control propellers were fabricated using polymer inks with free NCO groups but without chloroplasts. The controlled propellers were also damaged, healed, and assembled onto the remotely controlled boat (Fig. 64G). 8.4 Results 8.4.1 Mechanism of photosynthesis-assisted strengthening To design a polymer network that allows for an additional crosslinking reaction with the photosynthesis- produced glucose, we design a polymer resin that features both acrylate and isocyanate distal groups (NCO) and then blend the resin with chloroplasts extracted from spinach leaves (Figs. S43 - S44, Methods) 324 . The acrylate groups can be utilized for the photopolymerization-based 3D-printing (such as stereolithography), because the acrylate groups allow for a photo-initiated addition reaction to polymerize the resin (Fig. S45) 141,321 . The printing is rapid with a speed of 75-400 μm/s, and the resolution can reach as low as ~25μm. After the 3D-printing process, the NCO groups become free side groups within the polymer matrix (Fig. S46). The NCO groups can enable a relatively strong reaction with hydroxyl groups (OH) on a glucose molecule to form urethane linkages (-NH-CO-O-) (Figs. 60B and 8-S46) 325 . Since a glucose molecule has multiple OH groups, it is hypothesized that the OH groups on the chloroplast- produced glucose can bridge multiple NCO groups to create new crosslinks additional to the acrylate- enabled crosslinks within the polymer matrix (Figs. 60B and S46). Such additional crosslinks are expected to significantly enhance the modulus and strength of the polymer 326,327 . To demonstrate the strengthening concept, we 3D-print a tree-like structure whose Young’s modulus and tensile strength gradually increase as the photosynthesis illumination period increases (white light intensity 69.3 𝑊/𝑚 ( , Figs. 60C and S47). The strengthened structure with 2-h illumination shows a 168 better weight-sustaining capability than the unstrengthened structure (Figs. 60D and S48). Note that the photosynthesis process includes 2-h illumination of white light for glucose generation plus 2-h darkness for glucose export from the chloroplast 324,328,329 . As an educational example, we 3D-print Popeye the Sailor, an American cartoon character who can strengthen his muscles by eating spinach (Fig. 60E). We show that the 3D-printed Popeye-like structure strengthens upon light exposure, by leveraging the photosynthesis process of the embedded spinach chloroplasts (2-h illumination and 2-h darkness). We demonstrate the strengthening effect by showing a reduced deformation upon loading (Figs. 60F and S49). 169 Figure 60. Concept of the photosynthesis-assisted remodeling of 3D-printed structures. (A) Schematics to illustrate photosynthesis-assisted remodeling of plants. The photosynthesis-produced glucose undergoes a condensation reaction to form stiff polysaccharide (e.g., cellulose). (B) Schematics to illustrate photosynthesis-assisted remodeling of a synthetic polymer. The photosynthesis-produced glucose undergoes a reaction with isocyanate (NCO) side groups to form additional crosslinks. (C) Image sequence of a 3D-printed tree-like structure with various light illumination periods (white light intensity 69.3 𝑊/𝑚 ( ) of the photosynthesis process. (D) Unstrengthened and strengthened 3D-printed tree-like structures loaded by the same weight (1 g). (E) Image sequence of a 3D-printed Popeye-like structure with various light illumination periods of the photosynthesis process. (F) Unstrengthened and strengthened 3D-printed Popeye-like structures loaded by the same weight (200 g). The red dash boxes denote glass slides. The unstrengthened Popeye’s height reduces by 34.7%, but the strengthened Popeye only by 7% (Fig. S49). 170 We follow three steps to verify the hypothesized mechanism of photosynthesis-assisted strengthening (Fig. 61). In step 1, we verify that both light and chloroplasts are required to strengthen the designed polymer. We study three sample groups for comparison: The experimental group includes polymer samples with free NCO groups and embedded chloroplasts, going through 4-h illumination and 4-h darkness (Fig. 61A). To verify the effect of light, we employ control 1 group that includes polymer samples with free NCO groups and embedded chloroplasts, going through 8-h darkness (Fig. 61B). To verify the effect of chloroplasts, we employ control 2 group that includes polymer samples with free NCO groups but without chloroplasts, going through 4-h light illumination and 4-h darkness (Fig. 61C). We present the differences among these groups in three aspects. First, from the sample color, the initially green experimental samples turn to pale yellow, because light illumination can transform green chlorophyll to yellow lutein (Fig. 61D) 330 . In contrast, control 1 and 2 samples remain green and semi- transparent, respectively (Figs. 61EF). Second, since the photosynthesis-produced glucose is expected to consume free NCO groups to form additional crosslinks, the concentration reduction of free NCO groups can reveal the occurrence of the crosslinking reaction. To indicate the concentration of free NCO groups within the polymer matrix, we employ a Fourier transform infrared (FTIR) spectrometer to measure the transmittance of the sample around 2260 cm -1 that is corresponding to the NCO bond stretching vibration 321 . We find an evident peak at 2260 cm -1 in the initial state of all three sample groups (Fig. 61D-F). After the respective processes, the peak of the experimental group drastically drops, indicating the decreasing of the NCO concentration (Figs. 61D and S50A); however, the peaks of controls 1 and 2 remain almost the same (Figs. 61EF and S50BC). Third, we compare the mechanical properties of three sample groups via uniaxial tensile tests (Fig. 61G). Compared to controls 1 and 2, the experimental group exhibits higher Young’s modulus and tensile strength by factors of 620% and 350%, respectively (Fig. 61H and S51A). Since the strengthening is due to the formation of additional permanent covalent crosslinks, the strengthened Young’s modulus and tensile strength do not degrade within at least 6 months (Fig. S52). We further find that the fracture energy of the experimental sample is almost three times those of controls 1 and 2 (Figs. 61H, S51B, and S53) 322,323 . The toughening mechanism is similar to that in particle- 171 reinforce composites, because the regions around chloroplast fillers is strengthened by forming new crosslinks. Note that the required water for the photosynthesis process is supplied by the water storage within the chloroplasts 328,329 , and the required carbon dioxide is supplied by the existing carbon dioxide within the matrix and diffusion from the atmosphere 331 . A rough estimation shows these supplies of water and carbon dioxide are sufficient for the experiments (Table S2, Appendix B.2). In step 2, we verify that chloroplasts can generate glucose and export glucose to the polymer matrix. To detect the exported glucose within the polymer matrix, we employ a polymer sample with embedded chloroplasts but without free NCO groups (Fig. S54). FTIR spectra show that the concentration of the OH group (3300-3500 cm -1 ) 332 increases in the matrix after the photosynthesis process, implying the existence of free glucose that is not consumed by NCO groups (Fig. S55). In step 3, we verify that glucose can directly strengthen the designed polymer with free NCO groups but without chloroplasts. FTIR spectra show that the peak for the NCO groups disappears when glucose concentration is sufficiently high (e.g., 0.398 M), indicating that the glucose completely consumes the free NCO groups (Fig. S56). Tensile tests show that both Young’s moduli and tensile strengths increase as the glucose concentration increases (Fig. S57). Next, we study the effects of two vital factors on the strengthening performance: concentration of embedded chloroplasts and light illumination period (Figs. 61IJ). First, we investigate polymer samples with chloroplasts of various weight concentrations (0-7 wt%) and free NCO groups (processed with 4-h illumination and 4-h darkness). Tensile stress-strain curves show that both Young’s moduli and tensile strengths first increase with increasing chloroplast concentrations over 0-5 wt%, and then decrease afterward (5-7 wt%) (Figs. 61I and S58A). The decrease after 5 wt% is probably because that the chloroplasts serve as soft fillers within the polymer matrix, and that a high concentration of soft fillers compromises the mechanical properties of the chloroplast-embedded polymer. Second, we employ various light illumination periods (white light intensity 69.3 𝑊/𝑚 ( ) to process the polymer samples with 172 5 wt% chloroplasts and free NCO groups. Tensile stress-strain curves show that both Young’s moduli and tensile strengths first increase (or reach a plateau) with increasing illumination time within 0-4 h, and then decrease afterward (4-6 h) (Figs. 61J and S58B). The decrease after 4-h is probably because that extra- long illumination time may degrade the chloroplasts, associated with a reduction of the exported glucose concentration within the polymer matrix (similar behaviors for both 5 wt% (Fig. 61J) and 7 wt% of chloroplasts (Fig. S58C)) 328,329 . Note that the effects of the chloroplast concentration and illumination period can be quantitatively explained by a theory that models the free energy of polymer networks with additional crosslinks (Appendix B.2, Figs. S59-S64, Table S3). A key difference between the presented hybrid synthetic-living material and the existing synthetic material is that the material property can be modulated by tuning the living activity of the involved biological element (i.e., chloroplast). Here, we employ a chilling temperature (0-4℃) to temporarily freeze the activity of the embedded chloroplasts 333 , and thus the material remains at the soft state after 2- h illumination and 2-h darkness (Figs. 61K and Fig. S65A-C). Once the temperature returns to 25 ℃, the material can be strengthened to the stiff state via the photosynthesis process. This temporary freezing behavior cannot be achieved using traditional photoresins without living elements (Figs. S65D-F). Another interesting feature of the presented material is that the photosynthesis-assisted strengthening can be reversed by cleaving the glucose crosslinkers with periodic acids (Figs. 61L and S66) 334 . With 2 M periodic acid, the Young’s modulus and tensile strength of the initially strengthened polymer (with 4-h illumination and 4-h darkness) are reduced by 61% and 51%, respectively. 173 Figure 61. Mechanism of photosynthesis-assisted strengthening (A) Schematic of an experimental sample with free NCO groups and embedded chloroplasts undergoing 4-h light illumination and 4-h darkness. (B) Schematic of a control 1 sample with free NCO groups and embedded chloroplasts undergoing 8-h darkness. (C) Schematic of a control 2 sample with free NCO groups but without chloroplasts undergoing 4-h light illumination and 4-h darkness. (D-F) Samples and FTIR spectra before and after respective processes for (D) experiment, (E) control 1, and (F) control 2 cases, respectively. (G) Uniaxial tensile stress-strain curves of three groups of samples. (H) Young’s moduli, tensile strengths, and fracture toughnesses of three groups of samples. (I) Young’s moduli and tensile strengths of experimental samples with embedded chloroplasts of various weight concentrations (processed with 4-h illumination and 4-h darkness). (J) Young’s moduli and tensile strengths of experimental samples with 5 wt% chloroplasts after the photosynthesis processes with various light illumination periods. (K) Young’s moduli and tensile strengths of the processed experimental samples at three states: after 4-h darkness, after 2-h light and 2-h darkness at 0℃, and after 2-h light and 2-h 174 darkness at 0℃ followed by 2-h light and 2-h darkness at 25℃. (L) Young’s moduli and tensile strengths of processed experimental samples at three states: after 8-h darkness, strengthened with 4-h light illumination and 4-h darkness, strengthened and treated with 2 M HIO 4 solution to cleave the glucose crosslinkers. Error bars in (H-L) represent standard deviations of 3-5 samples 8.4.2 Photosynthesis-assisted strengthening with patterned light Next, we show the photosynthesis-assisted strengthening can be tuned by patterned light (Fig. 62). We demonstrate localized strengthening by exposing a plate sample to a patterned light with an “S” shape (Fig. 62A). After the photosynthesis with 4-h illumination and 4-h darkness, the illuminated S-shaped region turns from green to pale yellow (Figs. 62B and S67). Indentation tests show that the average stiffness of the strengthened region is around 4.3 times that of the unstrengthened region (Figs. 62CD and S68). This local strengthening capability can be harnessed to detour crack paths within the material (Figs. 62E-H). Due to the higher fracture toughness in the strengthened region, an initially straight crack detours a strengthened circle. The load-displacement curve shows that the toughness of the material is enhanced by 30% when a strengthened circle is installed (Fig. 62G). In addition, judiciously patterning the strengthened regions can guide the crack to follow a wavy path, while the crack path in the virgin material is almost a straight line (Fig. 62H). Photosynthesis can also be harnessed to strengthen 3D-printed structures. Similar to the tree-like and Popeye-like structures in Figs. 60C-F, homogeneous light illumination can strengthen an Octet lattice to sustain a weight that is 830 times of the lattice’s own weight, without buckling the beams (Fig. S69). In contrast, the unstrengthened lattice is significantly buckled by the same weight. This strengthening mechanism can further be used to fabricate lattices with a graded stiffness (Figs. 62I-M). Creating materials with graded functional properties has been a long-standing challenge in 3D printed materials, because grading properties requires continuously switching printing inks during fabrication 335 . Here, we expose an initially homogenous Octet lattice to a light pattern with graded intensity, to impart a gradient in stiffness (Fig. 62I and S70). This is because higher illumination doses lead to higher stiffness within a certain illumination dose range (Fig. 61J). The functionally graded lattice assumes a pale-yellow color at one end and remains green at the other end (Figs. 62J and S70). We compare the results with two control 175 samples, one stored in a dark environment for 8-h (fully soft, green lattice) and the other exposed to 4-h of homogeneous light illumination and 4-h darkness (fully stiffened, pale-yellow lattice). Indentation tests show that the effective Young’s modulus of the graded lattice decreases from1.7 MPa at one end to 0.3 MPa at the other end (Fig. 62K). We apply a compressive load to the lattice with a relatively high loading rate (10 mm/s, Fig. 62L) and find that the absorbed energy in the graded lattice is around 1.7 times that of the soft lattice and 3.3 times that of the fully stiffened lattice (Figs. 62M). Figure 62. Photosynthesis-assisted strengthening with patterned light 176 (A) Schematic of an experimental setup for the localized strengthening through a patterned light with an “S” shape. (B) Samples at the as-printed state and after 4-h illumination with an S-shaped light and 4-h darkness. (C) Young’s modulus distribution of the patterned sample measured with indentation tests. (D) Average stiffness of the unstrengthened and strengthened regions. (E) Crack detouring in a plate sample with a strengthened circle. (F) Straight crack in a plate sample without a strengthened circle. (G) Load- displacement curves of samples with and without the strengthened circle. The inset shows the loading setup. (H) Crack paths of samples with and without wavy strengthened regions. (I) Schematic to illustrate a 3D-printed lattice structure processed by a graded light (left to right: 69.3 to 0 𝑊/𝑚 ( ). (J) Samples of functionally graded, fully soft, and fully stiffened lattices. (K) Effective Young’s modulus distribution of three samples measured with indentation tests. (L) Compressive force-displacement curves of three samples with a loading rate of 10 mm/s. The loading is along the longitudinal gradient direction (x- direction). (M) The absorbed energy of the three samples. The error bars in (D) and (M) represent standard deviations of 3-5 samples. Note that the inhomogeneous green-color in (E), (F), and (H) is possibly due to some clusters of broken chloroplasts produced during the extraction experiments, which do not influence the result quality. 8.4.3 Photosynthesis-assisted strengthening regulated by pre-loads Mechanical loads can regulate plant-remodeling through mechanotransduction pathways, to achieve higher stiffness and strength than that without the mechanical loads 317 . Inspired by plants, we here show that the photosynthesis-assisted strengthening of the experimental polymer can be regulated by mechanical pre-loads (Fig. 63A). We apply a pre-stretch to a sample, followed by a photosynthesis process (4-h illumination and 4-h darkness). The processed sample with a pre-stretch of 1.3 shows higher Young’s modulus and tensile strength by factors of 228% and 159%, respectively, compared to that without a pre-stretch (Fig. 63B). The enhancement of Young’s modulus and tensile strength is not due to the density increase of additional crosslinks, because FTIR spectra reveal that the density of additional crosslinks in the processed pre-stretched sample is almost the same as that without a pre-stretch (Fig. 63C). We hypothesize that the enhancement is probably attributed to the architecture change of the additional crosslinks corresponding to the deformation of the primitive network (Fig. 63A), because the formation of additional crosslinks is based on the side chains with NCO groups. Further experiments show that Young’s moduli and tensile strengths of the processed samples increase with increasing pre- stretches (Figs. 63D and S72). This mechanism can be harnessed to realize a non-uniform stiffness distribution with non-uniform pre-stresses. For example, we apply non-uniform pre-stresses on a sample plate with a 3D-printed foot, and then illuminate light to enable the photosynthesis process (Fig. 63E). Indentation tests reveal an inhomogeneous stiffness distribution on the sample (Fig. 63F). To translate the 177 stiffness mapping to a pre-strain mapping, we need to obtain a master curve between a homogeneous compressive pre-strain on a sample disk and the resultant stiffness of the sample after the photosynthesis process (4-h illumination and 4-h darkness) (Fig. 63G). With such a master curve, a pre-strain mapping (Fig. 63H) can be predicted from the stiffness mapping in Fig. 63F. The demonstrated function may facilitate the design of future customized footwear by fabricating shoe soles with an inhomogeneous stiffness distribution that exactly matches the inhomogeneous stress distribution applied by the foot. Note that the post-curing of a partially-cured photoresin can enhance the stiffness 336,337 . However, the mechanism of forming additional crosslinks is drastically different from that in the current work, because the post-curing is based on the free monomers that are typically not connected to the primitive network (Fig. S73A). Thus, the pre-stretch of the primitive network would have a negligible effect on the architecture of additional crosslinks. Experiments show that pre-stretch can hardly regulate the stiffness and strength of the post-cured polymer (Figs. S73B-D). 178 Figure 63. Photosynthesis-assisted strengthening regulated by pre-loads (A) Schematics to illustrate the photosynthesis-assisted strengthening in experimental samples without and with a pre-stretch. (B) Stress-strain curves of three samples: with a pre-stretch of 1.3 after 4-h light illumination and 4-h darkness, without a pre-stretch after 4-h light illumination and 4-h darkness, and without a pre-stretch after 8-h darkness. (C) FTIR spectra corresponding to the above three processed samples. (D) Young’s moduli and tensile strengths of the processed samples with various pre-stretches. Error bars represent standard deviations of 3-5 samples. (E) Schematics to illustrate the photosynthesis process on a sample plate under non-uniform pre-stresses applied by a 3D-printed foot. (F) Young’s modulus distribution of the processed sample plate. (G) The master curve between the applied compressive pre-strain and the resultant Young’s modulus of the sample after the photosynthesis process (4-h illumination and 4-h darkness). (H) The compressive pre-strain distribution translated from the Young’s modulus distribution in (F). 8.4.4 Photosynthesis-assisted healing Some plants exhibit outstanding healing capability during grafting and wound repairing 338,339 . Inspired by plants, we here show that photosynthesis can assist the healing of a fractured polymer sample by forming 179 additional crosslinks between free NCO groups and photosynthesis-produced glucose at the fracture surfaces (Fig. 64A). To demonstrate the healing process, we 3D-print a dumbbell-shaped sample with free NCO groups and embedded chloroplasts, cut it into two parts, and then bring the two parts in contact (Fig. 64B, Methods). After 4-h illumination and 4-h darkness, the fractured sample is healed with a smooth healing interface, verified by a microscopic image around the interface (Fig. 64B). The healed sample can be stretched up to 1.8 times of original length without breaking (Fig. S74). To quantify the healing performance, we measure the tensile stress-strain behaviors of the healed samples after the photosynthesis process with different illumination periods (Fig. 64C). We find that the tensile strength ratio (tensile strength of the healed sample normalized by that of the virgin sample) increases with increasing illumination periods within 0-4 h and then decrease afterward (4-8h) (Fig. 64D). The healing strength ratio for 4-h illumination can reach as high as 70±7%. The decrease of the healing strength ratio after 4-h is probably because that extra-long illumination periods may degrade the chloroplasts, associated with the reduction of the exported glucose concentration 328,329 . As a contrast, the control 2 polymer with free NCO groups but without embedded chloroplasts exhibit a poor healing performance with the healing strength ratio as low as 9% (Fig. S75A). The microscopic image shows that the contacted fracture interface still leaves an evident gap after 4-h illumination and 4-h darkness (Fig. S75B). The photosynthesis-assisted healing mechanism can be harnessed to repair a propeller 3D-printed with the experimental polymer ink (Fig. 64E-G). A crack is installed on each wing of the propeller, and these cracks can be healed after the photosynthesis process (4-h illumination and 4-h darkness, Fig. 64E). On the contrary, cracks on the wings of a propeller 3D-printed with the control 2 polymer ink cannot be healed with the illumination process (Fig. S76). To demonstrate the performance, the healed experimental propeller that assembled on a remotely controlled boat can facilitate the forward movement of the boat (Fig. 64F). However, the unhealed control propellers cannot push the boat forward due to the lack of enough propulsion force (Fig. 64G). 180 Figure 64. Photosynthesis-assisted healing (A) Schematic of photosynthesis-assisted healing of a fractured polymer through forming additional crosslinks between free NCO groups and photosynthesis-produced glucose around the fracture surface. (B) Samples and interfacial microscope images at the virgin, damaged, and healed states. The healing process consists of 4-h light illumination and 4-h darkness. (C) Uniaxial tensile stress-strain curves of samples with various periods of light illumination time compared with that of the virgin sample. The virgin sample went through the photosynthesis process with 4-h light illumination and 4-h darkness. (D) Healing strength ratios of healed samples for various illumination periods. The healing strength ratio is defined as the tensile strength of the healed polymer normalized by that of the virgin sample. The error bars represent standard deviations of 3-5 samples. (E) 3D-printed experimental propeller structure at the virgin, damaged, and healed state. The insets show crack regions on a sector wing. (F) The healed experimental propellers assembled on a remotely controlled boat can facilitate the forward movement. (G) 181 The unhealed propellers made of control 2 polymer ink (with free NCO groups but without chloroplasts) assembled on a remotely controlled boat cannot facilitate the forward movement. 8.5 Conclusive remarks We harness photosynthesis in chloroplasts embedded in a synthetic polymer matrix, to remodel 3D- printed structures and demonstrate strengthening and healing. While the field of engineered photosynthesis shows a promising capability in producing energy fuels 340,341 , the current work extends the concept to advanced materials, by introducing a downstream reaction mechanism to use the photosynthesis-produced glucose. Besides, the presented photocurable polymers can be used in various photopolymerization-based 3D-printing systems, such as stereolithography 141,321 , polyjet 335 , photopolymer waveguides 142 , two-photon lithography 144,161 , continuous liquid production 148 , and volumetric lithography 342,343 . To the end, the communication between living photosynthesis and synthetic 3D-printable polymers may open doors for hybrid synthetic-living materials with both complex architectures and biomimetic properties. In the future study, maintaining the long-term living states of chloroplasts or even regenerating chloroplasts is a very important aspect. One possible solution would be refreshing of living chloroplasts using a flow system 344 , such as a microfluidic flow of chloroplasts through a porous material framework. 182 Chapter 9: Mechanics of Photosynthesis Assisted Polymer Strengthening 9.1 Objective Plant cells utilize photosynthesis to produce glucose that is delivered to selected locations to form stiff polysaccharides (e.g., chitin, chitosan, and cellulose), which strengthen the plant structures. Such a photosynthesis-assisted strengthening behavior in plants has rarely been imitated in synthetic material systems. We here propose a synthetic polymer system embedded with extracted plant chloroplasts, which allow for the photosynthesis-assisted mechanical strengthening of the polymer matrix. The strengthening mechanism relies on an additional crosslinking reaction between the photosynthesis-produced glucose and side groups within the polymer matrix. We develop a theoretical framework to model the photosynthesis-assisted strengthening behaviors of polymers. The glucose production of the embedded chloroplasts will be first modeled with a general photosynthesis theory, and the exportation of glucose to the polymer matrix is modeled with an enzyme-assisted mass transport theory. Next, a polymer strengthening network model with glucose molecules as additional crosslinkers is presented. Effects of the illumination period, the concentration of embedded chloroplasts, and the light intensity on the stiffness strengthening are studied. The theoretical results consistently agree with the experimental results of the photosynthesis-assisted polymer strengthening. 9.2 Introduction Plants offer continuous sources of inspiration for the engineering endeavor. Engineering materials inspired by plants provide great promise for designing and optimizing material properties and functionalities, such as hydrophobicity 345-347 , mechanical properties 348-350 , remodeling 351 , self-healing 352,353 , and shape-changing 348,354-356 . Of particular interest is plants’ strengthening behavior: Plant cells utilize photosynthesis to produce glucose that is delivered to selected locations to form stiff polysaccharides (e.g., chitin, chitosan, and cellulose), which strengthen the plant structures (Fig. 65a) 357,358 . For example, the stiffness of a young stem is typically in the order of kilopascal, while the stiffness 183 of a mature trunk can reach as high as several gigapascals 316 . Although such a photosynthesis-assisted strengthening behavior is the basis of plants’ growth and remodeling, how to imitate such strengthening behavior in a synthetic material system remains largely elusive. Here, we propose a synthetic polymer system embedded with extracted plant chloroplasts, which allow for the photosynthesis-assisted mechanical strengthening of the polymer matrix (Fig. 65b) 359 . The strengthening mechanism relies on an additional crosslinking reaction between the photosynthesis- produced glucose and side groups within the polymer matrix, thus forming a stiff region with additional crosslinks (Fig. 65b). This material system provides a unique platform for strengthening and remodeling engineering materials via the communication between synthetic polymers and natural photosynthesis processes, thus opening the door for the design of hybrid synthetic-living materials, for applications such as smart composites and soft robotics. Moreover, the photosynthesis-assisted strengthening can usually be delivered locally to achieve on-demand strengthening performance, or to impart graded stiffness with graded light intensity, which has been a long-standing challenge in traditional fabrication processes that require continuously switching materials during fabrication 360 . Despite the great potential, the fundamental understanding of this class of hybrid synthetic-living materials with living chloroplasts has been left behind due to two key reasons. First, the underlying mechanism between the living chloroplasts and the synthetic polymer system hasn’t been well understood. Although several biochemical models have been proposed to capture the photosynthesis behavior of plants 361,362 , there is no theoretical model to quantitatively understand the photosynthesis process of extracted chloroplasts within a polymer matrix. It remains elusive how photosynthesis-produced glucose molecules interact with the polymer network. It is also unclear how to mechanistically understand the effects of the concentration and photosynthesis conditions of embedded chloroplasts on the material strengthening behavior. Second, the understanding of strengthening networks based on additional crosslinking remains elusive. How the additional crosslinks affect the existing polymer networks remains unknown. How the additional crosslinks affect the polymer chain evolution is also ambiguous. The missing of these two aspects of theoretical understanding would significantly drag down the innovation of photosynthesis-assisted hybrid synthetic-living materials. 184 In this paper, we present a theoretical framework to model the self-strengthening behaviors of polymers assisted by the photosynthesis process. The strengthening mechanism of the synthetic polymer is shown in Fig. 65b. The photosynthesis-produced glucose can facilitate additional crosslinking reactions in the polymer matrix upon exposure to white light. The photosynthesis-assisted crosslinking is forming due to the reaction of open free isocyanate (NCO) groups in the material matrix and hydroxyl (OH) groups on the glucose, which enables the enhancement of mechanical properties of materials including Young’s modulus and tensile strength (Figs. 65c-e). The photosynthesis-assisted glucose production of the embedded chloroplasts will be first modeled with a general photosynthesis theory. Then, the exportation of glucose from the chloroplasts to the polymer matrix is modeled with an enzyme-assisted mass transport theory. Next, the original polymer matrix is modeled as a network model with homogeneous chain length distribution. When the photosynthesis-produced glucose is introduced in the polymer matrix and form the additional crosslinks, inhomogeneous chain lengths are considered following two different algorithms. The formation of additional crosslinks will be examined by the comparison between experimental and theoretical results. Effects of the illumination period, the concentration of embedded chloroplasts, and the light intensity on the stiffness strengthening will be studied. The theoretical model can consistently explain experimentally observed photosynthesis-assisted strengthening. The plan of the paper is as follows. section 9.3 introduces the experiments about the photosynthesis-assisted strengthening of a chloroplast-embedded polymer system. In section 9.4, we present the theoretical model system by first considering the general theory for the photosynthesis process in the material matrix, then the model for polymer strengthening by additional crosslinking. In section 9.5, we present the theoretical results from the photosynthesis model and then from the polymer strengthening model. With respective experiments and theories, the effects of the illumination period, the concentration of embedded chloroplasts, and the light intensity will be studied. The concluding remarks will be presented in section 9.6. 185 Figure 65. Schematics and properties of the photosynthesis-assisted remodeling (a) Schematics to illustrate photosynthesis-assisted remodeling of plants. The photosynthesis-produced glucose undergoes a condensation reaction to form stiff polysaccharides (e.g., cellulose). (b) Schematics to illustrate photosynthesis-assisted remodeling of a synthetic polymer. The photosynthesis-produced glucose undergoes a reaction with isocyanate (NCO) side groups to form additional crosslinks. (c) Schematic and sample with free NCO groups and embedded chloroplasts before and after undergoing 4-h light illumination and 4-h darkness. (d) Uniaxial tensile stress-strain curves of one experimental group and two control groups. The experimental group includes samples with free NCO groups and embedded chloroplasts undergoing 4-h light illumination and 4-h darkness. The control 1 group includes samples with free NCO groups and embedded chloroplasts undergoing 8-h darkness. The control 2 group includes samples with free NCO groups but without chloroplasts undergoing 4-h light illumination and 4-h darkness. (e) Young’s moduli of three groups of samples. 9.3 Experimental The polymer was prepared by embedding the extracted chloroplasts in a synthetic polymer matrix. The polymer with free NCO groups was prepared by preheating 0.01 mole of Poly(tetrahydrofuran) 186 (PolyTHF, average molar mass 650 g/mol) at 100℃, and exposed to the nitrogen environment for 1 h to remove moisture and oxygen. 0.02 mole of isophorone diisocyanate (IPDI), 10 wt% of dimethylacetamide (DMAc), and 1 wt% of dibutyltin dilaurate (DBTDL) were mixed with the preheated PolyTHF at 70℃, and stirred with a magnetic stir bar for 1 h. After reducing the temperature to 40℃, 0.01 mole of 2- Hydroxyethyl methacrylate (HEMA) was added and mixed for 1 h to complete the synthesis (0.02 mole of HEMA was added for the polymer without free NCO groups). Then, we extracted living chloroplasts from spinach leaves 324 . The HEPES buffer solution was prepared by mixing HEPES buffer (30×10 @F M, pH 5.0-6.0), poly(ethylene glycol) (𝑀𝑤.8000,10% (𝑤/𝑣)), 𝑀 { 𝐶𝑙 ( (2.5×10 @F 𝑀), 𝐾 F 𝑃𝑂 B (0.5×10 @F 𝑀), and DI Water. The HEPES buffer solution was then magnetically stirred for 3 h. NaOH solution was added to adjust the pH value to be around 7.6. The HEPES buffer solution was then stored in the fridge at 4°C for 3 h before use. Then, the fresh baby spinach leaves (Spinacia oleracea L.) were washed with DI water and then dried to remove the surface water. Next, the middle veins of the leaves were removed to obtain 65 g leaf meat from about 100 g of fresh leaves. Then, the leaf meat was ground with 100 ml HEPES buffer solution in the pre-chilled kitchen blender for about 2 minutes until the mixture became homogeneous. The mixture was centrifuged with 4000 RPM for 15 min at 4 °C (Eppendorf 5804R). Then, the supernatant was removed, and the chloroplast pellet was re-suspended in the HEPES buffer solution. After adding the suspended mixture on the top of 5 mL of 40% Percoll in two pre-chilled tubes, we centrifuged the mixture at 3636 RPM for 8 min at 4 °C. Later, we removed the supernatant and kept the pellet. Next, we washed the pellet by adding 10 mL HEPES buffer solution and piped it out twice to remove Percoll. Before using the extracted chloroplast, we put the tubes upside down in the fridge for 1 h to get rid of the remained water or buffer solution from the chloroplast pellet. Extracted chloroplasts of various weight percent from 0 wt% to 5 wt% were gently mixed with the prepared polymer inks (with or without free NCO groups) using a magnetic stir bar for 30 min at 4℃ in a dark environment to prevent the degradation of chloroplasts. Then, 2 wt% of photoinitiator 187 (phenylbis(2,4,6-trimethylbenzoyl) phosphine oxide) was mixed with the polymer inks. The polymer was fully cured under white light from a white-light projector for 60 s. To allow for the photosynthesis process, we placed the prepared chloroplast-embedded polymer samples in a white-light chamber (CL-1000 Ultraviolet Crosslinker with five UVP 34-0056-01 bulbs, light intensity 69.3𝑊/𝑚 ( ) and undergone various light illumination periods (0-4 h) and the respective darkness periods (same length of the illumination period). For example, the 15-minute group went through 15-minute light illumination and 15-minute darkness. For the samples with various weight concentrations (0-5 wt%) of chloroplasts, they went through 4-h light illumination and 4-h darkness. After the illumination and darkness process, the samples were then uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 with a mechanical tester (Instron, model 5942). The Young’s modulus of each sample was calculated from the obtained tensile stress-strain curves (Figs. 65de). To verify that photosynthesis can indeed assist the polymer strengthening, we study three sample groups for comparison: The experimental group includes polymer samples with free NCO groups and embedded chloroplasts, going through 4-h illumination and 4-h darkness, control 1 group that includes polymer samples with free NCO groups and embedded chloroplasts, going through 8-h darkness, and control 2 group that includes polymer samples with free NCO groups but without chloroplasts, going through 4-h light illumination and 4-h darkness. We compare the mechanical properties of three sample groups via uniaxial tensile tests (Fig. 65d). Compared to controls 1 and 2, the experimental group exhibits higher Young’s modulus by a factor of 620% (Fig. 65e) and higher tensile strength by a factor of 350%. In addition, we study the effects of two vital factors on the strengthening performance: concentration of embedded chloroplasts and light illumination period (Fig. 66). First, we employ various light illumination periods (white light intensity 0-69.3 𝑊/𝑚 ( ) to process the polymer samples with 5 wt% chloroplasts and free NCO groups. Tensile stress-strain curves show that Young’s moduli increase with increasing illumination time within 0-2 h (Fig. 66a-c). Then, we investigate polymer samples with chloroplasts of various weight concentrations (0-5 wt%) and free NCO groups (processed with 4-h 188 illumination and 4-h darkness). Tensile stress-strain curves show that Young’s moduli increase with increasing chloroplast concentrations over 0-5 wt%, (Figs. 66d-f). Figure 66. Experimental results of photosynthesis-assisted remodeling (a) Samples with 5 wt% chloroplasts after the photosynthesis processes with various light illumination periods. (b) Uniaxial tensile stress-strain curves, (c) Young’s moduli of samples with 5 wt% chloroplasts after the photosynthesis processes with various light illumination periods. Note that each light illumination period follows up with the same period of darkness period. (d) Samples with embedded chloroplasts of various weight concentrations. (e) Uniaxial tensile stress-strain curves, (f) Young’s moduli of various weight concentrations samples undergo 4-h light illumination and 4-h darkness. 9.4 Theoretical model In this section, we will establish a theoretical framework to understand the fundamental mechanics of photosynthesis-assisted polymer strengthening. The theory will explain the mechanisms of two processes: (1) Glucose is produced by the photosynthesis process within chloroplasts and then exported from the chloroplasts to the polymer matrix (Section 9.4.1), and (2) additional crosslinks are formed within the polymer network through the reaction between glucose and the NCO side groups (Section 9.4.2). 189 9.4.1 Part 1: Glucose production and exportation With the extracted chloroplasts embedded in the polymer matrix, the energy from light can trigger the photosynthesis process to produce glucose. The overall process of photosynthesis is shown in Fig. 67a 328,329 . During the daytime, chloroplasts first convert light energy to the energy-carrier molecules, and these molecules are simultaneously used to produce starch that is stored in the chloroplast. During the night, the accumulated starch is broken down as glucose and exported out of the chloroplast (Fig. 67a). In Section 9.4.1.1, we will model the conversion of light energy to chemical energy by considering a light- dependent reaction (Fig. 67b). In Section 9.4.1.2, we will model the production of starch by considering a photosynthetic carbon reduction (PCR) cycle or usually called the Calvin cycle (Fig. 67c). In Section 9.4.1.3, we will model the starch degradation and glucose export by using the Michaelis-Menten kinetic. Figure 67. Schematics of glucose production and exportation Schematics of chloroplast to illustrate (a) overall photosynthesis process during day and night (b) light- dependent reaction (c) photosynthetic carbon reduction (PCR) cycle. 190 9.4.1.1 Kinetics of the light-dependent reaction In the light-dependent reaction, the pigment chlorophyll can convert light energy to chemical energy in the form of adenosine triphosphate (ATP) and nicotinamide adenine dinucleotide phosphate (NADPH) (Fig. 67b), which are later used to produce glucose in the next stage of photosynthesis 328,329 . Photochemically, one molecule of the pigment chlorophyll absorbs one photon and loses one electron 363 . This electron transfers to a modified form of chlorophyll called pheophytin, which passes the electron to a quinone molecule, starting the flow of electrons down to an electron transport chain that leads to the ultimate reduction of NADP to NADPH (Fig. 67b). In addition, this process creates a proton gradient (energy gradient) across the chloroplast membrane, which is used by photophosphorylation in the synthesis of ATP (Fig. 67b). The chlorophyll molecule ultimately regains the electron when a water molecule is split in a process called photolysis (or water splitting), which releases a dioxygen (O ( ) molecule. The overall equation of the light-dependent reaction is written as 2 H ( O+2 NADP [ +3 ADP+3 Pi+4 ℎ𝜈 →2 NADPH+2 H [ +3 ATP+O ( (9-1) The net-reaction can be reduced as 363-366 2 H ( O+4 ℎ𝜈 →4 H [ +O ( (9-2) We consider a light source with an initial light intensity 𝐼 ' is illuminated on a polymer matrix with embedded chloroplasts. Due to the semitransparent color of the chloroplast-embedded sample, the light propagation will be attenuated through the polymer matrix, which can be described with the Beer- Lambert law 191,192,367,368 , )*(𝐳) )𝐳 =−𝐴𝐼(z) (9-3) where the light illumination is along the z-axis, 𝐼(z,𝑡) is the light intensity at position 𝐳 along the z-axis at time t, 𝐴 is the absorption coefficient of the material. The light propagation direction is along a single axis (the z-axis); thus, we consider the light attenuation as a 1D problem (Fig. 68). The absorption coefficient can be estimated as 369 𝐴 =𝛼 2 𝜂 (9-4) 191 where 𝛼 2 is the light absorption coefficient, and 𝜂 is the mass concentration of the chloroplast within a unit volume of material (e.g., 0-5%, dimensionless). Here, we assume the polymer is incompressible, and thus the amount of chloroplast per unit volume will remain constant throughout the deformation. With a constant initial light intensity 𝐼 ' , the light intensity along the sample thickness direction (z-axis) can be written as (Eq. 9-3 and Fig. 68b), 𝐼(z)=𝐼 ' 𝑒𝑥𝑝(−𝐴𝑧) (9-5) The chloroplasts embedded in the matrix absorb the photons via pigment chlorophyll and release electrons in the chloroplast. The governing equation of the absorbed photon concentration by the chlorophyll 𝐶 } (z,t) can be written as 191,192,367,368,370 , )6 E (~,.) ). =𝜀 9 𝜂 𝛼 ( 2 A M *(~) E9/Z (9-6) where 𝜀 9 is the photosynthetic energy conversion efficiency of photon energy, 𝜂 (mol/m 3 ) is the molar concentration of the chlorophyll, 𝛼 ( is the molar absorptivity of chlorophyll, 𝑁 g =6.02×10 (F 𝑚𝑜𝑙 @2 is the Avogadro number, ℎ =6.63×10 @FB 𝐽𝑠 is the Plank constant, 𝑐 =3×10 K 𝑚𝑠 @2 is the speed of light, and 𝜆 =550 𝑛𝑚 is the mean wavelength of white light. Note that, 𝜂 should be in a linear relationship with 𝜂, i.e., 𝜂 =𝜑𝜂, where 𝜑 ≈2.2×10 @F 𝑚𝑜𝑙/𝑚 F 363 . In practice, chloroplasts do not convert all radiation energy into biomass energy, mainly due to the respiration requirements, reflection, and the need for optimal solar radiation levels. The overall photosynthetic efficiency is estimated between 3-6% of total photon energy 371,372 . From Eqs. 9-1 and 9-2, the absorbed photon by the chlorophyll is used to create a proton gradient and then store the biomass energy in the chemical forms of ATP and NADPH. Since the formation of ATP and NADPH both require protons, to simplify the problem, we here consider the production of protons 𝐶 e N as an irreversible chemical kinetic with photon energy to represent the formation of ATP and NADPH written as 373 )6 O N ). =𝑘 2 𝐶 } (z,t) (9-7) where 𝑘 2 (𝑠 @2 ) is the reaction rate to produce protons. 192 Figure 68. Light propagation in the materials matrix (a) Schematics to illustrate the experiment procedure of light illuminate on the sample. (b) The global Cartesian coordinate system is constructed on the testing area. The light illumination direction is along the z-axis. 9.4.1.2 Photosynthetic carbon reduction (PCR) cycle After the NADPH and ATP are generated from the light-dependent reaction, these energy-carrier molecules are simultaneously used to produce the glucose through the photosynthetic carbon reduction cycle (PCR cycle). In the PCR cycle, an enzyme called RuBisCO captures carbon dioxide from the atmosphere and uses the energies from NADPH and ATP to release hydrocarbon sugar (Fig. 67c). During the daytime, the released hydrocarbon sugar is temporarily stored in the chloroplast in the form of starch 374,375 . The overall equation for PCR cycle is written as 328,329,363 3 CO ( +2 ATP+6 NADPH+6 H [ 5y>"86 Á⎯⎯⎯⎯⎯ÃC F H c O F −phosphate +2 ADP+8 Pi+3 H ( O+ 6 NADP [ (9-8) Equation 9-8 can be reduced by normalizing the coefficients as 2 B CO ( + H [ 5y>"86 Á⎯⎯⎯⎯⎯Ã 2 (B C c H 2( O c + 2 B H ( O (9-9) The chemical kinetics between proton (H [ ) and the produced C c H 2( O c in the form of starch during PCR cycle can be explained by the enzyme activity of RuBisCO following the Michaelis-Menten kinetics 376- 378 , written as, )6 P Q R 0( S Q TU$7%) (B ⁄ ). = < %$U0 6 !VW#T%X 6 O N 6 O N[< Y0 −𝑘 . 6 P Q R 0( S Q TU$7%) (B (9-10) 193 where 𝐶 Q 0( Q 8.4$9E is the concentration of the produced C c H 2( O c in the form of starch, 𝑘 94.2 (𝑠 @2 ) is the catalytic rate of RuBisCO, 𝐶 5yC"89w is the concentration of the enzyme RuBisCO, 𝑘 2 is the Michaelis constant of RuBisCO, and 𝑘 . is the termination rate of starch synthesis. We assume the gradually increased accumulation of starch in the chloroplast will result in termination of starch production, which has been found as a self-limiting process once the chloroplasts become saturated with transitory starch 379 . Note that the formation of starch typically requires a condensation reaction between a number of C c H 2( O c molecules, which kick out water molecules 328,329,363 . However, the molar mass of starch is typically unknown; therefore, we only consider the amount of the smallest unit C c H 2( O c within the starch, but not directly consider the amount of the large starch molecule. The production of starch during the photosynthesis process involves both the light-dependent reaction and the PCR cycle. The photon energy will first facilitate the production of biomass energies in the light-dependent reaction, and the enzyme will then facilitate the biomass energies to produce starch stored in the chloroplast 374 . Therefore, these two processes are strongly coupled. Light can facilitate the production of biomass energy, and at the same time, the biomass energies are utilized by the enzyme to produce starch. This kinetic equation can effectively represent the overall photosynthesis chemical reaction, which is summarized as 328,329,363 6 𝐻 ( 𝑂+6 𝐶𝑂 ( 2(Ep Á⎯⎯Ã𝐶 c 𝐻 2( 𝑂 c +6 𝑂 ( (9-11) 9.4.1.3 Glucose exportation to matrix During the night (darkness period), the accumulated starch in the chloroplast is first broken down into simple sugar such as maltose and glucose, which are then exported through the chloroplast membrane to the polymer matrix by glucose transporter (Fig. 67a) 380,381 . It is noteworthy that both maltose and glucose molecules have hydroxyl groups (OH), which can have a strong reaction with NCO groups within the initial polymer network. Since glucose is the simplest form of sugar and maltose is merely a form of multiple condensed glucose molecules, for simplicity, we here consider the product exported from the chloroplasts is glucose. 194 The breaking-down process of starch to form glucose molecules can be considered as a simple relationship with the darkness time 375,382,383 , written as 76 Z#[ 7. =− 76 P Q R 0( S Q TU$7%) 7. =𝑘 7 𝐶 Q 0( Q 8.4$9E (9-12) where 𝐶 {"; is the concentration of glucose in the chloroplasts, 𝑘 7 is the degradation rate of starch and 𝐶 Q 0( Q 8.4$9E is the C c H 2( O c concentration in the form of starch. The glucose molecules can be transported across the membrane of the chloroplast, assisted by the transportation enzyme 384 . The enzyme-catalyzed transportation of glucose from chloroplast to material matrix can be explained with the Michaelis-Menten kinetics 384 , written as 7A 7. = < %$U( 6 U7$[T 6 Z#[ 6 Z#[ [< Y( (9-13) where 𝑑𝑁 𝑑𝑡 ⁄ is the export rate of the glucose through the membrane transporter, 𝑘 94.( is the catalytic rate of glucose transport, 𝐶 .$4;8 is the concentration of transportation enzyme, and 𝑘 ( is the Michaelis constant of the enzyme. The incremental concentration of glucose per unit volume in the material matrix can thus be calculated as 7A XVU = 2 XVU < %$U( 6 U7$[T 6 Z#[ 6 Z#[ [< Y( 𝑑𝑡 (9-14) where 𝑉 wy. is a unit volume of the material matrix. Therefore, the total concentration of glucose in a unit volume of the material matrix at darkness time 𝑡 74$< can be calculated as 𝐶 {wy. = 2 XVU ∫ 𝑑𝑁 . '$75 ' = 2 XVU ∫ < %$U( 6 U7$[T 6 Z#[ 6 Z#[ [< Y( 𝑑𝑡 . '$75 ' (9-15) Note that the chloroplast-produced glucose in the material matrix is a function of light intensity, light illuminating time, darkness time, and concentration of the embedded chloroplasts. We will further discuss the effects of these factors on the strengthening behaviors in Section 9.5. 9.4.2 Part 2: Polymer strengthening by additional crosslinking The initial polymer matrix is first crosslinked by the photoradical initiated addition reaction of the acrylate groups (Fig. 69a). Within this initial polymer network, NCO groups are active sites that can have a strong 195 reaction with hydroxyl groups (OH) on the chloroplast-produced glucose to form urethane linkages (-NH- CO-O-). We here consider these newly formed urethane linkages as the new crosslinks additional to the acrylate-enabled crosslinks within the designed polymer matrix. In Section 9.4.2.1, we will first model the initial polymer network by considering a homogeneous chain length distribution network model; and in Section 9.4.2.2, we will model the strengthening of material by considering the formation of inhomogeneous chain lengths due to the additional crosslinks. 9.4.2.1 Initial polymer network Before strengthening, the polymer network is assumed to feature a homogenous chain length. The chain length is described by the Kuhn length, denoted as 𝑁 ' and chain number per unit volume as 𝑛 ' . The strain energy density of the polymer network can be written as 103,385 𝑊 ' =𝑛 ' 𝑘 > 𝑇𝑁 ' k Q 2 .4;EQ 2 +𝑙𝑛 Q 2 8";EQ 2 l (9-16) where 𝑘 > is the Boltzmann constant, 𝑇 is the temperature in Kelvin, and 𝛽 ' =𝐿 @2 HA 2 (9-17) where 𝐿 @2 ( ) is the inverse Lagrange function and Λ is the chain stretch. Here, we follow an affine deformation assumption that the microscopic deformation at the polymer chain level affinely follows the macroscopic deformation at the material level in three principal directions; therefore, the chain stretch can be expressed as Λ=W𝜆 2 ( +𝜆 ( ( +𝜆 F ( (9-18) This affine deformation assumption has been widely adopted for deriving the constitutive models for rubber-like materials, such as neo-Hookean model 103 and Arruda-Boyce model 385 . Note that Eq. 9-18 is slightly different from the corresponding relationship in the Arruda-Boyce model where the relationship is Λ=W(𝜆 2 ( +𝜆 ( ( +𝜆 F ( ) 3 ⁄ . The chain stretch expressed in Eq. 9-18 is adopted for deriving the neo-Hookean model 103,386 . We here adopt the network architecture from the neo-Hookean model but not the Arruda- Boyce network model, because a general network architecture that does not necessarily follow the eight- 196 chain structure is more consistent with the network structure with additional crosslinks shown in Section 9.4.2.2. If the material is incompressible, the Cauchy stresses in three principal directions can be written as ⎩ ⎪ ⎨ ⎪ ⎧ 𝜎 2 =𝜆 2 ) 2 )Z 0 −𝑃 𝜎 ( =𝜆 ( ) 2 )Z ( −𝑃 𝜎 F =𝜆 F ) 2 )Z * −𝑃 (9-19) where 𝑃 is the hydrostatic pressure. Under uniaxially stretch with 𝜆 2 =𝜆 and 𝜆 ( =𝜆 F =𝜆 @2/( , the Cauchy stresses 𝜎 ( and 𝜎 F vanish. The Cauchy stress 𝜎 2 can be formulated as 𝜎 2 =𝜆 2 ) 2 )Z 0 −𝜆 ( ) 2 )Z ( (9-20) The corresponding nominal stress 𝑠 2 along 𝜆 2 direction can be formulated as 𝑠 2 = 0 Z 0 =𝑛 ' 𝑘 > 𝑇W𝑁 ' Z@Z 8( √Z ( [(Z 80 𝐿 @2 un Z ( [(Z 80 A 2 v (9-21) Through Eq. 9-21, we can obtain the uniaxial tensile stress-strain behaviors of polymer samples before strengthening. Only two fitting parameters (chain number density 𝑛 ' and polymer chain length 𝑁 ' ) are required. 9.4.2.2 Strengthening by forming additional crosslinks Once the glucose is exported to the polymer matrix, the reactions between the free NCO groups and the OH groups on the glucose will form additional crosslinks (Fig. 69a). For forming a crosslink, one glucose molecule (with 5 OH groups) is only required to bridge two NCO groups. Thus, one glucose molecule is able to at best form 2.5 crosslinks within the network. The number of the introduced glucose molecules per unit volume is denoted as 𝑛 { and the formed additional crosslink number per unit volume is denoted as 𝑛 4 . We should have 𝑛 { ≤𝑛 4 ≤2.5𝑛 { . As shown in Fig. 69b, two polymer chains with chain length 𝑁 ' will become four polymer chains with shorter lengths after introducing an additional crosslink. In a general case, these four polymer chains may have different chain lengths. Here, to capture the essential physics with a simple mathematic 197 formulation, we assume these four polymer chains have the same chain length, as 𝑁 ' 2 ⁄ . In a more general case shown in Fig. 69c, we assume the crosslink formed between a chain with length 𝑁 ' 2 " ⁄ and a chain with length 𝑁 ' 2 ⁄ induces four chains with respective half lengths, where 𝑖 =0,1,2⋯ and 𝑗 =0,1,2⋯. After introducing 𝑛 4 additional crosslinks per unit volume, the initially homogeneous chain length (𝑁 ' ) will become inhomogeneous, with a chain length distribution over length of 𝑁 ' , 𝑁 ' 2 ⁄ , …., and 𝑁 ' 2 3 ⁄ , where 𝑚 ≥1. The value of 𝑚 can be constrained by choosing the largest 𝑚 to ensure A 2 ( . ≥𝑁 3"; (9-22) where 𝑁 3"; is the admissible smallest chain length. Figure 69. Schematics to show the formation of additional crosslinks (a) Schematics to show the formation of additional crosslinks through the reaction between the free NCO groups and the glucose. (b) Schematics to show the formation of one crosslink between two chains with the length of 𝑁 ' . We assume each chain with the initial length of 𝑁 ' becomes two chains with the length of 𝑁 ' 2 ⁄ . (c) Schematics to show the formation of one crosslink between a chain with the length of 𝑁 ' 2 " ⁄ and a chain with the length of 𝑁 ' 2 ⁄ . We assume the crosslink formed between a chain with the length of 𝑁 ' 2 " ⁄ and a chain with the length of 𝑁 ' 2 ⁄ induces four chains with respective half lengths, where 𝑖 = 0,1,2⋯ and 𝑗 =0,1,2⋯. 198 To estimate the chain number of each type of chain length per unit volume, we treat the additional crosslinking process as 𝑚 steps. In each step, a certain amount of additional crosslinking point is introduced. We employ two methods as follows. Method 1: Equal number of incremental crosslinking points In method 1, we assume that probabilities of forming a crosslinking on the chain with length 𝑁 ' 2 " ⁄ and the chain with length 𝑁 ' 2 ⁄ are equal, where 𝑖 =0,1,2⋯ and 𝑗 =0,1,2⋯ . Under this assumption, the incremental additional crosslinking density for each step is equal, denoted as 𝑑𝑛 4 : 𝑑𝑛 4 = ; $ 3 (9-23) In the following, we will go through each step to calculate the volume density of polymer chains with length 𝑁 ' 2 ⁄ and denote it as 𝐶 , where 𝑗 =0,1,2⋯. In step 1, some of the initial chains with length 𝑁 ' become shorter chains with length 𝑁 ' 2 ⁄ after adding 𝑑𝑛 4 crosslinking point if 2𝑑𝑛 4 ≤𝑛 ' . At the end of step 1, we have: 𝐶 ' =𝑛 ' −2𝑑𝑛 4 (9-24) 𝐶 2 =4𝑑𝑛 4 (9-25) In step 2, three possible routes to form the crosslinking: between two chains with length 𝑁 ' , between two chains with length 𝑁 ' 2 ⁄ , and between a chain with length 𝑁 ' and a chain with length 𝑁 ' 2 ⁄ . The probabilities for partitioning chains with length 𝑁 ' and chains with length 𝑁 ' 2 ⁄ are equal. Therefore, at the end of step 2, we have: 𝐶 ' =𝑛 ' −2𝑑𝑛 4 −2(𝑑𝑛 4 2 ⁄ ) (9-26a) 𝐶 2 =4𝑑𝑛 4 +4(𝑑𝑛 4 2 ⁄ )−2(𝑑𝑛 4 2 ⁄ ) (9-26b) 𝐶 ( =4(𝑑𝑛 4 2 ⁄ ) (9-26c) Similarly, at the end of step 3, we have: 𝐶 ' =𝑛 ' −2𝑑𝑛 4 −2(𝑑𝑛 4 2 ⁄ )−2(𝑑𝑛 4 3 ⁄ ) (9-27a) 𝐶 2 =4𝑑𝑛 4 +4(𝑑𝑛 4 2 ⁄ )−2(𝑑𝑛 4 2 ⁄ )+4(𝑑𝑛 4 3 ⁄ )−2(𝑑𝑛 4 3 ⁄ ) (9-27b) 199 𝐶 ( =4(𝑑𝑛 4 2 ⁄ )+4(𝑑𝑛 4 3 ⁄ )−2(𝑑𝑛 4 3 ⁄ ) 9-(27c) 𝐶 F =4(𝑑𝑛 4 3 ⁄ ) (9-27d) Eventually, at the end of step m, we have: 𝐶 ' =𝑛 ' −2𝑑𝑛 4 k1+ 2 ( + 2 F +⋯+ 2 3 l (9-28a) 𝐶 2 =2𝑑𝑛 4 +2𝑑𝑛 4 k1+ 2 ( + 2 F +⋯+ 2 3 l (9-28b) 𝐶 ( =2(𝑑𝑛 4 2 ⁄ )+2𝑑𝑛 4 k 2 ( + 2 F +⋯+ 2 3 l (9-28c) …… 𝐶 =2(𝑑𝑛 4 𝑗 ⁄ )+2𝑑𝑛 4 k 2 + 2 [2 +⋯+ 2 3 l (9-28d) …… 𝐶 3 =4(𝑑𝑛 4 𝑚 ⁄ ) (9-28e) The volume density of chains with length 𝑁 ' 2 ⁄ at the end of step 𝑚 can be summarized as 𝐶 = ⎩ ⎪ ⎨ ⎪ ⎧ 𝑛 ' − (; $ 3 k1+ 2 ( + 2 F +⋯+ 2 3 l , 𝑗 =0 (; $ 3 k ( + 2 [2 +⋯+ 2 3 l , 1≤𝑗 ≤𝑚−1 B; $ 3 ( , 𝑗 =𝑚 (𝑖𝑓 𝑚 ≥2) (9-29) After strengthening, the polymer chain length is inhomogeneous with a chain length distribution over length of 𝑁 ' , 𝑁 ' 2 ⁄ , …., and 𝑁 ' 2 3 ⁄ , where 𝑚 ≥1. The chain length distribution is shown in Eq. 9- 29. We assume that under deformation, each polymer chain deform following an affine deformation assumption that the microscopic polymer chain deformation affinely follows the macroscopic deformation in three principal directions; thus, the chain stretch of the chain with length 𝑁 ' 2 ⁄ (𝑗 =0,1,2⋯) can be expressed as 84,99,115,174,264,265,387 Λ =W𝜆 2 ( +𝜆 ( ( +𝜆 F ( (9-30) The strain energy of the whole polymer network per unit volume can be formulated as 84,99,115,174,264,265,387 𝑊 8 =∑ Ð𝐶 𝑘 > 𝑇k A 2 ( \ l Q \ .4;EQ \ +𝑙𝑛 Q \ 8";EQ \ Ñ 3 b' (9-31) 200 𝛽 =𝐿 @2 \ HA 2 ( \ ⁄ (9-32) where the chain stretch Λ is given in Eq. 9-30. Under uniaxial tension with 𝜆 2 =𝜆 and 𝜆 ( =𝜆 F =𝜆 @2/( , the tensile nominal stress of the incompressible polymer after strengthening can be calculated as 𝑠 82 =∑ t𝐶 𝑘 > 𝑇W𝑁 ' 2 ⁄ Z@Z 8( √Z ( [(Z 80 𝐿 @2 un Z ( [(Z 80 A 2 ( \ ⁄ vw 3 b' (9-33) In method 1, there is a hidden requirement for the relationship between 𝑛 4 and 𝑚. For example, if 𝑚 =1, the maximal possible crosslinking point density is 𝑛 ' 2 ⁄ . This condition is to ensure the chain density of chains with length 𝑁 ' is not negative. For a certain 𝑚 , the requirement of the possible crosslinking point density is (𝑚−1) d2k1+ 2 ( + 2 F +⋯+ 2 3@2 le <𝑛 4 𝑛 ' ≤𝑚 d2k1+ 2 ( + 2 F +⋯+ 2 3 le ⁄ (9-34) Method 2: Unequal number of incremental crosslinking points In method 2, we assume that the probability of forming a crosslinking on the chain with length 𝑁 ' 2 " ⁄ is higher than that of forming a crosslinking on the chain with length 𝑁 ' 2 ⁄ when 𝑖 <𝑗. In an extreme case, the crosslinking occurs first on the chain with length 𝑁 ' 2 " ⁄ , and then on the chain with length 𝑁 ' 2 "[2 ⁄ . In other words, the crosslinking reaction on the longer chains always happens before the crosslinking reaction on the short chains. Following the assumption, we can naturally define the ith step as the step with the occurrence of the crosslinking reaction on the chain with length 𝑁 ' 2 "@2 ⁄ . The process will move to the next step only when there are enough crosslinkers to consume all the chains with length 𝑁 ' 2 "@2 ⁄ . If the crosslinking reaction stops at step 1, there are only two types of chains: chains with length 𝑁 ' and 𝑁 ' 2 ⁄ . Their volume densities can be calculated as 𝐶 ' =𝑛 ' −2𝑛 4 (9-35a) 𝐶 2 =4𝑛 4 (9-35b) The requirement is 0<𝑛 4 𝑛 ' ⁄ ≤1 2 ⁄ . 201 If the crosslinking reaction stops at step 2, there are only two types of chains: chains with length 𝑁 ' 2 ⁄ and 𝑁 ' 2 ( ⁄ . Their volume densities can be calculated as 𝐶 2 =2𝑛 ' −2k𝑛 4 − ; 2 ( l =3𝑛 ' −2𝑛 4 (9-36a) 𝐶 ( =4k𝑛 4 − ; 2 ( l (9-36b) The requirement is 1 2 ⁄ <𝑛 4 𝑛 ' ⁄ ≤3 2 ⁄ . If the crosslinking reaction stops at step 𝑚, at the end of step m, there are only two types of chains: chains with lengths 𝑁 ' 2 3@2 ⁄ and 𝑁 ' 2 3@2 ⁄ . Their volume densities can be calculated as 𝐶 3@2 =2 3@2 𝑛 ' −2d𝑛 4 −k2 3@( − 2 ( l 𝑛 ' e=(2 3 −1)𝑛 ' −2𝑛 4 (9-37a) 𝐶 3 =4d𝑛 4 −k2 3@( − 2 ( l 𝑛 ' e=4𝑛 4 −4(2 3@( − 2 ( )𝑛 ' (9-37b) The requirement is for the additional crosslink density to reach step m is ( .80 @2 ( <𝑛 4 𝑛 ' ⁄ ≤ ( . @2 ( (9-38) After strengthening, the strain energy function can be formulated as 84,99,115,174,264,265,387 𝑊 8 =∑ Ð𝐶 𝑘 > 𝑇k A 2 ( \ l Q \ .4;EQ \ +𝑙𝑛 Q \ 8";EQ \ Ñ 3 b3@2 (9-39) 𝛽 =𝐿 @2 \ HA 2 ( \ ⁄ (9-40) where the chain stretch Λ is given in Eq. 9-30 and 𝐶 for 𝑗 =𝑚−1 and 𝑗 =𝑚 are given in Eq. 9-37. Under uniaxial tension with 𝜆 2 =𝜆 and 𝜆 ( =𝜆 F =𝜆 @2/( , the nominal tensile stress of the incompressible polymer after strengthening can be calculated as 𝑠 82 =∑ t𝐶 𝑘 > 𝑇W𝑁 ' 2 ⁄ Z@Z 8( √Z ( [(Z 80 𝐿 @2 un Z ( [(Z 80 A 2 ( \ ⁄ vw 3 b3@2 (9-41) 9.5 Results In this section, we first present the theoretical results calculated from the theory for glucose production and exportation (Section 9.5.1) and then from the theory for polymer strengthening by additional crosslinks (Section 9.5.2). In Section 9.5.3, we will integrate two parts of the theories and 202 discuss the results for glucose-enabled additional crosslinks in the polymer matrix. By coupling the photosynthesis theory in Section 9.4.1 and the strengthening model in Section 9.4.2, we examine the effects of the illumination period, the concentration of chloroplasts, and the light intensity on the strengthening performance. The theoretical results are compared with the experimental results. All used parameters are presented in Table 5. 9.5.1 Results of Part 1 theory In Section 9.4.1, a theoretical framework for the production and exportation of glucose was presented. During the illumination period, light intensity attenuates following the Beer-Lambert law (Eq. 9-3). Considering a relatively thin sample (𝐻~2 𝑚𝑚), we can calculate the mean light intensity across the thickness, written as, 𝐼 ̅ ≈ * 2 ( [1+𝑒𝑥𝑝(−𝐴𝐻)] (9-42) where 𝐻 is the sample thickness. Note that in a real situation the light intensity is inhomogeneous across the thickness: more protons are produced at the locations closer to the light incident surface. It means that the glucose production and additional crosslinks will vary across the interface in the later process. We here simplify the problem by considering the thin sample thickness used in the experiment and consider an effectively homogeneous strengthening across the interface. Using Eq. 9-42 and integrating Eq. 9-7, we obtain the governing equation for the production of protons, expressed as, ) ( 6 O N ). ( =𝑘 2 𝜀 9 𝜂 𝛼 ( 2 A $ * ̅ E9/Z (9-43) Coupling Eqs. 9-43 and 9-10, we can calculate the concentration of the produced C c H 2( O c in the form of starch (𝐶 Q 0( Q 8.4$9E ). A typical curve for the production of C c H 2( O c is shown in Fig. 70a. During the illumination period (2 h), the concentration of the produced C c H 2( O c in the form of starch increases over time and gradually reaches a plateau if the illumination time is long enough (Fig.70). The plateau is determined by the termination of the starch synthesis which is governed by the self-metabolism of the chloroplast. 203 During the darkness period, the starch begins to break down to form small glucose molecules which are then exported to the polymer matrix. Since the glucose exportation speed is dependent on the concentration of glucose within the chloroplast (Eq. 9-13), the starch breaking-down and the glucose exportation are strongly coupled. Coupling Eqs. 9-12 to 9-15, we can compute the evolution of the starch breaking-down and the glucose exportation, which are shown in Figs. 70a and 70b, respectively. As shown in Figs. 70a, the starch rapidly breaks down within 0.5 h. All of the produced C c H 2( O c molecules within chloroplasts are exported to the polymer matrix (as glucose molecules); thus, the concentration of the exported glucose increases over time and then reaches a plateau (Fig. 70b). Figure 70. Theoretical results of the production and exportation of glucose (a) The evolution of C c H 2( O c concentration in the form of synthesized starch in the chloroplast and (b) the evolution of the concentration of the exported glucose in the matrix over the illumination period (2 h) and the darkness period (2 h). 9.5.2 Results of Part 2 theory We consider the polymer strengthening via forming additional crosslinks in the polymer matrix. To estimate the chain number of each type of chain length per unit volume, we employ two methods to calculate the amount of additional crosslinking in each crosslinking step in Section 9.4.2.2. As shown in Figs. 71ab and 71cd, the polymer with initial chain length 𝑁 ' =100 becomes stronger with increasing 204 additional crosslinks for both method 1 and method 2. We here define the strengthening factor as the strengthened Young’s modulus (within 10% strain region) normalized by the non-strengthened Young’s modulus (Figs. 71bd). When the additional crosslinks density is low (e.g. 𝑛 4 𝑛 ' ⁄ ≤1 2 ⁄ ), there is only one-step strengthening in either method 1 or method 2, i.e., m=1 (Figs. 71ac, red and green lines, Figs. 71bd). The strengthening behavior and factor show the same results by both methods. When the additional crosslinks density is slightly larger than 1/2 (e.g. 𝑛 4 𝑛 ' ⁄ =0.75), the stress-strain curve and the strengthening factor calculated from method 1 and 2 are still similar (Figs. 71ac, blue line, Figs. 71bd). However, when 𝑛 4 𝑛 ' ⁄ increases to 1, the stress-strain curve and strengthening factor calculated from method 1 are much larger than those calculated from method 2 (Figs. 71ac, magenta line, Figs. 71bd). This is because the step number of method 1 reaches a larger number (m=5) than the step number of method 2 (m=2), corresponding to shorter chains in the polymer matrix according to Eqs. 9-29, 9-33, and 9-37. Figure 71. Theoretical results for various normalized additional crosslink density 𝑛 4 𝑛 ' ⁄ . (a) Nominal tensile stress-strain curves for method 1. (b) Strengthening factor in a function of the normalized additional crosslink density for method 1. The strengthening factor is defined as the 205 strengthened Young’s modulus normalized by the unstrengthened Young’s modulus. (c) Nominal tensile stress-strain curves for method 2. (d) Strengthening factor in a function of the normalized additional crosslink density for method 2. To investigate the relationships between additional crosslinks density 𝑛 4 𝑛 ' ⁄ and the step number m, we calculate the step numbers for method 1 and 2 with 𝑛 4 𝑛 ' ⁄ from 0 to 5 (Fig. 72). When 𝑛 4 𝑛 ' ⁄ ≤ 1 2 ⁄ , the step numbers m for methods 1 and 2 are both in the first step strengthening thus m values are the same. When 𝑛 4 𝑛 ' ⁄ increases to 5, the step number m for method 1 drastically increases to 45. However, the step number m is still 4 when 𝑛 4 𝑛 ' ⁄ =5 for method 2. To further investigate the effect of large step numbers on the polymer strengthening, we take a relatively large crosslinking number as an example (e.g., 𝑛 4 𝑛 ' ⁄ =2.5). When 𝑛 4 𝑛 ' ⁄ =2.5, the step number for method 1 increases to 21 (Fig. 72a), which means that the shortest chain length in the polymer matrix becomes 𝑁 ' 2 (2 ⁄ . This value should be constrained by the admissible smallest chain length 𝑁 3"; and the initial chain length 𝑁 ' of the polymer in Eq. 9-22. Considering the stress-strain curve shape of the studied polymer (Fig. 66), the initial chain length 𝑁 ' is estimated between 60 and 2000. 𝑁 ' 2 (2 ⁄ becomes an invalid number for the chain length. Therefore, under such a situation that additional crosslink density is relatively large, method 1 cannot effectively model the strengthening behavior, and we can only employ method 2. Figure 72. Relationships between the step number m and additional crosslink density Relationships between the step number m and additional crosslink density 𝑛 4 𝑛 ' ⁄ for (a) method 1 and (b) method 2 206 Using method 2, we study the effect of the initial chain length 𝑁 ' of the polymer on the strengthening effect (Fig. 73). When the initial chain length 𝑁 ' is very small (e.g. 𝑁 ' =40), the polymer can be significantly strengthened. When the initial chain length 𝑁 ' >500, the strengthening factor reaches a plateau of around 6 (Figs. 73ab). When the initial chain length 60≤𝑁 ' ≤2000, the strengthening factor varies from 6 to 7.9. Figure 73. Theoretical results for method 2 with m = 3 and 𝑛 4 𝑛 ' ⁄ =2.5. (a) Nominal tensile stress-strain curves and (b) strengthening factor for various initial chain lengths 𝑁 ' . 9.5.3 Results of the integrated theory Integrating Part 1 and Part 2 theories, we can link the experimental conditions, such as light illumination and chloroplast concentration, to the resulting polymer strengthening. The connection between the Part 1 theory and Part 2 theory is the relationship between the concentration of the exported glucose and the concentration of additional crosslinks. We assume that all the exported glucose molecules are consumed by forming additional crosslinks, because the concentration of the NCO group is high enough. In addition, as a starting point, we assume one glucose molecule only bridges two NCO groups to form one additional crosslink, that is, 𝑛 4 =𝑛 { =𝐶 {wy. 𝑁 g (9-44) Equation 9-44 constructs the connections between Part 1 theory and Part 2 theory. The concentration of the exported glucose calculated in Part 1 theory can be directly passed to Part 2 theory to determine the strengthening effect. 207 In the following sub-sections, we will first verify our theory for the glucose production/exportation with experimental results (Section 9.5.3.1), and then discuss the effects of the illumination period, the concentration of chloroplasts, and the light intensity on the polymer strengthening (Sections 9.5.3.2-4). 9.5.3.1 Verify the theory of glucose production via experiment After the chloroplast-embedded polymer samples go through the photosynthesis process (illumination and darkness period), the glucose will be exported from the chloroplast to the polymer matrix. Since the photosynthesis-produced glucose is expected to consume free NCO groups to form additional crosslinks, the concentration reduction of free NCO groups can reveal the production and exportation of glucose. To indicate the concentration of free NCO groups within the polymer matrix, we employ a Fourier transform infrared (FTIR) spectrometer to measure the transmittance of the sample around 2260 cm -1 that is corresponding to the NCO bond stretching vibration 321 . We find an evident peak at 2260 cm -1 in the initial state of the sample (Fig. 74a). After the photosynthesis processes (illumination period and the corresponding darkness period of the same length), the peak at 2260 cm -1 drops, indicating the reduction of the NCO concentration. With increasing illumination periods (0-2 h), the peak height drops more. The initial concentration of NCO groups is denoted as 𝐶 ' A6 , and the concentration of NCO groups after the photosynthesis process with illumination period 𝑡 " us denoted as 𝐶 A6 (𝑡 " ). To quantify the concentration reduction of NCO groups, we calculate the area under the FTIR peak (𝑆(𝑡 " )) and normalize the area with the initial peak area at 0 h (𝑆 ' ) (Fig. 74a). We approximate the concentration ratio of NCO groups as 6 ]C^ (. # ) 6 2 ]C^ = x(. # ) x 2 (9-45) Since the consumed NCO groups have reacted with glucose molecules and one glucose molecule is assumed to consume two NCO groups, we obtain the exported glucose concentration as 𝐶 {wy. (𝑡 " )=2𝐶 ' A6 k1− x(. # ) x 2 l (9-46) where 𝐶 {wy. (𝑡 " ) is the concentration of the exported glucose after the illumination period of 𝑡 " and darkness period of 𝑡 " , and 𝐶 ' A6 can be calculated from the material recipe (1.75×10 @B 𝑚𝑜𝑙/𝑚 F ). 208 Figure 74b shows the relationship between the exported glucose concentration and the illumination period. The theoretically calculated concentration of the exported glucose agrees well with the experimental results obtained from Eq. 9-46. As shown in Fig. 74b, the exported glucose concentration increases with the illumination period and gradually approaches a plateau when the illumination period is long enough. Figure 74. FTIR spectra and results of exported glucose concentration (a) FTIR spectra of experimental group samples (with free NCO groups and embedded chloroplasts) with various light illumination periods. The zoom-in view of FTIR spectra in the range of 2200 cm-1 to 2350 cm-1 indicates the concentration of the free NCO groups. (b) Experimentally measured and theoretically calculated exported glucose concentration in a function of the illumination time. The experimental results are obtained using Eq. 9-46. 9.5.3.2 Effect of the illumination period With a longer illumination period, the photosynthesis process of chloroplasts is holding longer, thus leading to a higher concentration of produced C 6H 12O 6 stored in the form of starch at the end of the light- dependent process (Fig. 75a). According to Eqs. 9-12 to 9-15, the stored starch in the chloroplast will degrade to glucose molecules and then transport to the material matrix, and the glucose molecules will serve as the additional crosslinks. With Eq. 9-44, the amount of the exported glucose molecules can be passed to Part 2 theory to obtain the stress-strain behaviors of the strengthened polymers with various light illumination periods (Fig. 75b). Subsequently, Young’s moduli of the strengthened polymers can be calculated within the strain range of 10% (Fig. 75c). As the illumination period increases, the concentration of the produced and exported glucose molecule increases, and the polymer thus becomes stiffer with a higher Young’s modulus. As the illumination period further increases, the concentration of 209 the exported glucose tends to approach a plateau; thus, Young’s modulus of the strengthened polymer also tends to gradually reach a plateau (Fig. 75c). The theoretically calculated Young’s moduli of the strengthened polymers for various illumination periods agree with the corresponding experimental results. Figure 75. Effect of the illumination period (a) The theoretically calculated C 6H 12O 6 concentration in the form of starch for various light illumination periods. (b-c) Experimentally measured and theoretically calculated stress-strain curves and Young’s moduli for various illumination periods. The Young’s modulus is calculated from the stress-strain curve within 10% strain. 9.5.3.3 Effect of the chloroplast concentration The chloroplast concentration greatly influences the polymer strengthening effect (Figs. 66d-f). The effect of the chloroplast concentration is displayed in two aspects. First, the color of chloroplast-embedded samples varies due to different concentrations of embedded chloroplasts (Fig. 66d). Due to the color difference, the light attenuation in the material matrix depends on the concentration of chloroplasts. This point can be modeled by Eqs. 9-3 and 9-4, where the light absorption of the material depends on the concentration of chloroplast embedded in the polymer matrix. With increasing concentration of chloroplasts, the light intensity is attenuated more, and thus the mean light intensity cross the thickness 𝐼 ̅ is lower (Eq. 9-42). Second, a higher concentration of chloroplasts (𝜂) leads to a higher concentration of chlorophyll (𝜂 in Eq. 9-6), and thus more photon energy will be absorbed to produce the glucose. Since a relatively thin sample (𝐻~2 𝑚𝑚) is employed here, the effect of light attenuation is much smaller than the effect of light absorption. Overall, with increasing concentration of chloroplasts, more C c H 2( O c is synthesized during the light-dependent process (Fig. 76a) and then is exported as glucose molecules in the 210 polymer matrix. The higher concentration of the exported glucose crosslinkers then leads to a stronger effect in the polymer strengthening. As shown in Figs. 76ab, as the concentration of chloroplasts increases from 0% to 5%, the resulting polymer matrix becomes stiffer with higher Young’s modulus. The theoretically calculated stress-strain curves and Young’s moduli agree with the respective experimental results (Figs. 76bc). Figure 76. Effect of the chloroplast concentration (a) The theoretically calculated C 6H 12O 6 concentration in the form of starch for samples with various concentrations of embedded chloroplasts. (b-c) Experimentally measured and theoretically calculated stress-strain curves and Young’s moduli for samples with various concentrations of embedded chloroplasts. 9.5.3.4 Effect of light intensity Next, we study the effect of the applied light intensity (𝐼 ' ) during the light-dependent process on the strengthening behavior. According to Eqs. 9-3, 9-6, 9-42, and 9-43, the higher photon energy absorbed by the pigment chlorophyll induces more biomass energy converted to generate sugars. Theoretical results show that the plateau C c H 2( O c concentration stored in starch increases with increasing illuminating light intensity 𝐼 ' (Fig. 77a). In addition, according to Eqs. 9-42 and 9-43, such an increasing trend should be most linear. Such a linear trend is verified by the theoretically calculated relationship between Young’s modulus of the strengthened polymer and the applied light intensity 𝐼 ' (Fig. 77b). The theoretically calculated Young’s moduli agree well with the experimentally measured results (Fig. 77b). 211 Figure 77. Effect of light intensity (a) The theoretically calculated C 6H 12O 6 concentration in the form of starch for various applied light intensities. (b) Experimentally measured and theoretically calculated Young’s moduli for various applied light intensities. 9.6 Conclusive remarks In summary, we presented experiments and theories to study plant-inspired photosynthesis-assisted strengthening behaviors in a synthetic polymer. The strengthening mechanism relies on an additional crosslinking reaction between the photosynthesis-produced glucose and side groups within the polymer matrix. We develop a theoretical framework to explain glucose production and exportation, and the corresponding polymer strengthening by forming additional crosslinks. The theoretical framework can quantitatively explain the experimentally observed photosynthesis-assisted polymer strengthening under different experimental conditions, such as various illumination periods, concentrations of embedded chloroplasts, and light intensities. The theoretical framework makes two significant advances in the field of solid mechanics. First, it, for the first time, proposes a simple and easy-to-implement theory to explain the polymer strengthening effect with additional crosslinks. This framework paves the way for the future mechanistic understanding of polymer network behaviors with incremental crosslinks, such as sequential crosslinking in double- network polymers/gels 323,388,389 . Second, it, for the first time, proposes a theoretical framework to bridge the communication between the natural photosynthesis process and synthetic polymer networks. The communication between living photosynthesis and synthetic polymers may open doors for hybrid synthetic-living materials with both complex microstructures and biomimetic properties. The theoretical 212 framework proposed in this paper may facilitate the mechanistic understanding of future hybrid synthetic- living materials. Of course, the theoretical framework in this paper has been significantly simplified in multiple aspects. These aspects may forecast future research opportunities. For example, to capture the essence of the theory, we only focus our attention on the stress-strain behaviors within 20% strain and the corresponding Young’s modulus (Figs. 75-77), but do not fully capture the stress-strain behaviors of the polymers until breaking during the tensile tests. As shown in Fig. 66, the stress-strain behaviors of the full strain regions until breaking may involve chain alternation and reorganization that may lead to softening or stiffening 99,115,174 . In addition, we do not consider the saturation of Young’s modulus over various chloroplast concentrations and light intensities. In Fig. 76, we show that Young’s modulus increases with increasing chloroplast concentration within 0-5%. With further increasing chloroplast concentration, we expect the modulus to saturate somewhere because a higher concentration of chloroplasts that effectively behave like soft fillers may compromise the material stiffness. In Fig. 77, we show that Young’s modulus increases linearly with the light intensity within 0−69.3 𝑊 𝑚 F ⁄ . With further increasing light intensity, we expect the modulus to saturate somewhere because strong light may damage the chloroplasts and thus result in less exportation of glucose to the material matrix. Although these saturation behaviors may be interesting, this paper primarily focuses on modeling the effect of photosynthesis-produced glucose on the polymer strengthening and does not include the saturation behavior in Figs. 76 and 77. Different from plants that chloroplast can be regenerated by their metabolisms, we chose moderate illumination periods, concentrations, and intensities to ensure the stability of the chloroplast activity in our material system 390 . How to maintain the long-term living states of chloroplasts or even regenerate chloroplasts is very important for the future study. As another example, in modeling the process of forming additional crosslinks, we consider that a crosslink would partition a chain into two halves with equal lengths. The realistic situation must follow a stochastic distribution. Besides, when considering the rule of forming additional crosslinks, we only 213 consider two scenarios, namely the equal probability of forming additional crosslinks in chains with various lengths (method 1 in Section 9.4.2.2) and forming additional crosslinks in long chains (method 2 in Section 9.4.2.2). Only considering these two scenarios is for the sake of mathematical simplicity; however, the realistic situation should follow stochastic variations. We hope future models can include more careful considerations of the stochastic aspect. Table 5. Definition, value, and estimation source of the employed parameters. The estimation source is given for each parameter. 𝐼 ' , 𝜂, and 𝑡 are directly from experiments. 𝑁 ' and 𝑛 ' is estimated based on the stress-strain behaviors of the polymer. Parameter Definition Fig. 70 Fig. 71,72 Fig. 73 Fig. 74, 75 Fig. 76 Fig. 77 Estimation source 𝐼 9 (𝐽 𝑠 _: 𝑚 _> ) Initial light intensity 69.3 N/A N/A 69.3 69.3 0-69.3 Experimental data 𝛼 : (𝑚 _: ) Light absorption coefficient of the chloroplast 2000 N/A N/A 2000 2000 2000 369 𝜂 (%) Mass concentration of the chloroplast 5 N/A N/A 5 0-5 5 Experimental data 𝜀 ` (%) Photosynthetic energy conversion efficiency of photon energy 5 N/A N/A 5 5 5 371,372 𝛼 > (𝑚 > 𝑚𝑜𝑙 _: ) Molar absorptivity of chlorophyll 1×10 a N/A N/A 1×10 a 1×10 a 1×10 a 391 𝑘 : ( 𝑠 _: ) Reaction rate to produce proton 1×10 b N/A N/A 1×10 b 1×10 b 1×10 b 373 𝑘 `<=: ( 𝑠 _: ) Catalytic rate of RuBisCO 3.13 N/A N/A 3.13 3.13 3.13 376,377 𝐶 ?cdAHGe (𝑚𝑜𝑙 𝑚 _a ) Concentration of RuBisCO 0.008 N/A N/A 0.008 0.008 0.008 376 𝑘 f: (𝑚𝑜𝑙 𝑚 _a ) Michaelis constant of RuBisCO 0.0021 N/A N/A 0.0021 0.0021 0.0021 376 𝑘 = ( 𝑠 _: ) Termination rate of the starch synthesis 0.0004 N/A N/A 0.0004 0.0004 0.0004 Fitting parameter 𝑘 g ( 𝑠 _: ) Degradation rate of starch 0.003 N/A N/A 0.003 0.003 0.003 383 𝑘 `<=> ( 𝑠 _: ) Catalytic rate of glucose transport 240.28 N/A N/A 240.28 240.28 240.28 384 𝐶 =B<hH (𝑚𝑜𝑙 𝑚 _a ) Concentration of transportation enzyme 0.02 N/A N/A 0.02 0.02 0.02 384 𝑘 f> (𝑚𝑜𝑙 𝑚 _a ) Michaelis constant of enzyme 19.3 N/A N/A 19.3 19.3 19.3 384 𝑁 9 Initial chain length N/A 100 40- 2000 400 400 400 Chosen based on the material 𝑛 9 (𝑚 _a ) Initial chain number density N/A 4.5 ×10 :i 4.5 ×10 :i 4.5 ×10 :i 4.5 ×10 :i 4.5 ×10 :i Chosen based on the material 𝑛 < /𝑛 9 Normalized additional crosslink density N/A 0-5 2.5 N/A N/A N/A Chosen based on the material 𝑡 (ℎ) Illumination time 2 N/A N/A 0-2 4 4 Experimental data 214 Chapter 10: Constructive adaptation of 3D-printable polymers in response to the typically destructive aquatic environment 10.1 Objective In response to the environmental stressors, the biological systems exhibit extraordinary adaptive capacity by turning destructive environmental stressors into constructive factors; however, the traditional engineering materials weaken and fail. Take the response of polymers to the aquatic environment as an example, water molecules typically compromise the mechanical properties of the polymer network in the bulk and on the interface through swelling and lubrication, respectively. Here, we report a class of 3D- printable synthetic polymers that constructively strengthen their bulk and interfacial mechanical properties in response to the aquatic environment. The mechanism relies on a water-assisted additional cross-linking reaction in the polymer matrix and on the interface. As such, the typically destructive water can constructively enhance the polymer’s bulk mechanical properties such as stiffness, tensile strength, and fracture toughness by factors of 746-790%, and the interfacial bonding by a factor of 1000%. This work opens the door for the design of synthetic materials to imitate the constructive adaptation of the biological systems in response to environmental stressors, for applications such as artificial muscles, soft robotics, and flexible electronics. 10.2 Introduction Although engineering and biological systems are surrounded by similar destructive environmental stressors, such as load imposition, light exposure, and water immersion, their responses are typically different. The biological systems exhibit extraordinary adaptive capacity by turning destructive environmental stressors into constructive factors. For example, bone and muscle turn the typically destructive mechanical loads into constructive factors to build mass and mechanical strength 327,392-396 . Plants harness sunlight, which otherwise degrades substance 397 , to constructively synthesize polysaccharides and grow stiffness and strength 359,398 . The engineering systems, on the contrary, typically 215 do not possess the intelligence of constructive adaptation but weaken in response to environmental stressors. Take the response of polymers to the aquatic environment as an example, water molecules typically compromise the mechanical properties of the polymer network in the bulk and on the interface. When water molecules migrate into a bulk polymer network, the polymer network swells, and its stiffness and strength reduce (Fig. 78A) 399-401 . When water molecules exist on the polymer interface, they lubricate the interface and reduce the interfacial adhesion or bonding (Fig. 78B) 402,403 . Such destructive responses may drastically limit the use of synthetic polymers in the fields that require the stability of bulk and interfacial mechanical properties in the aquatic environment. Inspired by the biological systems, we here report a class of 3D-printable synthetic polymers that constructively strengthen their bulk and interfacial mechanical properties in response to the typically destructive aquatic environment (Figs. 78CD). The mechanism relies on a water-assisted additional cross- linking reaction in the polymer matrix and on the interface, thus overcoming the property compromise due to swelling and lubrication. The proposed mechanism can constructively enhance the bulk mechanical properties such as stiffness, tensile strength, and fracture toughness by factors of 746-790% (Fig. 78C), and the interfacial bonding by a factor of 1000% (Fig. 78D). The proposed polymer is molecularly designed to be photocurable, thus facilitating 3D printing of various complex structures via the stereolithography system. To highlight the impact of the constructive adaptation, we show a 3D-printed robotic arm can strengthen its lifting capability after training in the water, though it weakens after training in the air. We also demonstrate a robotic fish with a 3D-printed polymer fin can swim faster and heal cracks after training in the water. Moreover, the proposed polymer can be used as a water-healable packaging material that can efficiently resist water-induced performance degradation of flexible electronics. The paradigm in this work provides a unique platform for innovating the bioinspired constructive adaptation of engineering materials in response to the typically destructive aquatic environment. 216 Figure 78. The overall mechanism of constructive adaptation in the aquatic environment (A) Schematic illustration of water-swelling induced stiffness decrease of a conventional bulk polymer network and the corresponding stiffness change ratio of a conventional polyurethane polymer after being immersed in the water for 24 h. The stiffness change ratio is calculated as (𝐸 Y −𝐸 " ) 𝐸 " ⁄ , where 𝐸 " is Young’s modulus of the initial sample and 𝐸 Y is Young’s modulus of the sample after water-immersion. (B) Schematic illustration of water-induced bonding decrease of a fractured conventional polymer network and the corresponding bonding change ratio of a fractured conventional polyurethane polymer after being immersed in the water for 24 h. The bonding change ratio is calculated as (𝐵 Y −𝐵 " ) 𝐵 " ⁄ , where 𝐵 " is the bonding force of a fractured polymer put into contact immediately after damaged and 𝐵 Y is the bonding force of a fractured polymer after water-immersion. (C) Schematic illustration of water- induced stiffness increase of the proposed polymer network and the corresponding stiffness change ratio after being immersed in the water for 24 h (data from Fig. 79F). (D) Schematic illustration of water- induced bonding increase of a fractured proposed polymer and the corresponding bonding change ratio after being treated with water (data from Fig. 80G). (E) Water-induced strengthening of a 3D-printed Octet lattice structure (0.11 g) that is loaded with a 100-g metal ball, and the corresponding compressive stress-strain curves of the structure before and after being immersed in the water for 24 h. (F) Water- induced crack healing of a 3D-printed pipe fitting (details in Fig. S82). 0.0 0.2 0.4 0 2 4 6 8 10 Stress (kPa) Strain (mm/mm) Before After 100 g 100 g 4 mm Loaded lattice: buckled Water -NCO -NCO -NCO -NCO -NCO -NCO -1 0 2 4 6 8 Stiffness change ratio -1 0 2 4 6 8 Stiffness change ratio Stiffness decreasing: swelling A Stiffness increasing: additional crosslinks C Conventional polymer network Proposed polymer network B Bonding increasing: interfacial bonds D Fractured conventional polymer network Fractured proposed polymer network -1 0 2 4 6 8 Bonding change ratio -1 0 2 4 6 8 10 Bonding change ratio Water Bonding decreasing: lubrication Fractured interface Water Water Water -NCO O N H N H Urea bond ≡ NCO Isocyanate group ≡ -NCO E F 3D-printed pipe fitting: cracked & leaking Water Water flow in 3D-printed pipe fitting: healed Water flow in 5 mm 5 mm Water flow out Water level Water leaking Crack healed Stiff Soft Water-induced strengthening Water-induced healing Loaded lattice: unbuckled 217 10.3 Materials and methods 10.3.1 Materials Poly(tetrahydrofuran) (Poly THF, average molar mass 650 g/mol), isophorone diisocyanate (IPDI), dimethylacetamide (DMAc), dibutyltin dilaurate (DBTDL), 2-Hydroxyethyl methacrylate (HEMA), phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide (PTPO), and Sudan I were purchased from Sigma- Aldrich. 10.3.2 Synthesis of polymers The new polymer was synthesized as follows: 0.05 mol of Poly THF was preheated to evaporate moisture and oxygen for 1 h at 100°C and stirred with a magnetic stir bar. 0.1 mol of IPDI, 10 wt% of DMAc, and 1 wt% of DBTDL were added in the preheated Poly THF at 70°C, and the mixture was stirred for 1 h. After the temperature decreased to 40°C, 0.05 mol of HEMA was added, and the mixture was stirred for another 1 h to complete the synthesis. The entire synthesis process was conducted in a nitrogen environment. The conventional polyurethane polymer was prepared following similar steps as the new polymer, except that a total of 0.1 mol HEMA was added in the last step. To prepare the 3D-printing polymer ink, 1 wt% of photoinitiator PTPO and various weight percentages of Sudan I (0%-0.02%) were mixed with the polymer liquids and stored in a dark amber bottle until use. 10.3.3 3D printing process The stereolithography (SLA) 3D printing process implemented in this paper was similar to our previous work 404,405 (Fig. S78). The basic idea was to polymerize the synthesized resin layer by layer with prescribed thickness under a light source to form a 3D structure. To prepare the image layers of the 3D structure, a computer-aided design (CAD) model was first converted to an STL file and then sliced into an image sequence. A bottom-up SLA 3D printer was used to print the structure. The setup of the bottom-up SLA 3D printer included a white-light projector at the bottom, an acrylic-made top-open resin box right above the projector, and a motor-controlled printing stage above the resin box. The resin box was firstly 218 pre-filled with the prepared polymer resin. The printing stage was moved down into the polymer resin, leaving a prescribed distance between the stage and the bottom of the resin box. The image of the first layer in the image sequence was then projected from the projector to the bottom of the resin box to polymerize the resin for a prescribed time. After the first layer was formed on the printing stage, the stage was lifted to a distance of the thickness of the next layer. In the meantime, the polymer resin refluxes to fill the space caused by stage lifting. The image of the second layer was then projected to the bottom of the resin box to polymerize the second layer. The second layer then bonds covalently with the first layer after polymerization. A 3D structure was finally formed by repeating the above-mentioned process. A Teflon membrane with low surface tension (~20 mN/m) was used to reduce the separation force between the polymerized part and the bottom of the resin box. 10.3.4 Characterization of water-induced strengthening A rectangular sample (width 10 mm, length 40 mm, and thickness 1 mm) was 3D-printed with the new polymer resin. The as-printed sample was immersed in the DI water for 24 h and then set in the air for 2 days. The optical transmittances of the sample at different stages were tested with a UV-vis spectrometer (Cary 60 UV-Vis spectrometer, Agilent) within the range of 380 nm to 720 nm. The FT-IR analyses of the sample at different stages were carried out with a Spectrum TWO FT-IR Spectrometer (PerkinElmer) with a scanning range of 450 to 4000 cm -1 and a resolution of 0.5 cm -1 . The uniaxially tensile stress-strain behavior of the sample was tested with a mechanical tester (model 5942, Instron) with a strain rate of 0.05 s -1 . The fracture toughness of the sample was measured by using the pure-shear fracture test 405 . Testing dimensions for the unnotched sample were 30 mm in length (𝑎 ' ), 5 mm in width (𝐿 ' ) and 1mm in thickness (𝑏 ' ) (Fig. S84A). For the notched samples, a notch of 15 mm was cut with a razor blade from the edge before testing. The load was applied from the two ends of the clamps to uniaxially stretch the samples at a strain rate of 0.05 𝑠 @2 . A high-speed camera was used to record the critical distance (𝐿 9 ) on the notched samples when the crack started to propagate. Fracture toughness energy was calculated as 219 𝑈(𝐿 9 ) (𝑎 ' 𝑏 ' ) ⁄ , where 𝑈(𝐿 9 ) was defined as the area under stress-strain curves in the un-notched test before the corresponding critical distance in the notched test (Figs. S84B-E) 405 . To understand the diffusion-limited strengthening behavior, we molded cylindrical polymer samples in a plastic tube with a diameter of 5 mm and length of 20 mm. The samples were then immersed in the water and taken out for study after different periods of time. Only the central part of the sample was used for the study to eliminate the boundary effect. The cross-sections of the samples were imaged using a Canon camera (EOS 70D). The Young’s moduli of the treated samples along the longitudinal direction with various water-immersion periods were measured with the Instron mechanical tester with a strain rate of 0.05 s -1 . 10.3.5 Localized water-induced strengthening Rectangular sample plates (35 mm x 35 mm x 1 mm) were first 3D-printed with the new polymer resin. Thin acrylic covers (thickness of 1 mm and height of 3 mm) with desired hollow patterns (i.e., wavy- pattern and circular-pattern) were cut with a laser cutter (Pro-Tech 60W CO ( laser cutter) and placed on the top of the plate samples. Another cover made with EcoFlex 00-30 (Smooth-on) was then placed outside of the acrylic covers to prevent water leakage between acrylic and polymer plate (Fig. S85A). Water was then filled into the acrylic covers to allow water to penetrate the polymer plate from the top surface for 24 h, followed by resting in the air for 2 days (Fig. S85B). The stiffness map of the processed samples was measured using indentation tests with the Instron mechanical tester (Fig. S85C). A compressive force F is applied on the sample by a flat-end indenter with the radius of R=1 mm with a strain rate of 0.05 s -1 . A depth 𝛿 is applied by the cylinder indenter on the sample (Fig. S85C). The Young’s modulus is calculated as 𝐸 =𝐹(1−𝜈 ( )/(2𝑅𝛿)), where υ is the Poisson’s ratio of the sample. 10.3.6 Characterization of water-induced healing and bonding For the water-induced healing experiment, a rectangular sample (20 mm x 3 mm x 2 mm) was first 3D- printed with the new polymer resin. The sample was then cut in half with a razor blade, put into contact, and immersed in different-temperature water for different periods of time. For the control experiment, the 220 fractured sample after being put into contact was stored at room temperature without water for different periods of time. Microscopic pictures were taken with an optical microscope (Nikon Eclipse LV100ND) around the fractured interface at the fractured and healed states at a scale of 500 µm. Samples healed with various healing periods are uniaxially stretched until rupture at a strain rate of 0.05 s -1 . The healing percentage was defined as the tensile strength of the healed sample normalized by that of the virgin sample processed with water-immersion for the same periods of time. To enable sample healing at 0°C, fractured samples were put in an ice bath sealed within a petri dish containing ice-water mixture as shown in the inset schematic in Fig. 80D. For the water-induced interfacial bonding experiment, two rectangular samples (40 mm x 10 mm x 1 mm) were first 3D-printed with the new polymer resin. The samples were then stacked together with only half of the area being in contact (20 mm x 10 mm) with and without water spraying in between the contacting area. After stacking for 2 days, the interfacial bonding of the samples was measured by using the 180° peeling test as shown in the inset schematic in Fig. 80H at a strain rate of 0.05 s -1 . 10.3.7 Constructive training of robotic arms Pneumatic robotic arms were 3D-printed with the new polymer resin and actuated using a syringe by changing the pressure of the internal air channel. The first robotic arm was first actuated to successfully lift a weight of 30 g, and then actuated in the air for 20 times, followed by resting in the air for 24 h. The trained robotic arm was actuated again but failed in lifting the 30 g weight. The second robotic arm was first actuated but failed in lifting a weight of 55 g. Then, it was actuated in the water for 20 times, followed by resting in water for 24 h. The trained robotic arm was actuated again to successfully lift the 55 g weight. The lifting distance of the weight was measured by the images taken with the Canon camera. 10.3.8 Strengthening and healing of robotic fish fins The fish caudal fins were 3D-printed with the new polymer resin and installed on a commercial radio remote control robotic fish (CREATE TOYS, Amazon) (Fig. S86). After the virgin robotic fish swam in 221 the water bath (within 10 s), the fish continuously swims in the water for another 8 h, followed by resting in the air overnight. Besides, another as-printed fin was imposed by a cut with a razor blade, followed by contacting the cutting surface and immersing in water for 8 h (with resting in the air overnight) for healing the crack. During the healing process, gentle support was provided to the fin to ensure the fractured surfaces are well aligned. The moving distance and velocity of the robotic fish at various states were captured by the Canon camera. 10.3.9 Healable packaging polymer for flexible circuits The flexible circuits were fabricated with a thin polyimide substrate (thickness of 800 μm) upon which silver ink circuits were drawn using a silver ink pen (Circuit Scribe, Amazon) (Fig. S87). The silver ink has a resistance of around 1 ohm per cm. The current on the circuit was powered and measured by a source meter (2400 SourceMeter, KEITHLEY) (Fig. S87A). In the experimental case, when there was water contamination on the circuit surface, we spread a thin layer of the new polymer ink on the surface, followed by the illumination of white light for 10 min. In the control case, the new polymer ink was replaced by a photocurable polyurethane ink 406 . Next, a crack was installed on the packaged layer with a razor blade for both the experimental and control cases. A water droplet was dripped on the crack area and the current change during the healing process was continuously monitored by the source meter. Three-points bending tests were conducted using the Instron mechanical tester with a strain rate of 0.05 s - 1 . 10.4 Results 10.4.1 The overall mechanism of constructive adaptation in the aquatic environment We have designed a class of 3D-printable polymers that incorporate active chemical groups to constructively strengthen the material matrix and interface in the aquatic environment (Figs. 78CD). To synthesize the polymer, we molecularly design a polymer resin that features both acrylate and isocyanate distal groups (NCO) (Fig. S77). The acrylate groups can facilitate the photoradical-initiated addition 222 reaction for diverse photopolymerization-based 3D-printing processes (such as stereolithography, Fig. S78) 141,404,406 . After photopolymerization, the NCO groups become tails on side chains within the polymer matrix (Fig. S79). One water molecule can bridge two side chains by reacting with two NCO groups to form urethane bonds (Fig. S80) 407-409 . Within the polymer matrix, such a chemical bridging mechanism enables the formation of new crosslinks, additional to the crosslinking during the photopolymerization process (Fig. 78C). The additional crosslinks within the matrix can constructively enhance the material stiffness and strength 327,359,394,395 , which thus offset the stiffness reduction effect due to the water-induced polymer swelling. Around the polymer interface, the chemical bridging can also constitute relatively strong interfacial bonding, thus healing the interfacial cracks (Fig. 78D). As a quick demonstration of the concept, we 3D-print a lattice structure that drastically increases the weight- sustaining capability after being immersed in the water for 24 h (Figs. 78E and S81). The strengthened lattice structure is able to sustain a weight of 100 g that is around 900 times its own weight without buckling beams, while the unstrengthened lattice buckled. As another example, a broken 3D-printed pipe fitting can heal the crack and resume water flow after being immersed in the water for 24 h (Figs. 78F and S82). 10.4.2 Water-induced bulk strengthening To systematically characterize the water-induced bulk strengthening, we first investigate different stages of the strengthening process with a sample strip (Fig. 79A). When the sample is as-fabricated (the virgin state, thickness ~1 mm), the sample is nearly transparent with an optical transmittance of around 85 % within 450-720 nm (Figs. 79AB). Once being immersed in the water for 24 h, the sample’s color gradually turns opaque and milky with an optical transmittance of nearly 0% within the whole visible light range (400-720 nm). Such color change is primarily due to the water diffusion into the polymer matrix and its reaction with the NCO groups. After being taken out of the water, the sample is resting in the air for 2 days to allow full reaction between the diffused water molecules and the NCO groups within the matrix, and then the sample color becomes semi-transparent with an optical transmittance of around 223 50% within 450-720 nm. To examine the concentration evolution of the NCO groups in the polymer matrix, we employ Fourier transform infrared (FTIR) spectrometer to measure the transmittance of the sample around 2,270 𝑐𝑚 @2 that is corresponding to the NCO bond stretching vibration 359,405 . A distinct peak centered at 2,270 𝑐𝑚 @2 is observed in the virgin state (Figs. 79C and S83). After the water immersion for 24 h, the peak dramatically drops, indicating that most of the NCO groups have been consumed by water molecules. After full reaction in the air for 2 days, the FTIR peak disappears, revealing that all the NCO groups are fully reacted in the material matrix. We further investigate the mechanical properties of the sample in the virgin and fully-reacted state. When loaded with a weight of 100 g, the virgin sample is stretched 40% more compared to the fully-reacted sample (i.e., strengthened sample), indicating higher stiffness of the fully-reacted sample (Fig. 79D). Under uniaxial tensile tests, the fully-reacted sample exhibits higher Young’s modulus and tensile strength than those of the virgin sample by factors of 746% and 784%, respectively (Figs. 79E and F). We also employ pure-shear fracture tests to measure the fracture toughnesses (Fig. S84) and find that the fracture toughness of the fully- reacted sample is 7.9 times that of the virgin sample (Fig. 79F). Our results imply that the water-induced formation of additional crosslinks not only stiffens the polymer network, but also enhances the material capability in resisting crack propagation. We hypothesize that the water-NCO reaction within the material bulk is facilitated by the water diffusion through the polymer matrix. To test this hypothesis, we image the cross-section of cylindrical samples (the length of 20 mm much larger than the diameter of 5 mm) after being immersed in the water for various periods of time. From the cross-section images, the water molecules gradually migrate toward the center of the sample as the immersion time increases (Fig. 79G). After various water-immersion periods, we take out the samples, allow the full reaction in the air for 2 days, and then measure the stiffness of the cylindrical samples along the longitudinal direction. We find that the stiffnesses of the cylindrical samples increase with increasing immersion periods until reaching a plateau after 24 h (Fig. 79H). The results in Figs. 79GH not only verify that the water-induced material strengthening is facilitated and limited by water diffusion, but also confirm that the water molecules can thoroughly react 224 with the sample strip (thickness ~1 mm) in Figs. 79A-F. The mechanism of diffusion-limited material strengthening allows us to harness confined water to enable local strengthening (Figs. 79IJ and S85). With patterned water supplies on a plate sample, only the locations in direct contact with water for 24 h turn milky (Figs. 79IJ). After full reaction in the air for 2 days, indentation tests reveal that the stiffnesses of the reacted regions are around 7 times those of the non-reacted regions (Figs. 79IJ). Figure 79. Water-induced bulk strengthening. (A) Image sequence of a strip sample at the virgin, strengthening, 24 h in water, and fully-reacted states. (B) Optical transmittance spectra of the strip sample at different states. (C) FTIR spectra within the range of 2200 𝑐𝑚 @2 to 2375 𝑐𝑚 @2 of the sample at different states. (D) A strip sample at the virgin and fully- reacted states loaded with a weight of 100 g. The zoom-in images show the length difference of the 2.5 2 1.5 1 0.5 0 Stiffness (MPa) Wavy pattern 2 mm Virgin 24 h in water 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.0 0.2 0.4 0.6 0.8 1.0 Stress (MPa) Strain (mm/mm) Virgin Fully reacted 0.0 0.5 1.0 1.5 2.0 2.5 Young's modulus (MPa) 0.0 0.2 0.4 0.6 0.8 1.0 Tensile strength (MPa) 0.0 0.5 1.0 1.5 Fracture toughness (J/m 2 ) Virgin Fully reacted A B C E F Virgin Fully-reacted 5 mm D 5 mm Virgin Strengthening 2 days in air: Fully-reacted 5 mm 5 mm 1 cm Water 5 mm 24 h in water H G 400 500 600 700 0 20 40 60 80 100 Optical Transmittance (%) Wavelength (nm) 2200 2250 2300 2350 FTIR transmittance (a.u.) Wavelength (cm -1 ) Virgin Fully reacted 24 h in water Virgin Fully reacted 24 h in water 100 g 100 g 0 h 3 h 6 h 12 h 30 h 1 mm 2.5 2 1.5 1 0.5 0 Stiffness (MPa) Circular pattern 2 mm Virgin 24 h in water J I 0 6 12 18 24 30 0.0 0.5 1.0 1.5 2.0 2.5 Young's modulus (MPa) Water immersion time (h) Sample Water Water diffusion direction 225 sample at two states. (E) Uniaxial tensile stress-strain curves of the sample at virgin and fully-reacted states. (F) Young’s moduli, tensile strengths, and fracture toughnesses of the sample at virgin and fully- reacted states. (G) Cross-section images of a cylindrical sample immersed in water for various periods of time. (H) The longitudinal Young’s modulus of the cylindrical sample as a function of the water- immersion time. The inset illustrates the water diffusion direction. (IJ) Water-induced local strengthening of a plate sample with wavy and circular patterns of water supplies, and the corresponding stiffness mapping of the strengthened samples. Error bars in (F) and (H) represent standard deviations over 3-5 samples. 10.4.3 Water-induced interfacial healing and bonding The water-NCO reaction around two interfaces can facilitate the interfacial healing of a fractured polymer (Fig. 78D). To demonstrate this concept, we cut a sample strip into two parts and then bring back into contact, followed by immersing the sample in the water (Fig. 80A). After water immersion for 8 h, the fractured interface can be nicely healed, verified by the smooth interface shown in the microscopic images (Figs. 80AB). To quantify the healing performance, we uniaxially stretch the healed sample with various water-immersion periods until rupture, and then calculate the healing percentage by normalizing the healed tensile strength over the tensile strength of the unfractured sample immersed in water for the same period. We find that the healing percentage increases with increasing the water-immersion time until reaching a plateau of around 85% after 8 h (Fig. 80C, black data points). As control experiments, we cut samples into two parts and then bring them back into contact, followed by resting in the air for various periods of time. The control experiments reveal that the interfacial bonding remains below 20% of the virgin tensile strength, without increasing over 25 h (Fig. 80C, gray data points). It is noted that the bonding at the water immersion time of 0 h shown in Fig. 80C represents the material adhesion of the fractured surface. In addition, we find that the water-induced interfacial healing performance is not drastically compromised by lowering the temperature to 0℃. The healing percentage for the water- immersion of 4 h at 25℃ is around 75%, while it only slightly reduces to 65% when the water temperature changes to 0℃ (Fig. 80D). It may be because the reaction rate between water molecules and NCO groups is only slightly compromised when the temperature reduces from 25℃ to 0℃ 407-409 . Not only assisting healing of cracked interfaces, the water-NCO reaction can also assist the interfacial bonding of two bulk polymers. To evaluate the water-induced interfacial bonding, we spray water on the 226 interfaces of two rectangular samples, stack two samples together for 2 days, and then conduct a 180° peeling test to measure the interfacial toughness (Fig. 80E). We find that the water-treated samples can establish a strong bonding with a sticky interface during the peeling test, indicating new bonding formed between two materials (Fig. 80E). In contrast, the samples that stack together without spraying water on the contacting interface exhibit a clean interface during the peeling test (Fig. 80F). Such a sharp difference in the peeling interface is because that the former strong bonding is primarily attributed to water-induced newly formed chemical bridging on the interface, while the latter weak bonding is merely due to the polymer adhesion. Quantitatively, the interfacial toughness of the bonded samples with the water-spraying is around 400 J m @( that is 10 times that without the water-spraying (Fig. 80G). Interestingly, the water-induced bonding between two bulk samples shows the capability of hanging a weight that is more than 200 times the samples’ own weight (Fig. 80H). Figure 80. Water-induced interfacial healing and bonding. 0 2 4 6 8 10 1 10 100 1000 Interfacial toughness (J/m 2 ) Displacement (mm) With water: Interfacial toughness ~ 400 𝐽/𝑚 % Without water: Interfacial toughness ~ 40 𝐽/𝑚 % G Force Stiff tape -NCO 0 15 30 45 60 0 20 40 60 80 100 Healing percentage (%) Temperature (°C) Experiment Control Ice bath Sample 0℃ water Fractured Healed Virgin 2 mm Fractured B 500 um 500 um A 0 5 10 15 20 25 0 20 40 60 80 100 Healing percentage (%) Healing time (h) C D Without water on the interface Clean interface Healed With water on the interface E F Sticky interface Strong bonding: interfacial bonds Weak bonding: adhesion 2 mm 2 mm 100g Sample self-weight ~0.5g H 5 mm 227 (A) A strip sample at the the virgin, fractured, and healed states. The sample is cut into two parts with a blade, brought into contact, and then immersed in the water for 8 h to heal. (B) Microscope images of the crack interface at fractured and healed states. (C) Healing percentages of the experimental (with water) and control (without water) groups for various healing time. The healing percentage is defined as the tensile strength of the healed sample normalized by that of the virgin sample with the same water- immersion time. (D) The healing percentage of the samples healed at different water temperatures. The inset schematic shows the experimental setup of the sample healing at an ice-water bath of 0°𝐶. (E) 180° peeling test of two sample plates stacked with water spray in between for 2 days. The inset illustrates the sticky interface during the peeling test. (F) 180° peeling test of two sample plates stacked without water spray for 2 days. The inset illustrates the clean interface during the peeling test. (H) The interfacial toughness of the experimental and control samples during the 180° peeling test. The interfacial toughness is calculated as 2𝐹 𝑤 ⁄ , where 𝐹 is the loading and w is the width of the tested samples. (G) Two sample plates (0.5 g) stacked with a strong water-induced bonding loaded by a weight of 100 g. 10.4.4 Constructive training of robotic arms in the aquatic environment Next, we show that the constructive adaptation of the new polymer in the aquatic environment can nicely mimic the constructive training of the human muscle (Fig. 81). Human muscle after training may experience fatigue by partially damaging the muscle microstructures, leading to a capability compromise in exerting the maximum force. The fatigued muscle can be restored and strengthened by resting to reconstruct and remodel its microstructures, thus being stronger to exert a larger force 327,392-395 (Fig. 81A). Here, we try to mimic the constructive training of the human muscle with a 3D-printed robotic arm (Fig. 81B). The 3D-printed robotic arm can be pneumatically actuated to reversibly bend by 130° (Fig. 81C). Since the bending angle is larger than 90°, we expect the actuated robotic arm to imitate the real arm to lift weights. In the first example shown in Fig. 81D, the as-printed robotic arm can successfully lift a weight of 30 g in its first pneumatic actuation; however, after 20 cycles of actuation in the air (4 s per cycle) followed by resting in the air for 24 h, the robotic arm fails in lifting the same weight of 30 g (Figs. 81DE). The performance degradation after training in the air is because that the continuous actuation of the robotic arm causes the fatigue and stress-softening of the polymer by damaging the polymer network microstructure during the actuation 410 . In the second example shown in Fig. 81F, the as-printed robotic arm fails in lifting a weight of 55 g that is over the arm’s initial carrying capability. After being trained for 20 cycles in the water (4 s per cycle) followed by resting in the water for 24 h, the trained robotic arm can successfully lift the weight of 55 g (Figs. 81FG). The performance improvement after training in the 228 water reveals that the water-induced material strengthening can constructively overcome the cyclic-load- induced material fatigue. Figure 81. Constructive training of robotic arms in the aquatic environment (A) Schematics of arm training, fatigue, and reconstruction process (B) Cross-section view of the computer-aided design model and the 3D-printed pneumatic robotic arm. (C) Reversible actuation of the 3D-printed robot arm. (D) Image sequence to show the actuation of the as-printed robotic arm for lifting a 30 g weight before and after the training in the air for 20 cycles (followed by resting in the air for 24 h). (E) Displacement and time history of the weight in (D). (F) Image sequence to show the actuation of the as-printed robotic arm for lifting a 55 g weight before and after the training in the water for 20 cycles (followed by resting in water for 24 h). (G) Displacement and time history of the weight in (F). A Muscle fatigue Weaker Intense exercise Strong Muscle reconstructed after resting 3D-printed sample 5 mm Air channel Cross-section view Training Actuated Initial 1 cm Lifting As-printed robotic arm: succeed in lifting 30 g before training Remodeled robotic arm: succeed in lifting 55 g after training As-printed robotic arm: fail in lifting 55 g before training 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.5 1.0 1.5 2.0 Dx (cm) Time (s) Before training After training Fail in lifting 0 1 2 3 0 2 4 6 8 Dx (cm) Time (s) Before training After training Fail in lifting B C D E G Lifting Lifting ∆x Lifting Lifting Lifting As-printed robotic arm: fail in lifting 30 g after training Lifting Lifting Lifting Lifting Lifting Lifting Training 20 cycles in air F Training 20 cycles in water 130° 229 10.4.5 Strengthening and healing of robotic fish fin in the aquatic environment The constructive adaptation in the aquatic environment can also facilitate the performance enhancement and recovery of a robotic fish with a flexible fin made from the new polymer (Fig. 82). Although the recent developments of swimming soft robots have highlighted their great potential in underwater operation and ocean exploration 411-416 , their performance may still be threatened by the material degradation and damage of the employed soft polymers in the aquatic environment 29 . In sharp contrast to the typically employed soft polymers, the newly proposed polymer here can constitute soft robotic systems that self-strengthen operation performance and self-heal cracks in the aquatic environment. Following the shape of the caudal fin of a commercial remotely-controlled robotic fish, we employ the new polymer to 3D-print a caudal fin and then install it on the commercial robotic fish (Figs. S86 and 82A). The robotic fish with the as-printed caudal fin can swim with a steady speed of 4.7 cm/s in the first practice (Figs. 82AD). After the robotic fish swims in the water bath for 8 h followed by resting in the air overnight, the robotic fish can swim with a steady speed of 6.6 cm/s, which increases by a factor of 140% compared to its virgin state (Figs. 82BD). Note that the tail oscillating frequencies of two swimming operations are the same (i.e., 6 Hz). The speed enhancement is because of the water-induced strengthening of the fin that provides the higher propulsive force with the same tail oscillating frequency. Next, we intentionally make fatal damage to the polymer fin by cutting a large crack in the middle (Fig. 82C(i)). The damaged robot loses the capability of swimming in the water. After we bring the crack interfaces into contact and immerse the sample in the water for 8 h (with resting in the air for overnight), the cracked interfaces can be nicely healed (Fig. 82C(ii)). The robotic fish then resumes the capability of swimming in the water with a steady speed of around 6 cm/s (Figs. 82CE), which is higher than the virgin speed (4.7 cm/s) and close to the strengthen speed (6.6 cm/s). 230 Figure 82. Strengthening and healing of robotic fish fins (A) (i) A 3D-printed fish fin at the virgin state installed on a robotic fish. (ii) Zoom-in view of the fish fin at the virgin state. (iii) Image sequence of the robotic fish with the virgin-state fin swimming in water. (B) (i) A 3D-printed fish fin at the strengthened state on a robotic fish. (ii) Zoom-in view of the fish fin at the strengthened state. (iii) Image sequence of the robotic fish with the strengthened-state fin swimming in water. (C) (i) A damaged fish fin installed on a robotic fish. (ii) Zoom-in view of the fish fin after being healed in water for 8 h. (iii) Image sequence of the robotic fish with the healed fin swimming in water. (D) Moving distances as functions of the swimming time for the virgin and strengthened states, and the corresponding steady velocities. (E) Moving distances as functions of the swimming time for the virgin and healed states, and the corresponding steady velocities. 10.4.6 Healable packaging polymers for flexible electronics One of the big challenges for flexible electronics is electronic leakage during the operation in the wet environment 417,418 . We here present a class of novel packaging polymers that can help avoid water- induced electronic leakage of flexible electronics through reaction and healing processes. We first employ a silver ink pen to write a conductive circuit on a flexible polyimide substrate (Figs. 83A(i) and S87A), 0 1 2 3 4 0 5 10 15 20 25 Dx (cm) Time (s) Strengthened Virgin D E 0 1 2 3 4 0 5 10 15 20 25 Dx (cm) Time (s) Healed Virgin Virgin Strengthened Damaged & healed A Fin healed via water B C Slowly moving forward t=0 s t=1 s t=2 s t=3 s t=4 s t=0 s t=2 s t=3 s t=4 s t=0 s t=1 s t=2 s t=3 s t=4 s Resume fast moving forward Fast moving forward t=1 s 0 2 4 6 8 Steady velocity (cm/s) 0 2 4 6 8 Steady velocity (cm/s) Virgin Strengthened Virgin Healed 1 cm 1 cm 1 cm 1 cm 1 cm 1 cm i ii iii i ii iii i ii iii Fractured 231 and then use a source meter to monitor the current passing one conductive route (Fig. S87B). When a water droplet (non-deionized) is contaminating the circuit, the current in the main conductive route drastically drops because of the leakage to other routes (Figs. 83A(ii) and B). We then apply a thin layer of the new polymer ink (viscous liquid) on the contaminated circuit and employ a visible light to solidify the polymer ink to package the circuit (Fig. 83A(iii)). During the packaging process, the water droplet is gradually absorbed by the packaging polymer through the water-NCO reaction, and the current through the initial conductive route gradually increases and resumes to the initial current level (Figs. 83A(iv) and 83B). As a control, we packaged the contaminated circuit using a photocurable polyurethane polymer; however, the measured current remains low over the 1-h packaging process as the electronic leakage is not stopped (Fig. 83B). In contrast to the control case, the new polymer features free NCO groups that can continuously absorb and react with water molecules and thus eliminate electronic leakage. In addition, the proposed packaging polymer can also turn the destructive water contamination into a constructive factor to heal cracks. If the packaging polymer is cracked (Fig. 83C(i)), the external water molecules may enter the cracking region to induce electronic leakage with a sharp current drop (Figs. 83C(ii) and D). However, the water molecules in the crack region will be gradually consumed by the packaging polymer to form interfacial chemical bridging to heal the crack (Fig. 83C(iii)), along with the recovery of the current leakage of the circuit (Fig. 83D). The healed packaging material can sustain a flexural bending deformation, without cracking the healed region (Fig. 83C(iv) and E). Compared to the virgin sample, the healed sample exhibits a larger bending stiffness (Fig. 83E and S87C), because the water molecules around the crack interface not only heal the crack but also strengthen the material by forming additional crosslinks. Note that the control case with traditional polyurethane polymer as the packaging layer does not show a quick current resume because the control packaging polymer cannot harness the water to heal the crack (Fig. 83D). 232 Figure 83. Healable packaging polymers for flexible electronics (A) Schematics and sample images to show: (i) a flexible circuit and the corresponding conductive route, (ii) the flexible circuit contaminated by a water drop and the current being leaked from the initial conductive route, (iii) the contaminated flexible circuit being packaged with the new polymer ink, and (iv) the flexible circuit packaged with the new polymer after absorbing the water contaminant. (B) Measured current of the initial conductive route in the flexible circuit packed with the new polymer (experiment) and photocurable polyurethane (control). (C) schematics and sample images to show: (i) a crack in the packaging polymer above flexible circuit, (ii) the crack contaminated by a water drop, (iii) the crack being healed by the water drop, and (iv) the fully healed packaging polymer. (D) Measured current of the initial conductive route in the flexible circuit packed with the new polymer (experiment) and photocurable polyurethane (control). (E) Load-displacement curves of the original, damaged, and healed packaged flexible circuit under three-point-bending tests. 0 20 40 60 0.6 0.7 0.8 0.9 1.0 Current (mA) Time (min) Experiment Control Current resumed by healing crack (i) (ii) (iii) (iv) 0 3 6 9 0.0 0.2 0.4 0.6 Load (N) Displacement (mm) Original Damaged Healed Load 0 20 40 60 80 0.0 0.2 0.4 0.6 0.8 1.0 Current (mA) Time (min) Experiment Control Current resumed by packaging (i) (ii) (iii) (iv) A Conductive silver ink (i) (ii) (iii) (iv) Contaminated Initial Packaging Packaged Water drop -NCO Isocyanate distal groups NCO N R' H Urea network R N N R' H H O Backbone chain CH 2 CH O O R' " ` -NCO (i) (ii) (iii) (iv) C Contaminated Damaged Healing Healed Water between substrate & polymer Polyimide substrate Water drop Water absorption Polyimide substrate Polyimide substrate Current leaking Current leaking Initial current path Polyimide substrate Crack Polyimide substrate B Water drop Planar view (Top) Planar view (Top) Cross-section view Cross-section view Planar view (Cross-section) Planar view (Cross-section) D E 1 cm 1 cm 233 10.5 Conclusive remarks In summary, we report a class of 3D-printable polymers that can strengthen the material matrix and heal cracks in response to the typically destructive aquatic environment. Such a constructive adaptation capability has been widely observed in the biological systems 327,359,392-395,398 , while rarely in traditional engineering materials that typically respond destructively to destructive environmental stressors. The key mechanism of the presented paradigm relies on chemical groups that react with the environmental stressors to form constructive crosslinks, thus reversing the negative impact of the environmental stressors. This paradigm echoes the recent advance in polymer mechanochemistry where mechanophores are employed to respond to the destructive force stressors and form constructive crosslinks 327,394,395 or lengthen polymer strands 396 . The difference of the proposed paradigm is that the employed active groups directly interact with the imposed environmental stressors, without going through the mechanochemical transductions of the mechanophores 327,394-396 ; therefore, the proposed paradigm may drastically expand the existing scope that is limited to force stressors, but potentially be able to extend to other destructive environmental stressors, such as sunlight 359 , greenhouse gases, high temperature, or even radiation. Besides, we present a new class of 3D-printable photopolymers that can constructively adapt to environmental stressors. Given that the presented photopolymers may be used in various photopolymerization based 3D-printing technologies, such as stereolithography 141,321 , polyjet 335 , photopolymer waveguides 142 , two-photon lithography 144,161 , continuous liquid production 148 , and volumetric lithography 342,343 , integrating features of constructive adaptation and complex structures may enable promising applications in artificial muscles, soft robotics, and flexible electronics, where constructive responses to environmental stressors are highly desirable. 234 Chapter 11: Conclusions and Outlook This dissertation has focused on understanding and developing bioinspired self-healing materials and novel engineered living materials from three major aspects: (1) Establishing theoretical models to understand the fundamental mechanics and physics of novel bio-inspired materials. (2) Developing multi- functional materials and structures by exploiting the theoretical understanding. (3) Exploring new engineering applications with developed new materials. The significant findings and outlooks in this dissertation are as follows: 1. Chapter 2 presents a theoretical framework that can analytically model the constitutive behaviors and interfacial self-healing behaviors of dynamic polymer networks crosslinked by various dynamic bonds, including dynamic covalent bonds, hydrogen bonds, and ionic bonds. The theories can predict the stress-stretch behaviors of original and self-healed dynamic polymer networks, as well as the corresponding healing strength over the healing time. We expect our model to be further extended to explain the self-healing behaviors of dynamic polymer networks with a wide range of dynamic bonds. 2. Chapter 3 proposes a molecularly designed photoelastomer ink that enables stereolithography- based additive manufacturing (AM) of elastomers with rapid and full self-healing. The dual functions of photopolymerization and self-healing are achieved by molecularly balancing the thiol and disulfide groups in the material ink. As a model self-healing photoelastomer, the material system with adequate modifications should be easily translatable to other photopolymerization-based AM systems. The AM of self-healing elastomers with various tailored 3D architectures is expected to open multiple application possibilities, including artificial organs, biomedical implants, bionic sensors, and robotics. The presented strategy may motivate molecular designs of various unprecedented material inks for emerging AM systems to enable rapid prototyping of 3D structures that cannot be fabricated with traditional shaping methods. 235 3. Chapter 4 presents a theoretical framework to understand the light-activated interfacial self- healing of soft polymers with inorganic and organic photophores. The self-healing process is considered as a coupled phenomenon that which polymer chains diffuse across the interface and reform the dynamic bonds assisted by the free radicals. We theoretically relate the light property and the interfacial self-healing strength of the polymers. We apply the theory to two types of soft polymers with inorganic and organic photophores, respectively. The theory can consistently explain the experimentally measured stress-strain behaviors of the original and self-healed samples. To the best of our knowledge, this paper presents the first network-based theory for the light-activated self-healing mechanics. 4. Chapter 5 reports that a tough TiO ( nanocomposite hydrogel can be activated by UV light to demonstrate highly efficient self-healing, heavy-metal adsorption, and dye degradation. Our strategy for the treatment of wastewater harnesses the ultrahigh specific surface area of nanoparticles while demonstrating a novel framework to preclude the negative side effects of the commonly employed nanomaterial-assisted water treatment. Furthermore, the high toughness and crack-healing capability of the hydrogel matrix offer great robustness to the adsorbent materials. We expect this strategy of stimuli-assisted water treatment with resilient hydrogel materials could be extended to various applications beyond wastewater treatment, such as resilient and pollutant- free artificial organs, tissue dressings, contact lenses, and soft-material glues, and hydrogel electronics. 5. Chapter 6 presents a theoretical framework explaining the constitutive and self-healing behaviors of self-healable thermoplastic elastomers with both dynamic bonds and crystalline phases. We consider the virgin thermoplastic elastomer by employing a general spring-dash model that couples the soft rubbery phase and the stiff crystalline phase. During the self-healing process, we use a diffusion-reaction model to model the interfacial healing process. The theoretical framework can explain the stress-strain behaviors of original and self-healed thermoplastic elastomers, as well as the corresponding healing strengths over the healing time. We show that 236 the theoretical framework can nicely explain our own experiments on self-healable thermoplastic elastomers polyurethane with dynamic disulfide bonds and the documented results of thermoplastic materials with disulfide bonds and pi-pi interactions. We expect that our model can be further extended to explain the self-healing behaviors of thermoplastic polymers with a wide range of dynamic bonds. 6. Chapter 7 reports a class of transformable lattice structures enabled by fracture and shape- memory assisted healing that can enable reversible transformations of lattice configurations, shifting properties among states of different stiffnesses, vibration transmittances, and acoustic absorptions. We expect that self-healable lattice structures can promote the future exploration of next-generation healable and reusable, lightweight materials. In addition, the shape-memory- assisted healing of lattice structures revolutionizes the state-of-the-art healing paradigms that primarily rely on manual contacts to align fracture interfaces. This paradigm may greatly facilitate the healing of undetected cracks or cracks deep within a structure without external tethered intervention, thereby potentially enabling broad applications in next-generation aircraft panels, automobile frames, body armor, impact mitigators, vibration-dampers, and acoustic modulators. Furthermore, the existing transformable structures primarily harness the nonfracture geometrical change of smart materials; the structural transformations enabled by the fracture- memory-healing cycles open a unique avenue by adding a fracture-healing tool, probably enabling previously impossible modulation of functionalities. 7. Chapter 8 harnesses photosynthesis in chloroplasts embedded in a synthetic polymer matrix to remodel 3D-printed structures and demonstrate matrix strengthening and crack healing. The current work extends the concept to advanced materials by introducing a downstream reaction mechanism to use the photosynthesis-produced glucose. Besides, the presented photocurable polymers can be used in various photopolymerization-based 3D-printing systems, such as stereolithography, polyjet, photopolymer waveguides, two-photon lithography, and continuous liquid production, and volumetric lithography. The communication between living photosynthesis 237 and synthetic 3D- printable polymers may open doors for hybrid synthetic-living materials with both complex architectures and biomimetic properties. 8. Chapter 9 presents a theoretical framework to study plant-inspired photosynthesis-assisted strengthening behaviors in a synthetic polymer. The theory explains glucose production, exportation, and the corresponding polymer strengthening by forming additional crosslinks. The theory quantitatively explains the experimentally observed photosynthesis-assisted polymer strengthening under different experimental conditions, such as various illumination periods, concentrations of embedded chloroplasts, and light intensities. This theoretical framework paves the way for the future mechanistic understanding of polymer network behaviors with incremental crosslinks, such as sequential crosslinking in double-network polymers/gels. This theoretical framework bridges the communication between the natural photosynthesis process and synthetic polymer networks. The communication between living photosynthesis and synthetic polymers may open doors for hybrid synthetic-living materials with both complex microstructures and biomimetic properties. The theoretical framework proposed in this paper may facilitate the mechanistic understanding of future hybrid synthetic-living materials. 9. Chapter 10 reports a class of 3D-printable polymers that can strengthen the material matrix and heal cracks in response to the typically destructive aquatic environment. The key mechanism of the presented paradigm relies on chemical groups that react with the environmental stressors to form constructive crosslinks, thus reversing the negative impact of the environmental stressors. The proposed paradigm may be able to extend to other destructive environmental stressors, such as sunlight, greenhouse gases, high temperature, or even radiation. Integrating features of constructive adaptation and complex structures may enable promising applications in artificial muscles, soft robotics, and flexible electronics, where constructive responses to environmental stressors are highly desirable. 238 Appendices A. Supplementary Information SI Tables Table S1. Model parameters used in this study. Parameter Definition Value (s -1 ) Forward reaction rate 2x10 -7 (s -1 ) Reverse reaction rate 4x10 -4 (m) The distance along the energy landscape coordinate 1.2x10 -9 b (m) Kuhn segment length 2x10 -10 Minimum chain length 10 Maximum chain length 120 Average chain length 49 Chain length distribution width 0.18 Chain alteration parameter 0.5 (N/m) Rouse friction coefficient 2.4x10 -6 for 60°C (K) Vogel temperature 383.2 B (K) Parameter for the Vogel relationship 486.5 A Parameter for the Vogel relationship -5.96 Table S2. Experimental data for measuring the mass percentage of water within the extracted chloroplast. Sample # The initial mass of extracted chloroplast (g) Mass after 8-h evaporation in a dark environment (g) Mass of water (g) Mass percentage of water (%) 1 0.3092 0.0592 0.25 80.9 2 0.3019 0.0529 0.249 82.5 3 0.3097 0.0567 0.253 81.7 4 0.3042 0.0452 0.259 85.1 5 0.3 0.041 0.259 86.3 6 0.3075 0.0405 0.267 86.8 Mean 83.9 Standard deviation 2.5 0 f i k 0 r i k x D 1 n m n a n d a x ¥ T 239 Table S3. Parameters used for the theoretical calculations. Parameter Physical meaning Figs. S64AB Figs. S64CD 𝑁 9 Initial chain length 400 400 𝑛 9 Initial chain number density (m -3 ) 4.5×10 :i 4.5×10 :i 𝑇 Temperature (K) 300 300 𝑛 < 𝑛 9 ⁄ Normalized additional crosslink density 0 for 0% 0.6 for 1% 1.1 for 3% 2.1 for 5% 0 for 0 h 0.5 for 0.25 h 1 for 0.5 h 1.8 for 1 h 2.3 for 2h 240 SI Figures Figure S1. Chemical Structures of (a) MMDS and (b) V-PDMS. Figure S2. Microscopic image to show the manufacturing resolution. The image is taken using a Nikon microscope (Eclipse LV100ND). 241 Figure S3. Molecular design of the control elastomer. MMDS and V-PDMS directly have a thiol-ene photopolymerization reaction to form an elastomer network without disulfide bonds. Figure S4. Raman spectra of the control elastomer (No IBDA) and the experiment elastomer (IBDA concentration 2.6wt%). The new band ~520 cm -1 is corresponding to the disulfide bond. 242 Figure S5. (a) Nominal stress-strain curves of the self-healed experiment elastomer samples after various healing cycle (each 2 h at 60°C). (b) The experiment elastomer sample at the healing state of cycles 1 ad 10. The sample does not shrink after the 10-cycle healing process. The scale bar represents 5 mm. Figure S6. Nominal stress-strain curves of original experiment elastomer and the elastomer after being immersed in DI water for 24 h. Figure S7. (a) The storage and loss moduli of the experiment elastomer over frequency 0.1-10 Hz in a frequency sweep test. (b) The storage and loss moduli of the experiment elastomer over temperature 25- 165°C in a frequency sweep test with frequency 1 Hz. 243 Figure S8. Nominal stress-strain curves of the experiment elastomer over three sequential tensile loading- unloading cycles with the maximal strain at (a) 0.6 mm/mm and (b) 1.1 mm/mm. Figure S9. Schematics to illustrate an interpenetrating network model. m types of networks interpenetrate in the material bulk space. The ith network is composed of the ith polymer chains with Kuhn segment number ni ( ). Each type of polymer chain self-organizes into eight-chain structures. m i£ £ 1 244 Figure S10. (a) Schematic to show the association-dissociation kinetics of the dynamic bond on the ith chain. We consider the reaction from the associated state to the dissociated state as the forward reaction of the ith chain with reaction rate ( ), and corresponding reaction from the dissociated state to the associated state as the reverse reaction with reaction rate . (bc) Potential energy landscape of the reverse reaction of the dynamic bond on the ith chain with chain force (b) and (c) . “A” stands for the associated state, “D” stands for the dissociated state, and “T” stands for the transition state. Figure S11. A schematic to show the self-healing process. f i k m i£ £ 1 r i k 0 = i f 0 ¹ i f 245 Figure S12. (a, b) Schematics of the eight-chain network model before and after the cutting process. The cutting is assumed to be located in a quarter position of the cube. (c) A schematic to show the diffusion behavior of the ith polymer chain across the interface. Figure S13. (a) Chain length distribution of the self-healing elastomer network. (b) The experimentally measured and theoretically calculated (b) stress-stretch curves of the original and self-healed elastomer samples, (c) healing strength ratios as a function of the healing time for various healing temperatures, and (d) the equilibrium healing time as a function of the healing temperature. The equilibrium healing time is defined as the healing time corresponding to 90% healing strength ratio. 246 Figure S14. Experimental setup for the self-healing 3D soft actuator. Figure S15. Schematics to show the experimental setup of the multimaterial stereolithography system. 247 Figure S16. (a) The fabricated sample of the nacre-like stiff-soft composite. During the AM process, the soft phase undergoes a thiol-ene reaction, the stiff phase acrylate addition reaction, and the soft-stiff interface thiol-acrylate reaction. “hv” represents the light exposure. The scale bar represents 3 mm. (b) The uniaxial nominal stress-strain curves of the original experiment composite (1st load), the self-healed experiment composite (2nd load), pure HDDA, and pure self-healable elastomer. (c) The uniaxial nominal stress-strain curves of the original control composite (1st load) and the self-healed control composite (2nd load). Figure S17. (a) Stress-stress behaviors of the original nanocomposite hydrogel and the nanocomposite hydrogel after the treatment of heavy metal solution for 2 h under UV exposure (light intensity 37 𝑊/𝑚 ( ). (b) Stress-stress behaviors of the nanocomposite hydrogel after heavy metal experiment and the corresponding healed samples for healing time 60 min and 120 min. 248 Figure S18. (a) Storage and loss moduli of an experimental polymer with both crystalline domain and disulfide bonds (PTMEG molar mass 250 g/mol) as functions of temperature. The glass transition temperature T g is estimated as ~71 °C through the decreasing onset of the storage modulus, and as ~65 °C through the peak of the loss modulus. Overall, the glass transition temperature is within 65-71 °C. (b) Storage and loss moduli of an experimental polymer with PTMEG molar mass 1000 g/mol as functions of temperature. The glass transition temperature T g is estimated as ~39 °C through the decreasing onset of the storage modulus. (c) Storage and loss moduli of an experimental polymer with PTMEG molar mass 1810 g/mol as functions of temperature. The glass temperature is not determinable and should be below 25 °C. Figure S19. Differential scanning calorimetry thermographs of experimental polymers with various PTMEG molar masses (with crystalline domains) and the control polymer (without crystalline domains). 249 The curves of heat flow show a narrow peak ranging from 110° to 150°C, corresponding to the dissociation of the crystalline domains. Based on the calculation method from reference 267 , the integration of the endothermic transition ranging from 110° to 150°C gives the enthalpy for melting the crystalline domains per unit mass of the dry sample 𝐻 843}i% . The estimation detail is as follow: 𝐻 (f' =𝑎𝑟𝑒𝑎 𝑓𝑟𝑜𝑚 𝐷𝑆𝐶 𝑊 𝑔 ∗℃∗𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑟𝑎𝑡𝑒 ℃ 𝑠𝑒𝑐 ≈ (140℃−110℃)∗0.41 𝑊 𝑔 2 ∗6 ℃ 𝑠𝑒𝑐 =36.9( 𝐽 𝑔 ) 𝐻 2''' =𝑎𝑟𝑒𝑎 𝑓𝑟𝑜𝑚 𝐷𝑆𝐶 𝑊 𝑔 ∗℃∗𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑟𝑎𝑡𝑒 ℃ 𝑠𝑒𝑐 ≈ (140℃−110℃)∗0.22 𝑊 𝑔 2 ∗6 ℃ 𝑠𝑒𝑐 =19.8( 𝐽 𝑔 ) 𝐻 2K2' =𝑎𝑟𝑒𝑎 𝑓𝑟𝑜𝑚 𝐷𝑆𝐶 𝑊 𝑔 ∗℃∗𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 𝑟𝑎𝑡𝑒 ℃ 𝑠𝑒𝑐 ≈ (140℃−110℃)∗0.105 𝑊 𝑔 2 ∗6 ℃ 𝑠𝑒𝑐 =9.45( 𝐽 𝑔 ) Therefore, the crystallinity of the sample can be calculated as 𝑋 (f' = 𝐻 (f' 𝐻 }.3%{(f' ' ≈ 36.9 74 𝐽 𝑔 ≈49.86% 𝑋 2''' = 𝐻 2''' 𝐻 }.3%{2''' ' ≈ 19.8 57( 𝐽 𝑔 ) =34.7% 𝑋 2K2' = 𝐻 2K2' 𝐻 }.3%{2K2' ' ≈ 9.45 47 𝐽 𝑔 =20.1% The 𝐻 }.3%{(f' ' , 𝐻 }.3%{2''' ' , and 𝐻 }.3%{2K2' ' are the enthalpy of fusion of 100 wt % crystalline PTMEG 250, 1000 and 1810, estimated from references 268,269 . 250 Figure S20. Additive manufacturing of self-healable and shape-memorizable structures (a) A CAD model is first sliced into a sequence of images. These 2D slice images, illuminated with UV/blue light from a light-emitting diode, are sequentially projected onto a transparent window. On the window, the liquid photoresin, capped into a prescribed height by a printing stage, is cured by the light and attached to the printing stage. As the printing stage is lifted off, the fresh resin refluxes beneath the printing stage. By lowering down the stage by a prescribed height and illuminating the resin with a subsequent slice image, a new layer can be printed and bonded onto the former layer. To eliminate the adhesion between the solidified resin and bath, an oxygen-permeable membrane (Teflon fluoropolymer, CSHyde, USA) is attached on the bottom, inducing a thin layer (~5-20µm) of the oxygen-rich dead zone to quench the photopolymerization. After repeating these processes, a 3D-architected polymer structure can be printed. (b) Printing height as a function of printing time. (c) Microscopic image (taken by Nikon Eclipse LV100ND) to show the manufacturing resolution. 251 Figure S21. Synthesis process of the experimental polymer ink. 0.00829 mole of PTMEG was preheated at 90°C and bubbled with nitrogen for 1 h to remove oxygen and water. After lowering down the temperature to 70°C, the preheated PTMEG was mixed with 7.369 g IPDI, 5 g DMac and 0.15 g DBTDL with magnetic stirring for 1 h (step 1). Then, a solution with 2.557 g HEDS in 20 g DMac was added drop-wisely to the mixture with magnetic stirring for another 1 h (step 2). After cooling the mixture to 40°C, 2.147g HEMA was added in with magnetic stirring for one more hour to complete the reaction (step 3). During the whole process, nitrogen was bubbled in the solution. The obtained solution was then put in a vacuum chamber for 12 hours to evaporate 90% of solvent. 252 Figure S22. (a) FTIR spectrum to verify the synthesis. The featured peak at around 2260𝑐𝑚 @2 which correspond to the N=C=O stretching band, was first found decrease after mixing the backbone polymer solution with the diol-terminated disulfide. The remain N=C=O stretching band was not disappear until the hydroxyl-ended acrylate group was added in and mixed for another hour. The disappearance of the N=C=O stretching band suggests that aromatic disocyanate was totally converted to urethane linkages and the synthesis of prepolymer solution was completed. (b) FTIR spectrum to verify the photopolymerization. The full photopolymerization of prepolymer solution to a crosslinked solid sample was found from the absence peak at 1630𝑐𝑚 @2 which corresponding to the absorption band of the acrylate group (C=C). Figure S23. (a) Schematics to show the disulfide-bond enabled self-healing process. The fractured interface can be healed through a disulfide metathesis reaction. (b) Photo-initiated addition reaction of acrylate groups. Figure S24. (a) Molecular structure schematics of an experimental polymer with both disulfide bonds and crystalline domains, and a control 1 polymer with only crystalline domains. (b) Raman spectra of experimental polymers with various PTMEG molar masses (with disulfide bonds) and the control 1 polymer (without disulfide bonds). The new band ~520 cm -1 is corresponding to the disulfide bond. 253 Figure S25. The synthesis process of the ink for the control 1 polymer with crystalline domains but without disulfide bonds. The synthesis process is similar to that of experimental polymer inks (Fig. S21) except that the HEDS was replaced by BDO that has a similar chemical structure as HEDS but without disulfide bonds. Figure S26. (a) Molecular structure schematics of an experimental polymer with both disulfide bonds and crystalline domains and a control 2 polymer with only disulfide bonds 300 . (b) Differential scanning calorimetry thermographs of experimental polymers with various PTMEG molar masses (with crystalline domains) and the control 2 polymer (without crystalline domains). 254 Figure S27. Microscopic images to show the healing interfaces at the shape-recovered state and the fracture-healed state of the lattice wing shown in Fig. 55k. The healing condition is 6 h at 80 °C. 255 Figure S28. (a) Storage, loss moduli and tan 𝜹 of an experimental polymer with both crystalline domain and disulfide bonds (PTMEG molar mass 250 g/mol) as functions of temperature. The glass transition temperature T g is estimated as ~71 °C through the decreasing onset of the storage modulus, and as ~65 °C through the peak of the loss modulus according to the basis reference 303 . Overall, the glass transition temperature is within 65-71 °C. (b) Storage, loss moduli and tan 𝜹 of an experimental polymer with PTMEG molar mass 1000 g/mol as functions of temperature. The glass transition temperature T g is estimated as ~39 °C through the decreasing onset of the storage modulus according to the basis reference 303 .. (c) Storage, loss moduli and tan 𝛿 of an experimental polymer with PTMEG molar mass 1810 g/mol as functions of temperature. The glass temperature is not determinable and should be below 25 °C. Figure S29. (a) Molecular structure schematic to show a control 1 polymer with crystalline domains but without disulfide bonds. (b) Microscope images to show the damaged interface before healing and still damaged interface after healing for 18 h. The fractured interface is not healed. Scale bars represent 200 µm. (c) Tensile stress-strain curves of a virgin control 1 polymer and the polymer after healing for 18 h at 80 o C. 256 Figure S30. Zoom-in view of the tensile stress-strain behavior of the polymer with PTMEG molar mass 250 g/mol. Small-strain Young’s modulus is 500 MPa. Figure S31. Schematic to show the three-point-bending (3PB) test on a lattice structure. The effective Young’s modulus (stiffness) of the lattice is calculated as M : * Be * , where F is the applied load, L is the span between two supporting points, W is the width of the lattice, H is the height of the lattice, and 𝛿 is the displacement in the 3PB test. The effective flexural strength of the lattice is calculated as F: . (e ( , where 𝐹 3 is the maximal load during the 3PB test. 257 Figure S32. Computer-aided design models and flexural stress-flexural strain curves of virgin, first- healed, and second-healed octet lattices of various relative densities (ρ/ρ 0=13.1%, 23.4%, 37.9%, and 53%) in 3PB tests. Figure S33. Experimental process of the self-healing of lattice structures. A virgin lattice is first fractured using the three-point-bending load. Two fractured parts are brought into contact and placed in a glass container with the exact inner volume of the lattice. The healing condition is 6 h at 80 o C. 258 Figure S34. (a) Load-displacement curves of the cyclically healed octet lattices with relative density 𝜌 𝜌 ' ⁄ =13.1% on three-point bending tests. (b) The effective relative Young’s moduli and flexural strengths of the cyclically healed octet lattices. Figure S35. Samples and schematics to show the process of shape-memory-assisted healing. Specifically, the shape memory process at 80 °C can help align the initially separated fracture surfaces to the contacted state. Then a healing process can repair the contacted fracture surfaces. Scale bar denotes 4 mm. 259 Figure S36. (a) Stress-strain-temperature behavior of synthesized polymers with PTMEG molar mass 250 g/mol within a shape-memory cycle. The shape-memory cycle consists of five segments: (1) Loading: a polymer sample is uniaxially stretched to a prescribed strain 𝜀 i at 60 o C. (2) Cooling 1: the strain slightly changes to 𝜀 9 after cooling to 35 o C with the maintained load. (3) Unloading: the applied load is relaxed at 35 o C with the strain reducing to 𝜀 y . (4) Recovering: the temperature increases again to 80 o C with the strain further reducing to 𝜀 $ . (5) Cooling 2: the temperature decreases to 60 o C. The shape fixity and recovery ratios are defined as 𝑅 # =𝜀 y 𝑚𝑎𝑥(𝜀 i ,𝜀 9 ) ⁄ and 𝑅 $ =1−𝜀 $ 𝜀 y ⁄ , respectively. This shape- memory cycle is employed for applications shown in Figs. 58d, 58i, and S37. (b) Shape fixity ratios R f and shape recovery ratios R r of the polymer within the above shape-memory cycle. Figure S37. Experimental image sequence of the shape-memory process of the impact-induced denting of an octet lattice: (i) virgin lattice, (ii) impact-induced damaged lattice, (iii-iv) shape-recovering lattice, and (v) shape-recovered lattice. Scale bar represents 4 mm. 260 Figure S38. (a) The meshed periodic unit used in the vibration band simulation of the triangle lattice. The mesh element number is 482. The simulation accuracy is ensured through a mesh refinement study. (b) Irreducible Brillouin zone of the triangle lattice 304 . (c) Simulated vibration band structure of the triangle lattice within a frequency range of 20-50 kHz. The band gap is 32-33.5 kHz. (d) The experimentally measured vibration transmittance over frequency 31.5-34 kHz. The load transmittance (<0.2) exhibits at 32.2-33.2 kHz. (e) The meshed periodic unit used in the vibration band simulation of the Kagome lattice. The mesh element number is 480. The simulation accuracy is ensured through a mesh refinement study. (f) Irreducible Brillouin zone of the Kagome lattice 304 . (g) Simulated vibration band structure of the Kagome lattice within a frequency range of 20-50 kHz. (h) The experimentally measured vibration transmittance over frequency 20-50 kHz. Note that the vibration band structures in c and g are very similar to those in 304 . Figure S39. Schematic to show the experimental setup for the vibration transmittance experiment. Figure S40. (a) Schematics to show the memory-healing assisted structural transformation: (i) virgin triangle lattice, (ii) programmed Kagome lattice through fracturing the virgin lattice, (iii) Shaped- recovered lattice with fractured interfaces, and (iv) fracture-healed lattice. (b) Measured vibration 261 transmittances of virgin triangle lattice, programmed Kagome lattice, shaped-recovered lattice, and fracture-healed lattice as functions of the acoustic frequency. Figure S41. Schematic to show the experimental setup for the acoustic transmittance experiment. Figure S42. (ab) Configurations for acoustic simulations for virgin lattice (a) and programmed lattice (b). (c) Numerically simulated and (d) experimentally measured acoustic transmittances of virgin lattice and programmed lattice as functions of acoustic frequency. 262 Figure S43. Synthesis of polymer resin with acrylate and isocyanate (NCO) groups. 0.01 mole of PolyTHF was preheated at 100℃ and exposed to a nitrogen environment for 1 h to remove moisture and oxygen. 0.02 mole of IPDI, 10 wt% of DMAc and 1 wt% of DBTDL were mixed with preheated PolyTHF at 70℃ and stirred with a magnetic stir bar for 1 h. After reducing the temperature to 40℃, 0.01 mole of HEMA was added and mixed for 1 h to complete the synthesis. 263 Figure S44. Preparation of experiment polymer sample. Extracted spinach chloroplasts were gently mixed with prepared polymer resin with acrylate and NCO groups by using a magnetic stir bar for 30 min at 5℃ in a dark environment to prevent the degradation of chloroplasts. The mixed polymer resin then went through a photoradical-initiated addition reaction with the photopolymerization-based stereolithography system to photopolymerize the polymer resin. Figure S45. (A) 3D-printing of polymer structures. A CAD model was first sliced into a sequence of images. These 2D slice images, illuminated with UV/blue light from a light-emitting diode, were sequentially projected onto a transparent window. On the window, the liquid photoresin, capped into a prescribed height by a printing stage, was cured by the light and attached to the printing stage. As the printing stage was lifted off, the fresh resin refluxed beneath the printing stage. By lowering down the stage by a prescribed height and illuminating the resin with a subsequent slice image, a new layer could be printed and bonded onto the former layer. To eliminate the adhesion between the solidified resin and bath, we attached an oxygen-permeable membrane to the bottom, inducing a thin layer (~5-20µm) of the oxygen-rich dead zone to quench the photopolymerization. After repeating these processes, a 3D- architected polymer structure could be printed. (B) The relationships between the printing depth and the printing time for polymer inks with embedded chloroplasts of various weight concentrations. (C) Printed strips to illustrate the printing resolution (~25 μm). 264 Figure S46. Schematics to show the bond formation process between OH groups on the chloroplast- produced glucose with free NCO groups. The zoom-in view of the initial network shows the chemical structure of free NCO groups and chloroplast-created glucose. The zoom-in view of the strengthened network shows the chemical structure with the new crosslink. 265 Figure S47. Young’s moduli and tensile strengths of the polymers in the 3D-printed tree-like structures with various light illumination periods. The data of Young’s modulus and tensile strengths were measured using dumbbell-shaped samples. Figure S48. Load sustaining ability 3D-printed tree-like structures. In the top case, the tree structure went through 2-h light illumination (white light intensity 69.3 𝑊/𝑚 ( ) and 2-h darkness. In the bottom case, the tree structure went through 4-h darkness. The mass of the metal ring is 1 g. Figure S49. Load-sustaining ability of the 3D-printed Popeye-like structures. (A) Unstrengthened Popeye-like structure. (B) Unstrengthened Popeye-like structure loaded by a weight of 200 g. Its height reduces by 34.7%. (C) Strengthened Popeye-like structure. (D) Strengthened Popeye-like structure loaded by a weight of 200 g. Its height reduces by 7%. 266 Figure S50. Full FTIR spectra of samples with three groups. (A) FTIR spectra of experimental group samples (with free NCO groups and embedded chloroplasts) before and after 4-h light illumination and 4- h darkness. (B) FTIR spectra of control 1 samples (with free NCO groups and embedded chloroplasts) before and after 8-h darkness. (C) FTIR spectra of control 2 samples (with free NCO groups but without embedded chloroplasts) before and after 4-h light illumination and 4-h darkness. The zoom-in view shows the spectra in the range of 2150 cm -1 to 2400 cm -1 , which indicates the concentration of the free NCO groups. 267 Figure S51. Sample geometries of tensile and pure-shear fracture toughness tests. (A) Geometry of a tensile test sample. The sample thickness is 2mm. (B) Geometry of a notched sample for pure-shear fracture toughness test. The fracture toughness test was conducted by testing an unnotched and notched sample. Each sample has a testing length 𝑎 ' =40 𝑚𝑚, thickness 𝑏 0 =1 𝑚𝑚 and distance between two clamps 𝐿 ' =5𝑚𝑚. A 20-mm notch on the notched sample was prepared by using a razor blade. Both samples were tensile stretched with a strain rate of 0.05 𝑠 @2 and recording using a high-speed camera to record the critical distance between the clamps when the crack starts propagating on the notched sample 𝐿 9 . The fracture energy of the material was calculated as 𝑈(𝐿 9 ) (𝑎 ' 𝑏 ' ) ⁄ , where 𝑈(𝐿 9 ) is the work done by the applied force before critical distance, illustrated as the area beneath the force-distance curve in the unnotched test. Figure S52. Stress-strain curves of a polymer sample right after the strengthening with 4-h light illumination and 4-h darkness and the strengthened polymers after 6 months. The employed polymer sample was 3D-printed with polymer inks with free NCO groups and embedded chloroplasts. The results show that the strengthened polymer maintains its Young’s modulus and tensile strength after 6 months. 268 Figure S53. Force-distance curves and experiment images for fracture-toughness tests. Force-distance curves of notched and unnotched samples under uniaxial stretch for (A) the experimental case, (B) control 1 case, and (C) control 2 case. The experimental sample has free NCO groups and embedded chloroplasts, and undergoes 4-h light illumination and 4-h darkness. The control 1 sample has free NCO groups and embedded chloroplasts, and undergoes 8-h darkness. The control 2 sample has free NCO groups but no embedded chloroplasts, and undergoes 4-h light illumination and 4-h darkness. The critical points indicate the point when the crack starts propagating on the notched sample. Sample images of notched and unnotched samples under uniaxial stretch for (D) the experimental case, (E) control 1 case, and (F) control 2 case. 269 Figure S54. Synthesis of polymer resin with only acrylate groups but without free NCO groups. 0.01 mole of PolyTHF was preheated at 100℃ and exposed to a nitrogen environment for 1 h to remove moisture and oxygen. 0.02 mole of IPDI, 10 wt% of DMAc and 1 wt% of DBTDL were mixed with preheated PolyTHF at 70℃ and stirred with a magnetic stir bar for 1 h. After reducing the temperature to 40℃, 0.02 mole of HEMA was added and mixed for 1 h to complete the synthesis. Figure S55. Experiments on polymer samples with embedded chloroplasts but without free NCO groups. (A) The polymer samples with embedded chloroplasts but without free NCO groups went through 4-h light illumination (white light intensity 69.3 𝑊/𝑚 ( ) and 4-h darkness. (B) The polymer samples with embedded chloroplasts but without free NCO groups went through 8-h darkness. (C) The zoom-in views showing the spectra in the range of 3000 cm -1 to 3800 cm -1 , which indicates the concentration of OH groups 332 . (D) Tensile stress-strain curves of polymer samples with embedded chloroplasts but without free NCO groups after 4-h light illumination and 4-h darkness, and 8-h darkness. 270 Figure S56. Full FTIR spectra of polymer ink with free NCO groups but without embedded chloroplasts before and after being mixed with 0.398 mol/L of glucose.The zoom-in view shows the spectrum in the range of 2100 cm -1 to 2500 cm -1 , which indicates the concentration of free NCO groups. Figure S57. (A) Uniaxial tensile stress-strain curves of polymer samples with free NCO groups and various concentrations of glucose. (B) Young’s moduli and tensile strengths in functions of the glucose concentration. The error bars represent the standard deviations of 3-5 samples. Figure S58. (A) Uniaxial tensile stress-strain curves of polymer samples with free NCO groups and embedded chloroplasts of various weight concentrations. (B) Uniaxial tensile stress-strain curves of polymer samples with free NCO groups and 5 wt% chloroplasts after the photosynthesis processes with various light illumination periods. (C) Young’s moduli and tensile strengths of experimental samples with 7 wt% chloroplasts after the photosynthesis processes with various light illumination periods. 271 Figure S59. Schematics for the polymer network. (A) Schematics to show the formation of additional crosslinks through the reaction between the free NCO groups and the glucose. (B) Schematics to show the formation of one crosslink between two chains with the length of 𝑁 ' . We assume each chain with the initial length of 𝑁 ' becomes two chains with the length of 𝑁 ' 2 ⁄ . (C) Schematics to show the formation of one crosslink between a chain with the length of 𝑁 ' 2 " ⁄ and a chain with the length of 𝑁 ' 2 ⁄ . We assume the crosslink formed between a chain with the length of 𝑁 ' 2 " ⁄ and a chain with the length of 𝑁 ' 2 ⁄ induces four chains with respective half lengths, where 𝑖 =0,1,2⋯ and 𝑗 =0,1,2⋯. 272 Figure S60. Theoretical results for step number m=1. (A) Nominal tensile stress-strain curves for various normalized additional crosslink density 𝑛 4 𝑛 ' ⁄ . (B) The Young’s modulus of the polymer in a function of the normalized additional crosslink density 𝑛 4 𝑛 ' ⁄ . The Young’s modulus is calculated from the stress- strain curve within 10% strain. (C) Nominal tensile stress-strain curves for various initial chain length 𝑁 ' and 𝑛 4 𝑛 ' ⁄ =0.5. (D) Strengthening factor in a function of the chain length for 𝑚 =1 and 𝑛 4 𝑛 ' ⁄ =0.5. The strengthening factor is defined as the strengthened Young’s modulus normalized by the unstrengthened Young’s modulus. Figure S61. Relationships between the step number 𝑚 and additional crosslink density 𝑛 4 𝑛 ' ⁄ for (A) method 1 and (B) method 2. Figure S62. Theoretical results for m=2 and 𝑛 4 /𝑛 ' =2/3. Stress-strain curves and strengthening factors for various initial chain lengths 𝑁 ' based on (AB) method 1 and (CD) method 2. 273 Figure S63. Theoretical results for 𝑛 4 /𝑛 ' >2/3. Stress-strain curves and strengthening factors for various initial chain lengths 𝑁 ' and (AB) 𝑚 =5 and 𝑛 4 𝑛 ' ⁄ =1 (method 1), (CD) 𝑚 =2 and 𝑛 4 𝑛 ' ⁄ =1 (method 2), and (EF) 𝑚 =3 and 𝑛 4 𝑛 ' ⁄ =3.05 (method 2). 274 Figure S64. Comparison between the theory and experiment. (A) Stress-strain curves and (B)Young’s moduli of polymer samples with free NCO groups and chloroplasts of various weight concentrations after 4-h light illumination and 4-h darkness. (C) Stress-strain curves and (D)Young’s moduli of polymer samples with free NCO groups and 5 wt% chloroplasts after various illumination periods and the corresponding periods of darkness. The parameters used to calculate the theoretical results are listed in Table S3. The error bars in (B) and (D) represent standard deviations of 3-5 samples. 275 Figure S65. Effect of chilling temperature on the proposed hybrid synthetic-living material and traditional photopolymer. (A) Schematics to illustrate the procedure for an experimental sample first undergoing 2-h light illumination and 2-h darkness at 0℃, and then undergoing 2-h light illumination and 2-h darkness at 25℃. (BC) Stress-strain curves, Young’s moduli, and tensile strengths of the processed experimental samples at three states: after 4-h darkness, after 2-h light and 2-h darkness at 0℃, and after 2-h light and 2-h darkness at 0℃ followed by 2-h light and 2-h darkness at 25℃. The error bars represent standard deviations of 3-5 samples. Results show that chilling temperature can temporarily freeze the living activity of the embedded chloroplasts. (D) Schematics to illustrate the post-curing procedure for a partially-crosslinked control 2 sample undergoing 2-h light illumination and 2-h darkness at 0℃. Since the control 2 sample can be fully crosslinked with light illumination of 60s, we employed 20s to enable a partial crosslinking. (EF) Stress-strain curves, Young’s moduli, and tensile strengths of the processed control 2 samples at three states: after 2-h light and 2-h darkness at 25℃, after 2-h light and 2-h darkness at 0℃, and after 4-h darkness at 25℃. The error bars represent standard deviations of 3-5 samples. 276 Results show that the post-curing of a partially-crosslinked photoresin cannot be frozen by a chilling temperature. Figure S66. Cleavage of glucose crosslinkers with period acids (HIO4). (A) Chemical reaction for cleaving a glucose molecule with period acids. (BC) Stress-strain curves, Young’s moduli, and tensile strengths of strengthened samples, and strengthened samples treated with solvent DMAc only, and strengthened samples treated with HIO 4 solution (2 M HIO 4 with solvent DMAc). The mechanical tests were carried out after evaporating the residual solvents. Results show that the HIO 4 can cleave the glucose crosslinkers to reverse the strengthened samples back to the soft state. The error bars represent standard deviations of 3-5 samples. Figure S67. Sample images of a locally strengthened sample through a patterned light with an “S” shape. 277 Figure S68 Experimental set-up of an indentation test. A round-flat end cylinder indenter with radius R=1 mm is loaded on the Instron mechanical tester to indent the sample by applying force F to a certain indentation depth 𝛿. The Young’s modulus is calculated as 𝐸 =𝐹(1−𝜐 ( ) (2𝑅𝛿) ⁄ , where 𝜐 is the Poisson’s ratio. Figure S69. Strengthening of Octet lattice with homogeneous light illumination. (AB) 3D-printed Octet lattice structure with free NCO groups and embedded chloroplasts went through 4-h light illumination and 4-h darkness and sustained a 100g weight (lattice weight 0.12 g). (CD) 3D-printed Octet lattice structure with free NCO groups and embedded chloroplasts went through 8-h darkness and sustained a 100g weight. (E) Compressive stress-strain curves of the strengthened and unstrengthened Octet lattice structures. (F) Zoom-in view of the compressive stress-strain curve of the 3D-printed Octet lattice structure. The strengthened lattice exhibits Young’s modulus that is 20 times that of the non-strengthened lattice. The scale bars represent 4 mm. 278 Figure S70. Schematic to show the experimental setup for the 3D-printed structures with a gradient light intensity. A transparent cover was attached with different layers of vinyl-coated white tape and covered on top of the printed sample. The entire setup was then placed in the chamber with light intensity varies from 0 to 69.3 𝑊/𝑚 ( on the long edge direction of the sample for each unit distance (2 mm). Figure S71. (a) Front, back, and cross-section views of the functionally-graded lattice structure. (bc) Front and cross-section views of the (b) fully-soft and (c) fully-stiffened lattice structures. 279 Figure S72. Stress-strain curves of experimental polymer samples (with free NCO groups and embedded chloroplasts) with various pre-stretches after the photosynthesis process (4-h light and 4-h darkness). Figure S73. Effect of pre-stretch on the mechanical property of post-cured control 2 polymer (with free NCO groups but without chloroplasts). (A) Schematics to illustrate the post-curing of control 2 samples without and with a pre-stretch. The post-curing condition is the same as the photosynthesis condition: 4-h light illumination and 4-h darkness. (B) Stress-strain curves of post-cured control 2 samples (printed with 60 s, close to fully cured) without a pre-stretch and with a pre-stretch of 1.3. (C) Stress-strain curves of post-cured control 2 samples (printed with 20 s, partially-cured) without a pre-stretch (𝜆 =1) and with various pre-stretches (𝜆 =1.1−1.3). (D) The Young’s moduli and tensile strengths of the post-cured control 2 samples (printed with 20 s, partially-cured) in functions of the pre-stretch 𝜆. Experimental procedure: The samples were prepared by 3D printing process using control 2 polymer ink (with free NCO groups but without chloroplasts) under different light exposure time (20 s or 60 s). When the light exposure time was 60 s, the sample was fully crosslinked; when the light exposure time was 20 s, the sample was partially-cured. The fabricated samples were then uniaxially pre-stretched with various stretches (𝜆 =1−1.3) and undergone 4-h light illumination and 4-h darkness. The pre-stretched section of the samples was then cut into dumbbell-like shape, and uniaxially stretched until rupture with a strain rate of 0.05 𝑠 @2 . 280 Figure S74. Stretching of a healed sample after 4-h light illumination and 4-h darkness. Figure S75. Self-healing of the control sample. (A) Uniaxial tensile stress-strain curves of control samples with free NCO groups but without embedded chloroplasts at the virgin state and after the healing process (4-h illumination and 4-h darkness). (B) control samples and interfacial microscope images at the virgin, damaged, and healed states. Figure S76. Healing process of 3D-printed propeller made by control 2 polymer with free NCO group but without embedded chloroplasts. (A) Image of sample damaged with sharp blade (B) Image of the unhealed sample after 4-h light illumination and 4-h darkness. The scale bars represent 4 mm. 281 Fig. S77. Synthesis of the new polymer ink. 0.05 mole of Poly THF was first preheated to evaporate moisture and oxygen at 100°C for 1 h and the mixture was stirred with a magnetic stir bar. 0.1 mole of IPDI, 10 wt% of DMAc, and 1 wt% of DBTDL were added in the preheated Poly THF at 70°C, and the mixture was mixed for 1 h. After the temperature declined to 40°C, 0.05 mole of HEMA was added, and stirred for another 1 h to complete the synthesis. The entire synthesis process was conducted in a Nitrogen environment. Fig. S78. Stereolithography (SLA) 3D printing process. The setup of the bottom-up SLA 3D printer includes a white-light projector at the bottom, an acrylic-made top-open resin box right above the projector, and a motor-controlled printing stage above the resin box. The resin box was firstly pre-filled with the prepared polymer resin. The printing stage was moved down into the polymer resin, leaving a prescribed distance between the stage and the bottom of the resin box. The image of the first layer in the image sequence was then projected from the projector to the bottom of the resin box to polymerize the resin for a prescribed time. After the first layer was formed on the printing stage, the stage was lifted to a distance of the thickness of the next layer. In the meantime, the polymer resin refluxes to fill the space 282 caused by stage lifting. The image of the second layer was then projected to the bottom of the resin box to polymerize the second layer. The second layer then bonds covalently with the first layer after polymerization. A 3D structure was finally formed by repeating the above-mentioned process. A Teflon membrane with low surface tension (~20 mN/m) was used to reduce the separation force between the polymerized part and the bottom of the resin box. Fig. S79. Photopolymerization of polymer ink. The polymer resin with 1 wt% of photoinitiator (phenylbis(2,4,6-trimethylbenzoyl)phosphine oxide) and various weight percentages of Sudan I (0%- 0.02%) went through a photoradical-initiated addition reaction with the photopolymerization-based stereolithography system to photopolymerize the polymer resin. Fig. S80. The chemical reaction between isocyanate groups and water molecules. (A) Chemical schemes to show the reaction between one water molecule and two NCO groups. (B) Schematic to illustrate the water-induced chemical bridging to form additional crosslinks. Fig. S81. Water-assisted strengthening of a 3D-printed lattice structure. (A) As-printed lattice structure. (B) lattice structure after being immersed in the water for 24 h. (C) Fully-reacted lattice structure after resting in the air for 2 days. 284 Fig. S82. Water-assisted healing of a 3D-printed pipe fitting. (A) A 90° pipe fitting with a water flow. (B) A crack installed on the pipe fitting. (C) Water leaks out of the pipe fitting when there is a water flow. (D) A temporary tape wrapped around to contact the crack surface of the damaged pipe fitting. (E) The wrapped pipe fitting immersed in water along with the inner water flow. (F) The healed pipe fitting sustaining a water flow without leaking. Fig. S83. Full FTIR spectra of the new polymer sample at virgin state. A distinct peak centered at 2,270 𝑐𝑚 @2 was observed to indicate the existence of the NCO group. 285 Fig. S84. Fracture tests of the polymer samples. (A) Sample geometry of pure-shear fracture toughness tests. (B) Force-distance curves of notched and unnotched samples at the fully-reacted state. (C) Force- distance curves of notched and unnotched samples at the virgin state. (D) Experiment images of notched and unnotched samples at fully-reacted state. (E) Experiment images of notched and unnotched samples at the virgin state. 286 Fig. S85. Experiments for the water-induced local strengthening. (A) Rectangular sample plates (35 mm x 35 mm x 1 mm) were first 3D-printed with the synthesized polymer resin. Thin acrylic covers (thickness of 1 mm and height of 3 mm) with desired hollow patterns (i.e., wavy-pattern) were cut with a laser cutter (Pro-Tech 60W CO ( Laser Cutter) and placed on the top of the plate samples. Another cover made with EcoFlex 00-30 (Smooth-on) was then placed outside of the acrylic covers to prevent water leakage between the acrylic and polymer plate. (B) Water was then filled into the acrylic covers to allow water to penetrate the polymer plate from the top surface for 24 h, followed by resting in the air for 2 days. (C) Indentation test to measure the stiffness map of the processed sample. A compressive force F is applied on the sample by a flat-end indenter with the radius of R=1 mm with a strain rate of 0.05 s -1 . A depth 𝛿 is created by the cylinder indenter on the sample. The Young’s modulus is calculated as 𝐸 =𝐹(1− 𝜈 ( )/(2𝑅𝛿)), where υ is the Poisson’s ratio of the sample. 287 Fig. S86. A commercial remotely-controlled robotic fish with a rubber caudal fin and the telecontroller. Fig. S87. (A) The fabrication process of a flexible circuit with a silver conductive ink pen (B) Schematic of the flexible circuit connected to a source meter (C) Schematic of the packaged circuit under three- points bending test. 288 B. Supplemental Methods B.1 Analytical modeling of disulfide-bond enabled self-healing We develop a polymer-network based model to explain the experimentally measured self-healing behaviors of the created elastomer with disulfide bonds. This model is an extension of a model we recently developed for self-healing hydrogels crosslinked by nanoparticles 84 . We first model the constitutive behavior of the original elastomer and then model the interfacial self-healing behavior of the fractured elastomer. Constitutive modeling of original elastomer We assume that the elastomer is composed of m types of networks interpenetrating in the material bulk space (Fig. S9) 99 . The ith network is composed of the ith polymer chains with Kuhn segment number. The length of the ith chain at the freely joint state is determined by the Kuhn segment number as , where b is the Kuhn Segment length. Researchers usually denote the “chain length” as 100 . Without loss of generality, the Kuhn segment number follows an order . We denote the number of ith chain per unit volume of material as . Therefore, the total chain number per unit volume of material is . The chain number follows a statistical distribution as (B.1-1) The summation of the statistical distribution function is a unit, i.e., . The chain-length distribution is usually unknown without a careful experimental examination. Although researchers usually accept that the chain length is generally non-uniform 101 , the most prevailing models for the rubber elasticity still consider the uniform chain length, such as three-chain model, four-chain model, and eight- chain model 100,102,103 . The consideration of non-uniform chain-length to model the elasticity behaviors of i n i n b n r i i = 0 i n m n n n £ £ ..... 2 1 i N å = = m i i N N 1 ( ) N N n P i i i = 1 1 = å = m i i P ( ) i i n P 289 rubber-like materials was recently carried out by Wang et al. 99 and Vernerey et al. 419 . Because of the limited experimental technique to characterize the chain length distribution to date, the selection of chain- length distribution is still a little ambiguous. Wang et al. tested a number of chain-length distribution functions including uniform, Weibull, normal, and log-normal, and found that the log-normal distribution can best match the material’s mechanical and mechanochemical behaviors 99 . In this study, we simply employ the log-normal chain-length distribution, while other distributions may also work for our model. The log-normal chain-length distribution is written as (B.1-2) where and are the mean of and standard deviation of , respectively. For the ith chain, if the end-to-end distance at the deformed state is , the chain stretch is defined as . The free energy of the deformed ith chain can be written as (B.1-3) where is the Boltzmann constant, is the temperature in Kelvin, and is the inverse Langevin function. Considering the chain as an entropic spring, the force within the deformed ith chain can be written as (B.1-4) To link the relationship between the macroscopic deformation at the material level and the microscopic deformation at the polymer chain level, we consider an interpenetrating model shown in Fig. S9 99 . We assume the ith chains assemble themselves into regular eight-chain structures 102 . We assume the material follows an affined deformation model 100,103 , so that the eight-chain structures deform by three principal stretches ( ) under the macroscopic deformation ( ) at the material level. Therefore, the stretch of each ith chain is ( ) ( ) ú ú û ù ê ê ë é - - = 2 2 2 ln ln exp 2 1 d p d a i i i i n n n n P a n d i n i n ln i r 0 i i i r r = L ÷ ÷ ø ö ç ç è æ + = i i i i B i i T k n w b b b b sinh ln tanh B k T ( ) i i i n L L = -1 b ( ) 1 - L i B i i i b T k r w f b = ¶ ¶ = 3 2 1 , , l l l 3 2 1 , , l l l 290 (B.1-5) At the undeformed state, the number of the ith chain per unit material volume is . As the material is deformed, the active ith chain number decreases because the chain force promotes the dissociation of the dynamic bonds. We assume at the deformed state, the number of the active ith chain per unit material volume is . Since every ith chain undergoes the same stretch , the total free energy of the material per unit volume is (B.1-6) where and is given in Eq. B.1-5, and the active ith chain density is obtained in the following sections. We consider the material as incompressible and it is uniaxially stretched with three principal stretches ( ), the nominal stress along direction can be calculated as (B.1-7) Next, we consider the association-dissociation kinetics of dynamic disulfide bonds (Fig. S10). We model the bond association and dissociation as a reversible chemical reaction 108,109 . The forward reaction rate (from the associated state to the dissociated state) is and reverse reaction rate is . For simplicity, we assume that only two ends of a chain have ending groups for the dynamic bond 24 . If two end groups are associated, we consider this chain as “active”; otherwise, the chain is “inactive”. The chemical reaction in Fig. S10a averagely involves one polymer chain; that is, the chemical reaction represents the transition between an active chain and an inactive chain. Here we denote the active ith chain per unit volume is and the inactive ith chain per unit volume is . The chemical kinetics can be written as 3 2 3 2 2 2 1 l l l + + = L i i N a i N i L å = ÷ ÷ ø ö ç ç è æ + = m i i i i i B i a i T k n N W 1 sinh ln tanh b b b b ( ) i i i n L L = -1 b i L a i N 2 / 1 3 2 1 , - = = = l l l l l 1 l ( ) å = - - - - ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ + + - = m i i i a i B n L n N T k s 1 1 2 1 1 2 2 1 3 2 6 3 l l l l l l f i k r i k a i N d i N 291 (B.1-8) Since the total number of ith chain per unit volume defined as , the chemical kinetics can be rewritten as (B.1-9) At the as-fabricated undeformed state, the reaction rates are and , respectively. As the material is fabricated as an integrated solid, we simply assume the association reaction is much stronger than the dissociation reaction at the fabricated state, i.e., . Otherwise, the polymer is unstable under external perturbations. Therefore, most of the ith chains are at the associated state, as the equilibrium value of at the undeformed state is (B.1-10) At the deformed state, the ith chain is deformed with stretch . Since the bond strength of the dynamic bonds is much weaker than those of the permanent bonds such as covalent bonds, the chain force would significantly alter the bonding reaction 108,109 . Specifically, the chain force tends to pull the bond open to the dissociated state. This point has been well characterized by Bell model for the ligand-receptor bonding for the cell adhesion behaviors, as well as for biopolymers 110 . We here employ a Bell-like model and consider the energy landscape between the associated state and dissociated state shown in Fig. S10bc 99 . We consider an energy barrier exists between the associated state (denoted as “A”) and the dissociated state (“D”) through a transition state (“T”). At the undeformed state of the ith chain, the energy barrier for A D transition is and the energy barrier for D A transition is (Fig. S10b). Under the deformed state of the ith chain, the chain force lowers down the energy barrier of A D transition to and increases the energy barrier for D A transition to , where is the distance along the energy landscape coordinate (Fig. S10c). Since the occurrence of the chemical reaction d i r i a i f i a i N k N k dt dN + - = d i a i i N N N + = ( ) i r i a i r i f i a i N k N k k dt dN + + - = 0 f i f i k k = 0 r i r i k k = 0 0 r i f i k k << a i N i i f i r i r i a i N N k k k N » + = 0 0 0 i L ® f G D ® r G D i f ® x f G i f D - D ® x f G i r D + D x D 292 requires the overcoming of the energy barriers, the higher energy barrier is corresponding to the lower likelihood of the reaction. According to the Bell model, the reaction rates are governed by the energy barrier through exponential functions as 110,111 . (B.1-11a) (B.1-11b) Where and are constants and is treated as a fitting parameter for the given material. If the material is loaded with increasing stretch ( ) with a very small loading rate, the deformation of the material is assumed as quasi-static. It means that in every small increment of the load, the chemical reaction already reaches its equilibrium state with an equilibrium active ith chain number . Under this condition, the active ith chain number per unit material volume is expressed as (B.1-12) with the chain force as expressed in Eq. B.1-4. In addition to the above association-dissociation kinetics, we also consider the effect of the network alteration 112,113 . During the mechanical loading, a portion of dissociated short chains may reorganize to become active long chains 112,113 . To capture this effect, we follow the network alteration theory to model the number of active chains to be an exponential function of the chain stretch as (B.1-13) where is the chain alteration parameter. Similar network alteration model has been employed to model the chain reorganization for the Mullin’s effect of rubber 112,113 , double-network hydrogels 114 , and nanocomposite hydrogels 115 . It has been shown that the network alteration is a unique network damage ÷ ÷ ø ö ç ç è æ D = ÷ ÷ ø ö ç ç è æ D - D - = T k x f k T k x f G C k B i f i B i f f i exp exp 0 1 ÷ ÷ ø ö ç ç è æ D - = ÷ ÷ ø ö ç ç è æ D + D - = T k x f k T k x f G C k B i r i B i r r i exp exp 0 2 1 C 2 C x D 2 / 1 3 2 1 , - = = = l l l l l a i N ÷ ÷ ø ö ç ç è æ D - + ÷ ÷ ø ö ç ç è æ D ÷ ÷ ø ö ç ç è æ D - = T k x f k T k x f k T k x f k N N B i r i B i f i B i r i i a i exp exp exp 0 0 0 i f i L ( ) [ ] 1 exp - L = i i a i N N a a 293 mechanism that facilitates the stiffening effect of the stress-stretch curve 112,113,115 . Here, we harness this network alteration effect to better capture the stress-stretch curve shapes of the original elastomer. Self-healing behavior of the fractured elastomer We consider a self-healing elastomer sample shown in Fig. S11. We cut the sample into two parts and then immediately contact back. After a certain period of healing time t, the sample is uniaxially stretched until rupturing into two parts again. Here, we consider the self-healed sample is composed of two segments (Fig. S11): Around the healing interface, the polymer chain would diffuse across the interface to form new networks through forming new dynamic bonds. We call this region as “self-healed segment”. Away from the self-healed segment, the polymer networks are intact, and we call this region as “virgin segment”. As we assume in section 3.1, the ith chains form network following eight-chain structures (Fig. S9). For simplicity of analysis, we assume the cutting position is located at a quarter part of the eight chain cube, namely the center position between a corner and the center of the eight-chain cube (Fig. S12a). This assumption is just for the sake of symmetry to enable easy analysis. Other anti-symmetry cutting positions can also be analyzed using an averaging concept. The cutting process forces the polymer chains to be dissociated from the dynamic bond around the corner or center positions. Since we immediately contact the material back, we assume the ending groups of the dynamic bonds are still located around the cutting interface, yet without enough time to migrate into the material matrix (Fig. S12b) 84 . Driven by weak interactions between ending groups of the dynamic bonds, the ending groups on the interface will diffuse across the interface to penetrate into the matrix of the other part of the material to form new dynamic bonds. Specifically shown in Fig. S12b, the ending groups of the part A will penetrate into part B towards the center position of the cube, and the ending groups of part B will penetrate into Part A towards the corner positions of the cube. These interpenetration behaviors can be simplified as a 1D model shown in Fig. S12c. As shown in Fig. S12c, an open ending group around the 294 interface penetrates into the other part of the material to find another open ending group to form a dynamic bond. Once the dynamic bond reforms, the initially “inactive” chain becomes “active”. This behavior can be understood as two processes: chain diffusion and ending group reaction. In the disulfide bond system shown in Fig. 15c, when we cut the material into two parts, the dissociated sulfide bonds undergo disulfide metathesis reactions (assisted by a catalyst tributylphosphine) to reform disulfide bonds around the interface. When the two material parts are brought into contact, these disulfide bonds will be mobilized by the catalyst tributylphosphine to move across the interface to exchange sulfide groups to form disulfide bonds to bridge the interface. Our generalized model shown in Fig. S12 and discussed above can approximately capture the key physics of the healing behaviors of the disulfide bond system. To model the chain diffusion, we consider a reptation-like model shown in Fig. S12c 100,117-119 . We assume the polymer chain diffuses along its contour tube analogous to the motion of a snake. The motion of the polymer chain is enabled by extending out small segments called “minor chains”. The curvilinear motion of the polymer chain is characterized by the Rouse friction model with the curvilinear diffusion coefficient of the ith chain written as (B.1-14) where is the Rose friction coefficient per unit Kuhn segment. We note that the chain motion follows a curvilinear path; therefore, we construct two coordinate systems s and y, where s denotes the curvilinear path along the minor chains and y denotes the linear path from the interface to the other open ending group. When the ith chain moves distance along the curvilinear path, it is corresponding to distance along y coordinate. Here we assume the selection of the curvilinear path is fully stochastic following the Gaussian statistics 121-123 . Therefore, the conversion of the distances in two coordinate systems is expressed as (B.1-15) x i B i n T k D = x i s i y b s y i i = 295 According to the eight-chain cube assumption, the distance between the corner and the center within the ith network cube at its freely joint state is (B.1-16) The distance between the ending group around the interface and the other ending group in the matrix is . According to Eq. B.1-15, the positions and are corresponding to and , respectively. If we only consider the polymer chain diffusion, the diffusion of the ith chain can be modeled with the following diffusion equation along the curvilinear coordinate s, (B.1-17) where is the inactive ith chain number per unit length (with the unit area) along the coordinate s ( ) at time t. However, the chain behavior is more complicated than just diffusion, because during the diffusion the ending group would encounter another ending group to undergo a chemical reaction to form a new dynamic bond. Although the chemical reaction may only occur around the ending group (relatively immobile ending group at ), the reaction forms dynamic bonds to transit an inactive chain into an active chain, and this reaction would reduce the amount of the inactive ending groups and further drive the motion of the other inactive ending groups. Therefore, the chain diffusion and ending group reaction actually are strongly coupled. Therefore, we consider an effective diffusion- reaction model to consider the effective behaviors of the chain and the ending group as 124 (B.1-18) (B.1-19) b n L i i » 2 i L 0 = y 2 i L y= 0 = s b L s i 4 2 = ( ) ( ) 2 2 , , s s t C D t s t C d i i d i ¶ ¶ = ¶ ¶ ( ) s t C d i , b L s i 4 0 2 £ £ b L s i 4 2 = ( ) ( ) ( ) t s t C s s t C D t s t C a i d i i d i ¶ ¶ - ¶ ¶ = ¶ ¶ , , , 2 2 ( ) ( ) ( ) s t C k s t C k t s t C a i f i d i r i a i , , , 0 0 - = ¶ ¶ 296 where is the active ith chain number per unit length (with the unit area) along the coordinate s ( ) at time t. As the polymer chain is freely joint during the diffusion process, we here use the chemical reaction rates and . In the initial state of the self-healing, all mobile open-ending groups of the ith chains are located around the healing interface. Therefore, the initial condition of the diffusion-reaction model is (B.1-20) (B.1-21) where . For a self-healing polymer that is capable of forming a stable solid form and enabling relatively short healing time, the basic requirement is . Here, we further focus our attention on polymers with good healing capability, so that the polymers can easily self-heal under relatively mild conditions. This requirement further implies that should be much larger than , i.e., . Under this condition, Eqs. B.1-S18 and B.1-S19 can be reduced as (B.1-22) At the same time, around the location , all open ending groups form dynamic bonds. This leads to the vanishing of inactive chains around the location , written as (B.1-23) Along with above initial and boundary conditions, the reaction-diffusion equation (Eq. B.1-S22) can be solved analytically or numerically. Once in the diffusion-reaction model is solved, we can further obtain the active ith chain number per unit volume of the self-healing segment at healing time t, written as ( ) s t C a i , b L s i 4 0 2 £ £ 0 f i k 0 r i k ( ) ( ) s N s t C i d i d = = , 0 ( ) 0 , 0 = = s t C a i ( ) 1 = ò ¥ ¥ - ds s d 0 0 r i f i k k < 0 r i k 0 f i k 0 0 f i r i k k >> ( ) ( ) ( ) s t C k s s t C D t s t C d i r i d i i d i , , , 0 2 2 - ¶ ¶ = ¶ ¶ b L s i 4 2 = b L s i 4 2 = ( ) 0 4 , 2 = = b L s t C i d i ( ) s t C d i , 297 (B.1-24) where is for the self-healed segment at the undeformed state ( ), and the superscript “h” denotes “healed”. At the deformed state, the active ith chain number in the self-healed segment decreases with the increasing stretch. If we consider a quasistatic load with principal stretches ( ), the active ith chain number per unit volume of the self-healing segment can be calculated as (B.1-25) with the chain force expressed as (B.1-26) Therefore, the free energy per unit volume of the self-healed segment can be written as (B.1-27) where and is given by Eq. S25. The nominal stress along direction can be written as (B.1-28) where t is the healing time and is the uniaxial stretch in the self-healed segment. We consider a self-healed sample (length ) with a self-healed segment (length , ) and two virgin segments (Fig. S11). Under a uniaxial stretch, the lengths of the whole sample and the ( ) ( ) ò - = b L i d i i i h i i ds N s t C L b N t N 4 0 2 2 , 4 1 ( ) t N h i 1 3 2 1 = = = l l l ( ) 2 / 1 3 2 1 , - = = = h h l l l l l ( ) ( ) ÷ ÷ ø ö ç ç è æ D - + ÷ ÷ ø ö ç ç è æ D ÷ ÷ ø ö ç ç è æ D - = T k x f k T k x f k T k x f k t N t N B i r i B i f i B i r i h i ah i exp exp exp 0 0 0 ( ) ( ) ÷ ÷ ÷ ø ö ç ç ç è æ + = - - i h h B i n L b T k f 3 2 1 2 1 l l ( ) å = ÷ ÷ ø ö ç ç è æ + = m i h i h i h i h i B i ah i h T k n t N W 1 sinh ln tanh b b b b ( ) ( ) ÷ ÷ ø ö ç ç è æ ú û ù ê ë é + = - - i h h h i n L 3 2 1 2 1 l l b ( ) t N ah i 1 l ( ) ( ) ( ) ( ) ( ) ( ) å = - - - - ú ú ú û ù ê ê ê ë é ÷ ÷ ÷ ø ö ç ç ç è æ + + ÷ ø ö ç è æ - = m i i h h i ah i h h B h h h h n L n t N T k t s 1 1 2 1 1 2 2 1 3 2 6 3 , l l l l l l l h l H h H H H h << 298 self-healed segment become and , respectively. The stretch of the self-healed segment is . The stretch of the virgin segment is approximately equal to the stretch of the whole sample because . We assume the initial cross-sections of the virgin segment and the self-healed segment are the same; then, the uniaxial nominal stresses in the self-healed segment and the virgin segment should be equal, written as (B.1-29) where is referred to Eq. B.1-28, and is referred to Eq. B.1-7. From Eq. B.1-29, we can determine the stress-stretch behaviors of the self-healed sample for various healing time t. The comparisons between the experimentally measured self-healing behaviors of the studied elastomers and theoretically calculated results are shown in Fig. S13. We employ an inhomogeneous chain-length distribution shown in Fig. S13a. The employed parameters are shown in Table S1. The chain dynamics parameters and Rouse friction coefficients are within the reasonable order compared with limited experimental or simulation results in the references 84,122,125,126 . The theoretically calculated stress- strain curves can consistently match the experimentally measured results (Fig. S13b). In addition, the theoretically calculated relationships between the healing strength ratio and the healing time also agree well with the experimental results (e.g., 60°C in Fig. S13c). Effect of temperature on the self-healing behavior The temperature term is directly involved in the expression of the nominal stress of the original hydrogel and self-healed hydrogel shown in Eqs. B.1-7 and B.1-27. However, the existence of both expressions results in the vanishing of the temperature term in the healing strength ratio. Here, we more focus on the effects of temperatures on the Rouse friction coefficient (Eq. B.1-13). The curvilinear diffusivity can be affected by the temperature from two aspects: First, the temperature term explicitly appears in Eq. B.1-13 through k BT. Then, the Rouse friction coefficient monotonically decreases with increasing temperature 100 . This behavior can usually be modeled by Vogel relationship as 23,100,122 , h h h h h h H h = l l ( ) ( ) h h H H h h H h - - » = l ( ) ( ) l l 1 1 s s h h = ( ) h h s l 1 ( ) l 1 s x 299 (B.1-30) where is the Vogel temperature, B (positive) and A are constant parameters. By judiciously selecting these three parameters, we can quantitatively reveal the relationship between the temperature and self- healing strength ratio. Using , and , we are able to theoretically capture the relationships between the healing strength ratio and the healing time, which show good agreement with experimental results for various temperatures from 40°C to 60°C (Fig. S13c). We further define the equilibrium healing time as the healing time corresponding to 90% healing strength ratio. We find out that the theoretically calculated relationship between the equilibrium healing time and the healing temperature is consistent with the experimental result (Fig. S13d). ÷ ÷ ø ö ç ç è æ - - µ ¥ A T T B exp x ¥ T K T 2 . 383 = ¥ K B 5 . 486 = 96 . 5 - = A 300 B.2 Mathematical model of polymer strengthening by additional crosslinking In the current work, the polymer ink is first crosslinked by the photo-initiated addition reaction of the acrylate groups (Fig. S44). Within this primary polymer network, NCO groups are active sites that can have a strong reaction with hydroxyl groups (OH) on the chloroplast-produced glucose to form urethane linkages (-NH-CO-O-). Since a glucose molecule has multiple OH groups, it is hypothesized that the OH groups on the chloroplast-produced glucose can bridge multiple NCO groups to create new crosslinks additional to the acrylate-enabled crosslinks within the designed polymer matrix (Fig. S59A). Before strengthening Before strengthening, the polymer network is assumed to feature a homogenous chain length. The chain length is described by the Kuhn length, denoted as 𝑁 ' and chain number per unit volume as 𝑛 ' . The strain energy density of the polymer network can be written as 103,385 𝑊 ' =𝑛 ' 𝑘 > 𝑇𝑁 ' k Q 2 .4;EQ 2 +𝑙𝑛 Q 2 8";EQ 2 l (B.2-1) where 𝑘 > is the Boltzmann constant, 𝑇 is the temperature in Kelvin, and 𝛽 ' =𝐿 @2 HA 2 (B.2-2) where 𝐿 @2 ( ) is the inverse Langevin function and Λ is the chain stretch. Here, we follow an affine deformation assumption that the microscopic polymer chain deformation affinely follows the macroscopic deformation in three principal directions; thus, the chain stretch can be expressed as Λ=W𝜆 2 ( +𝜆 ( ( +𝜆 F ( (B.2-3) This affine deformation assumption has been widely adopted for deriving the constitutive models for rubber-like materials, such as the New-Hookean model 103 and the Arruda-Boyce model 385 . The chain stretch expressed in Eq. B.2-3 is directly adopted from the New-Hookean model 103,386 . If the polymer is incompressible, the Cauchy stresses in three principal directions can be written as 301 ⎩ ⎪ ⎨ ⎪ ⎧ 𝜎 2 =𝜆 2 ) 2 )Z 0 −𝑃 𝜎 ( =𝜆 ( ) 2 )Z ( −𝑃 𝜎 F =𝜆 F ) 2 )Z * −𝑃 (B.2-4) where 𝑃 is the hydrostatic pressure. Under uniaxial tension with 𝜆 2 =𝜆 and 𝜆 ( =𝜆 F =𝜆 @2/( , the Cauchy stresses 𝜎 ( and 𝜎 F vanish. The Cauchy stress 𝜎 2 can be formulated as 𝜎 2 =𝜆 2 ) 2 )Z 0 −𝜆 ( ) 2 )Z ( (B.2-5) The corresponding tensile nominal stress (engineering stress) can be calculated as 𝑠 2 = 0 Z 0 =𝑛 ' 𝑘 > 𝑇W𝑁 ' Z@Z 8( √Z ( [(Z 80 𝐿 @2 un Z ( [(Z 80 A 2 v (B.2-6) Equation B.2-6 can be used to explain the stress-strain behaviors of polymer samples before strengthening. Only two fitting parameters (polymer chain length 𝑁 ' and chain number density 𝑛 ' ) are required. Strengthening by forming additional crosslinks Once the glucose is introduced, additional crosslinks form through the reactions between the free NCO groups and the OH groups on the glucose (Fig. S60A). One glucose molecule with 5 OH groups is only required to bridge two NCO groups to form a crosslink. Thus, one glucose molecule is able to at most form 2.5 crosslinks within the network. The number of the introduced glucose molecules per unit volume is denoted as 𝑛 { and the formed additional crosslink number per unit volume is denoted as 𝑛 4 , which should follow 𝑛 { ≤𝑛 4 ≤2.5𝑛 { . As shown in Fig. S60B, two polymer chains with chain length 𝑁 ' become four polymer chains with shorter lengths after introducing an additional crosslink. In a general case, these four polymer chains may have different chain lengths. Here, to capture the essential physics with a simple mathematic formulation, we assume these four polymer chains have the same chain length, as 𝑁 ' 2 ⁄ . In a more general case shown 302 in Fig. S60C, we assume the crosslink formed between a chain with a length of 𝑁 ' 2 " ⁄ and a chain with a length of 𝑁 ' 2 ⁄ induces four chains with respective half lengths, where 𝑖 =0,1,2⋯ and 𝑗 =0,1,2⋯. After introducing 𝑛 4 additional crosslinks per unit volume, the initially homogeneous chain length (𝑁 ' ) will become inhomogeneous, with a chain length distribution over lengths of 𝑁 ' , 𝑁 ' 2 ⁄ , …., and 𝑁 ' 2 3 ⁄ , where 𝑚 ≥1. The value of 𝑚 is constrained by choosing the largest 𝑚 to ensure A 2 ( . ≥𝑁 3"; (B.2-7) where 𝑁 3"; is the admissible smallest chain length. To estimate the chain number of each type of chain length per unit volume, we treat the additional crosslinking process as 𝑚 steps. In each step, additional crosslinks of a certain amount are introduced. We employ two methods: Method 1: Equal number of incremental crosslinks In method 1, we assume that probabilities of forming a crosslink on the chain with a length of 𝑁 ' 2 " ⁄ and the chain with a length of 𝑁 ' 2 ⁄ are equal, where 𝑖 =0,1,2⋯ and 𝑗 =0,1,2⋯. Under this assumption, the incremental additional crosslinking density for each step is equal, denoted as 𝑑𝑛 4 : 𝑑𝑛 4 = ; $ 3 (B.2-8) In the following, we will go through each step to calculate the volume density of polymer chains with length 𝑁 ' 2 ⁄ , where 𝑗 =0,1,2⋯. We denote it as 𝐶 , where 𝑗 =0,1,2⋯. In step 1, some of the initial chains with length 𝑁 ' become shorter chains with a length of 𝑁 ' 2 ⁄ after adding 𝑑𝑛 4 crosslinks if 2𝑑𝑛 4 ≤𝑛 ' . At the end of step 1, we have: 𝐶 ' =𝑛 ' −2𝑑𝑛 4 (B.2-9a) 𝐶 2 =4𝑑𝑛 4 (B.2-9b) 303 In step 2, three possible routes to form crosslinks: between two chains with the length of 𝑁 ' , between two chains with the length of 𝑁 ' 2 ⁄ , and between a chain with the length of 𝑁 ' and a chain with the length of 𝑁 ' 2 ⁄ . The probabilities for partitioning chains with length 𝑁 ' and chains with length 𝑁 ' 2 ⁄ are equal. Therefore, at the end of step 2, we have: 𝐶 ' =𝑛 ' −2𝑑𝑛 4 −2(𝑑𝑛 4 2 ⁄ ) (B.2-10a) 𝐶 2 =4𝑑𝑛 4 +4(𝑑𝑛 4 2 ⁄ )−2(𝑑𝑛 4 2 ⁄ ) (B.2-10b) 𝐶 ( =4(𝑑𝑛 4 2 ⁄ ) (B.2-10c) Similarly, at the end of step 3, we have: 𝐶 ' =𝑛 ' −2𝑑𝑛 4 −2(𝑑𝑛 4 2 ⁄ )−2(𝑑𝑛 4 3 ⁄ ) (B.2-11a) 𝐶 2 =4𝑑𝑛 4 +4(𝑑𝑛 4 2 ⁄ )−2(𝑑𝑛 4 2 ⁄ )+4(𝑑𝑛 4 3 ⁄ )−2(𝑑𝑛 4 3 ⁄ ) (B.2-11b) 𝐶 ( =4(𝑑𝑛 4 2 ⁄ )+4(𝑑𝑛 4 3 ⁄ )−2(𝑑𝑛 4 3 ⁄ ) (B.2-11c) 𝐶 F =4(𝑑𝑛 4 3 ⁄ ) (B.2-11d) Eventually, at the end of step m, we have: 𝐶 ' =𝑛 ' −2𝑑𝑛 4 k1+ 2 ( + 2 F +⋯+ 2 3 l (B.2-12a) 𝐶 2 =2𝑑𝑛 4 +2𝑑𝑛 4 k1+ 2 ( + 2 F +⋯+ 2 3 l (B.2-12b) 𝐶 ( =2( 7; $ ( )+2𝑑𝑛 4 k 2 ( + 2 F +⋯+ 2 3 l (B.2-12c) …… 𝐶 =2(𝑑𝑛 4 𝑗 ⁄ )+2𝑑𝑛 4 k 2 + 2 [2 +⋯+ 2 3 l (B.2-12d) …… 304 𝐶 3 =4(𝑑𝑛 4 𝑚 ⁄ ) (B.2-12e) The volume density of chains with length 𝑁 ' 2 ⁄ at the end of step m can be summarized as 𝐶 = ⎩ ⎪ ⎨ ⎪ ⎧ 𝑛 ' − (; $ 3 k1+ 2 ( + 2 F +⋯+ 2 3 l ,𝑗 =0 (; $ 3 k ( + 2 [2 +⋯+ 2 3 l ,1≤𝑗 ≤𝑚−1 B; $ 3 ( ,𝑗 =𝑚 (B.2-13) After strengthening, the polymer chain length is inhomogeneous with a chain length distribution over lengths of 𝑁 ' , 𝑁 ' 2 ⁄ , …., and 𝑁 ' 2 3 ⁄ , where 𝑚 ≥1. The chain length distribution is shown in Eq. S13. We assume that under deformation, each polymer chain deform following an affine deformation assumption that the microscopic polymer chain deformation affinely follows the macroscopic deformation in three principal directions; thus, the chain stretch of the chain with the length of 𝑁 ' 2 ⁄ (𝑗 =0,1,2⋯) can be expressed as 84,99,115,174,264,265,387 Λ =W𝜆 2 ( +𝜆 ( ( +𝜆 F ( (B.2-14) The strain energy of the whole polymer network per unit volume can be formulated as 84,99,115,174,264,265,387 𝑊 8 =∑ Ð𝐶 𝑘 > 𝑇k A 2 ( \ l Q \ .4;EQ \ +𝑙𝑛 Q \ 8";EQ \ Ñ 3 b' (B.2-15) 𝛽 =𝐿 @2 \ HA 2 ( \ ⁄ (B.2-16) where the chain stretch Λ is given in Eq. S14. Under uniaxial tension with 𝜆 2 =𝜆 and 𝜆 ( =𝜆 F =𝜆 @2/( , the nominal tensile stress of the incompressible polymer after strengthening can be calculated as 𝑠 82 =∑ t𝐶 𝑘 > 𝑇W𝑁 ' 2 ⁄ Z@Z 8( √Z ( [(Z 80 𝐿 @2 un Z ( [(Z 80 A 2 ( \ ⁄ vw 3 b' (B.2-17) 305 In method 1, there is a requirement for the relationship between 𝑛 4 and 𝑚. For example, if 𝑚 =1, the maximal possible crosslinking point density is 𝑛 ' 2 ⁄ . This condition is to ensure the chain density of chains with length 𝑁 ' is not negative. For a certain 𝑚 ≥1, the requirement of the possible crosslink density is (𝑚−1) d2k1+ 2 ( + 2 F +⋯+ 2 3@2 le <𝑛 4 𝑛 ' ≤𝑚 d2k1+ 2 ( + 2 F +⋯+ 2 3 le ⁄ (B.2-18) Method 2: Unequal number of incremental crosslinks In method 2, we assume that the probability of forming a crosslink on the chain with the length of 𝑁 ' 2 " ⁄ is higher than that of forming a crosslink on the chain with the length of 𝑁 ' 2 ⁄ when 𝑖 <𝑗. In an extreme case, the crosslink occurs first on the chain with the length of 𝑁 ' 2 " ⁄ , and then on the chain with the length of 𝑁 ' 2 "[2 ⁄ . In other words, the crosslinking reaction on the longer chains always happens before the crosslinking reaction on the shorter chains. Following the assumption, we can naturally define the ith step as the step with the occurrence of the crosslinking reaction on the chain with the length of 𝑁 ' 2 "@2 ⁄ . The process will move to the next step only when there are enough crosslinkers to consume all the chains with the length of 𝑁 ' 2 "@2 ⁄ . If the crosslinking reaction stops at step 1, there are only two types of chains: chains with length 𝑁 ' and 𝑁 ' 2 ⁄ . Their volume densities can be calculated as 𝐶 ' =𝑛 ' −2𝑛 4 (B.2-19a) 𝐶 2 =4𝑛 4 (B.2-19b) The requirement is 0<𝑛 4 𝑛 ' ⁄ ≤1 2 ⁄ . If the crosslinking reaction stops at step 2, there are only two types of chains: chains with length 𝑁 ' 2 ⁄ and 𝑁 ' 2 ( ⁄ . Their volume densities can be calculated as 𝐶 2 =2𝑛 ' −2k𝑛 4 − ; 2 ( l =3𝑛 ' −2𝑛 4 (B.2-20a) 306 𝐶 ( =4k𝑛 4 − ; 2 ( l (B.2-20b) The requirement is 1 2 ⁄ <𝑛 4 𝑛 ' ⁄ ≤3 2 ⁄ . If the crosslinking reaction stops at step 𝑚, at the end of step m, there are only two types of chains: chains with lengths 𝑁 ' 2 3@2 ⁄ and 𝑁 ' 2 3@2 ⁄ . Their volume densities can be calculated as 𝐶 3@2 =2 3@2 𝑛 ' −2d𝑛 4 −k2 3@( − 2 ( l 𝑛 ' e= (2 3 −1)𝑛 ' −2𝑛 4 (B.2-21a) 𝐶 3 =4d𝑛 4 −k2 3@( − 2 ( l 𝑛 ' e=4𝑛 4 −4k2 3@( − 2 ( l 𝑛 ' (B.2-21b) The requirement is for the additional crosslink density to reach step m is ( .80 @2 ( <𝑛 4 𝑛 ' ⁄ ≤ ( . @2 ( (B.2-22) After strengthening, the strain energy function can be formulated as 84,99,115,174,264,265,387 𝑊 8 =∑ Ð𝐶 𝑘 > 𝑇k A 2 ( \ l Q \ .4;EQ \ +𝑙𝑛 Q \ 8";EQ \ Ñ 3 b3@2 (B.2-23) 𝛽 =𝐿 @2 \ HA 2 ( \ ⁄ (B.2-24) where the chain stretch Λ is given in Eq. S14 and 𝐶 for 𝑗 =𝑚−1 and 𝑗 =𝑚 are given in Eq. S21. Under uniaxial tension with 𝜆 2 =𝜆 and 𝜆 ( =𝜆 F =𝜆 @2/( , the nominal tensile stress of the incompressible polymer after strengthening can be calculated as 𝑠 82 = ∑ t𝐶 𝑘 > 𝑇W𝑁 ' 2 ⁄ Z@Z 8( √Z ( [(Z 80 𝐿 @2 un Z ( [(Z 80 A 2 ( \ ⁄ vw 3 b3@2 (B.2-25) Strengthening with m=1 When 𝑛 4 𝑛 ' ⁄ ≤1 2 ⁄ , there is only one-step strengthening. After the strengthening, only chains with lengths of 𝑁 ' and 𝑁 ' 2 ⁄ coexist in the system. The strengthening can be modeled by either method 1 or method 2. 307 As shown in Figs. S60AB, the polymer with an initial chain length 𝑁 ' =100 becomes stronger after forming more additional crosslinks. The Young’s modulus (within 10% strain region) increases linearly with increasing the crosslink density (Fig. S60B). We define the strengthening factor as the strengthened Young’s modulus normalized by the unstrengthened Young’s modulus. We find that the strengthening factor decreases with increasing the initial chain length 𝑁 ' (Figs. S60CD). When the initial chain length 𝑁 ' is very small, the polymer can be significantly strengthened. According to the stress-strain curve shapes of the studied polymers in this work (Figs. S58), the initial chain length should be 𝑁 ' ≥60. The initial chain length cannot be too small. When the initial chain length 𝑁 ' >500, the strengthening factor reaches a plateau of around 1.96. When the initial chain length 60≤𝑁 ' ≤2000, the strengthening factor varies from 1.96 to 2.2. According to the results shown in Figs. 61G-J and S58, the strengthening factor of the studied polymer in this work can reach as high as 6.2; therefore, we have to study the cases for 𝑚 >1. Strengthening with m>1 When the density of the formed additional crosslinks 𝑛 4 𝑛 ' ⁄ >1 2 ⁄ , the chain length distributions modeled by methods 1 and 2 are different. Figure S61 shows the relationships between step number m and the density of the formed additional crosslinks for methods 1 and 2. For method 1, when 𝑛 4 𝑛 ' ⁄ increases to 5, the step number m drastically increases to 45. However, the step number m is still 4 when 𝑛 4 𝑛 ' ⁄ =5 for method 2. When 𝑛 4 𝑛 ' ⁄ is slightly larger than 1 2 ⁄ (e.g., 2/3), the strengthening factors calculated from methods 1 and 2 are still almost the same (Fig. S62). However, when 𝑛 4 𝑛 ' ⁄ increases to 1, the strengthening factors calculated from methods 1 are larger than those calculated from method 2 (Figs. S63A-D). It is because that the step number of method 1 is larger, corresponding to shorter chains. When 𝑛 4 𝑛 ' ⁄ is relatively large (e.g., 3.05), the step number for method 1 is 21, which means that the shortest chain length becomes 𝑁 ' 2 (2 ⁄ . Considering the stress-strain curve shape of studied polymer 308 (Figs. S58), the initial chain length 𝑁 ' is estimated between 60 and 2000. 𝑁 ' 2 (2 ⁄ becomes an invalid number for the chain length. Therefore, under such a situation that additional crosslink density is relatively large, method 1 cannot model the strengthening behavior. We can only employ method 2 (Figs. S63EF). Comparison between theory and experiment Using method 2, we can explain the stress-strain curves and Young’s moduli of the polymers before and after strengthening (used parameters shown in Table S3). For example, for polymers with chloroplasts of various weight concentrations (0 to 5 wt%), the theoretically calculated stress-strain curves and Young’s moduli agree with the respective experimental results (Fig. S64AB). It also works for polymers with 5 wt% chloroplasts under various illumination periods from 0 to 2 h (Fig. S64CD). 309 B.3 Supplies of water and carbon dioxide Since the chloroplasts are embedded in the polyurethane-based polymer matrix, external water supply cannot be provided to support the photosynthesis of the chloroplasts. The water for the photosynthesis process should be supplied by the water storage within the chloroplasts 324,328,329,363 . To estimate the mass percentage of water within the extracted chloroplast, we placed the extracted chloroplast in a dark environment and applied a gentle airflow to evaporate the water for 8 h. Through measuring the mass before and after the evaporation process, we estimated the mass percentage of the water within the extracted chloroplast was 83.9±2.5 wt% (Table S2). If the weight percentage of the chloroplast is 5 wt%, with the density of polyurethane-based polymer as 1.25 g/cm 3 , we can roughly estimate the volume density of water supply as 𝐶 e ( ' = f%×KF.%×2.(f {/93 * 2K {/3wi =2.91𝑚𝑜𝑙/𝐿 (B.3-S1) In plants, the carbon dioxide is digested by stomas and then gradually diffuse into cells at a deeper location 328,329,363 . In this study, since the polyurethane-based polymer has a relatively high permeability for carbon dioxide, with the diffusivity experimentally measured as 𝐷 =3.5×10 @ −3.9×10 @ 𝑐𝑚 ( 𝑠 @2 331,420 , we hypothesize that the carbon dioxide that supports photosynthesis may be provided by the existing carbon dioxide within the polymer matrix and the diffusion of carbon dioxide through the polymer matrix during the photosynthesis process. The concentration of carbon dioxide in the atmosphere in year 2019 was around 410-415 ppm 421 , which calculated as 𝐶 6 ( ' =9.318×10 @F −9.432×10 @F 𝑚𝑜𝑙/𝐿 (B.3-S2) At the as-fabricated state, we assume the carbon dioxide within the polymer matrix is already in equilibrium with that in the atmosphere. During the photosynthesis process, the carbon dioxide within the polymer matrix is gradually consumed, and external carbon dioxide diffuses from the atmosphere into the polymer matrix. 310 The key question is whether the supplies of water and carbon dioxide are sufficient for the conducted experiment. To answer this question, we carry out the following estimation. According to the theoretical modeling shown in above section, the initial chain density is estimated as 𝑛 ' =4.5×10 2 𝑚 @F =7.475×10 @K 𝑚𝑜𝑙/𝐿 (Table S3). The concentration of the required additional crosslinks 𝑛 4 for strengthening the polymer network with 5 wt% embedded chloroplasts should scale with 𝑛 ' , written as 𝑛 4 =𝛽𝑛 ' (B.3-S3) where 𝛽 is a parameter (<10) dependent on the light illumination time. For example, for 2-h light illumination, 𝛽 =2.3; and for 4-h light illumination, 𝛽 =3−3.5. One glucose molecule with 5 OH groups is only required to bridge two NCO groups to form a crosslink. Thus, one glucose molecule is able to at most form 2.5 crosslinks within the network. The number of the introduced glucose molecules per unit volume is denoted as 𝑛 { , which follows 𝑛 { ≤𝑛 4 ≤2.5𝑛 { . Therefore, the possible highest concentration of the required glucose is 𝑛 { =𝑛 4 =𝛽𝑛 ' (B.3-S4) For a photosynthesis process, the overall effective chemical reaction can be written as 328,329,363 6 𝐻 ( 𝑂+6 𝐶𝑂 ( Ep Á Ã𝐶 c 𝐻 2( 𝑂 c +6 𝑂 ( (B.3-S5) Equation S30 shows that the production of 1 glucose molecule requires 6 water molecules and 6 carbon dioxide molecules. Therefore, the concentrations of the required water and carbon dioxide are estimated as 𝐶 e ( $ =𝐶 6 ( $ =6𝛽𝑛 ' (B.3-S6) For 4-h light illumination (along with the subsequent 4-h darkness), 6𝛽𝑛 ' ~1.35×10 @c − 1.57×10 @c 𝑚𝑜𝑙/𝐿. 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Abstract (if available)
Abstract
Living organisms are continuous sources of inspiration for engineering materials and structures. However, synthetic materials are typically different from living creatures because the latter consist of living cells to support their metabolisms, such as self-healing, response to stimuli, remodeling, and reproduction. Bio- inspired self-healing materials have been developed to mimic natural living materials to show the spectacular capability of repairing fractures or damages and restoring mechanical strengths. However, existing self-healing polymers still face two central challenges in their development: missing the fundamental understanding of self-healing mechanics and deficiency in 3D shaping. This dissertation aims to provide a comprehensive theoretical understanding of bio-inspired self-healing polymers and propose novel polymer design strategies to address the challenges. This dissertation starts by presenting a general analytical model to understand the interfacial self-healing behaviors of dynamic polymer networks. Based on the theoretical understanding, a self-healable elastomer polymer ink is molecularly designed to enable stereolithography-based additive manufacturing with rapid and full self-healing. Guided by the theoretical and experimental methods, four examples of novel bio-inspired polymer systems are proposed to provide comprehensive scientific advances to solve different engineering problems. In the first example, we propose a theoretical framework to understand the light-activated interfacial self-healing of soft polymers with light-responsive photophores. We introduce a tough and self-healable nanocomposite hydrogel that can be activated by ultraviolet (UV) light to efficiently adsorb heavy metal ions and degrade dye molecules in wastewater. In the second example, we propose a model to understand self-healable thermoplastic elastomers' constitutive and healing behaviors with both dynamic bonds and semi-crystalline phases. We present a class of transformable lattice structures enabled by fracture and shape-memory-assisted healing. In the third example, we harness photosynthesis in chloroplasts embedded in a synthetic polymer matrix to remodel 3D-printed structures and demonstrate matrix strengthening and crack healing. We propose a theoretical framework to model the self- strengthening behaviors of polymers assisted by the photosynthesis process. In the last example, we report a class of 3D-printable synthetic polymers that constructively strengthen their bulk and interfacial mechanical properties in response to the typically destructive aquatic environment. In the end, concluding remarks and an outlook of future work are provided to summarize the dissertation.
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University of Southern California Dissertations and Theses
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Asset Metadata
Creator
Yu, Kun-Hao
(author)
Core Title
Mechanics and additive manufacturing of bio-inspired polymers
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Civil Engineering
Degree Conferral Date
2022-08
Publication Date
07/19/2022
Defense Date
05/02/2022
Publisher
University of Southern California
(original),
University of Southern California. Libraries
(digital)
Tag
additive manufacturing,bio-inspired,dynamic bonds,engineered living materials,OAI-PMH Harvest,polymer network model,self-healing,self-remodeling
Format
application/pdf
(imt)
Language
English
Contributor
Electronically uploaded by the author
(provenance)
Advisor
Wang, Qiming (
committee chair
), Chen, Yong (
committee member
), Ghanem, Roger (
committee member
), Lee, Vincent (
committee member
)
Creator Email
kunhao0629@gmail.com,kunhaoyu@usc.edu
Permanent Link (DOI)
https://doi.org/10.25549/usctheses-oUC111373213
Unique identifier
UC111373213
Legacy Identifier
etd-YuKunHao-10856
Document Type
Dissertation
Format
application/pdf (imt)
Rights
Yu, Kun-Hao
Type
texts
Source
20220719-usctheses-batch-955
(batch),
University of Southern California
(contributing entity),
University of Southern California Dissertations and Theses
(collection)
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The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given.
Repository Name
University of Southern California Digital Library
Repository Location
USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA
Repository Email
cisadmin@lib.usc.edu
Tags
additive manufacturing
bio-inspired
dynamic bonds
engineered living materials
polymer network model
self-healing
self-remodeling