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Content INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type o f computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. Oversize materials (e.g., maps, drawings, charts) are reproduced by sectioning the original, beginning at the upper left-hand comer and continuing from left to right in equal sections with small overlaps. Each original is also photographed in one exposure and is included in reduced form at the back o f the book. Photographs included in the original manuscript have been reproduced xerographically in this copy. Higher quality 6” x 9” black and white photographic prints are available for any photographs or illustrations appearing in this copy for an additional charge. Contact UMI directly to order. UMI A Bell & Howell Information Company 300 North Zed) Road, Ann Arbor MI 48106-1346 USA 313/761-4700 800/521-0600 POLYMER AGGREGATION DRIVEN BY SPECIFIC INTERACTIONS W enjun Wu A Dissertation Presented to the FACULTY OF THE GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (Chemistry) August 1995 Copyright 1995 W enjun Wu UMI Number: 9621651 UMI Microform 9621651 Copyright 1996, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 UNIVERSITY OF SOUTHERN CALIFORNIA THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 90007 This dissertation, written by WenJ uij .H V l............................................................... under the direction of h.sx Dissertation Committee, and approved by all its members, has been presented to and accepted by The Graduate School, in partial fulfillment of re quirements for the degree of DOCTOR OF PHILOSOPHY — C . . Dean of Graduate Studies Date DISSERTATION COMMITTEE Chairperson Acknowledgments I am very grateful to my research advisor, Professor Eric J. Amis, for his patience, support and direction during my graduate career. I deeply appreciate his continual concerns and efforts that he has exhibited through the years. I have benefited immensely from the scientific meetings and discussions he encouraged me to attend. I m ust acknowledge Dr. Tom Seery and Dr. Donald Hodgson, who patiently taught me the operation and data analysis of light scattering experiments. For the help and suggestions that they have provided me, I owe them a debt of gratitude. I would like to thank all the colleagues in the group, including Dr. Donald Hodgson, Tom Seery, Ning Hu, Qun Yu, Xinhao Gao, Diane Valachovic, Brett Ermi, and Chevan Goonetilleke, for being helpful resources and creating a friendly and productive working environment. I would also like to thank a group of graduate students in the chemistry department, Chuck Xu, Pingfan Yang, Bo Wu, Gerard Jensen, Jessie Chu, Claudine Ashvar, and Joe Finley for their help, encouragement and friendship. I thank my parents for their support, love and hope. Finally, I am most grateful to my husband, Dongyi, for his love, patience and understanding. TABLE OF CONTENTS Page Acknowledgments........................................................................................ ii List of Figures................................................................................................ v i List of Tables.................................................................................................. xiv Abstract........................................................................................................... xv Chapter 1. Introduction................................................................................ 1 References........................................................................................... 10 Chapter 2. Experimental Techniques........................................................ 15 Introduction....................................................................................... 15 Viscometry.......................................................................................... 15 Capillary Viscometers........................................................... 18 Magnetic Sphere Viscometer............................................... 21 Light Scattering.................................................................................. 25 Static Light Scattering........................................................... 26 Dynamic Light Scattering.................................................... 28 References........................................................................................... 39 Chapter 3. Matched Linear and Cyclic Homopolymers........................ 42 Introduction....................................................................................... 42 Theoretical Predictions..................................................................... 44 Unperturbed Cyclic Homopolymers................................. 44 Perturbed Cyclic Homopolymers....................................... 49 Experimental Agreements............................................................... 53 Unperturbed Cyclic Homopolymers................................. 54 -Perturbed Cyclic Homopolymers....................................... 55 Summary............................................................................................ 57 iv References........................................................................................... 58 Chapter 4. Matched Linear Triblock and Cyclic Diblock Copolymers.................................................................62 Introduction....................................................................................... 62 Experimental Section........................................................................ 62 Results and Discussions................................................................... 67 Static Light Scattering........................................................... 67 Dynamic Light Scattering.................................................... 74 Conclusions........................................................................................ 8 6 References........................................................................................... 89 Chapter 5. Aggregation of Linear Triblock and Cyclic Diblock Copolymers.................................................................91 Introduction....................................................................................... 91 Review: Linear Block Copolymer Micellization......................... 92 Experimental Section........................................................................ 98 Results and Discussions....................................................................99 DLS of Linear Triblock Copolymer.................................... 99 DLS of Cyclic Diblock Copolymer...................................... 105 Total Intensity Measurements............................................ 108 Comparisons.......................................................................... 112 Conclusions........................................................................................ 116 References........................................................................................... 117 Chapter 6 . Hydrophobically M odified Water Soluble Polymers 120 Introduction....................................................................................... 120 Random Copolymers........................................................................ 121 Telechelic Polymers.......................................................................... 127 Theoretical Approaches........................................................ 129 Experimental Work............................................................... 138 References........................................................................................... 142 Chapter 7. Fluorocarbon Telechelic PEOs................................................ 147 Introduction........................................................................................ 147 Experimental Section........................................................................ 148 Results and Discussions.................................................................... 154 Viscosity.................................................................................. 154 Light Scattering...................................................................... 164 Conclusions......................................................................................... 183 References........................................................................................... 185 Chapter 8 . Hydrogen-Bonding Aggregation in Nonpolar Solvent................................................................. 188 Introduction....................................................................................... 188 Review................................................................................................. 188 Experimental Section........................................................................ 193 Results and Discussions......................................................................198 Characterization of Individual Copolymers.................... 198 Absence of Self-Association in Donor Copolymers 202 Effect of Donor to Acceptor Ratio...................................... 207 Concentration Effect.............................................................. 216 Effect of Acceptor Comonomer Content........................... 220 Solvent Effect......................................................................... 226 Conclusions........................................................................................ 228 References........................................................................................... 230 Chapter 9. Future W ork................................................................................. 233 Matched Linear Triblock and Cyclic Diblock............................... 233 Fluorocarbon End-Capped PEOs.................................................... 237 References........................................................................................... 241 vi LIST OF FIGURES Figure Page Figure II-l One Bulb Ubbelohde capillary viscometer............... 20 Figure H-2 Diagram of the magnetic sphere viscometer setup........................................................... 2 2 Figure II-3 Typical Zimm plot showing double extrapolations.................................................................. 29 Figure II-4 Schematic of Bi-200SM laser light scattering instrument................................................... 35 Figure III-l (a) A cyclic chain with two Gaussian subchains originating in segment i and ending in segment j, where one subchain consists of m segments and the other of N-m. (b) Topological state of two ring polymers. Average intermolecular interaction is repulsive......................................................................... 45 Figure III-2 Double contact cluster diagram for two interacting rings. The dashed lines denote the segment pairs in contact....................................... 51 Figure IV-1 Synthesis of linear triblock and cyclic diblock copolymers...................................................... 64 Figure IV-2 Zimm Plots of linear (upper) and cyclic (bottom) copolymers at 25 °C..................................... 6 8 Figure IV-3 Weight averaged molecular weights measured by SLS for linear triblock (□) and cyclic diblock (O) copolymers over the temperature range of 1 2 to 35 °C............................... 69 Figure IV-4 Radii of gyration determined by SLS for linear triblock (□) and cyclic diblock (O) copolymers over the temperature range of 12 to 35 °C.................................................................. 70 vii Figure IV-5 Second virial coefficients determined by SLS for linear triblock (□) and cyclic diblock (O) copolymers over the temperature range of 12 to 35 °C............................... 71 Figure IV- 6 Concentration dependence of g< 2)(t) functions from DLS at 14.9 °C and scattering angle of 30°. Concentrations (mg mL'1) for (a) cyclic (top): 15.5 (O), 10.9 (♦), 8.73 (A), 5.93 (•); (b) linear (bottom): 13.5 (O), 8.40 (♦), 7.30 (A), 3.59 ( • ) ......................................................... 76 Figure IV-7 Angular dependence of g^2Ht) functions from DLS at 14.9 °C. Concentrations for cyclic (top) and linear (bottom) polymers are (a) 20.8 and (b) 29.8 mg mL-1. Scattering angles 0 = 30° (O), 45° (•), 60° (■), 75° (□), 90° (▲), 120° (A), 135° (O)............................................ 77 Figure IV- 8 Angular dependence of DLS inverse relaxation time 1 /x for cyclic block copolymer (o), and the fast mode (□) and the slow mode (■) for linear block copolymer at 13.5 mg mL"1 and 14.9 °C................... 78 Figure IV-9 Temperature dependence of g^21(t) correlation functions from DLS for cyclic polymer (upper) and linear (bottom) at concentrations of 29.8 mg mL-1 and 20.8 mg mL"1 , respectively. Scattering angle is 45°. Temperature: 30.0 °C (•), 25.2 °C (O), 23.6 °C (♦), 21.2 °C (O), 19.2 °C (■), 17.2 °C (□), 15.9 °C (A)............................ 80 Figure IV-10 Temperature effect of g< 2Kt) correlation functions for cyclic diblock at 20.8 mg mL and 45° scattering angle. The experiment temperatures are 6.9 °C (O), 10.0 °C (O), 12.0 °C (A) and 14.9 °C (□)........................................ 82 Figure IV-11 DLS inverse fast relaxation time 1/ t viii Figure IV-12 Figure V-l Figure V-2 Figure V-3 Figure V-4 Figure V-5 Figure V-6 Figure V-7 for cyclic diblockat 12 °C (O), and linear triblock at 21.2 °C (□) under theta conditions....................................................................... 84 DLS inverse relaxation time 1/x for cyclic diblock (O), and linear triblock (□) at 30.0 °C......................................................................... 85 Intensity autocorrelation functions and CONTIN fits of linear triblock at concentration of 20.8 mg mL' 1 and 45° scattering angle. The temperatures are 15.9 °C (O), 17.2 °C (O), 19.2 °C (A), 21.2 °C(D).................................................................... 101 The CONTIN fits of linear triblock at 14.9°C and 45° scattering angle. The concentrations (mg mL*1) are 8.40 (O), 7.30 (O), 3.59 (A).......................................................... 103 The CONTIN fits of linear triblock at 20.8 mg mL-1 and 17.2°C. The scattering angles are 30°(O), 45°(0), 60°(A), 90°(D)....................... 104 The inverse relaxation time vs. the square of scattering vector q2 of the fast ( • ) and slow (O) modes of linear triblock copolymer at 15.9 °C...................................... 106 The intensity autocorrelation functions and CONTIN fits of cyclic diblock at 20.8 mg mL' 1 and 45 scattering angles. The temperatures are 6.9 °C (O), 10.0 °C (O), 12.0 °C (A) and 14.9 °C (□)......................................... 107 The intensity autocorrelation functions and CONTIN fits of cyclic diblock at 20.8 mg mL' 1 and 6.9 °C. The angles are 30° (O), 45° (O), 60° (A), 90° (□) and 135° (V)..............................................................................109 The inverse relaxation time vs. the square of scattering vector q2 of the Figure V-8 Figure V-9 Figure VI-1 Figure VI-2 Figure VI-3 Figure VI-4 Figure VI-5 Figure VII-1 ix single relaxation modes of cyclic diblock at c = 20.8 mg mL*1 and temperatures of 14.9 °C (♦), 19.2 °C (■), 23.7 °C (A) and 30.0 °C ( • ) ............................................................... 110 The inverse relaxation time 1/x vs. the square of scattering vector q2 of the fast (filled symbols) and slow (empty symbols) modes of cyclic diblock at temperatures of 6.9 °C (•), 8.0 °C (♦) and 9.0 °C (A)................................................................ I l l The scattered intensities of linear triblock and ring diblock at 45° angle and concentrations of 11.2 mg mL' 1 and 20.8 mg mL'1 , respectively................................... 113 Effect of shear rate on solution viscosity of copolymer acrylamide and 0.07 mol% FX-13 at various polymer concentrations: 0.3 wt% (■), 0.2 wt% (A), 0.1 wt% (♦) and 0.05 wt% ( • ) ..................................... 123 Viscosity of 0.5 wt% PAM copolymers vs. the content of fluorocarbon containing acrylate (■) or methacrylate comonomers ( • ) at 0.4 s' 1 and 25 °C......................... 125 Tanaka-Edwards model: internal rearrangm ent of the transient network due to thermal movements....................... 132 Annable model: (a) schematic illustration of possible states of chain association, (b) superstructures with a crosslink functionality greater than 2....................... 135 Rosette (flowers) micelles under (a) low shear (b) intermediate shear and (c) high shear rates..................................................... 137 Fluorocarbon telechelic polyethylene oxides (PEOs). ■ ■ is the perfluoroalkyl X sticker group, O is the urethane linkage and PEO is the hydrophilic backbone......................... 149 Figure VII-2 Preparation of fluorocarbon telechelic PEOs.................................................................................. 150 Figure VII-3 Viscosity vs. concentration for telechelic PEOs of Mw = 35,000 with -C8Fi7 ( • ) and -C16H33 (■) end groups..................................................155 Figure VIM Viscosity vs. concentration for fluorocarbon telechelic PEOs of Mw = 8000 with -C7F15 ( • ) and -Q F 17 (■) end groups................ 156 Figure VII-5 Viscosity vs. temperature for solutions of 8000 PEO end-capped with -C6F13 (•), "C7F15 (♦) and -C8Fi7 (A)............................................ 158 Figure VII- 6 Viscosity vs. temperature for solutions of -C8Fi7 end-capped PEO with Mw = 4600 (A), 8000 (♦), 15,000 ( • ) ........................................................ 159 Figure VII-7 Viscosity vs. concentration for dilute solutions of (C8Fi7)2PEO with Mw = 35,000 in methanol (O) and water ( • ) ................................... 163 Figure VII- 8 Zimm plot of (C8Fi7)2PEO with Mw = 35,000 in methanol...............................................165 Figure VII-9 Zimm plot of (C8Fi7)2PEO with Mw = 35,000 in water............................................................................. 167 Figure VII-10 g(1) correlation functions of (C8Fi7)2PEO with Mw = 35,000 in methanol (top) and water (bottom) at 40° scattering angle...................... 169 Figuree VII-11 The CONTIN fits to g ^ correlation functions of (C8Fi7)2PEO with Mw = 35,000 in methanol (top) and water (bottom) at 40° scattering angle.................................................. 170 Figure VII-12 The inverse relaxation time 1 /t vs. the sqaures of scattering vector q2 for the xi telechelic polymer in methanol at concentrations of 20.6 (•), 17.4 (♦), 14.0 (A), and 6.11 (A) mg mL' 1.................................................... 172 Figure VII-13 The inverse relaxation time 1/x vs. the sqaures of scattering vector q2 for the telechelic polymer in water at concentrations of 2.00 (*), 1.68 (O), 1.38 (O), 1.08 (A), 0.46 (♦) and 0.24 (□) mg mL' 1................... 173 Figure VII-14 Diffusion coefficients of (CsF^hPEO with Mw = 35,000 in methanol (O) and water ( • ) ......................................................................... 174 Figure VII-15 Hydrodynamic radii of (CsF^^PEO with Mw = 35,000 in methanol (O) and water ( • ) ........... 176 Figure VII-16 Possible branched structures and their g values.................................................................. 181 Figure VIII-1 Zimm plot of poly(p-t-butyl styrene- 25% 4- hydroxyl styrene) in toluene.........................................199 Figure VIII-2 Zimm plot of poly(styrene- 22% 4-vinyl pyridine) in toluene.......................................................2 0 0 Figure VIII-3 The inverse relaxation time vs. the square of scattering vector for poly(p-t-butyl styrene- 25% 4-hydroxyl styrene) ( • ) and poly(styrene- 22% 4- vinyl pyridine) (O) in toluene.................................... 201 Figure VIII-4 Excess scattering intensity at 40° scattering angle for poly(p-t-butyl styrene- 31 % 4-hydroxyl styrene) in toluene titrated with pyridine of same molarity (3.87 x 10-5 M) as the molar concentration of 4-hydroxyl styrene comonomer........................................................204 Figure VIII-5 Zimm plot of poly(p-t-butyl styrene-31 % 4-hydroxyl styrene) in toluene with the presence of excess of pyridine (31% P 4 0 H : pyridine = 1 : 2 )................................................................205 Figure VIII- 6 The inverse relaxation vs. the square of scattering vector for poly(p-t-butyl styrene- 31 % 4-hydroxyl styrene) with ( • ) and without (O) added pyridine in toluene.................... 206 Figure VIII-7 The relaxation time vs. molar fraction of added pyridine in toluene at 40° scattering angle............................................................. 208 Figure VIII- 8 The relaxation times of the aggregates formed by poly(p-t-butylstyrene-25% 4- hydroxyl styrene) and poly(styrene-22% 4- vinyl pyridine) in toluene at c = 0.075 mg mL-1 210 Figure VIII-9 The intensity profile of the mixture of poly(p-t-butyl styrene-25% 4-hydroxyl styrene) and poly(styrene-22% 4-vinyl pyridine) in toluene at c = 0.075 mg mL' 1.................................. 211 Figure VIII-10 The dynamic light scattering results of a mixture of poly(p-t-butyl styrene-25% 4- hydroxyl styrene) and poly(styrene-22% 4-vinyl pyridine) in toluene at 0.075 mg mL' 1 and Fa = 0.70....................................................................2 1 2 Figure VIII-11 The relaxation times of the aggregates formed by poly(p-t-butyl styrene-25% 4- hydroxyl styrene) and poly(styrene- 22% 4- vinyl pyridine) in toluene at concentrations of 0.075 mg mL' 1 (O) and 0.017 mg mL' 1 (O).......... 217 Figure VIII-12 The scattering intensities of the aggregates formed by poly(p-t-butyl styrene-25% 4- hydroxyl styrene) and poly(styrene- 22% 4- vinyl pyridine) in toluene at concentrations of 0.075 mg mL' 1 (O) and 0.017 mg mL' 1 (o)................ 219 Figure VIII-13 The inverse relaxation time vs. the square of the scattering vector for the aggregates formed by poly(p-t-butyl styrene-25% 4- hydroxyl styrene) and poly(styrene- 22% 4- vinyl pyridine) in toluene at concentration of 0.14 mg mL' 1 and Fa = 0.57........................................ 221 xiii Figure VIII-14 Figure VIII-15 Figure VIIM 6 The relaxation times (upper) and intensities of the aggregates formed by poly(styrene-25% 4-hydroxyl styrene) and poly(styrene-14% 4-vinyl pyridine) in toluene at concentration of 0.75 mg mL' 1............................................................. 222 The relaxation times (upper) and intensities of the aggregates formed by poly(p-t-butyl styrene-25% 4-hydroxyl styrene) and poly(styrene- 6 % 4-vinyl pyridine) in toluene at concentration of 1.0 mg mL’1................................. 223 The relaxation times (upper) and intensities (bottom) of the aggregates formed by poly(p-t-butyl styrene-31 % 4-hydroxyl styrene) and poly(styrene- 14% 4-vinyl pyridine) in THF at concentration of 19.0 mg mL' 1...................... 227 dfcfev. xiv LIST OF TABLES Table Page Table III-l Comparisons of linear and cyclic homo polymers in theta and good solvents.............................57 Table IV-1 Results of linear and cyclic block copolymers in comparisons with theoretical predictions for homopolymer pairs in theta and good solvents.................................................................... 8 8 Table V-l The critical aggregation temperatures of linear triblock and cyclic diblock dtermined by light scattering......................................... 114 Table VII-1 Homo- and hydrophobically modified PEOs in water................................................................... 179 Table VIII-1 Characterization of donor and acceptor copolymers........................................................................ 196 XV Abstract Solution properties of various associating polymers have been studied with laser light scattering and viscometry. These polymers bearing the functional units associate via dipolar, hydrophobic and H- bonding interactions to form large aggregates in solution. The individual polymers are fully characterized and the aggregation is demonstrated by the increase in scattering intensity, large hydrodynamic radius and slow relaxation mode. A pair of molecular weight matched linear triblock and cyclic diblock copolymers has been studied in dilute solution of cyclohexane, a theta solvent for the middle PS block. The static and dynamic properties of linear and cyclic block copolymers are compared with theoretical predictions for homopolymer linear and cyclic pairs. Total scattering intensity and dynamic light scattering measurements show that the decrease of solution temperature can induce copolymer aggregation and the critical aggregation temperatures are determined for linear triblock and cyclic diblock respectively. The telechelic poly(ethylene oxides) containing fluorocarbon end groups have been studied in water. The association strength of fluorocarbon measured by viscosity and light scattering is compared to that of corresponding hydrocarbon hydrophobes. The mechanism of strong fluorocarbon association is examined in the light of recent xvi theoretical models. The possible structure of the aggregates in aqueous solution is deduced from the results of light scattering and viscosity experiments. Two copolymers bearing hydrogen-bonding donor and acceptor functional groups are mixed in a nonpolar solvent toluene. The aggregation through H-bonding has been investigated as a function of the ratio of donor to acceptor copolymers, total polymer concentration, acceptor comonomer content. A more polar solvent THF is used to study the solvent effect. 1 Chapter 1. Introduction Polymers are best known for their use as bulk materials, such as elastomers, plastics and fibers. The solution properties of polymers, however, have also excited tremendous experimental and theoretical interest due to the importance of macromolecules in chemical technology and biology. The applications of polymer solutions have covered fields as diverse as lubricants, oil field chemicals, water treatment chemicals, coatings, pharmaceuticals, food applications, etc.[l- 8 ] In these fields, polymers affect the flow behavior and thereby the performance of the fluid during and after applications. The power of polymers to influence fluid behavior arises from the intrinsically greater hydrodynamic volume (HDV) of a macromolecule in solution compared to the total molecular dimensions of the repeating units. The hydrodynamic volume is determined by polymer structure parameters (concerning polymer topology, chain length and stiffness) and polymer-solvent interactions, as well as polymer-polymer associations or repulsions. The effective HDV of a macromolecule is proportional to the cube of the root-mean-square end- to-end distance, / and is generally described by the product of the intrinsic viscosity [ri] and the molecular weight M in Flory's theory[9]: HDV s [r|]M = < ( > < r 2 >% (1-1) 2 where < ( > is a universal constant for all types of polymers. HDV also has a temperature, concentration, molecular weight and deformation rate dependence. Experimentally, light scattering and viscometry techniques have been frequently employed to study the solution properties of polymers. A discussion of these two techniques and experimental details is given in Chapter 2. Many features and thus applications of polymers are determined by the size and shape of polymer particles in solutions or suspensions. A combination of light scattering and viscosity measurements can usually provide the most important characteristics, such as the molecular weights and structures of individual polymers, as well as the large particles formed upon aggregation. Developing and characterizing the polymers of unique architectures have also become an emphasis of polymer physics. One of those interesting synthetic structures is the polymer ring. Dilute solution studies of cyclic polymers are intriguing in part because of the significance of circular biological macromolecules, DNAs. The effect of cyclization on the conformational statistics, molecular dimensions, thermodynamics and dynamic properties of linear polymers has been investigated by a number of authors.[10-17] The experimental results on linear and ring pairs of polystyrene, polydimethylsiloxane and poly(2 - vinyl pyridine) have been in excellent support of theoretical models. [18- 24] These theoretical predictions and experimental agreements of homopolymer linear and cyclic pairs are reviewed in Chapter 3. 3 For the past forty years, the experimental efforts have focused on the available linear and cyclic homopolymer pairs. No experimental work has been performed on the solutions of macrocyclic block copolymers due to the difficulty of synthesis. The recent success in synthesis has provided the molecular weight matched linear and cyclic block copolymer pairs [25, 26] for possible studies of fundamental differences arising from linear and cyclic topologies. Chapter 4 reports the first experimental results from static and dynamic light scattering on linear triblock poly(dimethylsiloxane)-polystyrene-poly(dimethyl- siloxane) (PDMS-PS-PDMS) and cyclic diblock PS-PDMS. Cyclohexane, a theta solvent for PS block, is chosen in the study. The thermodynamic and hydrodynamic properties of block copolymer pairs are compared with the theories proposed for homopolymer pairs. The comparisons prove that the theoretical predictions are still applicable to linear and cyclic block copolymers.[27] Besides developing new synthetic approaches to prepare polymers of different topologies, novel polymeric structures can also be achieved by polymer aggregation through specific interactions. Traditionally, the applications of polymers in solution often rely on their high molecular weights, chain entanglements and polymer-solvent interactions. Polymers that associate via physical interactions can build up equivalent high molecular weight, and sometimes even offer superior performance since polymer aggregation often results in unique solution or colloidal properties. [28] Therefore, alternative property control can be also 4 accomplished by virtue of phase changes and associations driven by specific interactions. Such specific interactions can be realized by the introduction of special functional groups into polymer chains. Polymers possessing these functional moieties can associate inter- and intramolecularly through hydrophobic, electrostatic, dipolar and hydrogen-bonding interactions in solution. In the systems where the specific interactions are operating, polymer is only needed at low concentrations to substantially modify the solution properties. Additionally, the solution properties can be optimized by varying the type, structure and the content of associating units. Therefore, this class of polymers has recently received a great deal of attention because of the efficiency and economy consideration in the applications of their solutions. The aggregation phenomena of block copolymers have been observed for various linear AB diblocks and ABA triblocks in selective solvents. [29-32] Block copolymer micellization is a result of thermodynamic forces (enthalpy driven process) arising from the chemical dissimilarity of the two component blocks. It is generally agreed, both theoretically and experimentally, that linear diblock and triblock copolymers in a poor solvent for the B block form uniform spherical micelles with a dense core of poorly solvated B blocks and a shell of swollen A blocks. Chapter 5 discusses the micellization theories of linear block copolymers and the light scattering results of a matched linear triblock PDMS-PS-PDMS and cyclic diblock PDMS-PS in 5 cyclohexane, a good solvent for the PDMS blocks but a poor solvent for the PS block at temperatures below 35 °C.[23] Both static and dynamic light scattering show that the apparent theta temperatures for the linear triblock and cyclic diblock are shifted to 20 °C and 1 2 °C, respectively. Aggregation of these block copolymers is accompanied with a sharp increase in the scattering intensities, a negative second virial coefficient A 2 and the appearance of a slower diffusion mode when the experimental temperatures are blow the critical aggregation (or apparent 0-) temperatures. Light scattering measurements provide the first experimental evidence that the aggregation of cyclic diblock copolymers does occur. The hydrodynamic properties of the aggregates formed by linear triblock and ring diblock are also discussed in Chapter 5. Since AB is assigned arbitrarily for linear diblocks, obviously, reversing the selective solvent for AB diblock will only result in micelles of reverse core and shell. But for the case of linear triblock copolymers in a poor solvent for the end blocks, there is still debate on whether intermolecular micellization occurs and what structure the micelles assume in solution if micellization does occur.[33-35] Experiments have provided evidence for the aggregation of some triblock copolymers, [35-37] but not others, [38-40] in such solvents. Some experimental observations have shown spherical but less compact structures,[31, 41] while others have suggested a network-like or branched structure [36, 37] for the triblock aggregates in a poor solvent for the terminal blocks. 6 Another category of associating polymers that are especially interesting is water soluble polymers. These polymers play important roles in a variety of areas as viscosity or rheology modifiers. [28, 42] Water soluble polymers containing hydrophobic groups tend to associate in water similar to the way amphiphilic surfactant molecules do. This class of polymers includes block, random copolymers, and comb or telechelic polymers depending on the placement of hydrophobic units relative to the polymer backbone. W ater soluble block polymers are composed of hydrophilic and hydrophobic blocks,[43] while random copolymers consist of hydrophobic units randomly distributed along the hydrophilic polymer chain. [44-46] In comb polymers, the hydrophobes are evenly spaced along the water soluble polymer chains.[47] The telechelic polymer bearing associating units at each end of a polymer chain often serves as the model associating polymer to investigate the association process because of its relatively simple structure. Chapter 6 discusses the previous experimental w ork on fluorocarbon and hydrocarbon modified random copolymers and hydrocarbon telechelic polyfethylene oxide) (PEO). Telechelic polymers have been employed in most theoretical models attempting to explain the enhancement of solution viscosity resulting from hydrophobic association. [48-51] Also, a variety of experimental techniques have been utilized to characterize hydrocarbon telechelic PEOs and their association processes.[48, 51-55] Recent models that recognize the co-existence of intermolecular and intramolecular 7 association and a transition from intramolecular loops to intermolecular bridges seem to explain the strong concentration dependence of solution viscosity and dynamic modulus. On the other hand, telechelic polymers in aqueous media can be viewed as a triblock copolymer in a poor solvent for the end blocks. Some theoretical attempts are base upon the micellization of such copolymers in a solvent good for the middle block. However, to this point no theoretical models have been successful in predicting the range of solution properties. Essentially, the structure of aggregates formed upon association is unknown and it is the key to understanding the macroscopic properties of associating polymers. The hydrophobic association is strongly dependent on the type, structure and the distribution of hydrophobes. It has been found that using fluorocarbons as the hydrophobic units gives rise to much stronger viscosifying ability than using the corresponding hydrocarbons in the case of random associating copolymers. [56, 57] To overcome the problems of random copolymers, such as large polydispersity, the uncertainty in comonomer content and microstructure, a better defined water soluble polymer containing fluorocarbon units is demanded to further understand the fluorocarbon association. Light scattering and viscosity experiments extending this work to a less polydisperse model telechelic polymer composed of a poly(ethylene oxide) backbone and dual perfluoroalkyl end groups are described in Chapter 7. The results of fluorocarbon telechelic PEOs are compared to hydrocarbon telechelic 8 polymers, as well as to theoretical models. Our results quantify, at the molecular level, the stronger association of fluorocarbons than hydrocarbons in terms of critical micelle concentration (cmc), activation energy Ea, average aggregation number N, and intrinsic viscosity [t)]. Combining light scattering and viscosity data, we are able to conclude that aggregates assume a statistically branched structure in water. In addition to the investigations of matched linear triblock and cyclic diblock copolymers and fluorocarbon telechelic PEOs, light scattering measurements are performed to monitor the formation of hydrogen-bonding complexes between two styrene-based copolymers. The background review of hydrogen bonding association and the experimental results are given in Chapter 8 . The copolymers, poly(styrene-4-hydroxyl styrene) and poly(styrene-4-vinyl pyridine), each consist of the random distribution of hydrogen donating and accepting comonomers. The individual donor or acceptor copolymer alone exhibits neither intramolecular nor intermolecular association in toluene. However, upon the mixing of these two complimentary copolymers, the formation of hydrogen-bonding complexes is demonstrated by the increase of scattering intensity and hydrodynamic radius. Complexing behavior is studied as a function of the concentration ratio of acceptor to donor copolymers, the acceptor comonomer content, and total polymer concentration. The dynamic light scattering results show that the aggregate size is independent of total polymer concentration, but decreases with decreasing acceptor 9 comonomer content in poly(styrene-4-vinyl pyridine) copolymers. This aggregation driven by the hydrogen-bonding interaction is sensitive to the solvent polarity. The same donor and acceptor copolymer pair do not form complexes in the polar solvent tetrahydrofuran (THF). Finally, future directions for their areas of research are discussed in Chapter 9. 10 References 1. A. Casale and R.S. Porter, Polymer Stress Reactions; vol.2; Academic Press: New York; P548, (1978). 2. N. Benfaremo and C.S. Liu, Lubrication 76(1), 1 (1990). 3. K.G. Shaw and D.P.J. Leipold, }. Coat Technol. 57, 63 (1985). 4. P.R. Norwar, E.L. Rosier, and E. J. Schaller, J. Coat. Technol. 64(804), 87 (1992). 5. S. P Gupta and S.P. Trushenski, Soc. Pet. Eng. ]. 5, 345 (1978). 6 . J. Bock, Jr., Valint, S.J. Pace, D.B. Siano, D.N. Schultz and S.R. Turner, in Water Soluble Polymers for Petroleum Recovery; G.A. Stahl and D.N. Schultz, Ed.; Plenum Press: New York, pp 147 (1988). 7. J. Huguet and M.J. Vert, Controlled Release 1, 217 (1985). 8 . S.E. Morgan and C.L. McCormick, Prog. Polym. Sci. 15, 507 (1990). 9. P.J. 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Da, T.E. Hogen-Esch, and G.B. Butler, J. Polym. Sci. Part A: Polym. Chem. 30, 1383 (1992). 15 Chapter 2. Experimental Techniques I. Introduction In this chapter the experimental techniques utilized in the studies on aggregation phenomena of various polymer systems are reviewed. Due to the complicated solution behavior of polymers containing complexing or associating moieties, a combination of experimental techniques has been attempted with an ultimate goal of completely characterizing each polymer solution system. Experimental approaches including viscometry and light scattering have been employed. Theoretical basics and experimental details necessary for the discussion of the results in subsequent chapters will be described. II. Viscometry Of all the polymer solution characterization techniques viscosity is probably the easiest and most fundamental method. [1, 2] When a polymer is dissolved in a solvent, the two-body interaction between polymer and solvent molecules results in an increase in polymer dimensions over that in the unsolvated state. Thus, polymer chain characteristics of dimension, stiffness, topology, etc. can be acquired through viscosity measurements. This is why viscosity is one of the most frequently used techniques in polymer characterization. 16 Due to the nature of large molecular sizes of polymers, there almost always exists a measurable increase in viscosity even for very dilute polymer solutions. The viscosity T| of a polymer solution depends on the molecular weight of the polymer, as first recognized in 1930 by Staudinger.[3] Since the frictional property is sensitive to the change of dimensions and topologies of the dissolved solute, the parameters determined by viscosity measurements can provide useful information on size and shape of polymer aggregates formed in solutions. Viscometry is thus an expedient technique for studying association phenomena occurring along with the change of size and shape of molecules. Extensive reviews of viscosity parameters and experimental details can be found in many textbooks. [2] The necessary equations and specific details particular to the systems under investigation will be discussed below. The increment of solvent viscosity by the addition of polymer is expressed by the specific viscosity T |S p , which is defined by (r) - ris)/r|s where t| and rj s are the solution and solvent viscosities respectively. The reduced viscosity T|r defined as, % p/c, describes the change in the specific viscosity with polymer concentration c. The reduced viscosity can then be expressed as a series expansion of rjR with respect to concentration c riR =-— = a-i + a2c + a3c2 + ••• (II-l) cris In the region of low solute concentration c, an expression for viscosity t ) r was developed by Huggins 17 % = — — = M(1 + + • • •) (H-2) dls where [r\] is the intrinsic viscosity, a characteristic parameter for the polymer in a particular solvent and kn is a shape dependent factor called the Huggins constant. The intrinsic viscosity measures the contribution by isolated polymer to the solution viscosity in the absence of polymer intermolecular interactions, and is obtained by extrapolating t j r to zero concentration. The Huggins constant characterizes specific hydrodynamic interactions of the polymer and solvent and has values between 0.4 and 0.76 for random coils. It has been shown theoretically that these two values correspond to the free-draining[4] and non draining [5] limits respectively. The alternative extrapolation method to obtain intrinsic viscosity involves an expansion of the relative viscosity T|rel = tl/Tls in c as ln^isL = l n - 5 - = [ri](l-p[Ti]c + - ) (II-3) c cns Where P is another shape dependent factor analogous to kh- For a given polymer-solvent system at a specified temperature, the intrinsic viscosity [r|] can be related to the polymer molecular weight through the Mark-Houwink-Sakurada (MHS) equation [6] [q] = KM“ (II-4) where K and a are constants over a wide range of molecular weights at a given temperature, and the exponent a is indicative of solvent quality. For linear polymer random coils, values of a range from 0.5 for a 1 8 polymer in a theta-solvent to about 0.8 in very good solvents.[1] The MHS equation offers a convenient means of determining the molecular weight of a polymer in a particular solvent. The intrinsic viscosity [t|], as mentioned before, can be affected by molecular weight, polydispersity, chain stiffness and topology, as well as temperature and solvent quality. For instance, the [t|] value of a branched polymer is smaller than that of its linear homolog. [7] Since viscosity is a measure of the energy dissipated by a fluid in motion as it resists an applied shearing force, two types of polymer solution flow behavior can be encountered: shearing-thickening (dilatant) — viscosity increases with shear rate or shear-thinning (pseudoplastic) — viscosity decreases with shear rate. This suggests that the effect of shear rate on [r|] can be considerable for an expanded polymer in good solvents. Reduced viscosity should therefore be extrapolated to zero shear rate to facilitate quantitative comparison of experiments to theories. In addition, the sensitivity of viscosity to temperature necessitates that the measurement tem perature be carefully controlled. Capillary Viscometers The dilute solution viscosity of polymers studied in this dissertation was measured with Cannon-Ubbelohde four bulb dilution viscometers (Cannon Instruments). Capillary viscometers have the advantage of high accuracy, easy and fast operation, and low cost of instrumentation. The size 25, 50 and 75 calibrated viscometers were employed to measure the kinematic viscosity (flow driven by gravitation) in the range of 0.3 to 8.0 centistokes within reasonable experiment time. The viscosity and shear rates were calculated from the solution and solvent flow times using the vendor supplied calibration constants. The calibration constants were also checked by comparison of m easured and literature values of solvent viscosities. An Ubbelohde suspension-type, one bulb capillary viscometer shown in Figure II-l is used for the illustration below. In practice, the capillary viscometer is vertically placed into a temperature controlled bath. An aliquot of solution of known volume is pipetted into bulb D through A and equilibrated at the experimental temperature prior to the measurement. The solution is sucked up to B with C closed off. When the pressure is released, the solution flows down the capillary under gravimetric force and drains along the sides of the bulb back into D. The flow time is recorded for the solution meniscus to pass from x to y in bulb E. In the multiple shear version the height and diameters of four bulbs and capillaries in series are designed to provide four different shear rates for solution flow. The addition of an appropriate amount of solvent to the solution in D followed by extensive mixing gives the next concentration in the series. Therefore, the relative and reduced viscosities at each concentration are calculated as follows: 20 D Figure II-l. One bulb Ubbelohde capillary viscometer. 21 n - J k = ! z io ( u . 6 ) Clls ct0 Where t and to are the solution and solvent flow times, respectively. All viscosity measurements described in future chapters were carried out in a water bath with the temperature controlled to ± 0.01 °C. Some shear dependence of the viscosity, particularly at the low shear rate of the fourth bulb, was observed for the polymer systems examined. Extrapolation to zero shear was performed for all viscosities measured with capillary viscometers. The measurements for each concentration were typically repeated three times and flow times for each bulb were within a repeatability of ± 0.01%. Magnetic Sphere Viscometer Versions of magnetic sphere viscometers (MSV) have been developed in several research groups. [8-14] The major advantage of this type of viscometer is the automation that facilitates easier and faster data acquisition for semi-concentrated and concentrated polymer solutions. A simple diagram of the instrument built in our lab is shown in Figure II-2. The magnetic sphere (MS) is levitated in the sample tube (ST) that contains the fluid whose viscosity is to be measured. The sample tube is immersed in a refractive index matching toluene bath and a temperature controlled water bath. A voltage generator (VG) supplies current to a magnetic field generating coil (CO) above the sphere, which generates a magnetic force to balance the weight and buoyancy of the 22 ST D = CO MS Lens MT MC VG ' CM A /D D/A PA A/Dx4 Figure II-2. Diagram of the magnetic sphere viscometer setup. MS: magnetic sphere; ST: sample tube; VG: voltage generator; CO: magnetic force generating coil; CM: current meter; MT: stepping motor; MC: motor controller; PA: preamplifier; LS: laser beam; A/Dx4: four channel converter; PC: computer; QD: quadrant detector. 23 sphere. The current Io through the coil is measured by a digital current meter (CM). The sample tube is moved up and down at controlled velocity driven by a stepping motor (MT) and motor controller (MC). During the entire course of measurement, the current is adjusted to maintain the sphere in a fixed position. Hence, the sphere experiences a viscous drag (i.e. frictional force) from the fluid in the tube. The resulting difference in the current AI (= I-Io) is a function of the velocity profile and allows the determination of fluid viscosity. The quadrant detector (QD) determines the sphere position from the shadow image of the sphere surrounded by projected laser light of a larger dimension. There are four forces acting on the magnetic sphere, Fm, Fq, Fg and Fb, representing the magnetic, viscoelastic, gravity and buoyance force, respectively. To keep the position of sphere stationary, the forces exerted on the sphere need to be balanced. So The magnetic force is produced by a magnetic field H through the current I where a is the radius of the sphere, J is the magnetism of the sphere and A is a proportionality constant. The viscosity force of a Newtonian fluid is related to the force by — F r| + F g F b (H-7) (II-8) Fq = 67tar|u (II-9) 24 where rj is the fluid viscosity, u is the velocity at which the sphere is moved, and a is the radius of the sphere. While the gravity is solely dependent on the mass of sphere, the buoyance force, Fb = m gpi/pS / is determined by the mass of sphere m, and the densities of the liquid pi and the sphere ps. Thus, for a given sphere, Fg and Fb are constants during the experiment and the resulting difference of these two forces is balanced by the magnetic force generated by initial current Io- Fm thus has to be regulated by adjusting current I to compensate the viscosity force Ft| Fm = AAI = Fp = 6jtar)u (11-10) Hence, the viscosity is given by T ] = — — = K — ( 1 1 - 11) 6na u u where K is a constant which can be calibrated with viscosity standards. The magnetic sphere viscometer was employed to measure the zero shear viscosities of semi-concentrated and concentrated associating polymer solutions. The extremely low shear rate is achieved by controlling the velocity of the sample tube translation. The magnetic sphere viscometer built in our lab has working shear rates ranging from 3 x 10‘3 to 4 s_1. Within this range, no shear dependence was observed for the associating polymer solutions studied and thus all viscosity data correspond to zero shear values. 25 Homogeneous solutions of fluorocarbon telechelic polymers were transferred into the sample tube of magnetic sphere viscometer (MSV). The tube was sitting in the toluene bath for at least one day to ensure air bubbles disappear before the measurements. For temperature studies, the solutions were equilibrated at the desired temperature. III. Light Scattering Two distinct classes of measurements are possible using light scattering techniques. Elastic or static light scattering (SLS) provides static properties of a polymer in solution, such as absolute weight- average molecular weight, molecular dimension and shape, as well as the degree of polymer-solvent interaction. Dynamic properties such as translational diffusion, rotational diffusion, and internal motions of a polymer in solution can be determined from quasi-elastic or dynamic light scattering (DLS). Many excellent review papers and textbooks have covered the theoretical background, the instrumentation and applications of light scattering.[15-21] A brief description of theories, sample preparation and data analysis relevant to the interpretation of the experimental results in later chapters are given here. When a beam of light encounters atoms or molecules, the electrons are perturbed or displaced and oscillate about their equilibrium positions with the same frequency as the incident light. This induces transient dipoles in the atoms or molecules that act as secondary 2 6 scattering sources by re-emitting the absorbed energy in all directions. Two different aspects of the scattered intensity are of concern respectively in the static light scattering and dynamic light scattering experiments. The angular distribution of time-averaged scattering intensity (SLS) reflects the equilibrium properties of chain dimension whereas the time-dependent scattered intensity at different scattering angles (DLS) corresponds to a spectrum of shifted frequencies of the re emitted light. In an analogy to the Doppler effect, frequencies are slightly increased or decreased depending on whether the scattering species is moving toward or away from the observer. From this we can determine apparent diffusion coefficients as described in the DLS section below. Static Light Scattering In static light scattering experiments, the reduced scattering intensity, referred to as Rayleigh's ratio, Re, is measured at a scattering angle 0. The Rayleigh ratio is defined as I r2 R0 = - s s _ = KcM (11-12) !o where c is the polymer concentration, M is the molecular weight of polymer, and Iex is the excess scattered intensity at a distance r from the scattering volume to the detector. The excess scattered intensity is given as Iex = 1(0) — Is(0 ), where 1(0) and Is(0) are the scattered intensities from the solution and solvent, respectively. The optical constant K for 27 vertically polarized incident light is K = (11-13) 4 n a dc 3n with n, N a, — and A - o being the refractive index, Avogadro's number, oc the refractive index increment, and wavelength of incident light in vacuo, respectively. The theoretical basis of static light scattering from polymer solutions was first established in the 1940s. [22] A relationship was developed between the scattering intensity from a polymer solution and the weight-averaged molecular weight M, as well as the size and shape of a polydisperse ensemble of macromolecules. This relationship is given as Kc 1 Re MP(0) + 2A 2c + --- (11-14) where M is the weight average molecular weight, P(0), defined by a ratio I0/Ie = = O, is the particle scattering factor, and A2 is the second virial coefficient characterizing the solvent quality. For solutions of Gaussian polymers, P(0) is given as P_1(0)= l + - q 2Rg - (11-15) 3 8 where Rg is the radius of gyration and q is the scattering vector whose magnitude is given by q = (4jrn/A.g)sin(0/2). In the limit of small angle 0, substituting for P_ 1 (0) in equation 11-14 by equation 11-15 leads to A clever treatment of scattering intensity data utilizing a double extrapolation method was proposed by Zimm. [23, 24] If the scattering intensities for the solutions of various concentrations are measured over a wide selection of angles, the data can be plotted as (Kc/Re) against {sin2(0/2)+kc}, where k is an arbitrary plotting constant chosen to provide a convenient spread of the data in a grid-like graph. A typical Zimm plot applying the above data analysis scheme is shown in Figure II-3. In this plot, and A2 are computed from the relations of limc_ o(Kc/R0) vs. sin2(0/2) and lime^ofKc/Rg) vs. c, respectively. The weight-averaged molecular weight is obtained as the inverse value of the intercept at double extrapolations of zero concentration and zero angle. Dynamic Light Scattering Dynamic light scattering is probably the best technique to study associating systems since the motions probed by DLS can be either Brownian motion of the individual particles or the motion of aggregates formed in solution. Dynamic light scattering (DLS) is a generic term covering all the light scattering methods that provide information on molecular dynamics. This name is sometimes used interchangeably with photon correlation spectroscopy (PCS) and quasielastic light scattering (QELS); they are essentially the same technique. More strictly, 0 o 6? 30 PCS refers to the light scattering experiments employing photon counting to compute the autocorrelation functions as opposed to the use of an analog signals in early experiments, while QELS is used to describe experiments performed in the absence of electric or hydrodynamic flow fields. The relaxation of a macroscopic concentration fluctuations produced by Brownian motion is described by Fick's law of diffusion J = -DVc (11-17) and the conservation equation ^ = - V .J (11-18) at where J is the diffusion flux in time t and D is the diffusion coefficient. The concentration fluctuation decays as — = -D 0q2aq(t)cos(q,r) (11-19) at n where q is the scattering vector defined in equation 11-15 and aq(t) is the spatial Fourier component of the concentration of scattering particles. The solution to equation 11-19 turns out to be aq(t) = aq(0)exp(-Dq2t) (11-20) The concentration fluctuation due to the particle diffusion results in the intensity fluctuation, i.e. the temporal behavior of scattering intensity. A direct analysis [15, 25] of the time dependence of the 31 scattering intensity would be to record the intensity as a function of time for a period T and then calculate G(2)(t) = (1(0) I(x)) = j j d t I(t) I(t -K) (11-21) where G<2K t) is the intensity-intensity autocorrelation function and I(t) and I(t+x) are the intensities at times t and t+x. The method of direct analysis involves recording, sorting and constructing the products of the intensities. This is a difficult tedious, and inefficient computational task. However, the advent of the photon correlation technique provides an alternative procedure to tackle the problem. The Onsager regression hypothesis states [15, 25] that on the average, a random fluctuation in a variable obeys the macroscopic relaxation equation for the decay of nonequilibrium values of the same variable. Therefore, in this analysis the intensity-intensity autocorrelation function G <2)(x) is related to the averaged particle motions by G(2)(t) = [G(1)(t)]2 + 12 (11-22) This is often known as the Siegert relation, in which G(1)(x) = | l I E0 I 2 a 2 exp(iq • [?j(t) - q(t + x)])^ = IE0 I 2 (aq(t)a_q(t + i)) (11-23) where G(1)(x) is the electric field correlation function with Eo, q, oq and fj being magnitude of the electric field, scattering vector, polarizability and location of particle i, respectively. Substituting equation 11-20 into equation 11-23 gives [26] 32 G(1)(x) = (I)exp(-Dq2x) where I = IE0 I 2 ^ 1 aq (0) l2^. Equivalently, G( 2)( t ) = Aexp(-2Dq2T) + B (11-24) (II-25) where A = (I2 )-(I)2 and B is the experimentally measured baseline <I>2 in the ideal case. The Wiener-Khintchine theorem states that statistically, the correlation function G<2Kx) and the optical power spectrum S*(co) are a Fourier transform pair,[25] namely In particular, if G(2)(t) is exponential as seen in equation 11-24, then the power spectrum is a Lorentzian: and 2Dq2 is the linewidth at the half-height of the spectrum S*(co). From equation 11-26 and 11-27, it is realized that frequency spectrum and the intensity-intensity autocorrelation function are a Fourier transform pair and hence contain the same information. By analyzing the exact shape of the decay curve G(2Kx), it is possible to extract the diffusion coefficient from the angular dependence and to eventually calculate the G(2)(x) = — H^dco S^co) exp[27ticox] 2 n (11-26) and Skco) = H o G ^ x ) exp[-27ticox] (11-27) 0) > 0 (11-28) 33 hydrodynamic size from the Stokes-Einstein equation kT Rh = - (II-29) 67iqoD where t|o is the solvent viscosity and k is the Boltzman constant. In a light scattering instrument, a digital correlator is the device that computes the correlation function of a fluctuating intensity signal by dividing time into contiguous intervals. The length of an interval is the "sample time". The number of photons n(tj) received during each sample time tj is stored electronically. The correlator then constructs the correlation function as a sum of products, M (1(0) I(aS)) = X n(tj) n(tj - aS) (11-30) i=l where S is the sample time, M is the total number of sample times taken in one experiment; the product of these two quantities, SM, is the experiment duration, and a is an integer that references the channel number. The values of <I(0) I(aS)> are stored in a series of accumulator circuits or channels. Data analysis methods for DLS can be divided into several operational categories. In the cumulant expansion of a polydisperse system of polymer solution, the field correlation function G(1)(x) derived from Siegert relation (equation 11-22) is related to the characteristic linewidth (T) distribution function G(H through a Laplace transform relation: 34 In I G(1)(t) I = - r x + -^H2't2 - ^ 3 x3 + "- w here oo r= jrG(r) dr (11-32) o jii = /(r -n 1 g(d dr (11-33) o For systems with multiple modes of relaxation, G^Ox) can be also represented as the convolution of a relaxation spectrum, s(t), and an exponential decay: The correlation functions can be deconvoluted using CONTIN, a constrained regularization method by Provencher for inverting Laplace transforms. [27, 28] The deconvolution yields the spectrum of relaxation times for the various processes in the scattering sample as a series of amplitudes, s(x), along a grid of x values. The amplitudes of the modes are indicative of the relative contributions of different relaxations. Figure II-4 is a schematic diagram of the light scattering instrum ent used in our laboratory. The experiments were performed using an Ar ion laser (Spectral Physics 2020-3) operating at a wavelength of 514.5 nm. The power output was between 0.3 and 1.2 W depending on the scattering intensity of the solution. The laser is directed to a focusing lens (100 mm) before entering the index matching vat. The vat G(1)(x) = s(x) exp(-t/x) dt (11-34) 35 S1 S2 / L a s e j / A L 1 k Figure II-4. Schematic of BI-200SM laser light scattering instrument. LI and L2 are lens; SI, S2, and S3 are apertures; B is a beam stop; P is an optional polarization analyzer; AW is an aperture wheel and FW is a filter wheel. 36 is filled with filtered toluene surrounding the scattering cell and the bath temperature is controlled to ± 0.05 °C. The scattered light is collected by a commercial light scattering goniometer (Brookhaven Instrument 200SM) with a stepping motor control which operates over scattering angles from 10 to 150°. A photomultiplier tube (PMT) (Thorn EMI 9863B) is mounted on the goniometer and the scattered light is directed into the PMT by a series of integrated optics including focusing lenses, filters and irises. The intensity measurements in SLS were conducted with a 264 channel multi-bit autocorrelator (Brookhaven Instrum ent 2030AT). The total intensity was also monitored concurrently with a separate 20 MHz photon counter. The correlator, counter, and goniometer stepping motor were all controlled by an IBM AT type microcomputer for automated data acquisition. The Brookhaven software installed in the microcomputer was used for primary data analysis of SLS measurements. A multi-tau correlator (ALV Instrument 5000) was employed to process the photon correlation functions. Both SLS and DLS data were typically transferred to a VAX 6320 or IBM RS/6000 990 and analyzed with a nonlinear least squares fitting program or curve fitting using a data analysis program on a personal computer (Igor for Macintosh). For associating systems, Debye [29] has introduced the following equation to determine the apparent molecular weight of aggregates. 37 Ryv ^cmc Mw K (c-cm c) 1 ^ | q2Rg2 ) + 2A2(c-cm c) (VII-32) cmc At concentrations much higher than cmc, the measured intensity is dominated by the scattering of large aggregates and equation VII-32 becomes equation 11-16. Therefore, the intensity contribution from single chains can be neglected and equation 11-16 can be used to calculate the apparent molecular weight of aggregates. In the studies of associating systems of polymer solutions, the SLS technique was employed to determine the molecular weights or apparent Mw of individual polymers and of aggregates using Zimm plots. The radii of gyration Rg and second virial coefficients A2 were also obtained from the analysis. The intensity fluctuation caused by the diffusion of both individual polymers and aggregates are monitored by dynamic light scattering. The diffusion coefficient D of each mode can be calculated from the relaxation time which is one of the standard outputs from the CONTIN program. The sizes of the species in solution then can be obtained through the Stokes-Einstein equation (11-29). The proper preparation of the sample prior to measurement is of decisive importance for the obtaining of reliable data. [19] In all the experiments, optically clear scattering cells were repeatedly cleaned by acetone-vapor washing. Polymer samples were freeze-dried before use and solutions were prepared in the concentration range that guarantees their optical clarity. PTFE and PVDF microporous (0.2 pm and 0.45 pm) *%«»<- 38 filters from Gelman Science were used to remove dust particles from the polymer solutions in organic and aqueous media respectively. For some water soluble associating polymer solutions, post-filtration was not possible because of the extremely high solution viscosity resulting from the strong associations. In those cases (e.g. polyacrylamide copolymers), all the reactants, solvents, initiator and surfactants were pre-filtered before the polymerization was started. [30, 31] The scattering solutions were then made by dilution of viscous stock solutions obtained directly from polymerization. Both static and dynamic light scattering measurements were carried out within the angular range of 20 to 140° at intervals of 5 or 10°. The total scattering intensity was measured 10 times for Is intervals at each angle and an average value was determined. A complete data series with varying concentrations and angles was taken in most cases for the construction of a Zimm plot. However, due to the complicated nature of the scattering from aggregates formed by linear and cyclic block copolymers the normal reduction of the intensities given by Kc/Re is not performed. Instead the subsequent analysis of the static light scattering follows a simple calculation of the excess scattered intensity at each tem perature and concentration. 39 IV. References 1. P.J. Flory, Principles of Polymer Chemistry; Cornell University Press, Ithaca, New York, (1976). 2. E. Schroder, G. Muller, and K.-F. Arndt, Polymer Characterization; Hanser, New York, (1988). 3. J.M.G. Cowie, Polymers: Chemistry & Physics of Modern Materials; Blackie Academic & Professional, Chapm an & Hall, p207 (1991). 4. N. Saito, /. Phys. Soc. Japan 7, 447 (1952). 5. K.F. Freed and S.F. Edwards, J. Chem. Phys. 67, 4032 (1975). 6. H. Fujita, Macromolecules 21, 179 (1988). 7. H. M orawetz, Macromolecules in Solution; John Wiley & Sons, pp299-314, (1965). 8. R. Hilfiker, B. Chu, and J. Shook, Rev. Sci. Instrum. 60, 760 (1989). 9. B. Chu and R. Hilfiker, Rev. Sci. Instrum. 60, 3047 (1989). 10. B. Chu and R. Hilfiker, Rev. Sci. Instrum. 60, 3828 (1989). 11. M. Adam, M. Delsanti, P. Pieransky, and R. Meyer, Rev. Phys. Appl. 19, 253 (1984). 12. C. Leyh and R. C. Ritter, Rev. Sci. Instrum. 55, 570 (1984). 40 13. B. Gauthier-Manuel, R. Meyer, and P. Pieranski, }. Phys. E: Sci. Instrum. 17, 1177 (1984). 14. N. Hu, Ph.D. Thesis, University of Southern California, Los Angeles, CA (1994). 15. B.J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology, and Physics; John Wiley & Sons, Inc. (1976). 16. R. Pecora, Dynamic Light Scatteing; Plenum: New York, (1985). 17. S.D. Dover, in An Introduction of the Physical Property of Large Molecules in Solution; E.G. Richards, Ed.; Cambridge University Press: N ew York, 1980; Chapter 7. 18. B. Chu, Laser Light Scattering; Academic: New York, (1991). 19. G.D.J. Philies and F.W. Billmeyer, in Treatise in Analytical Chemistry; P.J. Elving and E.J. Meeham, Ed.; Wiley- Interscience: New York, 1986; Part 1, Section H, Chapter 9. 20. H.-G. Elias, Light Scattering from Polymer Solutions; M.B. Huglin, Ed.; Academic Press: London, (1972). 21. K.S. Schmitz, An Introduction to Dynamic Light Scattering by Macromolecules; Academic Press, Inc. (1990). 22. B.H. Zimm, R.S. Stein, and P. Doty, Polymer Bull. 1, 90 (1945). 23. B.H. Zimm, J. Chem. Phys. 16, 1093 (1948). 24. B.H. Zimm, /. Chem. Phys. 16, 1098 (1948). 41 25. D.A. McQuarrie, Statistical Mechanics; Harper & Row: New York, Chapter 21 & 22; (1972). 26. J.L. Doob, Ann. Math. 43,351 (1942). 27. S.W. Provencher, Comput. Phys. Commun. 27, 213 (1982). 28. S.W. Provencher, Comput. Phys. Commun. 27, 229 (1982). 29. H.-G. Elias, Light Scattering from Polymer Solutions; M.B. Huglin, Ed.; Academic Press: London, p397, (1972). 30. T.A.P. Seery, Ph.D. Thesis, University of Southern California, Los Angeles, CA (1992). 31. T.A.P. Seery, M. Yassini, T.E. Hogen-Esch, and E.J. Amis, Macromolecules 25, 4784 (1992). 42 Chapter 3. Matched Linear and Cyclic Homopolymers I. Introduction Cyclic biological macromolecules have attracted interest for a long time and will continue to be important in the years ahead. In 1962, the velocity centrifugation and enzymatic degradation studies by Fiers and Sinsheimerfl] suggested that single-stranded DNA from bacteriophage < J> X 1 7 4 m ay exist as a "ring-shaped" molecule. Since then, other ring- shaped viral DNA's have been discovered by many groups in polyoma, [2] in the double-strained "replicating form" of <))X174,[3] and in T2.[4] Electron micrographs have directly proved the circularity of these DNA’ s. [2-4] Ring and linear macromolecules are topologically distinct. Differences in their properties and behavior are expected. At least in the case of the replicating form of < |> X 174, the circularity of the DNA has profound biological importance.[5] Spiegelman et al. have shown that, somehow, although yet unknown, the circularity assures that the correct strand of the DNA will be faithfully copied by RNA transcriptase. [5] In order to understand the biological importance associated with the peculiar macrocyclic structure of DNA's, it is certainly worthwhile to investigate thermodynamic and hydrodynamic properties of cyclic or ring polymers. In the past four decades, a large number of papers 43 concerning the effect of cyclization on the conformational statistics, molecular dimensions, thermodynamics, and dynamic properties of linear polymers have been published. [6 -2 1 ] On the experimental side, the hydrodynamic properties of cyclic DNA were investigated and compared to that of their linear cleavage products. DNA polymerases and recombinant DNA methodology have provided powerful tools to construct matched linear DNA molecules of the same sequences. However, these unique methods are not applicable to other polymers. Also, for more generalized physical studies, structurally simpler linear and cyclic pairs are needed. Despite the fundam ental interest in cyclic polymers, experimental work has been ham pered by difficulties in synthesizing well-defined narrow distribution materials. Almost a decade after the cyclic DNAs were discovered, the first synthetic cyclic homopolymer was prepared.[2 2 , 23] Polystyrene (PS), polydimethylsiloxane (PDMS), and poly(2-vinyl pyridine) (P2VP) have been prepared and studied as linear and cyclic matched pairs. With the successes in chemistry it has become possible to examine the structure-property relations of molecular weight matched linear and cyclic polymer pairs. 44 II. Theoretical Predictions Unperturbed Cyclic Homopolymers Mean Square Radius of Gyration Chain dimensions of cyclic polymers in dilute solution at the Flory temperature (0-temperature) was first calculated by Kramers in 1946.[6] One direct theoretical approach adopted by Zimm and Stockmayer[7] and later by Casassa[8 ] was the molecular model of statistical chains using configurational distributions. In the case of a simple end-to-end closed chain, the resulting configurational distribution can be found by a rather simple consideration. [8 ] In this approach, an unperturbed cyclic polymer is modeled as a sequence of segment vectors characterized by a Gaussian length distribution with the special constraint that the vectors form a closed ring. For a cyclic polymer with the degree of polymerization N, the segments can be numbered consecutively from 1 to N around the ring and the mean- square radius can be defined as The vector Ljj in Figure Ill-l(a) can be expressed by the vector sum over the m segments or by the sum over the rest of N-m bonds. If the (IH-2) 45 m N-m (b) Figure III-l (a) A cyclic chain with two Gaussian subchains originating in segment i and ending in segment j, where one subchain consists of m segments and the other of N-m. (b) Topological state of two ring polymers. Average intermolecular interaction is repulsive. 46 the subchains in a ring obey Gaussian statistics, then the corresponding distributions of these two subchains are p’(Lii)=,5 ^ ? ,3/2exp( ~3Lfj 2 mb2 r) (m-3) and P2(Lij) = (-------- j ] 2 ji(N - m)b > 3/2 exp<------ 2(N - m)b (in-4) where b is the segment length. The joint distribution of the ring when segment 1 and N are connected is the convolution of the above two distributions, i.e. P a irin g = Pi (Lij)•P2(Lij) f ” = ( 3 )3/2 N 3NLf 2 nb r n i 3/2 f ” J m N - m 2). exp- 2(mN - m 2 )b2 (m -5) Inserting equation III-5 into III-2 and then integrating over space leads to ^ ) = ( m N - m W Averaging over all i and j in equation (III-l), gives Nb2 (Rs)e = (m-7) '0 12 for large degree of polymerization N. Hence, under theta-conditions, the unperturbed mean-square radius of a cyclic polymer is only half that of the linear chain with identical degree of polymerization. 47 Second Virial Coefficient A2 Roovers and Toporowski[9] found that A 2 for cyclic polystyrene in cyclohexane has a definite positive value at the usual 0 -tem perature. This non-zero value of A2 at the linear polymer's 0-temperature leads to a lowering of the theta-temperature for cyclic chains. For the case of comb, star, and branched polymers, where there is a higher local segment density, a lowering of the 0 -temperature can be explained by considering the effect of the segment density on the cancellation of excluded volume interactions in the balance of long-range intramolecular interactions of polymer segments with the polymer- solvent interactions.[10] This explanation does not, however, provide nearly as strong an effect as is needed to justify the lowering in the case of cyclic polymers which have only marginally higher segment density than their corresponding linears. More recently, Iwata et al.[11,12] proposed a model that accounts for an additional topological interaction and repulsive force between cyclic polymers. Topological states of ring polymers are described by the degree of intertwining between two loops (Figure Ill-l(b)). This additional repulsive interaction, operating at the usual linear polymer 0 -temperature, would yield a positive second virial coefficient A2 and therefore a lower temperature to reach the 0 -condition. 48 Hydrodynamic Coefficients The intrinsic viscosity [rj], the friction coefficient f, and translational diffusion coefficient D of an unperturbed ring polymer were first calculated by Bloomfield and Zimm [13] and by Fukatsu and Kurata[14] using the Kirkwood-Riseman theory[15] with the preaveraged Oseen interaction tensor. In the non-draining limit their calculations yield [Del, [ills = 0.662 (in-8) = -^ 2 - = 0.849 (in-9) fi,e Dc,e Based on these results, one can derive the more interesting quantity, S the — factor, defined as R s ( H f r _ i & - < nH 0) s where Rh is the hydrodynamic radius. The --fac to r is independent of bond length and degree of polymerization. Burchard and Schmidt[16] found for cyclic and linear chains in unperturbed states (|)c.e = J-r = 1-2533 (in-11) > c,e = 1 | = i-: _> = J L 'r 1 /0 3 Vic 49 Perturbed Cyclic Homopolymers Mean Square Radius of Gyration In the perturbed states where polymer-solvent interactions overweigh polymer-polymer interactions, the excluded volume effect comes into play. The radius expansion factor a for perturbed spring head chains was calculated to first-order in the excluded-volume variable z by Casassa,[8 ] who obtained a 2 = 1 + k z (in-13) with z = ( - 1 t )3/2 N 1 /2P 2 jtb and k = 134/105 for linear and k = rc/2 for ring polymers. The variable p is the excluded volume for any pair of segments. The prefactor k for cyclic chains is larger than that of its linear counterpart, indicating that the ring swells more by intrachain repulsion than a linear chain of the same chain length . Computer simulations of self-avoiding cyclic chains have given information on the ratio /(R g )j at the limit of long chain length. The ratios estimated by Bruns and Naghizadel[17] from Monte Carlo simulations of off-lattice chains and by Chen[18] from Monte Carlo calculations on random-flight chains range from 0.56 to 0.57. These values were also confirmed by Prentis applying first-order renormalization group theory. [19] 50 Second Virial Coefficient Az The second virial coefficient has been calculated for the non twisted chain only within the double contact approximation [8 ] since A2 describes binary interactions. Figure III-2 displays the cluster diagram schematically. For two interacting cyclic polymers, the second virial coefficient A2 is given by A 2 = (-^ 4 r)S Z 2 M ij i2 1 ~ ,01Nl ,01N z z ji h (in-14) where N a denotes Avogadro's number and M is the molecular weight. The subscripts 1 and 2 refer to the two polymer rings of the bimolecular cluster. P(0j j j / 0 in 2 ) is the probability that a contact is formed between the segment ji of one ring and )z of another ring and simultaneously that a second contact is formed between the two segments ii and i2 of the two chains. The constraint of the fixed two chain ends in a ring keeps the chain segments confined to a smaller space. This necessarily increases the probability of a contact. The symmetry of the ring model simplifies the multiple summations or integrations. The second virial coefficient obtained from the double contact approximation by Casassa[8 ] is A = ( _ N a PN2 _ Bz + 2 M w ith B = 4.457 The coefficient B for cyclic polymers is much larger than the value 2.865 for linear chains. 51 Figure III-2. Double contact cluster diagram for two interacting rings. The dashed lines denote the segment pairs in contact. 52 On the basis of Casassa's work[8 ], Hocker et al.[20] expressed the ratio of A2's for expanded cyclic and linear coils as _ 5.73z, ln(l + 8.914zc) A 2l 8.914zc ln(l+ 5.731,) where the dimensionless binary interaction parameter z can be related to the dimension expansion factor a by combination of 2 = 4 - (in-17) a and a 5 - a 3 = k z (IE-18) to yield a 2 = 1 + k z (in-19) where k = 1.276 for linear polymers and k = n /2 for a cycle. The classic definition of a by Flory is “ 2 = T T T (m-20> (R l)e ( Rl ) . i Rl ) Given the known ratios of 7 ,C /— = 0.5 and /■ ■ ■ , v c = 0.56 under theta (Ri) ,e ( Rl\ and expanded-conditions, Amis et al.[21] combined equations 111-18 and 111-19 to calculate the ratio a^/o.\ to determine z for linear and cyclic chains. Substituting zc and z\ values into equation 111-16, one can 53 obtain the second virial coefficient ratio of cyclic to linear chain A 2,c A 2,l - 0.80 (in-21) Hydrodynamic Coefficients Chen applied the Kirkwood formula to Monte Carlo data for self- avoiding random flight ring and linear chains and obtained the diffusion coefficient ratio[18] -5b = 0.899 (IH-22) Dc The S/R-factor for perturbed linear and cyclic chains in good solvent was also obtained by Burchard and Schmidt [16] and the results are S « (—)c = 0 )c = 1.253(1 + 0.155z) (in-23) R r h f (-), = ( - ^ — )i = 1.508(1 + 0.029z) (IH-24) s (r | ) III. Experimental Agreements A number of techniques have been used to characterize cyclic polymers in solution including size exclusion chromatography, viscometry,[10, 24-37] static and dynamic light scattering,[10, 24-37] and 54 small angle neutron scattering. [20, 26, 36-44] In general, the experiments on linear and cyclic homopolymer pairs have shown good agreements with the theoretical predictions. U nperturbed Cyclic Homopolymers M ean Square Radius o f G yration One of the most basic predictions is that under 0-conditions the mean-square radius of gyration of a cyclic polymer will be exactly half that of its linear homologue of identical molecular weight. [6 -8 ] Experimentally, equation III-7 was verified by light scattering results of ring polystyrene in cyclohexane at 35 °C [37] as well as by small-angle neutron scattering data of Hadziioannou et al. [41] on ring polystyrene in d-cyclohexane at 33 °C. Confirmation of this ratio has also been obtained for polydimethysiloxane in perdeuterated benzene[24, 38] where <Rg>l,e/<Rg>c,e = 1.9 ± 0 .2 . Low er 6-tem perature At the same time a related observation is that the 0-tem perature for a cyclic polymer could be significantly lower than that for its linear counterpart in the same solvent. [10, 37] Light scattering measurements [37] have shown that the 0-temperature for cyclic polystyrene in cyclohexane is approximately 6 °C lower than that of linear polystyrene 55 (34.5 °C) and small angle neutron scattering shows a similar shift (40 °C for linear and 34 °C for cyclic) when perdeuterocyclohexane is used as the solvent. [42] Furthermore, in decalin, the corresponding theta- temperatures were 15 and 19 °C for cyclic and linear PS respectively. [27] H ydrodynam ic Coefficients Dodgson and Semiyen found [ilde/falle =0.67 ,[22] in excellent agreement with equation III- 8 for poly(dimethylsiloxane) in butanone, a theta-solvent at 20 °C over the molecular weight range of 2500 to 16000. The intrinsic viscosity results on cyclic polystyrene by Rempp et al. [35] also confirmed that [ti]c/[ti]i is 0.66 under 0-conditions. The ratio of friction coefficients from velocity sedimentation measurements[37] was 0 .8 6 for large molecular weight polystyrene in its theta solvent cyclohexane, which was consistent with the theoretical prediction. Perturbed Cyclic Homopolymers M ean Square Radius o f Gyration In good solvents or perturbed states, radii of gyration of ring and linear polystyrene in d-cyclohexane at 2 2 °C by SANS experiments[44] 2 2 give 0.56 for the ratio of <Rg>c/<Rg>i. Higgins et al. found this ratio to be 0.53 ± 0.05 for ring and linear poly(dimethylsiloxane) in D^-benzene at 25 °C.[24, 38] These results are in good agreement with the simulation values mentioned before. 56 Second Virial Coefficients A2 Edwards [24], Higgins [38] and Roovers[37] have measured second virial coefficients A2 for poly(dimethylsiloxane) and polystyrene using SANS and light scattering techniques. Experimental data taken from these literature yield A 2 values for linear and cyclic homopolymer pairs consistent with Wu and Amis' prediction of 0.80.[21] Hydrodynamic Coefficients The intrinsic viscosity or translation diffusion coefficient in a good solvent does not fully agree with theoretical values. Dodgson and Semiyen reported [ri]c/[ri]i to be 0.60 for poly(dimethylsiloxane) in cyclohexane and toluene (both are good solvents) at 25 °C.[22] Monte Carlo simulations by Chen[18] predicted the ratio of translational diffusion coefficients to be D i/D c = 0.899. Sedimentation coefficients of linear and cyclic DNA [45,46] give si/sc = 0.877 to 0.909. These results are consistent with theoretical calculations of 0.870 to 0.917 by Bloomfield [13] and others.[14] Edwards et a/.[36] and Higgins et al.[40] found Rhc/Rhl = 0.84 ± 0.02 for poly(dimethylsiloxane) in toluene from classic gradient diffusion and dynamic light scattering measurements, respectively. Probably, the macrorings studied by these authors were too low in molecular weight to be an adequate test of equation 111-22 which is expected to be valid at high molecular weights. 57 IV. Sum m ary The theoretical predictions and experimental verifications are summarized in Table III-l for a quick reference and comparison. Table III-l. Comparison of linear and cyclic homopolymers in theta and good solvents linear vs. ring Theoretical Experimental Theta- Solvent <Rg>i,e/<Rg>c,e 2.0 1.9 ± 0 .2 0 -tem perature lower lower fode/foile 0.662 0.66 - 0.67 Di.e/Dc.e 0.849 0.86 Good Solvent <Rg>c/<R^>l 0.56 - 0.57 0.53 ± 0.05 A2.c/D2,1 0.80 0.80 - 0.81 Di/D c 0.899 0.877 - 0.909 58 V. References 1. W. Fiers and R.L. Sinsheimer, J. Mol. Biol. 5, 408, (1962). 2. R. Weil and J. Vinograd, Proc. Natl. Acad. Sci. (U.S.) 50, 730 (1963). 3. A. Burton and R.L Sinsheimer, Science 142, 962 (1963). 4. C.A. Thomas, Jr., and L.A. MacHattie, Proc. Natl. Acad. Sci. (U.S.) 52,1297 (1964). 5. M. Hayashi, M.N. Hayashi, and S. Spiegelman, Proc. Natl. Acad. Sci. (U.S.) 51, 351 (1964). 6 . H.A. Kramers, J. Chem. Phys. 14, 115 (1946). 7. B.H. Zimm and W.H. Stockmayer, J. Chem. Phys. 17, 1301 (1949). 8 . E.F. Casassa, J. Polym. Sci., Part A 3, 604 (1965). 9. J. Roovers and P.M. Toporowski, Macromolecules 16, 843 (1983). 10. F. Candau, P. Rempp, and H. Benoit, Macromolecules 5, 627 (1972). 11. K. Iwata and T. Kimura, J. Chem. Phys. 74, 2039 (1981). 12. K. Iwata, Macromolecules 18, 115 (1985). 13. V. Bloomfield and B.H. Zimm, J. Chem. Phys. 44, 315 (1966). 14. M. Fukatsu and M. Kurata, J. Chem. Phys. 44, 4538 (1966). 59 15. H. Yamakawa, Moder Theory of Polymer Solutions; Harper & Row: New York, (1971). 16. W. Burchard and M. Schmidt, Polymer 21, 745 (1980). 17. W. Bruns and J. Naghizadeh, J. Chem. Phys. 65, 747 (1976). 18. Y. Chen, J. Chem. Phys. 78, 8 (1983). 19. J.J. Prentis, ]. Chem. Phys. 7 6 ,1574 (1982). 20. M. Ragnetti, D. Geiser, H. Hocker, and R.C. Oberthur, Makromol. Chem. 186, 1701 (1985). 21. E.J. Amis, D.F. Hodgson, and W. Wu, /. Polym. Sci., Polym. Phys. Ed. 31,2049(1993). 22. K. Dodgson and J. A. Semiyen, Polymer 18, 1265 (1977). 23. K. Dodgson, D. Sympson, and J. A. Semiyen, Polymer 19, 1285 (1978). 24. C.J.C. Edwards and R.F.T. Stepto, in Cyclic Polymers; J.A. Semiyen, Ed.; Elsevier: London, Chap. 4; (1986). 25. H. Zhang and Z-D. He, Polym. Commun. 32, 239 (1990). 26. G. Hild, E. Kohler, and P. Rempp, Eur. Polym. ]. 16, 525 (1980). 27. D. Geiser and H. Hocker, Macromolecules 13, 653 (1980). 28. D. Geiser and H. Hocker, Polym. Bull. (Berlin) 2, 591 (1980). 29. B. Vollmert and J. Huang, Makromol. Chem., Rapid Commun. 2,467 (1981). 6 0 30. H. Hocker, Angezv. Makromol. Chem. 87, 100 (1981). 31. G. Hild, C. Strazielle, and P. Rempp, Eur. Polym. J. 19, 721 (1983). 32. E.J. Amis and D.F. Hodgson, Polymer Preprints 32(3), 617 (1991). 33. G.B. McKenna, G. Hadziioannou, P. Lutz, G. Hilde, C. Strazielle, C. Straupe, P. Rempp, and A.J. Kovacs, Macromolecules 20, 498 (1987). 34. P. Lutz, G.B. McKenna, P. Rempp, and C. Strazielle, Makromol. Chem., Rapid Commun. 7, 599 (1986). 35. C.J.C. Edwards, R.F.T. Stepto, and J.A. Semiyen, Polymer 21, 781 (1980). 36. C.J.C. Edwards, S. Bantle, W. Burchard, R.F.T. Stepto, and J.A. Semylen, Polymer 23, 873 (1982). 37. J. Roovers, J. Polym. Sci., Polym. Phys. Ed. 23, 1117 (1985). 38. J.S. Higgins, K. Dodgson, and J.A. Semiyen, Polymer 20, 553 (1979). 39. G. Hadziioannou, P. Cotts, C. Hans, P. Lutz, C. Strazielle, P. Rempp, and A. Kovacs, Bull. Am. Phys. Soc. 30, 436 (1985). 40. J.S. Higgins, K. Ma, L.K. Nicholson, J.B. Hayter, K. Dodgson, and J.A. Semiyen, Polymer 24, 793 (1983). 41. G. Hadziioannou, P. Cotts, G.T. Brinke, C.C. Han, P. Lutz, C. Strazielle, P. Rempp, and A. Kovacs, Macromolecules 20, 493 (1987). 61 42. C. Strazielle and H. Benoit, Macromolecules 8 , 203 (1975). 43. Y. Matsushita, I. Noda, M. Nagasawa, T.P. Lodge, E.J. Amis, and C.C. Han, Macromolecules 17, 1785 (1984). 44. M. Ragnetti, D. Geiser, H. Hocker, and R.C. Oberthur, Makromol. Chem. 186, 1701 (1985) 45. J. Vinograd, J. Lebowitz, R. Radloff, and P. Laipis, Proc. Natl. Acad. Sci. U.S. 53, 1104 (1965). 46. A.D. Hershey, E. Burgi, and L. Ingraham, Proc. Natl. Acad. Sci. U.S. 49, 748 (1963). 6 2 Chapter 4. Matched Linear Triblock and Cyclic Diblock Copolymers I. Introduction The results from static and dynamic light scattering measurements on a new type of macrocyclic polymer are presented in this chapter. The results here report the first characterizations of the fundamental properties of molecular weight and radius of gyration by total intensity (static) light scattering and hydrodynamic radius by dynamic light scattering. Because these matched diblock and triblock copolymers are especially unique in having the ring and linear geometry this aspect of their structure is the focus of this chapter. Differences in their solution behavior, as evidenced by second virial coefficient and hydrodynamic diffusion coefficients, are considered as a function of tem perature in comparison to existing theories and previous experiments on cyclic and linear homopolymer pairs. II. Experimental Section The linear triblock and cyclic diblock copolymers were prepared by Dr. Rui Yin.[l, 2] Previous work by Hogen-Esch et al.[l, 2] on polymers of this type has included SEC analysis of relative hydrodynamic volumes and differential scanning calorimetry measurements of the variation of 63 the glass transition temperature as a function of molecular weight, fractional composition of the blocks, and chain topology. All these results supported the integrity and purity of the linear and cyclic copolymers. Details of the synthesis have been given elsewhere [1, 2] and will be repeated only briefly here. Dual ended living polystyrene precursor was prepared in THF at -78 °C by vapor-phase addition of styrene into a stirred initiator solution of lithium naphthalide (Figure IV-1). The polystyrene dianion was then deactivated at - 20 °C by reacting with a few equivalents of 2,2,5,5-tetramethyl-2,5-disila-l-oxycyclopentane (EDS, Petrarch). This capping step replaces the very active living polystyryllithium which is prone to side reactions and yet is still able (at 25 °C) to initiate hexamethylcyclosiloxane (D3, Aldrich) which is the m onomer for polydimethylsiloxane (PDMS). The reaction mixture was stirred for 12 hours following addition of the D3 in order to complete the conversion. The PDMS-PS-PDMS was split into two parts. One part was term inated by trimethylchlorosilane to provide the linear triblock copolymer. The second part of the living copolymer was cyclized in vacuo by carefully adding the copolymer solution and a stoichiometrically equivalent of dichlorodimethylsilane coupling agent to a large reaction vessel over the course of 2-3 hours. Unlike the cyclization of PS or Poly(2-vinyl pyridine) (P2VP), this reaction has no characteristic color change upon cyclization and therefore it was critical to determine the stoichiometry of the reactant solutions. Solutions of Initiator CH2= C H Initiator + PDMS-PS-PDMS P S "+ EDS/D3 ==> Figure IV-1. Synthesis of linear triblock and cyclic diblock copolymers 65 equal volumes of silanolate dianion and dichlorodimethylsilane of the same concentration were prepared and reacted by slow addition to a large volume of THF kept at 0 °C at precisely the same rate. Fractionation of the crude macrocyclic polymer was carried out by dissolution of the polymer in toluene at a concentration of approximately 1 wt%. Methanol was added dropwise to the toluene solution stirred with a magnetic spinbar to precipitate high molecular weight polycondensates which were obvious in the SEC analysis. A cloudy precipitate was formed with the dropwise addition of the precipitant methanol. The cloudy solution was stirred for several hours and followed by a few hour period for the high molecular weight fraction to settle to the bottom of the vessel in a "gel-like" phase. The supernatant was collected and monitored with SEC (Waters). The fractional precipitation was repeated until the molecular weight of the supernatant matched that of the linear counterpart. Yields, particularly of the cyclic polymers were typically low and thus only one sample pair of appropriate molecular weight was available in quantity sufficient for the present study. SEC of this sample pair gave a molecular weight of 4.15 x 104 and polydispersity of 1.24 (linear) and 1.23 (cyclic). There was not enough material to allow further fractionation, however, the SEC traces show that the high molecular shoulder present in the crude reaction product was removed. The linear and cyclic copolymers consist of 35.1 wt% polystyrene block as measured by the proton NMR. 6 6 The polymer samples were freeze-dried from cyclohexane and dissolved in freshly distilled cyclohexane (Fisher). Solutions were filtered through 0.45 gm PTFE filters directly into light scattering cells at concentrations ranging from 0.05 to 30.0 mg m L'1. Static and dynamic light scattering was performed on a Brookhaven goniometer (BI-200SM), modified for improved static scattering performance over the angular range 30° to 145°, using an Ar ion laser (Spectra Physics 2020-3) operating at 514.5 nm. Photon autocorrelation functions were obtained with a multi-tau log-time correlator (ALV Instruments 5000). Solution temperatures were controlled to ± 0.05 °C over a range of 6.9 to 35.0 °C. Static scattering was analyzed by Zimm plots to yield molecular weights, radii of gyration and second virial coefficients at each measurement temperature. The refractive index increment 0n/3c)x,p of block copolymers was taken as the weight average of 0n/3c)T,p for each block. [3] Because the refractive index of PDMS (no = 1-43) matches that for cyclohexane (no = 1.426), the refractive index increment (3n/3c)T,p for the diblock cycle and triblock linear was taken as Wpg0 n /3 cps) where the weight fraction of the PS block, Wpg, is 0.351 and the 0n/3cpg) of polystyrene in cyclohexane is 0.175 mL g*1. Refractive index increments, in fact, depend weakly on temperature and thus it is an approximation that (dn/dc) = 0 for the PDMS block. Nevertheless, this is a reasonable approximation compared to the large On/3c) for the polystyrene block. The dynamic light scattering auto-correlation functions were analyzed by the cumulant method and randomly checked with CONTIN 67 analysis which gave the same results. For the advantage of easy and fast data analysis, the dynamic light scattering results discussed in this chapter were obtained from cumulant method. Cumulant expansion takes into consideration polydispersity of molecular weights as shown in equation 11-31. For scattering functions that show two clearly separated relaxation modes, the cumulant analysis was performed individually on each section of the correlation function and compared to CONTIN fits on the same data. III. Results and Discussions Static Light Scattering Examples of typical static light scattering results are shown in Figure IV-2 for the cyclic (upper) and linear (lower) copolymers, respectively, at 25 °C. From these plots, molecular weights, radii of gyration, and second virial coefficients are extracted as described in Chapter 2. These data were obtained over a temperature range from 12 to 35 °C and compilations of the results are shown in Figure IV-3, IV-4 and IV-5. The molecular weights are the same for the cyclic diblock and the linear triblock when the temperature is above 20 °C (Figure IV-3). These molecular weights are comparable with the results from SEC. Because O n/3c) is corrected for the weight fraction of the "visible" polystyrene 6% o> % ,© !?.> j # * * % ? * * jooi 6 ‘ M X . * - 69 6x10 ____ 0____ 2 - 15 20 10 25 30 35 40 T, °C Figure IV-3. Weight averaged molecular weights measured by SLS for linear triblock (□) and cyclic diblock (O) copolymers over the temperature range of 12 to 35 °C. nm 70 25 20 15 0C 10 5 0 10 15 20 25 30 35 40 T , °C o o Figure IV-4. Radii of gyration determined by SLS for linear triblock (□) and cyclic diblock (O) copolymers over the temperature range of 12 to 35 °C. 6 |OLUgU J O ‘ 71 8x10 6 4 CM — o - ° —o _ 2 0 CM 2 4 -6 20 10 15 25 T, °C Figure IV-5. Second virial coefficients determined by SLS for linear triblock (□) and cyclic diblock (O) copolymers over the temperature range of 12 to 35 °C. 72 block and the mass concentration of the entire polymer was used in the Zimm plot calculations, the measured molecular weight of 4.31 x 104 is that of the entire copolymer. Alternatively one could use the scattering data to calculate the molecular weight of the polystyrene block by using O n/9c) for polystyrene in cyclohexane and using only the mass concentration of the styrene block, calculated with the known weight fraction. The molecular weight thus obtained, 1.50 x 104, is simply the weight fraction of the total (35.1% of 4.31 x 104). The self-consistency confirms the copolymer composition determined by proton NMR. To some extent, the independence of Mw with temperature is also a validation of the approximation that (d n /d c) for the PDMS segment, which we take as zero, is also independent of temperature. In the region just below 20 °C the data for the linear triblock become unreliable because of the strong fluctuations in the scattering near the apparent 0 - temperature. This is even more obvious in the analysis of the second virial coefficient. Measurement of radii of gyration from static light scattering is very difficult for polymers of these molecular weights and thus the Rg values are rather scattered (Figure IV-4). Both molecules give Rg values of about 13 nm for data above 20 °C. This value seems too large for this molecular weight although it may reflect the fact that the PDMS block is in good solvent and therefore expands the PS block. For the linear triblock the measured Rg appears to decrease at temperatures below about 20 °C. This could be expected for a selective solvent if the PS 73 section collapses before it associates into a micelle. The cyclic copolymer shows no such effect. Due to the scattered data of radii of gyration, it is not possible to compare the experimentally measured values to the theoretical ratios in theta and good solvents. [4, 5] Fortunately, the Rg values are not important for the remainder of the discussion. The second virial coefficients, A2, which are extracted from the concentration dependence of the zero angle scattering, are much more consistent and provide the most interesting information. Above 20 °C, the cyclic and linear molecules have positive A2 values indicative of good solvent conditions. All of this data (Figure IV-5) is taken at or below the 0-temperature of 35 °C for homopolystyrene. The presence of PDMS block(s) attached to the PS increases the apparent solvent quality because cyclohexane is a good solvent for PDMS (0 = -81 °C). For the linear triblock, A2 drops sharply and becomes negative at 20 °C. The fact that the drop is so sharp, rather than a smooth decrease more typical of behavior through the 0 -temperature, reflects that this is a block copolymer system. [6 ] The suppression of the 0-temperature of linear triblock is not by itself particularly surprising. The more significant result is that the closure of the linear triblock to form the cyclic diblock further shifts the 0-temperature below 12 °C. Positive A2 values are measured for the ring polymer over the entire temperature range of 1 2 to 35 °C and they show only a small decrease with temperature. As mentioned in Chapter 3, Iwata[7, 8 ] proposed that the added topological interaction arising from intertwining two loops creates a 74 repulsive force in the cyclic polymers and leads to an increase in A2 values and a decrease of the 0-temperature. For homopolymers the theory provides quantitative predictions, for example, the difference of 0-temperatures is calculated to be 6 °C for linear and cyclic polystyrene homopolymers in cyclohexane. [8 ] However, only qualitative arguments are possible for the block copolymers because of the presence of PDMS blocks and only apparent 0 -temperatures are observed for the block copolymers. Furthermore, this theory does not provide an explanation for the m agnitude of the 0 -temperature shift between linear and cyclic block copolymers. The ratio of A2,c/A 2,i in good solvents can be estimated for the two pairs of A2 values obtained at 25 °C and 35 °C. Both give a ratio A2,c/A 2,i = 0.81 which is in a good agreement with the theoretically calculated ratio of A2,c/A 2,1 = 0.80.[9] We would also like to estimate z and the expansion factor from the measured Rg values in order to calculate a consistent A2 ratio using equation 11-16 and compare the data to the predictions. However, it is not possible to do this with the quality of Rg data available now. These experiments would require larger cyclic polymers than are currently available to us. Dynamic Light Scattering Dynamic light scattering provides a further characterization of the difference between the linear and cyclic chains when solvent quality changes w ith temperature. The intensity-intensity autocorrelation 75 functions, g(2 Kt), were measured for several polymer concentrations, different scattering angles and varying temperatures. Figure IV- 6 and IV-7 illustrate the concentration and angular dependence of g< 2)(t) correlation functions of linear and cyclic copolymers in cyclohexane at 14.9 °C. Data for the cyclic polymer covering the concentration range from 5.0 to 20.8 mg mL*1 (Figure IV-6 a, top plot) and for several scattering angles ranging from 30° to 135° (Figure IV-7a, top plot) all show single exponential behavior typical of polymer diffusion in a good solvent. On the other hand, the linear triblock solution at 14.9 °C shows multimodal scattering functions for a similar concentration and angular range (Figures IV-6 b and IV-7b). These functions are fit by cumulant analysis to extract either one (cyclic polymer) or two (linear polymer) relaxation times. The inverse decay times thus determined are shown in Figure IV- 8 plotted against the square of the scattering wavevector. These plots are all linear with zero intercept indicative of free diffusion. The diffusion coefficients calculated from the slopes of the faster relaxations of the linear polymer or the only relaxation of the cyclic polymer are nearly independent of concentration, which are Di = 4.94 x 10' 7 and Dc = 5.58 x 10' 7 cm2 s'1, respectively. The diffusion coefficient for the slower relaxation of the linear chain scattering depends slightly on concentration and at 13.5 mg mL-1 as shown in Figure IV- 8 it is calculated as 1.30 x 10' 8 cm 2 s_ 1 . We also 76 1.15 tP° o ™ 1.05 0.001 0.01 0.1 1 10 t, ms Figure IV-6 . Concentration dependence of g< 2Ht) functions from DLS at 14.9 °C and scattering angle of 30°. Concentrations (mg m L'1) for (a) cyclic (top): 15.5 (O), 10.9 (♦), 8.73 (A), 5.93 (•), 5.00 (□); (b) linear (bottom): 13.5 (O), 8.40 (♦), 7.30 (A), 3.59 (•). I_______ I _______ I _______I ________ I ___ 0.001 0.01 0.1 1 10 t , ms Figure IV-7. Angular dependence of g< 2 Kt) functions from DLS at 14.9 °C. Concentrations for cyclic (top) and linear (bottom) polymers are (a) 20.8 and (b) 29.8 mg mL-1. Scattering angles 0 = 30° (O), 45° (•), 60° (■), 75° (□), 90° (A), 120° (A), 135° (o). 78 (/) E 6 x1 0 2 -2 q ,cm 3 c o Figure IV-8 . Angular dependence of DLS inverse relaxation time 1/x for cyclic block copolymer (O), and the fast mode (□) and the slow mode (■) for linear block copolymer at 13.5 mg mL-1 and 14.9 °C. 79 note that the slow relaxation occurs at a much longer time scale and its am plitude is much greater at higher concentrations. The relative am plitude of the slow mode decreases with lower concentrations and higher angles (also seen in Figures IV-6 b and IV-7b). Below 5.0 mg mL-1, the slow m ode is no longer measurable. This slow relaxation is most likely due to the aggregation of the PDMS-PS-PDMS triblock copolymers in the selective solvent because cyclohexane becomes a poor solvent for the PS block at 14.9 °C (below the apparent 0-temperature) but still a good solvent for the PDMS blocks. The data for the faster relaxation allows us to compare the diffusion coefficients, D, and therefore the hydrodynamic radii, for the cyclic and linear chains. The ratio of Dc/D i from the measurement at 14.9 °C is 1.13 and it is comparable to theoretical predictions[10-13] of 1.18. We note that the predictions are for the case when both the linear and cyclic chains are Gaussian; that is, both chains are in a common 0- solvent. However, the temperature of 14.9 °C is not far from the theta- point of either linear triblock or cyclic diblock copolymers as will be demonstrated later by the temperature dependence of dynamic light scattering data. By raising the temperature, the solutions of linear and cyclic polymers could both be moved away from the poor solvent regime. Dynamic light scattering results are illustrated in Figure IV-9 where the autocorrelation functions are shown for several temperatures from 15.9 to 30 °C. Over this temperature range, A2 for the cyclic polymers is 80 CM o> 1.1 - CM O) 0.001 t , ms Figure IV-9. Temperature dependence of g 12)(t) correlation functions from DLS for cyclic polymer (upper) and linear (bottom) at concentrations of 29.8 mg mL*1 and 20.8 mg mL'1, respectively. Scattering angle is 45°. Temperature: 30.0 °C (•), 25.2 °C (O), 23.6 °C (♦), 21.2 °C (O), 19.2 °C (■), 17.2 °C (□), 15.9 °C (A). 81 positive and comparable to values in good solvents. The dynamic scattering is consistent, and the correlation functions do not change over this temperature range. The linear chains show much different behavior with a clear transition from multimodal scattering below the 0 -temperature, two clear relaxations near 20 °C, and single relaxation at higher temperatures. The apparent 0-temperature at 20 °C is therefore confirmed independently by static and dynamic light scattering experiments. The slow diffusion observed in the photon correlation function gW(t) corresponds to the larger sized aggregates formed by the PDMS-PS-PDMS triblock when the temperatures are below the apparent 0 -tem perature. Thermodynamically, the theta-condition of the cyclic diblock in cyclohexane should be realized by lowering the solution temperature. As expected, further decrease of measurement temperature can indeed induce the critical condition for the diblock ring as evidenced by the appearance of a slow mode in the correlation functions (Figure IV-10). The correlation functions show two distinct relaxations for the diblock ring when the temperatures are pushed below 12 °C and the slow mode is more profound at the lower temperature. Hence, the apparent theta- temperature for the cyclic diblock is determined to be 12 °C by dynamic light scattering. The lower 0-temperature for ring than linear is confirmed even with block copolymer pairs, indicating that it results from the chain topology independent of the chemical composition. 82 C\J O) 0.1 1 10 0.001 0.01 t , ms Figure IV-10. Temperature effect of G(2)(t) correlation functions for cyclic diblock at 20.8 mg mL and 45° scattering angle. The experiment temperatures are 6.9 °C (O), 10.0 °C (O), 12.0 °C (a ) and 14.9 °C (□). 83 Figure IV-11 compares the plots of inverse relaxation time vs. the square of scattering vector for linear triblock and cyclic diblock under their theta-conditions, i.e., 21.2 °C and 12.0 °C, respectively. The diffusion coefficients obtained from the slopes of the two lines in Figure IV-11 are 5.67 x 10' 7 cm 2 s' 1 and 5.74 x 10' 7 cm2 s' 1 for the linear triblock and cyclic diblock at their 0-temperatures, respectively. Since the solvent viscosity changes with temperature, the viscosity for cyclohexane are calculated to be 0.96 cP and 1.1 cP at 21.2 °C and 12.0 °C, respectively.[15] The ratio Dc/D i calibrated with the solvent viscosity is 1.16 under theta-conditions, which is in a good agreement with the predicted ratio of 1.18.[10-13] W hen the solution temperature is 30.0 °C, single relaxations are observed for the linear and cyclic block copolymers in the good solvent regime. The diffusion coefficients calculated from Figure IV-12 at 30 °C for the linear and the cyclic samples are 7.59 x 10' 7 and 8.40 x 10-7 cm2 s '1 , respectively. The ratio Dc/D i of 1.11 is consistent with the value predicted by Monte Carlo calculation (Equation III-22).[16] The diffusion coefficient ratio is slightly smaller than the experimental result near the 0-condition and the prediction for Gaussian coils. In general, as the solvent quality improves and the coils expand, the apparent hydrodynamic interactions decrease and chains become more free draining. We admit however that such a small decrease in the ratio of Dc/D j (from 1.16 in theta solvent to 1.11 in a good solvent) is difficult to m easure experimentally. 84 7x10 0.2 0.4 0.6 0.8 2 -2 1.2x10 Figure IV-11. DLS inverse fast relaxation time 1/x for cyclic diblock at 12 °C (O), and linear triblock at 21.2 °C (□) under theta conditions. 1/t , ms* 85 100 80 60 40 20 0 20 40 80 120x10 0 60 2 -2 q , cm Figure IV-12. DLS inverse relaxation time 1/x for cyclic diblock (O), and linear triblock (□) at 30.0 °C (in good solvent). 86 The results presented in this paper are limited to a single pair of samples. We hope that further investigations of solution properties as a function of molecular weight and copolymer composition will follow from continuing success in the synthesis laboratories. Future experiments focusing on the differences in the apparent 0 -point between the linear triblock and cyclic diblock could be performed by looking for the onset of the aggregation. The investigations of the nature of these aggregates in comparison to previous work on micelle formation of block copolymers in selective solvents will be presented in Chapter 5. IV. Conclusions The results of dilute solution studies provide a comparison of solution properties of cyclic and linear block copolymers with theoretical predictions for homopolymer pairs. The dilute solution behavior of a linear triblock PDMS-PS-PDMS copolymer and its cyclized diblock PDMS-PS derivative shows that their 0-temperatures differ from each other by 8 °C. The triblock itself exhibits an apparent 0-temperature of 20 °C which is 15 °C lower than that of pure polystyrene. The further suppression of 0 -temperature for the cyclic diblock polymer may not require new theory since it is consistent with the predictions from theories for cyclic homopolymer. A comparison of second virial coefficients A2,c/A 2,i under good solvent conditions also demonstrates good agreement with the theoretical prediction. Dynamic light 87 scattering confirms the static light scattering results for the temperature dependence of solvent quality for both linear and cyclic copolymers. The comparisons of the diffusion coefficients for cyclic and linear block copolymers in both theta and good solvents agree with theories for homopolymer pairs. The data of the PDMS-PS-PDMS triblock linear and PS-PDMS diblock cyclic copolymers in cyclohexane is summarized in Table IV-1 along with theoretical predictions developed for homopolymer linear and cyclic pairs. 88 Table IV-1. Results of linear and cyclic block copolymers in comparisons with theoretical predictions for homopolymer pairs in theta and good solvents linear vs. ring H om opolym er Block Copolymer Theta- Solvent <Rg>c,e/<R^>i,e 0.5 N /A 0 -tem perature 35 °C vs. 29 °C 20 °C vs. 12 °C Dc.e/Di.e 1.18 1.16 Good Solvent <Rg>c/<R^>l 0.56 - 0.57 N /A A2.C/D2.1 0.80 0.81 Dc/Di 1 .1 1 1 .1 1 89 V. References 1. R.Yin and T.E. Hogen-Esch, Polymer Preprints 33(1), 239 (1992). 2. R. Yin, E.J. Amis, and T.E. Hogen-Esch, Macromol. Symp. 85, 217 (1994). 3. H. Benoit and D. Froelich, Light Scattering From Polymer Solutions; M.B. Huglin, Ed.; Academic Press: London, Chapt. 10; (1972). 4. B.H. Zimm and W.H. Stockmayer, J. Chem. Phys. 17, 1301 (1949). 5. E.F. Casassa, ]. Polym. Sci., Part A 3, 604 (1965). 6 . N.P. Balsara, P. Stepanek, T.P. Lodge, and M. Tirrell, Macromolecules 24, 6227 (1991). 7. K. Iwata and T. Kimura, /. Chem. Phys. 74, 2039 (1981). 8 . K. Iwata, Macromolecules 18, 115 (1985). 9. E.J. Amis, D.F. Hodgson, and W. Wu, ]. Polym. Sci., Polym. Phys. Ed. 31(13), 2049 (1993). 10. V. Bloomfield and B.H. Zimm, J. Chem. Phys. 44, 315 (1966). 11. H. Yamakawa, Modern Theory of Polymer Solutions; Harper & Row: New York, (1971). 12. M. Kumbar, J. Chem. Phys. 55, 5046 (1971). 13. M. Kumbar, J. Chem. Phys. 59, 5620 (1973). 90 14. M. Fukatsu and M. Kurata, J. Chem. Phys. 44, 4539 (1966). 15. C.S. Viswanath, Data Book on the Viscosity of Liquids; New York: Hemisphere Pub. Corp., pp200 (1989). 16. Y. Chen, J. Chem. Phys. 78, 8 (1983). 91 Chapter 5. Aggregation of Linear Triblock and Cyclic Diblock Copolymers I. Introduction The micellization of linear di- and triblock copolymers in selective solvents is reviewed in this chapter. The solution properties and the micellization of linear AB diblock and ABA triblock copolymers have attracted continuous interest because block copolymers can act as classic nonionic surfactants to form micelles in selective solvents and eventually form networks under certain experimental conditions. [1-5] However, there is no literature on the micellization of cyclic AB diblock copolymers. Fundamental differences are expected for the micellization of AB diblock rings in comparison with ABA triblocks or AB diblock linear copolymers due to the topological constraints on the ring polymers. Here the first investigation of the aggregation phenomena of linear ABA triblock and cyclic AB diblock copolymer pair is reported. Cyclohexane, a theta solvent for polystyrene is used as the selective solvent to induce the aggregation of PDMS-PS-PDMS linear and PDMS- PS cyclic block copolymers. Light scattering experiments show that aggregation takes place in solution when the temperature is below the critical aggregation temperatures (or apparent theta temperatures), 20 °C and 12 °C for the linear triblock and cyclic diblock, respectively. 92 II. Review: Linear Block Copolymer Micellization As a result of the thermodynamic interactions between chemically different blocks, block copolymers often exhibit unique solution behaviors. The colloidal properties of block copolymers in selective solvents (good for one block, bad for the other) recall those known from aqueous solutions of amphiphilic surfactants. Formation of micelles takes place in solution when the copolymer concentration is above critical micelle concentration (CMC). Micellization of linear AB diblock and ABA triblock copolymers in the dilute solution of selective solvents has been studied by various experimental techniques,[2-14] including small-angle X-ray scattering (SAXS), small-angle neutron scattering (SANS), light scattering, viscometry, sedimentation and fluorescence energy transfer. The diblock copolymer micelles have been found to have a narrow size distribution and a spherical core-shell structure, with the insoluble block(s) as core and solvated soluble blocks as shell, respectively. [1 ] Micellization of block copolymers obeys the closed association model characterized by an equilibrium between "unimer" (molecularly dissolved copolymer) and micelles.[2 -1 0 ] Theoretical methods and computer simulations have provided descriptions of micellar structures existing in solution and scaling laws for the micelles. [15-19] For AB diblock copolymers, theoretical work has directed at predicting the critical micelle concentration, the micelle size 93 distribution, the average association number, as well as the core radius and shell thickness of micelles. Triblock Copolymers in a Selective Solvent for End Blocks For the micellization of ABA triblock copolymers in a selectively good solvent for the terminal block, experimental results are often fit to theories developed for AB diblock copolymers.[15-17] Winnik et al.[9] found that the characteristic micelle size (Rh), the mean association number N, core radius (Rc), and Flory-Huggins % parameter for poly(ethylene oxide)-polystyrene-poly(ethylene oxide) are in good agreements with two theoretical models[15,16] proposed for AB diblock copolymers by simply considering ABA triblock as equivalent to two AB diblock copolymers of half the size. In a preferential solvent for the outer A blocks, triblock copolymers also aggregate into monodisperse spherical micelles with a core rich in B chains surrounded by a corona of A chains swollen by the solvent. These micelles are in equilibrium with molecularly dissolved copolymer coils (unimers).[2 -1 0 ] NU<— where U represents unimers (individual copolymer), M represents micelles, N is the association number, and K is the equilibrium constant. The equilibrium assumes a close association mechanism as in the micellization of AB diblock copolymer. 94 The association equilibrium, association num ber and micelle size can vary with the copolymer composition, chain length,[8 ] temperature,[13, 20, 21] and solvent quality.[10,14] For the system of poly(oxyethylene/oxybutylene/oxyethylene) triblock in water, the critical micelle and gel concentration decreased remarkably as chain length increased, while the molecular weights and sizes of micelles increased with increasing chain length. [8 ] Tem perature is another important param eter controlling the micellization process. The Rayleigh scattering data on a polystyrene- polybutadiene-polystyrene triblock copolymer in a mixed solvent of dioxane-ethanol,[20, 21] showed that at higher temperatures (>30 °C) the copolymer is present primarily in monomolecular form (unimer). Micelles were present almost exclusively at 20 °C, and both forms coexisted in the solution when temperature is between 20 and 30 °C. Also, an inverse temperature effect on the micelle formation of poly(oxyethylene)-poly(oxypropylene)-poly(oxyethylene) in aqueous solution was observed.[13] The association structures varied from hard sphere micelles, prolated ellipsoid, to large aggregates, as the tem perature increased. Among extensive studies, the use of mixed solvent has been the most favored approach to prepare micellar aggregates from block copolymers. Chu and coworkers[14] showed that the addition of water in o-xylene can induce the micellization of poly(oxyethylene)- poly(oxypropylene)-poly(oxyethylene) (PEO-PPO-PEO). The triblock 95 copolymers did not micellize in the absence of water or in the presence of a small amount of water (molar ratio, Z, of w ater/EO < 0.15). Micelles, consisting of a PPO shell and a PEO and water core, can also be formed and they changed from spherical (Z < 1.3) to a nonspherical (Z > 1.3) shape as the amount of water increased. Triblock Copolymers in a Selective Solvent for the Middle Block In a selective solvent which is a good solvent for the inner B block but a bad solvent for the end A blocks, the behavior of ABA triblock copolymers becomes more complicated. Experimental results and theoretical predictions are highly controversial at this point. Some of triblock systems show no multimolecular association in such solvents and only intramolecular association was observed. [22-24] However, in other cases, triblock copolymers were found to exhibit aggregation, [25, 26] but the structure of triblock copolymer aggregates did not fit a spherical core-shell model. The aggregates were expected to possess a network like or a loose branched structure. [25, 26] Theoretical arguments have been advanced for[27] and against[28] the formation of micelles by symmetric triblock copolymers in poor solvents for terminal blocks. From a thermodynamic viewpoint, ten Brinke and Hadziioannou[28] argued that neither micelles nor intramolecular association should exist in a solvent selective for the m iddle block. Computer simulations, however, support the formation of independent micelles under some conditions, and more complicated 96 structures consisting of clusters or networks of interconnected micelles were predicted under other conditions. [18] Monte Carlo simulations performed by Rodrigues and Mattice on a system of triblock ABA in a selective solvent for the middle block provided strong support for possible branched structures of aggregates.[18,19] The authors speculate that transitory aggregates, large independent micelles, and branched structures can coexist, depending on the strength of the interaction. The ABA linear chain contributes to transitory aggregates with a single A block and its other A block dangling in solvent. An micelle can also be formed with both A blocks participating in the core. In addition, the system may contain free unassociated chains as well as single loops formed by intramolecular association joining both end blocks from the same triblock chain. In branched structures, soluble center blocks act as bridges to connect dense micelles of insoluble terminal blocks. In contrast to the above arguments and experimental observations, Tuzar and coworkers investigated dilute and semidilute solutions of a triblock copolymer, polystyrene-poly(hydrogenated butadiene)-polystyrene in solvents selective for A or B blocks.[ll, 12] In both systems, micelles were detected with uniform spherical cores formed by insoluble copolymer blocks. When heptane was used as a good solvent for poly(hydrogenated butadiene), micelles were present with outer PS blocks as cores and aliphatic middle blocks as shells. In the mixed solvents, l,4-dioxane/25 vol.% heptane, micelles are then formed w ith aliphatic cores and PS shells. Unlike the former case where 97 PS blocks were densely packed in the core region, these micellar cores were found to be strongly swollen. Cyclic AB Diblock Copolymers Due to the difficulty in the synthesis of macrocyclic copolymers, no studies have been carried out for cyclic block copolymers in selective solvents. To a certain extent, the micellization of AB diblock rings in a selective solvent should resemble an AB linear diblock more than its linear precursor ABA triblock copolymer. When the solvent changed from a preferential solvent for A blocks to a preferential solvent for B blocks, the micellar cores and shells would simply be reversed for either the AB linear and cycle. On the other hand, the topological constraints of ring polymers result in fundamental differences in micellization of cyclic AB diblock copolymers compared to AB linear copolymers. As one can imagine, predictions for critical micelle concentration, micellar structure, micellar size, aggregation number and thus scaling relations would need to take account of the characteristics of ring topology. For example, the core and the corona of the aggregates are composed of the arches of insoluble and soluble blocks respectively, instead of free and stretchable linear block chains. Furthermore, the constraints of ring architecture and the additional topological repulsive force would reduce the number of the chains in core and shell regions. 98 The fact that a ring polymer exhibits larger expansion than its linear counterpart in a good solvent would perhaps favor a loosely packed core and shell. Thus, it will not be surprising if the micellar core size, shell thickness and association numbers do not fit theoretical models or experimental results of either AB or ABA linear block copolymers. Both theoretical and experimental studies are definitely required to understand the micellization phenomena of cyclic block copolymers. III. Experimental Section The same pair of linear triblock and cyclic diblock copolymers mentioned in Chapter 4 are used for the aggregation studies here. The block polymers in this work contain 35.1 wt% of styrene as determined by proton NMR. In the linear triblock polymer, the polystyrene is the center block with PDMS blocks on each side. Static light scattering measurements give 4.31 x 104 for the average molecular weight of the whole polymer. The sample preparations, purifications and dissolutions follow the same procedures discussed in Chapter 4. The temperatures of light scattering experiments ranged from 6.9 to 35.0 °C. A circulator controlled the temperature of the index- matching toluene bath to ± 0.05 °C. Filtered dry air was blown towards the metal parts of the light scattering instruments to avoid water condensation when the experimental temperature was below room 99 temperature. Dynamic light scattering autocorrelation functions were acquired at scattering angles from 30° to 135° with a multi-tau log-time correlator (ALV Instruments 5000). The relaxation time extracted from CONTIN analysis was related to hydrodynamic radius of the diffusing species by the Stokes-Einstein equation. Total intensity measurements at different temperatures were performed on a Brookhaven 264 channel correlator coupled with an automated goniometer. Due to the complex features of the aggregation, the method of complete Zimm plots was not utilized. Instead the excess scattering intensities (solution scattering intensity subtracting solvent scattering intensity) were measured for each solution concentration at various scattering angles. IV. Results and Discussions DLS o f Linear Triblock Copolymer Previous static and dynamic light scattering results[29, 30] both demonstrate that the linear triblock copolymer starts to associate when the solution temperature drops below 20 °C. The second virial coefficient from static light scattering changes from positive to negative as tem perature decreases, indicating an apparent theta temperature of 20 °C for the linear triblock copolymer. 10 0 Figure V-l shows the same temperature effect on the aggregation of linear triblock copolymer at a concentration of 20.8 mg mL'1 in cyclohexane and scattering angle of 45°. When temperatures are below 20 °C (top three curves of the upper plot), a slower relaxation mode is observed in addition to the normal single chain relaxation in the correlation functions. The slow relaxation corresponds to large aggregates diffusing in solution and the relative amplitude of the slow mode decreases as temperature goes up. The CONTIN peaks become broader as the temperature approaches the transition temperature. The change in relaxation spectra with temperature is consistent with the findings of Chu et al. on the temperature induced PS-P(t-butyl styrene) copolymer micelles. [31] Since the peak area represents the contribution of particle scattering intensity, the CONTIN fits as a function of temperature can provide a picture of the temperature-dependent dynamic equilibrium between single polymer chains and aggregates. After the calibration of solvent viscosity at each experiment temperature, the aggregate relaxation time exhibits only a weak temperature dependence. The increase in the relative amplitude of the slow mode suggests the lower temperature favors the formation of aggregates in the equilibrium between unimer and association complex. As can be seen in Figure V-l, the slow relaxation mode eventually disappears when temperature changes from 19.2 to 21.2 °C. The sharp transition temperature around 20 °C for linear triblock copolymer is demonstrated by dynamic light 0.001 0.01 0.1 1 10 100 t (ms) Figure V-l. Intensity autocorrelation functions and CONTIN fits of linear triblock at concentration of 20.8 mg mL' 1 and 45 0 scattering angle. The temperatures are 15.9 °C (O), 17.2 °C (O), 19.2 °C (A), 21.2 °C (□). 102 scattering data as well as by the second virial coefficient from static light scattering experiments. The intensity-intensity autocorrelation functions were measured for several polymer concentrations and scattering angles. Figure V-2 illustrates the typical concentration dependence of the relative proportion of single chain and copolymer aggregates scattering in solution. At the same temperature 14.9 °C, the amplitude of the slow m ode is more pronounced at higher concentration. However, the decay times of correlation functions (peak positions of CONTIN fits) display- only a weak concentration dependence. Since the CONTIN relaxation time is proportional to the hydrodynamic radius according to the Stokes- Einstein equation, hydrodynamic sizes of both triblock single chain and aggregates are independent of polymer concentration. Figure V-3 shows the angular dependence of intensity auto correlation functions at 17.2 °C which is below 20 °C, the critical aggregation temperature of the linear triblock. The CONTIN peak position is shifted to shorter decay time with increasing scattering angle. This is understandable because the relaxation time (i.e. peak position) is inversely proportional to the square of the wavevector q2, which is a function of sin2(0/2). The relative amplitude from the copolymer aggregates decreases with increasing scattering angle. The total intensity is more sensitive to the scattering of larger particles at low angles because of the particle structure factor. Thus, at lower angles, the aggregate scattering contributes more to the total intensity and results in amplitude, (norm.) 103 0.5 0.0 r r m r m rnrnrrr rnrtrrirnrrnrnrrriTrnTr 10'3 10‘2 10'1 10° 101 102 103 t , ms Figure V-2. The CONTIN fits of linear triblock at 14.9°C and 45° scattering angle. The concentrations (mg mL_ 1 ) are 8.40 (O), 7.30 (o), 3.59 (A). 104 O Z C D ~ o ZJ "5. e < 0 . 0 0.001 0.01 100 1000 105 an increase of the relative amplitude of slow mode. The disappearance of slow relaxation at high angles indicates the strong angular dependence of aggregate scattering intensity. This effect can be also seen in the inverse relaxation time 1 /x vs. the square of scattering vector q2 plot (Figure V-4). For the linear triblock at 15.9 °C, Figure V-4 shows that both fast (using the left axis) and slow modes (using the right axis) are diffusive. The corresponding hydrodynamic radii calculated from the diffusion coefficients (the slope of the lines) are 4.1 and 149 nm for the linear copolymer unimer and its aggregates in cyclohexane respectively. DLS of Cyclic Diblock Copolymer As expected, aggregation of the cyclic diblock copolymer occurs when the temperature is pushed below 12 °C. Figure V-5 shows the temperature dependence of dynamic light scattering for the cyclic diblock in cyclohexane. The aggregation of cyclic diblocks takes place in cyclohexane when the solution temperature is below 12 °C as evidenced by the slow relaxation mode in Figure V-5. The correlation functions display singular and bimodal relaxations for the cyclic diblock at temperatures above and below 12 °C, respectively. The apparent theta tem perature for the cyclic diblock is thus 8 °C lower than that of the linear triblock. This shift m ust be due to the constraints of the ring topology and it is in agreement with experimental findings and theoretical predictions on homopolymer linear and cyclic pairs. [31-33] The temperature effect on the relative amplitude of relaxation spectra is 106 3000 60x10 2500 50 2000 40 1500 - 20 1000 500 80 120x10 40 2 2 Figure V-4. The inverse relaxation time vs. the square of scattering vector q2 of the fast ( • ) and slow (O) modes of linear triblock copolymer at 15.9 °C. amplitude (norm.) 107 1.2 + -* O) 1.0 1.0 0.5 0.0 10'4 10'3 10'2 10'1 10° 101 102 ,3 t , ms Figure V-5. The intensity autocorrelation functions and CONTIN fits of cyclic diblock at 20.8 mg mL-1 and 45 scattering angles. The temperatures are 6.9 °C (O), 10.0 °C (O), 12.0 °C (A) and 14.9 °C (□). 108 similar to that for linear triblock observed in Figure V-l, i.e., the relative am plitude of the slow mode increases with decreasing temperature. Figure V- 6 demonstrates the angular dependence of intensity autocorrelation functions (upper) and relaxation distributions (bottom) extracted from CONTIN analysis. Again, the aggregate scattering (slow relaxation mode) is more profound at low scattering angles. When temperatures are above 12 °C, only a single relaxation was observed for diblock rings in dynamic light scattering experiments over a range of scattering angles. The linear angular dependence of relaxation times shown in Figure V-7 is indicative of diffusive behavior of the single chains in solution. The relaxation time corresponds to the motion of unassociated cyclic diblock in solution. However, two distinct relaxation modes are observed for the ring copolymer in solution when the temperature is below 12 °C. The linearity and zero intercepts in Figure V- 8 indicate that both the fast (using the left axis) and slow modes (using the right axis) are diffusive. The hydrodynamic radii corresponding to the single chain and aggregates of ring polymer are calculated to be 3.9 and 143 nm, respectively. Total Intensity Measurements The difference in the transition temperature (critical aggregation temperature) for linear triblock and cyclic diblock can also be determined amplitude (norm.) ik tl. 109 C\J O ) 1.1 - m \W k V A \w k W J i ■ t , ms Figure V-6 . The intensity autocorrelation functions and CONTIN fits of cyclic diblock at 20.8 mg mL' 1 and 6.9 °C. The angles are 30° (O), 45° (O), 60° (A), 90° (□) and 135° (V) 110 60 40 20 0 0 20 40 80 60 120x10 2 -2 q ,cm Figure V-7. The inverse relaxation time vs. the square of scattering vector q2 of the single relaxation modes of cyclic diblock at c = 20.8 mg mL' 1 and temperatures of 14.9 °C (♦), 19.2 °C (■), 23.7 °C (A) and 30.0 °C (•). 6x10 4000 5 4 3000 3 2000 2 1000 1 O ^ S .___ ■ « ______■ ■ 0.0 0.2 0.4 0.6 0.8 2 -2 q ,cm Figure V-8 . The inverse relaxation time 1/x vs. the square of scattering vector q2 of the fast (filled symbols) and slow (empty symbols) modes of cyclic diblock at c = 20.8 mg mL' 1 and temperatures of 6.9 °C (•), 8.0 °C (♦) and 9.0 °C (A). 112 from the scattering intensity measurements as shown in Figure V-9. For both linear and cyclic copolymers, as temperature decreases, the scattering intensity first stays constant and then increases steadily after a sudden leap. The sharp rise in scattering intensity reflects the formation of large aggregates in the solution. For linear triblock at 11.2 mg mL' 1 and 45° scattering angle, the intensity break-point occurs at the temperature at 19.5 °C, which agrees well with the results of dynamic light scattering and second virial coefficient. The intensity vs. temperature profile for the cyclic polymer is similar to that of linear copolymer. But the intensity jump takes place at 13 °C for the block copolymer ring at 20.8 mg mL-1, which falls in the range of 12 to 14.9 °C estimated from dynamic light scattering data. The internal consistency regarding the critical aggregation temperature between the results of the three approaches is summarized in Table V-l. The slight difference between the transition temperatures obtained from the time-averaged intensity measurements and intensity fluctuation experiments (DLS) has been reported by Chu et al. [31] Nevertheless, our results from three independent methods agree reasonably well within the experimental errors. C om parisons It is unexpected that the size of the aggregates formed by the linear triblock and cyclic diblock copolymers in cyclohexane is independent of solution temperature (Figure V-l and V-5) and copolymer concentration intensity (a.u.) 113 200 150 1 0 0 50 — - 0 0 - 0 - o - o — o - 0 20 5 10 15 25 30 T, °C Figure V-9. The scattered intensities of linear triblock and ring diblock at 45° angle and concentrations of 11.2 mg mL*1 and 2 0 .8 mg mL-1, respectively. 114 Table V-l. The critical aggregation temperatures of linear triblock and cyclic diblock determined by light scattering Critical Aggregation Tem perature A2 CONTIN Intensity Linear Triblock 2 0 19.2-21.2 19.5 Cyclic Diblock 12.0 -14.9 13 115 (Figure V-2). Mortensen and Pederson found the size and the structure of aggregates strongly depend on temperature.[13, 31] The temperature independence observed for our linear triblock and cyclic diblock may be due to the narrow range of experiment temperatures so the solvent, cyclohexane is not too far into the poor solvent regime for the PS block. Moreover, since the solvent is selectively good for the end blocks, the structure of the aggregates formed by the triblock PDMS-PS-PDMS in cyclohexane is expected to be spherical as predicted by theories. [4,5] The large hydrodynamic size and polydispersity of the aggregates, however, do not seem to support the model of uniform spherical micelles. Ideally, a spherical micelle consisting of a dense core of insoluble blocks is a compact structure and therefore has a size on the order of tens of nm. The formation of large aggregates rather than spherical micelles may be also resulted from the temperature range. With the temperature only a few degrees away from the apparent 0 -temperature, the association junctions formed by PS blocks are probably swollen by the solvent. It is thus less likely for the triblock copolymer to form compact spherical micelles. However, investigations at lower temperatures are not possible because of the high freezing point of cyclohexane (6.5 °C). Interestingly, the hydrodynamic size of the aggregates of diblock ring is only slightly smaller than that found for linear triblock aggregates. It is necessary to differentiate the mean aggregation number and the structures of the aggregates formed by linear triblock and cyclic diblock. Therefore, further characterization of the aggregates is needed 116 to understand the differences in association process of linear and cyclic block copolymers, such as the apparent molecular weight and the packing density of respective aggregates. V. Conclusion The light scattering technique has been employed to investigate the onset of aggregation by linear and cyclic block copolymers in a selective solvent, cyclohexane, which is a theta-solvent for the middle polystyrene block and a good solvent for the PDMS blocks in the entire tem perature range. The apparent theta-temperatures are realized by lowering the solution temperatures to 20 °C and 12 °C for the linear triblock and cyclic diblock respectively. These transition temperatures are also referred to as the critical aggregation temperatures below which the block copolymers start to aggregate into larger clusters in solution. The results in this chapter include the first report on the occurrence of cyclic diblock aggregation in a selective solvent. The aggregation is accompanied with a negative second virial coefficient, the existence of slow diffusive relaxation modes in CONTIN analysis of dynamic light scattering data, as well as a sudden jump of scattered intensity. The critical aggregation temperatures determined from different approaches are self-consistent with one another. The size of aggregates is independent of solution concentration and experiment temperature although the lower temperature favors the formation of aggregates. 117 VI. References 1. Z. Zhou, B. Chu, and D.G. Peiffer, Langmuir 11, 414 (1995). 2. J. Rassing and D. Attwood, Int. J. Pharm. 13, 4755 (1983). 3. G. Wanka, H. Hoffmann, and W. Ulbricht, Colloid Polym. Sci. 268,101 (1990). 4. W. Brown, K. Schillen, M. Almgren, S. Hvidt, and P. Bahadur, /. Phys. Chem. 95, 1850 (1991). 5. K. Mortensen, W. Brown, and B. Norden, Phys. Rev. Lett. 13, 2340 (1992). 6 . H.-W. Haesslin, Makromol. Chem. 186, 357 (1985). 7. K. Visscher and P.F. Mijnlieff, Rheologica Acta 30, 559 (1991). 8 . C.V. Nicholas, Y.-Z. Luo, N.-J. Deng, D. Attwood, J.H. Collett, C. Price, and C. Booth, Polymer 34, 138 (1993). 9. R. Xu, M.A. Winnik, G. Riess, B. Chu, and M.D. Croucher, Macromolecules 25, 644 (1992). 10. K. Prochazka, B. Medhage, E. Mukhtar, M. Almgren, P. Svoboda, J. Trnena, and B. Bednar, Polymer 34, 103 (1993). 11. J. Plestil, D. Hlavata, J. Hrouz, and Z. Tuzar, Polymer 31, 2112 (1990). 12. Z. Tuzar, C. Konak, P. Stepanek, J. Plestil, P. Kratochvil, and K. Prochazka, Polymer 31, 2118 (1990). 13. K. Mortensen and J.S. Pedersen, Macromolecules 26, 805 (1993). 14. G. Wu, Z. Zhou, and B. Chu, Macromolecules 26, 2117 (1993). 15. J. Noolandi and K.M. Hong, Macromolecules 16, 1443 (1983). 16. A. Halperin, Macromolecules 20, 2943 (1987). 17. R. Nagarajan and K. Ganesh, J. Chem. Phys. 90, 5843 (1989). 18. K. Rodrigues and W.L. Mattice, Polymer Bulletin 25, 239 (1991). 19. K. Rodrigues and W.L. Mattice, Langmuir 8 , 456 (1992). 20. Z. Tuzar and P. Kratochvil, Makromol. Chem. 160, 301 (1972). 21. Z. Tuzar and P. Kratochvil, Adv. Colloid Interface Sci. 6 , 201 (1976). 22. T. Kotaka, T. Tanaka, and H. Inegaki, Polym. J. 3, 327 (1972). 23. T. Kotaka, T. Tanaka, and H. Inegaki, Polym. J. 3, 338 (1972). 24. W.T. Tang, G. Hadziioannou, P.M. Cotts, B.A. Smith, and C.W. Frank, Polym. Prepr. 27, 107 (1986). 25. T. Kotaka, T. Tanaka, and H. Inegaki, Macromolecules 11,138 (1978). 26. E. Raspaud, D. Lariez, and M. Adam, Macromolecules 27, 2956 (1994). 27. N.P. Balsara, M. Tirrell, and T.P. Lodge, Macromolecules 24, 1975 (1991). 119 28. G.T. Brinke and G. Hadziioannou, Macromolecules 20, 486 (1987). 29. E.J. Amis, D. F. Hodgson, and W. Wu, J. Polym. Sci., Polym. Phys. Ed. 31(13), 2049 (1993). 30. E.J. Amis and W. Wu, Polymer Preprints 35(1), 632 (1994). 31. Z. Zhou, B. Chu, and D.G. Peiffer, Macromolecules 26, 1876 (1993). 32. J. Roovers, J. Polym. Sci. Polym. Phys. Ed. 23, 1117 (1985). 33. H. Zhang and Z-d. He, Polym. Commun. 32, 239 (1990). 34. K. Iwata, Macromolecules 18, 115 (1985). 120 Chapter 6. Hydrophobically Modified Water Soluble Polymers I. Introduction Hydrophobically modified water soluble polymers have received substantial interest due to their potential applications. Water soluble polymers containing a small number of hydrophobic substituents such as alkyl groups are often referred to as "associating polymers" because they undergo association in aqueous solution. [1] The association generates high molecular weight clusters by forming a transient network via hydrophobic interactions and therefore results in an appreciable increase in the viscosity of polymer solutions. [2-3] Because of the nature of the weak physical association, the high viscosity thus obtained depends strongly on shear rate. The network-like structures readily come apart when subjected to a high shear stress, resulting in lower viscosity — pseudoplastic or shear thinning behavior. Upon removal of shear, the network is formed again and the viscosity of associating polymer solutions goes back to its low shear value. Due to the above mentioned unique rheological property, the major technological application of these materials is as viscosity modifiers for aqueous solutions in coatings [4,5] and enhanced petroleum recovery.[6 ] Traditionally, these technologies relied on ultrahigh molecular weight polyacrylamide and xanthan. However, 121 ultrahigh molecular weight polyacrylamide has poor mechanical and thermal stability. Also, the ionic charge repulsion or polyelectrolyte effect in aqueous media often induces a conformational change of water soluble polymers. Fortunately, associating polymers can offer superior performance to ultrahigh molecular weight water soluble polymers since they are less sensitive to salt content and molecular weight. The viscosity enhancement results from hydrophobic interactions which consists of reversible association/dissociation processes. More recently, hydrophobically modified associating polymers have also been studied for the development of controlled drug release systems [7] and for drag reduction in water-based fluids. [8 ] As a consequence, there has been increasing interest in the synthesis and characterization of these hydrophobically modified water soluble polymers. [9-28] II. Random Copolymers Early studies of associating polymers focused on water soluble random copolymers. Many of these copolymers were prepared by free radical emulsion polymerizations. A small amount of associating stickers can be incorporated into polymers by either grafting hydrophobic units to a hydrophilic backbone[9,10] or copolymerizing hydrocarbon containing comonomers into a water soluble polymer. [11-16] 122 The nature of hydrophobic interactions depends strongly on the chain architecture, the type, the length and the placement of hydrophobic substituents. [17] For instance, Hogen-Esch et al. discovered that in both polyacrylamide copolymers and modified hydroxyethyl cellulose (HEC) systems, fluorocarbons as hydrophobic substituents lead to much higher viscosity than hydrocarbons as hydrophobe. [18-20] This is consistent with the fact that fluorocarbon surfactants have lower critical micelle concentrations (CMC), surface energies and surface tensions than their hydrocarbon analogs. [21] Also, experimental studies on poly(acrylamide) copolymers have shown that the solution viscosity increases with increasing spacing between the hydrophilic polymer backbone and pendant hydrophobic fluorocarbon units by inserting oxyethyl groups. [22] Evidently, the spacer effect which is a function of the length and flexibility of spacers increases the accessibility of the hydrophobes by decreasing the steric hindrance to association. This would lead to the formation of stronger micelle-like association structures (i.e. longer duration time of association junctions) and thus higher viscosity. As mentioned above, the main feature of associating polymers is the strong shear dependence of viscosity. A strong shear thinning effect has been observed for both hydrocarbon and fluorocarbon modified water soluble polymers. The effect is exemplified in Figure VI-1 for an associating poly(acrylamide) copolymer containing fluorocarbon acrylate (FX13) as hydrophobe. At the polymer concentration of 0.3 wt%, the T|,CP 123 3000 2500 0.07 mol% FX-13 ■ 0.3 wt% A 0.2 wt% ♦ 0.1 wt% • 0.05 wt% 2000 1500 1000 500 -0.5 0.0 0.5 logy, s'1 2.0 Figure VI-1. Effect of shear rate on solution viscosity of copolymer acrylamide and 0.07 mol% FX-13 at various polymer concentrations: 0.3 wt% (■), 0.2 wt% (A), 0.1 wt% (♦) and 0.05 wt% (•). 124 solution viscosity drops sharply from 2500 cP to 400 cP over a shear rate change of one decade. The shear thinning is explained by the destruction of intermolecular association junctions under high stress. Figure VI-1 also shows that the shear thinning effect is concentration dependent and is less profound at lower concentrations. This is presumably because the intermolecular association is substituted by intram olecular interactions in more dilute solutions. The comonomer content of associating polymers is another factor that alters the association and thus viscosity profile. A maximum is observed in a viscosity vs. comonomer content plot (Figure VI-2). The initial increase in viscosity with hydrophobe content suggests the formation of extended network of intermolecular associations. To a certain extent, further increase in comonomer content starts to favor intramolecular associations. More preferable intramolecular interactions at high hydrophobe concentrations would collapse the intermolecular association and decrease the solution viscosity. Figure VI-2 shows the viscosity is also dependent on the structure of hydrophobic comonomers. W hen fluorine containing methacrylate comonomer is used, higher comonomer content is needed to achieve the viscosity maximum. To illustrate the underlying molecular basis for the viscosity results, Seery and Amis recently carried out static and dynamic light scattering experiments on solutions of polyacrylamide copolymers with varying content of fluorocarbon units.[23] They found that associations lo g r\, cP 125 log comonomer, mol% Figure VI-2. Viscosity of 0.5 wt% PAM copolymers vs. the content of fluorocarbon containing acrylate (■) or methacrylate comonomers ( • ) at 0.4 s_1 and 25 °C. 126 occur at polymer concentrations as low as 10 ppm. The multichain aggregates of large hydrodynamic radii formed in solution provide the first direct evidence for explaining the viscosity enhancement. It is important to determine the exact degree of comonomer incorporation since the hydrophobe content plays an im portant role in the viscosifying ability of associating copolymers. In the synthesis of both hydrocarbon and fluorocarbon modified associating polymers, the hydrophobe content can be controlled by the ratio of the hydrophilic- hydrophobic comonomers. Since the content of hydrophobic comonomer has to be extremely low in order to ensure the copolymer solubility in water, it is very difficult to accurately measure the degree of hydrophobic units incorporated in the polymer chain. Although direct measurements by UV spectroscopy[12,13] and fluorescence techniques[24] have been reported for hydrocarbon hydrophobes, no methods have succeeded in determ ining fluorocarbon comonomer content so far. In addition to the uncertainty of comonomer content, another problem is the copolymer microstructure, i.e., a random or blocky distribution of the hydrophobic units. It has been claimed that the copolymer microstructure is affected by the presence of the surfactant micelles during the course of synthesis and in turn has a large effect on the rheological behavior of the polymer solutions. [16] On the other hand, Bock and coworkers reported a random distribution of hydrophobic units. [11, 25] However, this was challenged by McCormick 127 et a i,[26, 27] who suggested the formation of a blocky structure in copolymers synthesized by the emulsion technique. For fluorine containing poly(acrylamide) copolymers, *H and 19F NMR dual probes have been employed to investigate reaction kinetics and comonomer content. [28] Monitoring the disappearance rate of 19F NMR signals from fluorocarbon comonomer allows one to measure the incorporation rate (i.e. reactivity ratio). Yassini and Hogen-Esch found that flurocarbon comonomer incorporation into polyacrylamide chains is random when the acetone concentration in the reaction mixture is above 6 wt%.[28] However, the extremely broadened 19F NMR spectra hampers direct determ ination of comonomer content. Although the synthesis of random copolymers is straightforward, the large polydispersity and the uncertainty of comonomer distribution and hydrophobe content make experimental characterizations and data interpretation very difficult. Thus, despite their technological importance, characterization of these hydrophobically modified water soluble copolymers still remains limited. III. Telechelic Polymers To overcome the problems encountered in random copolymer systems, associating polymers with defined architecture, narrow molecular weight distribution and known sticker placement are needed. It is only very recently that experiments have been performed on a 128 model polymer, a telechelic, urethane-coupled polyethylene oxide (PEO) with long hydrocarbon alkyl end groups.[10,29-37] This class of end- functionalized PEO, known as " HEUR associating thickeners," is added at about 0.5-2 wt% to latex paint formulations to modify their rheology and to reduce splatter and sag. Among the characteristics of their solutions in water is the high viscosity at relatively low polymer concentrations and a very rapid rise in the zero-shear viscosity with increasing concentration. At higher shear rates there is often a transition region where the viscosity increases (shear-thickening), followed by a dramatic drop of solution viscosity (shear thinning). A typical linear HEUR associative thickener has a structure RO— (DI— O —PEO— O—)n DI— OR where DI is a diisocyanate, typically toluene diisocyanate (TDI) or isophorone diisocyanate (IDI). R is an alkyl or alkylaryl group. The HEUR polymers were prepared from commercially available dual hydroxyl-ended PEO by reacting with a diisocyanate (DI). The end modification is accomplished using an aliphatic alcohol or an alkylphenol and the mean chain length of polymers depends upon the DI/PEO ratio. These polymers have recently attracted widespread attention, in part because of their applications in paint and paper coatings technology, but also because of their relatively well-defined structure. They can serve as useful model polymers for molecular studies of the association process, both theoretically and experimentally. 129 Theoretical Approaches From a thermodynamic point of view, these telechelic associating thickeners are similar to nonionic surfactants because of their amphiphilic characteristics. However they differ from small molecule surfactants in that 1 ) two hydrophobic units are anchored to the polymer chain, one at each end; 2 ) the hydrophilic chains are much longer than any conventional nonionic surfactant headgroup. As a result of these differences, the influence of long chain dynamics and the relative location of the two end groups in aggregates have to be taken into account. Therefore, the formation and structure of the aggregates of these telechelic polymers may be far more complicated than simple surfactant micelles. On the other hand, it is generally believed that the association process of telechelic water soluble polymers is analogous to the micellization of triblock copolymers with insoluble end blocks, except for the fact that the driving force is an intermolecular hydrophobic interaction. The hydrophobic units tend to associate in aqueous media to minimize their exposure to water. This association process is accompanied by a breakdown of a highly ordered iceberg structure of water molecules around the hydrophobes. [38] Thus, the entropy gain arising from reorientation of water molecules favors the hydrophobic associations, [38] whereas the triblock copolymer micellization is entirely an enthalpy driven process. The different origins of thermodynamics may account for differences in the association structures. 130 In an attem pt to understand the molecular basis of the association mechanism, many theories have been developed to explain or simulate the experimental results of telechelic model polymers in aqueous solution. Early theoretical calculations by Green and Tobolsky[39] applied classical rubber elasticity theories to transient networks formed by either entanglements or breakable physical bonds. The theory predicted a constant steady-shear viscosity where x is the relaxation time representing the reciprocal rate of bond breaking and reformation, and where G oo is the high frequency storage modulus, v is the number of elastic chains, k is the Boltzman constant, and T is the absolute temperature. The Green and Tobolsky model, however, predicted neither shear thickening nor shear thinning which are typical features of HEUR-AT solutions at intermediate and high shear rates, respectively. In order to account for the non-Newtonian fluid behaviors, the disengagement rate of stickers within the network has to be allowed to depend upon shear rate. Generalized transient network theories were established by Jenkins[29] and Tanaka and Edwards[40] in the hope of correcting failures of the above model. The Tanaka and Edwards model considered an unentangled network made of telechelic polymer chains of uniform length, each t|(Y) = T|(0) = tGm (VI-1) G^ = vkT (VI-2) 131 connected to the association junctions through "sticky" end functional groups (Figure VI-3). There are two kinds of chains in the network: 1) elastically active (or effective) chains with both ends connected to separate junctions; 2 ) dangling chains with only one end attached to any junction while the other end dangles freely in solution. Hence two distinct time scales were proposed to characterize different molecular motions. The single-chain relaxation time Tr is described by the Rouse relaxation time. The other relaxation time X x represented the lifetime of a reversible bond in an association junction. The fundamental assumption of the theory is that Tx » Tr, meaning that a re-formed active chain relaxes into a stress-free configuration before it joins into or breaks from junctions at either end. Consequently, the slow dynamic properties of the system, such as zero shear viscosity is controlled predominantly by Tx instead of Tr. Tanaka and Edwards defined a bonding potential for the hydrophobe in a micelle that is characterized by an activation energy Em for disengagement. The disengagement rate po can then be expressed as Po=w 0e-Em/kT (VI-3 ) where co o is a characteristic frequency of thermal vibration, estimated by Tanaka and Edwards to be on the order of 108 to 109 s'1. The relaxation time Tx is the reciprocal of the disengagement rate Po as given below T x = 0)o1eEm/kT (VI-4) The number of elastically active chains is given as 132 DEFORMATION Figure VI-3. Tanaka-Edwards model: internal rearrangement of the transient network due to thermal movements. 133 (VI-5) where M is the molecular weight, n is the number of chains and co(M) is a weak function of molecular weight which is unity for large M. When Em » kT, the quantity in parenthesis approaches 1 and thus all the chains are elastically effective in this limit. Combining equations VI-1 and VI-2, the zero shear viscosity can be represented by Even though equation VI- 6 takes the Green and Tobolsky form, the relaxation time is controlled by the lifetime of the reversible bond, Tx, which changes exponentially with temperature in the case of an unentangled network (equation VI-4). Hence, the Tanaka and Edwards model predicts that solution viscosity decreases with the increase of the bond breakage frequency Po (or decrease of duration time Tx) and exponentially as temperature increases. The modified transient network theory of Tanaka and Edwards successfully predicted several experimental observations. It does not however explain the strong effect of concentration on the rheology at low concentrations. This is probably because the model oversimplifies available chain topologies by assuming there are only two kinds of chains in solution and that all chains are active for large Em. Based on the Tanaka and Edwards model, Annable et a/. [36] developed an T io = vkTxx (VI-6 ) 134 approximate theory to account for the changing topology of the network with concentration. Five possible single chain states (Figure VI-4a) were recognized in the statistical-mechanical model, which described the concentration dependence of the number of elastically effective chains. To explain the experimentally observed strong concentration dependence, Annable model suggests an entropically driven transformation process. It predicts that over the full concentration regime, there is a gradual transition from a network composed predominantly of loops at low concentrations to one mainly comprised of links at high concentrations. The numerical results of the Annable model [36] is presented below. The fraction of telechelic chains in a given state (Figure VI-4a) is defined as Fi, F2, F3, F4 and F5 , respectively. The fraction is a function of the number of micelles and the bonding energy of each state. Due to statistical reasons, the fractions F3, F4 and F5 are negligible compared to the fraction of bridging Fi and looped chains F2 . To estimate the num ber of micelles, Annable assumed that the number of chains surrounding a central chain is given by Z = (VI-7) 0.64 where < |> is the volume fraction of swollen chains: $ = nltr3 / 6 = i 2 ^ A 2 i (V,-8 ) 6 M where ro is the mean diameter of a chain. Then the fraction of bridging chains is 135 0 -— - 0 0 - — — ■ o c s 4a superbridge superloop dangling end 4b Figure VI-4. Annable model: (a) schematic illustration of possible states of chain association; (b) superstructures with a crosslink functionality greater than 2 . 136 F = 3Z + 2 -. (3Z + 2) - 4Z[2(Z +1) - N agg] 2Z The mean micelle crosslink functionality is FlNagg (VI-9) w = 2 _ Fj (VI-10) w here N agg is the aggregation number. By assuming that the functionality is binomially distributed, the distribution function will be PW = J . 'F i Tmax- % m ax. \ ,W IIiax-Y>! which eventually leads to the modulus G „ 1 - 'Fi (VI-11) max j nkT N (VI-12) « a g g tl-P(O)] These results predict a modulus which rises rapidly with concentration at low concentrations, but becomes linear at high concentrations. More recently, a "rosette" or flower micellar model as shown in Figure VI-5 was proposed by two groups independently. [41,42] A key feature of this model is that over a range of concentrations (above cmc of the telechelic polymer), the system is comprised of largely individual micelles formed by all looped chains. At higher concentrations a loop- to-bridging transition takes place and micelles are bridged up to form larger flower-like aggregates. It was assumed that the core size and association number in each micelle remain constant during and after the transition. Thus, the increase of concentration will enhance the macroscopic viscosity by increasing the number of bridges without Figure VI-5. Rosette (flower) micelles under (a) low shear (b) intermediate shear and (c) high shear rates. 138 perturbing the structure of individual micelles. Structures depicted in Figure VI-5 can be employed to qualitatively explain the shear thickening and shear thinning effects. The flower structure in 5a is stretched under intermediate shear stress to become structure 5b. Larger hydrodynamic volumes of the stretched structures 5b give rise to a viscosity increase at intermediate shear rate, while shear thinning occurs when the structure fractures and the micelles rearrange (5c). According to the authors[41, 42], the rosette or flower model was based on those for block copolymer micelles. As mentioned before, the thermodynamic driving forces are different for hydrophobic association and block copolymer micellization. The theories established for block copolymer micelles may not be applicable to the aggregation of associating polymers in water. It can be noted however that even in the case of triblock copolymers in a selective solvent for internal blocks, it is rare that compact spherical micelles are formed. The majority of experimental results[43, 44] and computer simulations [45, 46] support a loose network-like or branched structure at the strong segregation limit. Hence, similar loose structures are expected for the associating polymer aggregates if we visualize the telechelic polymers as a triblock copolymer with the end groups being short insoluble blocks. Experimental Work The experimental results obtained from viscosity, light scattering and fluorescence techniques all suggest that telechelic, hydrocarbon- 139 ended PEO forms "micelle-like clusters"(MLC) in aqueous solution. Extensive viscosity studies of these associative thickeners by Jenkins [29] show that the solution viscosity increases with increasing hydrocarbon length and decreasing molecular weight of PEO. The viscoelastic behavior of HEUR polymers is consistent with a Maxwell model consisting of a single elastic component connected in series with a single viscous element. [36] The systems can thus be characterized by a single stress relaxation time. [36] The spectroscopic studies using fluorescence probes or labeled polymers are useful complementary techniques to rheological experiments. [30-32, 35, 38] The use of a water insoluble fluorescence probe can provide a wealth of information on the presence and nature of hydrophobic sites from analysis of the microenvironment the probe experiences. For instance, by introducing pyrene as the fluorescent probe, it was established that hydrocarbon end groups associate to form hydrophobic domains. [30-32] Winnik and coworkers have also detected the critical micellar concentration (cmc) for hydrocarbon end-capped PEO associative thickeners using their fluorescence techniques. They found that this type of polymer exhibits an extremely low cmc in water. For fixed hydrophobe length, the cmc increases as molecular weight of PEO increases. The mean aggregation number estimated from fluorescence decay time is in the range of 13 to 25 end groups depending on the hydrophobe length and density of hydrophobes. For a particular associative sample HEUR-AT22-2, (-C16H 33 end-capped 35,000 molecular 4MICV 140 weight PEO), Winnik et al. found that the cmc is 0.1 mg mL_1 and 20 end groups associate to form a hydrophobic micelle-like cluster. [30] However, reliable information is difficult to obtain from the fluorescence quenching experiment because the lifetime of pyrene is influenced by impurities and by oxygen quenching. [47] In addition, the major assumption used to calculate the number of end groups in a micelle is that for maximum excimer formation (i.e. maximum Ie/ I m ratio) the concentration of pyrene molecules is exactly twice the micelle concentration. [30] This assumption relies on unperturbed efficiency of excimer formation. They also assumed that both end groups stay in the same hydrophobic domain (micellar core) with hydrophilic chains forming loops so the mean aggregation number is one half of the number of end groups in association junctions. This leads to the speculation[41] that these "rosette" micelles were composed of 10 polymer chains, all cyclized to form a micellar core containing 2 0 end groups ( N r ) and that at higher concentrations a loop-to-bridging transition occurs without perturbing the magnitude of the aggregation number or micellar core size. By comparing the excimer emission intensity Ie of dipyme in telechelic polymers to that of dipyme in SDS micelles, Winnik et al. [41] estimated the size of hydrophobic core of associating polymers to be 2 nm. However, given the above-mentioned assumptions and the differences in the micellar structures of the associating polymers compared to SDS, one has to be careful not to overinterpret these values. 141 For the same associative thickener, other authors estimate a m uch smaller aggregation number; 6 end groups instead of 20. [35-37] A small aggregation number value was also inferred from fitting viscoelastic response data by Annable and coworkers. [36] The association functionality of four end groups was also deduced from the combination of light scattering and viscosity measurements on similar telechelic polymers. However, the aggregates were concluded to resemble a statistically branched polymer structure. [33, 34] Despite the increasing research interest in these associative thickeners, to this point, no definitive description has been provided for the size and form of aggregates or how the polymer chains orient into aggregates. More experimental work to reveal the answers to these questions is needed. 142 IV . R eferences 1. Polymers in Aqueous Media: Performance through Association; E.J. Glass, Ed.; Advances in Chemistry 223; American Chemical Society: Washington, D.C., (1989). 2. G. Broze, R. Jerome, P. Teyssie, and G. Marco, Macromolecules 16,996 (1983). 3. P. Agarwal, R. T. Garner, and R.D. Lundberg, Macromolecules 17, 2794 (1984). 4. K.G. Shaw and D.P.J. Leipold, ]. Coat Technol. 57, 63 (1985). 5. P.R. Norwar, E.L. 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Glass, Ed.; Advances in Chemistry 223; American Chemical Society: Washington, D.C., pp 399 (1989). 26. S.A. Ezzell and C.L. McCormick, Macromolecules 25, 1881 (1992). 27. S.A. Ezzell, C.E. Hoyle, D. Creed, and C.L. McCormick, Macromolecules 25, 1887 (1992). 28. M. Yassini and T.E. Hogen-Esch, Polym. Prep. 33, 933 (1992). 29. R.D. Jenkins, Ph.D. Thesis, Lehigh University, Bethlehem, PA. (1990). 30. Y. Wang and M.A. Winnik, Langmuir 6 , 1437 (1990). 31. A. Yelta, J. Duhamel, P. Brochard, H. Adiwidjaja, and M.A. W innik, Macromolecules 26, 1829 (1992). 32. A. Yelta, J. Duhamel, H. Adiwidjaja, P. Brochard, and M.A. W innik, Langmuir 9, 881 (1993). 145 33. C. Maechling-Strasser, J. Francois, F. Clouet, and C. Tripette, Polymer 33(3), 627 (1992). 34. C. Maechling-Strasser, J. Francois, and F. Clouet, Polymer 33(5), 1021 (1992). 35. B. Richey, A. B. Kirk, E.K. Eisenhart, S. Fitzwater, and J.W. Hook, J. Coatings Technol. 63(798) 31 (1991). 36. T. Annable, R. Buscall, R. Ettelaie, and D. 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Introduction In this chapter a full characterization of fluorocarbon telechelic poly(ethylene oxide) (PEO) is presented. Viscosity and light scattering techniques have been employed to investigate the association process. The solution studies of these perfluoroalkyl terminated model polymers are motivated by 1 ) urethane coupled hydrocarbon telechelic polyethylene oxide and its application in latex paints have been investigated by many groups using various techniques; 2 ) previous viscosity and light scattering experiments have demonstrated that fluorocarbon hydrophobes offer greater solution viscosity to water soluble associative polymers than hydrocarbon homologs. The viscosity measurements are performed on the telechelic samples of varying molecular weights and fluorocarbon length as well as changing temperatures. Viscosity and light scattering experiments provide information on the size and structure of aggregates. The focus of the studies is to gain some insights into the fluorocarbon association mechanism, such as critical micelle concentration (cmc), average association number N, and the structure of aggregates formed in aqueous solutions. The results of fluorocarbon telechelic polymers are compared to those of hydrocarbon telechelic PEOs, as well as to theoretical models. 148 II. Experimental Section M aterials Telechelic associative polymers w ere prepared at Applied Biosystem Inc. by Dr. Steve Menchan, w ho generously provided us with the samples. These telechelic polymers are composed of polyethylene oxide as the hydrophilic chain and perfluoroalkyl end groups with urethane as the linkage. The general structure of these fluorocarbon telechelic polymers is schematically depicted in Figure VII-1 . Mono dispersed, dual hydroxyl-ended polyethylene glycol precursors were purchased from Fluka. The hydrophobic modification of PEO was achieved by sequential reactions of isophorone diisocyanate with perfluoroalcohols and polyethylene glycol (Figure VII-2). A large excess of isophorone diisocyanate w as first reacted with perfluoroalcohols so that the reaction only took place on the primary isocyanate and the secondary isocyanate was left intact for the end capping step. After the excess isophorone diisocyanate was removed, a ten fold excess of the above obtained isocyanate was then used to treat polyethylene glycol to yield fluorocarbon telechelic polymers. The modified polymers were precipitated in hexane, filtered and dried in vacuo to remove the solvent or precipitant. 19F NMR showed 100% conversion of end groups, i.e. the fluorocarbon telechelic PEO indeed has the hydrophobe at each end. Since the synthesis was truly an end group functionalization rather than a condensation reaction, the polydispersity 149 = Rp = C4 F9 , C6 F13, C7F15j CqF A = “ ^-CH2CH2o 17 Figure VII-1. Fluorocarbon telechelic polyethylene oxides. ■ 1 is the perfluoroalkyl sticker group, O is the urethane linkage and polyethylene oxide is the hydrophilic backbone. RF OH ---------------------------------► || large excess O Rf = C4F9j C6F13, C7F15, c 8f 17 H0(CH2CH20)nH n = 100, 180 340, 800 Fluorocarbon telechelic polyethylene oxides Figure VII-2. Preparation of fluorocarbon telechelic PEO's 10 eq. 151 indices of these fluorocarbon end-capped PEO's is much narrower than commercial hydrocarbon telechelic PEO's (typically PI > 1.7) prepared by condensation reactions. The fluorocarbon telechelic samples were freeze-dried from a mixed solvent of 9:1 benzene/m ethanol (v/v). To characterize the telechelic samples, a solvent in which the polymers do not undergo aggregation is desired. Methanol is chosen for this purpose since methanol is known to be a good dispersing solvent for PEO.[l, 2] For light scattering experiments, methanol solutions of polymers were prepared by dissolution of sample powders in spectro-grade methanol (Fisher Scientific) which was pre-filtered through Gelman 0.2 pm PTFE filters. The stock solutions of telechelic polymers in water were made by dissolving freeze-dried powder into deionized water. To exclude the possibility of PEO itself aggregating in water,[3] ultrapure water (resistivity > 18 MQ) pretreated by a Barnstead instrument (NANOpure 550) was filtered through 0.2 pm PVDF filters and used for the preparation of aqueous solutions. All stock solutions were gently stirred for 24 hours before use. Fresh solutions were used for light scattering experiments since PEO can degrade via a radical auto-oxidation mechanism. [4, 5] To avoid batch-to-batch variation, all the solutions used for concentration dependent experiments were m ade from one stock solution and experiments were carried out within three days. Dilute solutions for viscosity measurements were prepared similarly without filtration. For the viscosity of more concentrated 152 solutions, the telechelic samples were dissolved in a special solvent m ade of 6.67 M urea and 0.1 M boric acid in deionized water. The pH of the solutions was adjusted to 8.0 with 0.1 M NaOH solution and monitored by an Orion SA520 pH meter. Sample powders were dissolved in the above-made solvent at various weight concentrations. Hydroquinone inhibitor (5-20 ppm) was added to these polymer solutions to prevent radical degradation of poly(ethylene oxide).[4] The solutions then were vigorously agitated for at least 1 2 hours to ensure homogeneity prior to the measurements. Light Scattering Static and dynamic light scattering experiments were performed on a particular telechelic sample, -CsFi7 end-capped 35,000 PEO. The light scattering instrum ent consists of a Brookhaven goniometer (BI- 200SM) with an Ar ion laser (Spectra Physics 2020-3) operating at 514.5 nm. Photon autocorrelation functions were acquired at scattering angles ranging from 30 to 135° with a multi-tau correlator (ALV instrument 5000). Measurement temperatures were controlled at 25.00 ± 0.05 °C. Static light scattering data was analyzed by the Zimm method. The literature d n /d c values of 0.132 and 0.150 were used in calculations for methanol and water, respectively. [6 ] This should be a valid approximation since the content of fluorocarbon groups is so low ( 2 wt% for 35,000 PEO) that it should not cause a serious variation in the refractive index increment dn/dc. Dynamic light scattering auto 153 correlation functions were analyzed by Provencher's CONTIN. Hydrodynamic sizes of particles were calculated from relaxation times according to the Stokes-Einstein equation (11-29). Viscosity Since the magnetic sphere viscometer was designed to measure visocisty at extremely low shear rates, no shear dependence was found within the experimental shear range of 10’3 to 0.4 s '1. The solution viscosity thus m easured by the magnetic sphere viscometer can be taken as zero shear viscosities even for semi-concentrated solutions of fluorocarbon telechelic polymers. The viscous solutions of fluorocarbon associating polymers in the sample tube were sitting in the toluene bath for one day to clear air bubbles created during solution transfer and then equilibrate at the measurement temperature. The experimental temperatures were controlled to ± 0.01 °C. Capillary viscometers were used to obtain dilute solution viscosities. The flow times of polymer solutions and solvents were recorded using standard Ubbelohde four-bulb capillary dilution viscometers. The measurements were carried out in both methanol and water at 25.00 ± 0.01 °C. Zero shear rate viscosities at each concentration were determined by extrapolating the viscosity vs. shear rate plot. The intrinsic viscosity [t|] was obtained by extrapolating the reduced viscosity T )s —— to infinite dilution, c 154 III. Results and Discussions Viscosity The striking viscosifying effect of hydrophobically modified polyfethylene oxide) is observed in Figure VII-3. It shows strong concentration dependence for the viscosity of fluorocarbon and hydrocarbon telechelic PEOs in water at 25.0 °C. The solution viscosity of both fluorocarbon and hydrocarbon associating polymers increases rapidly with concentration in the fashion of a power law. The same result was also found on hydrocarbon HEUR-associating thickener (AT) systems. [4, 7-9] At the same polymer concentration and identical molecular weight (35,000), the solution viscosity of -C8F17 end-capped PEO is one order of magnitude higher than that of -C16F33 end-capped PEO, even though the fluorocarbon hydrophobe length(C8 ) is only half the hydrocarbon length (C16). In fact, it was found in hydrocarbon HEUR-AT systems, that the hydrocarbon length has to be longer than C8 in order to achieve useful viscosity enhancement of aqueous solutions.[4] This again demonstrates that fluorocarbons possess more effective hydrophobic character and are therefore more effective than hydrocarbons as viscosity or rheology modifiers as found by Hogen-Esch and coworkers. [1 0 , 1 1 ] Figure VII-4 shows the effect of hydrophobe length on the viscosity for aqueous solutions of -C7F15 and -C8F17 end-capped 8000 PEO. The viscosity increases dramatically with concentration which is a (cjo) ‘U 6o| 155 5 4 3 2 1 0.2 0.4 0.6 0.8 1.0 log C, (wt%) Figure VII-3. Viscosity vs. concentration for telechelic PEOs of Mw = 35,000 with -CsFl7 ( • ) and -C16H 33 (■) end groups. l o g t|, (cP) 156 6 5 4 3 2 1 0.0 0.2 0.4 0.6 0.8 1.0 log C, (wt%) Figure VII-4. Viscosity vs. concentration for fluorocarbon telechelic PEOs of Mw = 8000 with -C7F15 ( • ) and -CsFi7 (■) end groups. 157 typical behavior of hydrophobically modified water soluble polymers. Throughout the concentration range, the viscosity of -CsFi7 end capped PEO is much higher than that of -C7F15 end capped PEO of the same molecular weight. The increase of viscosity with increasing hydrophobe length has also been found for a series of hydrocarbon telechelic PEO samples by Jenkins. [4] This is a direct manifestation of hydrophobicity because longer hydrophobes offer greater association strength. The strong concentration dependence observed in Figure VII-3 and VIM can be explained by the transition of looping to bridging as predicted in the Annable model. As the polymer concentration increases, the fraction of intramolecular looping decreases and intermolecular association increases, resulting in a large increase in viscosity. Solution viscosity should eventually reach infinity when associating polymers form a physical gel at high concentrations. Unlike fluorocarbon modified high molecular weight polyacrylamide copolymers, the viscosity of fluorocarbon telechelic polymers obeys the Arrhenius relationship with respect to temperature. This result clearly indicates that a single process underlies the relaxation kinetics in solutions of fluorocarbon telechelic PEOs. The linearity of In viscosity vs. inverse temperature is displayed in Figure VII-5 and VII- 6 . The activation energy Ea for viscous flow can be derived from the slopes of the straight lines using lnri = lnA + ^ r: (VII-1) (d o ) ‘ ll U| 158 14 12 10 8 6 3.1 3.2 3.3 3.4 3.5 3.6x10 1/T, K'1 Figure VII-5. Viscosity vs. temperature for solutions of 8000 PEO end-capped with -C6F13 (•), -C7F15 (♦) and -CgF^ (A). I n ti, (cP) 159 13 12 11 10 9 L 3.1 3.2 3.3 3.4 3.5x10 1/T, K'1 Figure VII-6 . Viscosity vs. temperature for solutions of -CsFi7 end- capped PEO with Mw = 4600 (A), 8000 (♦), 15,000 (•). 160 Figure VII-5 shows the temperature dependence of viscosity for 8000 PEO end-capped with -C6Fi3, -C7F15 and -C8F17 perfluoroalkyl groups. For the same molecular weight polymer and same solution temperature, the viscosities of telechelic polymers increase progressively w ith increasing length of fluorocarbon groups. This is again consistent w ith the results seen in Figure VII-4 and the observations in hydrocarbon telechelic PEO's. Thus, it is clear that longer hydrophobes are expected to give greater viscosity in solutions of these water soluble associating polymers. The activation energy calculated from the slopes are 13.6,15.6 and 17.3 kcal mol*1 for -C6F13, -C7F15 and -CsFi7, respectively. The activation energy reflects the association strength according to the Tanaka-Edwards and Annable theories.[7,12] Evidently, the longer hydrophobe, characterized by a larger activation energy, leads to a stronger association and thus a higher viscosity. Brown [13] and Tanaka and Edwards [12] have proposed that the m agnitude of the viscosity is a function of the chain conformation and the hydrophobe length. But the chain conformation depends more on polymer concentration than hydrophobe length. Therefore the contributions of chain conformation and the association strength to the viscosity can be separated into the form rj = f(c)*g(n), where f(c) represents chain conformation and g(n) the association strength. Assuming that the chain conformation is independent of hydrophobe length, the huge difference in viscosity for telechelic polymers of varying hydrophobe length is attributed to the association strength. This 161 also explains the similarity of viscosity vs. concentration plots of -C7F15 and -C8F1 7 end capped PEOs (Figure VII-4). The two viscosity curves in Figure VII-4 can be vertically shifted to reproduce one another as the Brown model predicts. The increase of activation energy with increasing fluorocarbon length quantitatively proved that stronger association due to longer hydrophobe gives rise to a larger viscosity enhancement (Figure VII-4 and VII-5). Figure VII- 6 shows the temperature effect on viscosity profiles for -C8F17 end-capped PEOs of varying molecular weights. For the same perfluorooctyl end group, the solution viscosity at the same temperature decreases as polymer molecular weight increases from 4600 to 8000 and then to 15,000. In unassociating systems, solution viscosity normally increases with increasing polymer length. Apparently, for these fluorocarbon telechelic samples, the lower hydrophobe density, which results from increasing the polymer chain length, at fixed mass concentration, results in a lower viscosity. To a certain degree, this finding supports the Tanaka-Edwards model that the zero shear viscosity is controlled by slow relaxation rather than single-chain dynamics. This result can also be understood in terms of the fraction of looping in the Annable model. Shorter chains are expected to form fewer loops due to the greater entropy penalty. The associating end groups thus exist predominantly in the form of bridges in the network and the bridge topology contributes more to the increase of solution viscosity. 162 Another interesting feature of Figure VII-6 is that the three viscosity lines are perfectly parallel to each other and each slope gives approximately the same activation energy of 17 kcal mol-1. The invariant activation energy with polymer chain length directly supports the assumption of the Brown model, i.e., the independence of chain conformation on hydrophobe length. This is also consistent with the Tanaka-Edwards and the Annable models which introduce the activation energy to reflect the association strength regardless of molecular structure and polymer chain length. The value of 17 kcal m ol'1 is equivalent to 29 kT at 25 °C and is also comparable to 16 kcal m ol'1 for (Ci6H 3 3)2PEO obtained from rheological measurements by Annable et al.[7] This result again quantifies stronger association by fluorocarbons than corresponding hydrocarbon units. Dilute solution viscosity measurements were performed on (CsFi 7> 2PEO of 35,000 molecular weight in methanol and water at 25.0 °C. The reduced viscosity vs. polymer concentration is plotted in Figure VII-7 with the top axis representing the concentration of aqueous solution and the bottom axis representing the concentration of polymer in methanol. In methanol the reduced viscosity vs. concentration follows the linear relationship of the Huggins equation tired = N O + kH[tl]c) (VII-2) where [rj] is the intrinsic viscosity and kn is the Huggins constant. The Huggins equation describes the concentration dependence of viscosity 163 co n e, mg mL’1 0 1 2 3 4 5 6 O) E E 0.5 t p r 0.0 0 5 10 15 20 co n e, mg mL"1 Figure VII-7. Viscosity vs. concentration for dilute solutions of (C8Fi7> 2PEO with Mw = 35,000 in methanol (O) and water (•). 164 for unassociated polymers in dilute solution. The linear relationship for the methanol solution indicates that methanol is indeed a good solvent for the telechelic polymers and no polymer association is observed in methanol. The intrinsic viscosity, extracted from the intercept of this plot for the polymer in methanol, is 0.047 mL m g'1. For the aqueous solution of the polymer, the reduced viscosity displays a weak concentration dependence at concentrations below 2 mg mL-1, but increases rapidly with a further increase in concentration. The same behavior has been observed for hydrocarbon telechelic PEO in water.[4,8 ] The deviation of reduced viscosity vs. concentration from the linear relationship of Huggins equation, along with the higher intrinsic viscosity for the polymer in water, is attributed to the associations in aqueous media. The value of the intrinsic viscosity, 0.11 mL m g'1, turns out to be equal to that of -C16H 33 end-capped 35,000 PEO. [ 8 ] This result is consistent with the comparable activation energy between these two telechelic polymers, both suggesting the stronger hydrophobic association of fluorocarbons than hydrocarbons of equal length. Light Scattering A Zimm plot for the telechelic associative polymer in methanol is shown in Figure VII-8 . Static light scattering in the concentration range of 1.43 to 20.6 mg mL' 1 yields a weight-averaged molecular weight of 3.51 x 104. This value agrees well with the nominal molecular weight of polyethylene glycol precursor purchased from Fluka. The radius of Kc/Re , 10‘6mol g'1 165 120 1 0 0 80 60 4 0 20 01 I I ................................................ 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 sin2(6/2) + 20c Figure VII-8 . Zimm plot of (CsF^^PEO with Mw = 35,000 in m ethanol. 166 gyration Rg and second virial coefficient A2 calculated from the Zimm plot are 15.1 nm and 1.84 x 10*3 cm3 mol g '2, respectively. The large positive A 2 value confirms that methanol is a good solvent for this telechelic associative polymer and thus no association is expected in m ethanol. Static light scattering data in the concentration range of 0.46 to 2.00 m g mL"1 for the same (CsF^^PEO polymer in water is shown in Figure VII-9. The molecular weight and radius of gyration extracted from the Zimm plot in Figure VII-9 are 7.98 x 105 g mol"1 and 40.5 nm, respectively. These much larger values of the apparent molecular weight and radius of gyration evidence the formation of large aggregates in the aqueous solution. The negative second virial coefficient, -1.71 x 10"4 cm3 mol g"2 confirms that strong polymer-polymer associations occur in water. Taking 3.51 x 104 as the molecular weight of unassociated polymer, the mean aggregation number is estimated to be 23 by dividing the apparent aggregate molecular weight by the single chain molecular weight. This result suggests that each cluster is composed of 23 polymer chains. For (Ci6H 33> 2PEO of the same molecular weight, the mean aggregation number has been given as 10 or less[7,8,14]. In other words, static light scattering results directly prove, at a molecular level, that the -C8F17 end group achieves stronger hydrophobicity in water than -C16H 33 does. The stronger hydrophobe results in the formation of larger aggregates and builds up a higher macroscopic viscosity. Kc/Re , 1 0 mol g‘ 167 2.0 1.4 0.8 0.6 0.4 0.2 0.6 0.8 0.0 0.4 1.0 sin2(0/2) + 20c Figure VII-8. Zimm plot of (CsFi7)2PEO with Mw = 35,000 in water. 168 Dynamic light scattering of the 35,000 (CsFi7)2PEO sample has also been performed at a wide selection of scattering angles. Figure VII-10 shows some g ^ ) autocorrelation functions taken at 40° scattering angle for the telechelic polymer in methanol (top) and water (bottom). Since methanol is a good solvent for the polymer, a single relaxation is observed, as expected, for correlation functions in the concentration range of 1.43 to 20.6 mg mL-1. The single relaxation is attributed to the unassociated polymer chain diffusing in methanol. Dynamic light scattering in water also shows a single relaxation throughout the concentration range from 0.1 to 2.00 mg mL'1. However, the decay occurs at longer times corresponding to the larger-sized aggregates formed in water. The relaxation spectra of the CONTEM fits shown in Figure VII-11 provide a more obvious comparison when methanol (top) and water (bottom) are used as solvents. Sharp relaxation peaks observed in methanol indicates the narrow molecular distribution of the telechelic sample. Considerably broader and slower relaxation peaks are obtained when the polymer forms the large aggregates in water. The peak positions remain nearly constant for various concentrations of methanol solutions while a slight increase in the decay time is seen with increasing polymer concentration in water. The single relaxation of aggregates in water persists upon dilution, even when the polymer concentration is as low as 0.1 mg m L'1. This implies that the critical micelle concentration of (C sF ^ P E O telechelic in water is well below 0.1 mg mL'1. Such a low cmc is the result of strong 169 0'6I 0 .5 - ^ 0.4 - & 0.3 - 0.1 0.0 0.8 3 0.6 ~ 0.4 b ) 0.2 0.0 3 2 4 1 2 0 3 logt, (ms) Figure VII-10. g(^ correlation functions of (CsFi7)2PEO with Mw = 35,000 in methanol (top) and water (bottom) at 40° scattering angle. 170 0.20 0.15 0.10 TJ 3 0.05 C O 0.00 ( N tN tN tm m tM N h 0.10 0.05 Q . E co 0.00 t t f t t e& um / m m i w w w i t mmt mt M EBB. 3 4 2 2 -1 0 1 3 logt, (ms) Figure VII-11. The CONTIN fits to correlation functions of (CgFi7)2PEO with Mw = 35,000 in methanol (top) and water (bottom) at 40° scattering angle. 171 intermolecular associations of fluorocarbon modified polymers. The absence of the faster single chain relaxation in water suggests that the equilibrium between "unimer" (single polymer chain) and micelle is driven towards the formation of aggregates by the extremely strong intermolecular interaction of fluorocarbon end groups. The single relaxation of correlation functions from dynamic light scattering is consistent with the single stress relaxation in Annable's rheology measurements on hydrocarbon telechelic polymers. [8 ] The diffusion coefficient at each concentration is computed from the slope of the inverse relaxation time 1 /x vs. the square of the scattering vector q2. The straight lines in Figure VII-12 and VII-13 indicate the diffusive nature of the telechelic polymer in methanol and the aggregates in water solutions. The concentration dependence of the diffusion coefficient D is summarized in Figure VII-14 in which the top axis is the concentration of aqueous solutions and the bottom axis is the concentration of methanol solutions. A linear dependence of diffusion coefficient on polymer concentration exists for the polymer aggregates in water. The values of Do and ko are calculated to be 1.24 x 1 0 '^ cm^ s'* and -0 .2 2 1 , according to the equation below D = D0(l + k DC) (VII-3) where Do is the diffusion coefficient at the zero concentration limit and ko is a measure of a combination of hydrodynamic and thermodynamic effects. A negative ko usually correlates with a negative second virial coefficient. [15] Thus, the negative ko from dynamic light scattering is 172 8 x1 0 ' 6 4 2 0.8 1.0x101 0.2 0.4 0.6 2 -2 q ,cm Figure VII-12. The inverse relaxation time 1 /t v s . the square of scattering vector q2 for the telechelic polymer in methanol at concentrations of 20.6 (•), 17.4 (♦), 14.0 (A), and 6.11 (A) mg mL-1. 173 5000 40 0 0 - 3000 '</) H ^ 2000 1000 ° 0 1 2 3 4 5x10 2 -2 q ,cm Figure VII-13. The inverse relaxation time 1/x vs. the square of scattering vector q2 for the telechelic polymer in water at concentrations of 2.00 (★), 1.68 (O), 1.38 (O), 1.08 (A), 0.46 (♦) and 0.24 (□) mg mL*1. D , x 1 O'8 cm2s' 0.0 0.5 1.0 1.5 2.0 1 0 0 50 0 0 5 10 15 20 cone, mg mL’1 Figure VII-14. Diffusion coefficients of (CsF^hPEO with Mw = 35,000 in methanol (O) and water (•). 175 consistent with the negative A2 determined by static light scattering, both indicating strong polymer aggregation. The hydrodynamic radii Rh calculated from the Stokes-Einstein equation are shown in Figure VII-15. The hydrodynamic sizes of the polymer in methanol are rather small because they correspond to unassociated single polymer chains. This again verifies our assumption of no association in methanol. Even though the polymer concentrations in water are very dilute compared to the methanol solutions, the hydrodynamic size is substantially larger than Rh of the polymer in methanol because of the occurrence of polymer aggregation. Again, the dynamic light scattering data is consistent with the static light scattering results and both identify the formation of large aggregates in water due to the strong fluorocarbon associations. The viscosity and light scattering measurements on fluorocarbon telechelic PEO confirmed how fluorocarbons as hydrophobe lead to a great viscosifying effect in aqueous solutions of water soluble polymers. Physical quantities such as a higher intrinsic viscosity, activation energy for viscous flow, and larger apparent molecular weight, size and a negative second virial coefficient seem to adequately characterize the aggregates in water. However, the detailed structure of the aggregates is to this point still unknown. Fortunately, the ratio of radius of gyration to hydrodynamic radius Rg/Rhois characteristic of a polymer's conformation. It has been , nm 176 co n e , mg mL*1 2.0 0.5 o.o 40 30 20 sz c t 5 10 15 20 0 co n e, mg mL’1 Figure VII-15. Hydrodynamic radii of (CsF^^PEO with Mw = 35,000 in methanol (O) and water (•). 177 shown that this ratio is 0.75 for a hard sphere, 1.5 for an ideal coil and 2.0 for a highly branched structure. [16] Our experimentally determined Rg/Rho value is 2.05 for the polymer aggregates in water. This value suggests that the aggregates formed by telechelic (CsF^^PEO in water most likely assume a highly branched structure instead of a compact spherical micellar structure. However, the Rg/Rho ratio is not very sensitive to the degree of branching. Zimm and Stockmayer[17] have defined a structure parameter g to distinguish branched polymers of different shapes: 2 2 where Rgbo and R |i0 are the squares of the radii of gyration for branched and linear polymers, respectively, of same molecular weight at theta condition. Assuming the expansion factors a b = 0^ for linear and branched topologies, the above equation can be rewritten as By analogy a viscometric structure parameter g' can be defined from the intrinsic viscosities of branched and linear polymers (VII-5) (VII-6) [T ill g' can be related to g by applying the classical Fox-Flory law [18] 178 (VII-7) to equation VII- 6 above (VII-8 ) We can assume that unmodified homopolyethylene oxide takes a linear conformation in aqueous solution. The intrinsic viscosity and radius of gyration of the polymer aggregates are compared to those of unmodified polyethylene oxide of the same chain length. M easurements on unmodified homopolyethylene oxide need not be repeated since there has been a great deal of work done on linear unassociated PEO in water. [19-21] It has been established that for hydroxyl-ended PEO in water, the radius of gyration Rg[19] and intrinsic viscosity [t|][2 0 , 2 1 ] scale with molecular weight as Parameters for linear unassociated PEO calculated from the equations above are complied in the first two columns of Table VII-1 w hile the last column contains the experimental data for perfluoroalkyl end-capped PEO associative polymers. Our first comparison is between the telechelic polymer and homo-PEO of 35,000 which is the molecular weight of the unassociated telechelic polymer. The calculated values of Rgl = 0.0215 M^ 5 8 3 nm (VII-9) [T l] = 0.054 M0 6 6 mL g’ 1 (VII-10) 179 Table VII-1. Homo- and hydrophobically modified PEO in water H om o PEO* in water Modified PEO in water M W 35,000 798,000 798,000 Rg (nm) 9.6 59.3 40.5 [tj] (ml mg-1) 0.0539 0.424 0.112 Rho (nm) 19.8 Rg/Rho 2.05 g=(Rgb/Rgl)2 0.466 g'=([Tl]b/ [T ill)2/ 3 0.412 180 chain dimension and intrinsic viscosity are 9.6 nm and 0.0539 mL mg' 1 for 3.50 x 10^ unassociated linear PEO in water. The formation of larger polymer clusters (Mapp = 79,800 not 35,000) is responsible for the higher values in column 3 than in column 1. The second column contains the calculated results for 7.98 x 105 homo-PEO and the radius of gyration and intrinsic viscosity are 59.3 nm and 0.424 mL mg*1, respectively. There is still a noticeable discrepancy in the values of intrinsic viscosity and radius of gyration when column 2 and 3 are compared for 7.98 x 105 linear PEO and telechelic PEO aggregates, respectively. These differences come from differences in the structures. In other words, the aggregates assume different shapes in water than unmodified PEO of the same molecular weight. It is now necessary to obtain the structure factor g to determine what kind of branched structure the telechelic aggregates would form in aqueous solutions. There has been much theoretical work on the calculation of g for different topologies of branched polymers.[17, 22, 23] The theoretical g values for star, comb-like and statistically branched polymers are listed in Figure VII. For statistical branching, Zimm and Stockmayer[17] computed the g values for different functionalities. The structure parameter g decreases with increasing functionality. For a tetrafunctional branched polymer, g is expressed as (VII-11) where m is the average branching per chain. In the case of two 181 Star A g = 0.064 Star B g = 0.127 Comb-like g = 0.568 K m * Tetrafunctional Branch g = 0.466 Trifunctional Branch g = 0.546 Figure VII-16. Possible branched structures and their g values 182 hydrophobic end groups being involved in two different association junctions, m is then given by m = (N -l)/3 = 7.3, N is the mean aggregation number. Therefore, g calculated from equation VII-11 is equal to 0.466. Taking the calculated values of 59.3 nm and 0.424 mL mg' 1 as the radius of gyration and intrinsic viscosity for linear unassociated 7.98 x 105 PEO in water, the g values from light scattering and viscosity are 0.466 and 0.412, respectively (see Table VII-1), which agree well with the value of 0.466 for tetrafunctional branched polymers as predicted by Zimm and Stockmayer. Of course this is the extreme case of tetrafunctional junctions. In reality, for dilute solutions, there is a significant probability that some of the chains form loops with both end groups binding to the same junction. Given the same association number, 23 for this particular telechelic polymer, the increasing probability of looping would result in a smaller average branching m, thus a larger g and consequently a lower functionality for the junctions. However, the entropy penalty resulted from looping would limit the cyclization effect. [24] Therefore, the shape of aggregates seems to be analogous to a statistically branched polymer w ith tetrafunctional junctions formed by the hydrophobic fluorocarbon end groups. Francois et al. have also concluded the similar tetrafunctional topology for hydrocarbon end-capped PEO in water. [25, 26] This conclusion also seems consistent with results for triblock copolymer aggregates formed in a selective solvent for the middle block. [27, 28] 183 The experimentally determined g values do not support the flower or rosette structures proposed by Winnik[29] and Semenov[30]. Cluster structures formed by micelles of all cyclized chains are much denser than these statistically branched polymers. Denser structures like those would have a smaller Rg, Rg/Rho and thus a lower g. Energetically, the statistically branched structure is probably preferable over compact spherical micelles because the hydrophobic association has a saturating nature. [31] The number of end groups in a junction is limited below a certain maximum value by the additional entropy loss of chain looping and favorable packing density of a spherical micelle. It is difficult for a functional group to joint in a large junction around which the chains are already densely packed. Also, given the strength of fluorocarbon hydrophobes, a small fraction of loops can be expected. Therefore, the majority of associating end groups may be involved in two separate junctions and thereby provide elastically active chains as predicted by the Tanaka-Edwards theory[12] with a small number of chains in the looping state of the Annable model.[7] However, it remains to determine, by direct experiment the actual aggregate structure formed by these telechelic polymers in water. The association structure surely controls all resulting solution properties. IV. Conclusions Laser light scattering and viscosity measurements on the telechelic fluorocarbon end-capped PEO provided quantitative 184 information on the fluorocarbon association in aqueous solution. The solution behavior of these polymers is very similar to that of hydrocarbon end-capped PEO associative thickeners. In general, the solution viscosity increases with increasing polymer concentration and increasing fluorocarbon length. For a fixed hydrophobe length, the viscosity decreases with increasing molecular weight. The equilibrium between unassociated single chains and aggregates is favored towards the aggregate completion even at very low concentrations, which suggests a very low cmc. For concentrations above the cmc, a single relaxation is seen in dynamic light scattering, corresponding to large sized aggregates. Further increase in concentration results in a sharp increase of solution viscosity. Both light scattering and viscosity results confirmed that the fluorocarbon hydrophobe imparts greater viscosity to water soluble polymers in solution than do corresponding hydrocarbon hydrophobes. Stronger fluorocarbon association is manifested in higher zero shear viscosity, activation energy, intrinsic viscosity and aggregation number. For a particular telechelic (CsF^^PEO, the aggregates consist of an average of 23 polymer chains. The Zimm- Stockmayer structure parameter g calculated from static light scattering and intrinsic viscosity data suggests that aggregates in water probably assumed a branched structure with tetrafunctional junctions. 185 V. References 1. C. Stazielle, Makromol. Chem. 119, 50 (1968). 2. D.K. Carpenter, G. Santiago, and A.H. Hunt, Polym. Sci. Polym. Symp. 44, 75 (1974). 3. K. Devanand and J.C. Selser, Nature 343, 739 (1990). 4. R.D. Jenkins, Ph.D. Thesis, Lehigh University, Bethlehem, PA. (1990). 5. C.W. McGray, J. Polym. Sci. 46, 51 (1960). 6 . M.B. Huglin, Polymer Handbook; 3rd Edition; J. Brandrup and E.H. Immergut, Ed.; John Wiley & Sons, pp453 (1989). 7. T. Annable, R. Buscall, R. Ettelaie, and D. Whittlestone, J. Rheol. 37(4), 695 (1993). 8 . A. Yelta, J. Duhamel, H. Adiwidjaja, P. Brochard, and M.A. Winnik, Langmuir 9, 881 (1993). 9. G. Fonnum, J. Bakke, and F.K. Hansen, Colloid Polym. Sci. 271, 380 (1993). 10. Y.-X. Zhang, A.-H. Da, T.E. Hogen-Esch, and G.B. Butler, /. Polym. Sci., Polym. Lett. Ed. 28, 213 (1990). 11. Y.-X. Zhang, A.-H. Da, T.E. Hogen-Esch, and G.B. Butler, J. Polym. Sci., Part A: Polym. Chem. 30, 1383 (1992). 186 12. F. Tanaka and S.F. Edwards, J. Non-Newtonian Fluid Mech. 43, 247 (1992). 13. G. Brown and A. Chakrabarti, J. Chem. Phys. 96, 3251 (1991). 14. B. Richey, A.B. Kirk, E.K. Eisenhart, S. Fitzwater, and J.W. Hook, J. Coatings Technol. 63(798) 31 (1991). 15. B.U. Felderhof, J. Phys. A: Math. Gen. 11, 929 (1978). 16. W. Burchard, Adv. Polym. Sci. 48, 1 (1983). 17. B.H. Zimm and W.H. Stockmayer, J. Chem. Phys. 17, 130 (1949). 18. P.J. Flory and T.G. Fox, Jr. /. Am. Chem. Soc. 73, 1904 (1951). 19. K. Devanand and J.C. Selser, Macromolecules 24, 5943 (1991). 20. D.K. Thomas and A. Charlesby, }. Poly. Sci. 4 2 ,195-202 (1960). 21. H.G. Elias and H. Lys, Die Makromolekulare Chemie 92, 1 (1966). 22. W.H. Stockmayer and M. Fixman, Ann. N.Y. Acad. Sci. 57, 334 (1953). 23. T.A. Orofino, Polymer 2, 305 (1961). 24. G.T. Brinke and G. Hadziioannou, Macromolecules 20, 486 (1987). 25. C. Maechling-Strasser, J. Francois, F. Clouet, and C. Tripette, Polymer 33(3), 627 (1992). 26. C. Maechling-Strasser, J. Francois, and F. Clouet, Polymer 33(5), 1021 (1992). 187 27. T. Kotaka, T. Tanaka, and H. Inegaki, Macromolecules 11,138 (1978). 28. E. Raspaud, D. Lariez, and M. Adam, Macromolecules 27, 2956 (1994). 29. A. Yekta, B. Xu, J. Duhamel, H. Adiwidjaja, and M.A. Winnik, Macromolecules 28 956 (1995). 30. A.N. Semenov, J.-F. Joanny, and A.R. Khokhlov, Macromolecules 28 1066 (1995). 31. F. Tanaka and W.H. Stockmayer, Macromolecules 27, 3943 (1994). 188 Chapter 8. Hydrogen-Bonding Association in Nonpolar Solvent I. Introduction The aggregation via hydrogen-bonding interaction between a pair of hydrogen donor and acceptor copolymers in a nonpolar solvent, toluene, has been studied by light scattering techniques. The individual random copolymers, poly(styrene-4-vinyl pyridine) as acceptor and poly(t-butyl styrene-4-hydroxyl styrene) as donor are fully characterized in toluene. Unlike other associating systems, the individual donor or acceptor copolymers themselves do not exhibit intra- or intermolecular association in the investigated concentration range. The dramatic enhancement in the relaxation time and scattering intensity upon mixing demonstrates the formation of hydrogen bonding complexes. The H-bonding complexation in this chapter has been investigated as a function of the relative ratio of donor to acceptor copolymers, the comonomer content of acceptor copolymer, and total polymer concentrations. The H-bonding complexing ability of copolymers is greatly reduced when polar solvent THF is used as the solvent. II. Review It is well-known that hydrogen bonding plays a fundamental role in the structure of DNA and the secondary and tertiary structures of 189 proteins, as well as in the gelation of gelatin. To elucidate the complicated mechanism of these biological functions it is very useful to investigate synthetic polymers with simple structures as model systems. Practically, the formation of the aggregates through hydrogen bonding interactions have been found useful in enhancing the bulk miscibility of polymer blends. [1 , 2 ] Aggregation caused by non-covalent, physical interactions in a solution has attracted a great deal of interest because of the wide uses in the modification of solution properties. [3] In dilute solutions, molecular aggregation among the polymer chains can provide large "super molecules" and thus higher viscoelasticity[4, 5] or sometimes the phase separation in such polymer solutions. [ 6 ] The complexes formed through H-bonding interactions may have a compact or a gel-like structure. [7] A compact structure results in the precipitation of the polym er mixture from the solution, which tremendously reduces the viscosity. Whereas in the case of a gel-like structure, a dramatic increase in viscosity is observed even in dilute solution. [8 ] The structure of polymeric aggregates can be regulated by the composition, relative distribution, and most importantly, the nature of the specific interactions (i.e., ionic, hydrophobic and hydrogen bonding etc.) of the associating groups along the polymer backbone. For example, a ladder structure with linear sequences of cooperative functional groups (homopolymers) was found in complexes containing hydrogen bonds and oppositely highly charged polyelectrolytes.[9-ll] 190 Interpolymer aggregation has also been observed in the case of random copolymers that contain inert comonomers along the polymer chains. The statistical incorporation of inert comonomer units into polymer chains m ay not change the ability of active groups to form aggregates but will influence the composition, structure, and properties of the resulting complexes.[12] Therefore, aggregation can be induced not only by sufficiently long continuous sequences of the active groups but also by simultaneous interaction of a number of functional groups fixed at some distance one from the other in the chain. [1 2 ] The critical phenomena oftentimes exist in the complexation of binary homopolymer solutions, [4] such as the critical chain length, critical pH, etc. In the case of interpolymer complexes formed by random copolymers, a "gel type" complex is induced in solution by an array of hydrogen bonds formed among polymers bearing complementary proton acceptor and proton donor groups. [12] The degree of conversion in the complex formation is a linear function of the mole fraction of bonding comonomer units and, therefore, a critical comonomer content of copolymers is expected for two random copolymer systems. [1 2 ] The concentration effect on complex composition is rather complicated for interpolymer complexes. It has been found that the composition of hydrogen bonded complexes is 2 to 2 /3 of donor to acceptor molar ratio in dilute solution and 2/3 in concentrated solutions. [4] However, viscosity measurements have shown the 191 concentration independence of complexes of poly(methacrylic acid)- poly(N-vinyl pyrrolidone) in water. [12] On the other hand, an increase of concentration of the polymer components sometimes decreases the dissociation degree of a polyelectrolyte and thus influences the complex formation and the composition.[4] In the system of polyfacrylic acid) and polyacrylamide in water, PAA-PAAm-H 2 0 , Staikos and coworkers found that the structure of interpolymer complexes depend strongly on the composition of donor and acceptor polymers in the mixture. [8 ] A compact structure was formed when the polymer mixture is rich in PAA (weight fraction W p a a > 0 .2 0 ), whereas a gel-like interpolymer association was preferred at W p a a < 0 .2 0 .[8 ] As one category of associating polymer systems, relatively few studies have been carried out for hydrogen-bonding aggregation in solution compared to ionic or hydrophobic associations. Among the existing literature, the majority of the solution studies of synthetic hydrogen-bonding polymers have been limited to polyacid or polybase as one or both of the components in either aqueous medium or polar organic solvents. [13-15] The aggregates formed in water can be also stabilized or destabilized by the hydrophobic interaction of bulky backbones. Additionally, most investigations are complicated by hydrogen bonds formed between the donor or acceptor polymers and the solvents. And in some cases polyelectrolyte effects come into play, depending on the solution pH. [8 , 10] Most experimental results on 192 interpolymer complexes in aqueous solution are summarized in two review papers. [4,12] As one can imagine, the solvent effect is one of the most im portant controlling factors for the complex formed by hydrogen bonding. Complexing ability of two complementary polymers depends on the dielectric constant of solvent. [12] Some solvents can interact with polymers via hydrogen bonds. When the interaction between one polymer and solvent is stronger than that between two complementary donor and acceptor polymers, a complex can not form. It has been found that the complexes formed in water and organic solvent exhibit different composition and structure. [12] In some organic solvents, the destruction of polymer complexes may occur due to the weakening of the hydrophobic interactions[16, 17], but complex formation was reported in other organic solvents. [18] It will therefore be of interest to study polymer aggregation involving H-bonding interactions at low concentrations in a nonpolar solvent. A recent study of dilute solution viscosity has shown a "gel type" complex when polymer chains bearing statistically distributed proton acceptor and proton donor groups are mixed in toluene. [19] Toluene, as a nonpolar aprotic solvent, should practically exclude the interferences of hydrophobic interactions and polyelectrolyte effects. In addition, hydrocarbon-soluble associating polymers have been found useful as antimisting and drag reducing agents. [2 0 ] 193 The choice of pyridine (4-vinyl pyridine) and phenol (4-vinyl phenol) as the respective acceptor and the donor functional groups in our study, eliminates the complications arising from H-bonding self associations. The donor and acceptor copolymers, poly(styrene-co-4- vinyl phenol) and poly(styrene-co-4-vinyl pyridine) respectively, were characterized by viscosity and light scattering measurements. The polymer concentrations were kept extremely low to prevent the precipitation of mixtures. At such low concentrations, viscosity and the other rheological techniques may not be sensitive to the complex formation. Laser light scattering has been found effective in characterizing polymer aggregates at low concentrations [2 1 ] and is therefore employed in our study. III. Experimental Section Materials The donor and acceptor copolymers were prepared by Sanjay Malik in Julia Kornfield's laboratory at Caltech. The copolymers of the styrene and 4-vinyl pyridine were used as the proton acceptor polymers, while the copolymers of p-tertiary butyl styrene with 4-vinyl phenol w ere the proton donors. The acceptor copolymers were synthesized by means of emulsion polymerization. A clean, three necked, glass reactor was twice evacuated and filled with purified argon. Deionized water (400g), emulsifier (triton 194 X-100) (12g) and the purified monomers (lOOg) were sequentially added to the flask with the protection of Ar gas and stirred at a constant speed. The feed ratios of noninteracting styrene monomer and functional 4- vinyl pyridine comonomer were varied to obtain different comonomer compositions. An aqueous solution of ammonium persulfate (0.2g) was introduced into the reactor after the argon purged through the emulsion for 30 minutes. A drop of N,N,N',N'-tetramethylethylene diamine (TMEDA) into the emulsion quickly induced polymerization, as observed by a slight exotherm. The temperature of the reactor was maintained at 20 °C during the four-hour reaction period. The polymer was isolated from the emulsion by precipitation in cold methanol. The dried polymer was reprecipitated from toluene in methanol. The recovered polymer was dried in vacuo at 45 °C for several days. The donor copolymers were synthesized by solution polymerization of 4-acetoxy styrene and p-tertiary butyl styrene in 1,4- dioxane. A three neck, glass reactor was charged with the required quantity of 1,4-dioxane (lOOg) and the comonomer in appropriate proportions (total 25g). Prior to addition of the initiator, azoisobutyronitrile (AIBN) (0.4g), the contents of the flask were purged with argon, frozen, evacuated and thawed to remove any entrained oxygen. The temperature was raised and then maintained at 78 °C for 12 hours while the contents in the flask were agitated at a constant speed. The solution was allowed to cool to room temperature and the polymer was isolated by precipitating in cold methanol. The isolated copolymer 195 was then reprecipitated from toluene in methanol and then vacuum- dried at 45 °C to a constant weight. The resulting polymer was hydrolyzed to generate the proton donor phenolic group as follows. A two neck glass vessel was charged with a 5% (weight/volume) solution of the copolymer in tetrahydrofuran, THF, water (10% by the volume of THF) and a catalytic quantity of hydrochloric acid. The mixture was refluxed for one week with mild agitation and argon purging through. The isolation of the donor copolymers was the same as described above. The compositions, as determined by NMR and the solution characteristics of the proton donor and acceptor copolymers are compiled in Table VIII-1. Sample Preparation The copolymer samples were freeze-dried from 1,4-dioxane and then dissolved in toluene at concentrations ranging from 0 .0 1 to 10 mg m L '1. Solutions were filtered through 0.45 pm PTFE filters prior to scattering measurements. Mixtures of the proton donating and accepting copolymers were prepared from these solutions by filtering one stock solution into a filtered solution of the other. Two sets of these experiments were conducted simultaneously, one starting with the donor solution and the other with the acceptor solution titrated by consecutive addition of the acceptor solution and donor solutions, respectively. This allows the titration and thus light scattering measurement to cover the entire range of donor to acceptor ratio. The 196 Table VIII-1. Characterization of donor and acceptor copolymers Polymer C om onom er com position (mol %) 1 0 ' 6MW (g mol"1) Rg (nm) 104A2 (mol cm 3g’2) Rh (nm) 22% P4VP 0 .2 2 1.65 83 1.24 25 14%P4VP 0.14 2 .1 1 109 1.96 6 % P4VP 0.06 2.31 1 1 2 2.77 2% P4VP 0 .0 2 1.96 93 3.24 25% P40H 0.25 0.55 32.3 3.06 1 2 31% P40H 0.31 0 .1 0 14.6 3.44 6 .0 31% P40H +Pyridine 0.31 0 .1 1 15.1 3.90 5.7 197 donor and acceptor solutions were prepared at the same mass concentration so that the mass concentration of the mixtures would be independent of the fraction of donor or acceptor. Scattering Experiments Static and dynamic light scattering experiments were performed on a Brookhaven goniometer (BI-200SM) with an Ar ion laser (Spectra Physics 2020-3) operating at 514.5 nm. Photon autocorrelation functions w ere acquired with a multi-tau correlator (ALV instrument 5000). M easurement temperature was controlled to 25.00 ± 0.05 °C. Static scattering was analyzed by the Zimm method. The values of d n /d c for these samples were measured using the differential refractometer setup in our lab. [22] The device is calibrated with NaCl solutions of known refractive index. The dynamic light scattering auto-correlation functions were analyzed by CONTIN. The aggregation phenomena of donor and acceptor copolymers w ith varying composition of functional comonomers were studied as a function of the molar ratio of donor to acceptor copolymers. A donor copolymer solution in the scattering cell was titrated by consecutive addition of acceptor solutions and vice versa to obtain any given molar ratio of donor to acceptor copolymers. The mixture then was gently swirled and allowed to sit for ten minutes prior to the scattering measurements. The solution concentrations of copolymers were kept very low to avoid precipitation or phase separation of mixtures. 198 IV. Results and Discussions Characterization of Individual Copolymers All individual donor and acceptor copolymers are characterized in toluene with static light scattering. Examples of typical Zimm plots are shown in Figure VIII-1 and VIII-2 for the donor and acceptor copolymer composed of 25% 4-vinyl phenol (P40H) and 22% 4-vinyl pyridine (P4VP), respectively. Molecular weights, radii of gyration and second virial coefficients are extracted from the Zimm plots and the results are summarized in Table VIII-1. These data are comparable to data for polystyrenes of similar degree of polymerization. The radii correspond to radii observed for polystyrene of the same molecular weight [23, 24] and more importantly, the second virial coefficients are only slightly smaller than those seen for polystyrene. [24] These results indicate that the presence of the functional comonomers does not perturb the chain conformations or alter the solvent quality significantly. Dynamic light scattering data were acquired for the individual copolymers at several concentrations over scattering angle range 20-140°. The inverse relaxation times, x, obtained from the deconvolution of the autocorrelation functions using CONTIN, were plotted against the square of the scattering vector q2 (Figure VIII-3). The diffusion coefficients obtained from the slopes of such plots were independent of 199 O o.o 0.2 fig u r e V ijr 7 P°iy(p-t~ butyl sfyrene~ 25< y A . 4-hyd. roxyl $ co O o ’ * - .C o o ' & f o’ I / fJ 3 3 O 60 « ‘S’.* ? 201 5x 1 04 4 3 ’< /) ^ 2 1 %.0 0.2 0.4 0.6 0.8 1.0 1.4x10 2 -2 q ,cm Figure VIII-3. The inverse relaxation time vs. the square of scattering vector for poly(p-t-butyl styrene- 25% 4-hydroxyl styrene) ( • ) and poly(styrene- 22% 4-vinyl pyridine) (O) in toluene. 202 concentration for several samples observed below the overlap concentration c*. The hydrodynamic radii calculated from the diffusion coefficients using the Stokes-Einstein equation are also listed in Table VIII-1. Figure VIII-3 shows the typical angular dependence of the inverse relaxation time 1/x, for donor and acceptor copolymers of 25% 4- vinyl phenol and 22% 4-vinyl pyridine, respectively. Absence o f Self-Association in Donor Copolymers The existence of self-hydrogen bonds of poly(styrene-co-4-vinyl phenol) in bulk state is still a controversy. FTIR analysis of hydroxyl stretching bands by Coleman et al.[25] shows that self-associated hydroxyl group is the dom inant form in this polymer bulk. On the other hand, Frechet and coworkers[26] found that poly(4-vinyl phenol) is not compatible with copolymers of styrene and 4-vinyl phenol containing as much as 70% of 4-vinyl phenol comonomer, which indicates no specific hydrogen bonding interactions are present between the hydroxyl groups. These different observations perhaps resulted from the solvent from which the examined films were cast. [27] In the former case, polymer films were cast from tetrahydrofuran, while in the later paper, the tested films were prepared in pyridine, a strong H-bonding accepting solvent. A solvent effect was also observed by a fluorescence technique which demonstrates that compatibility of the blend of poly(styrene-co-4-vinyl phenol) and PMMA was optimized by casting from toluene rather than from dioxane or chloroform. [27] 203 To detect the existence of the self-hydrogen bonds among the donor copolymers in dilute solution, we titrated one donor copolymer, which contains 31 mol%, the highest content of 4-vinyl phenol, with same molarity of pyridine solution. Figure VIII-4 demonstrates the excess scattering intensity at 40° vs. molar fraction of pyridine added in polymer solution. The linearity of the excess scattering intensity vs. the concentration of pyridine (or donor copolymer concentration) implies that the size and conformation of the donor copolymer does not change with the addition of pyridine. The decrease in the intensity with increasing pyridine content simply reflects the dilution effect since the intensity is proportional to cMw, where c and Mw are the concentration and molecular weight of 4-vinyl-phenol copolymer, respectively. Figure VIII-5 shows a complete Zimm plot of styrene copolymer containing 31% 4-vinyl pyridine with the added pyridine in toluene (comonomer to pyridine molar ratio 1 : 2). The radius of gyration and molecular weight are calculated from the Zimm plot and complied in Table VIII-1. The values remain the same in the absence or the presence of excess volume of pyridine. We assume that d n /d c does not change with the addition of pyridine since the weight added is negligible. Insignificant self-hydrogen bonding interaction among donor polymers is also suggested by dynamic light scattering measurements. Figure VIII- 6 shows a plot of inverse relaxation time 1/x vs. q2 over the angle range of 40-135° for the copolymer in toluene with and without the addition of pyridine in molar ratio of 2 :1 relative to the 4-hydroxyl , kcsp 204 1 o 0.2 0.0 0.4 0.8 0.6 1.0 molar fraction of pyridine Figure VIII-4. Excess scattering intensity at 40° scattering angle for poly(p-t-butyl styrene- 31% 4-hydroxyl styrene) in toluene titrated w ith pyridine of same molarity (3.87 x 10"5 M) as the molar concentration of 4-hydroxyl styrene comonomer. 2 0 % 206 1.0x10 0.8 0.6 0.4 0.2 0.2 0.4 0.6 0.8 2 -2 q ,cm 1.2x10 Figure VIII-6. The inverse relaxation vs. the square of scattering vector for poly(p-t-butyl styrene-31 % 4-hydroxyl styrene) with ( • ) and without (O) added pyridine in toluene. 207 styrene comonomer concentration. As seen in Figure VIII-6 , the relaxation data do not show a significant change in the diffusion coefficient or hydrodynamic radius with the addition of organic base pyridine. The linear least square fits of two sets of data for this donor polymer with and without pyridine overlap well with each other to give the diffusion coefficients with a negligible difference. The relaxation time x (i.e. hydrodynamic radius) in Figure VIII-7 is measured at 40° with the continuous addition of pyridine solution. The relaxation time of the polymer shows only a small fluctuation over a broad range of molar fraction of pyridine. In the case of intermolecular association, the addition of H-bond accepting pyridine would compete against long chain 4-hydroxyl styrene copolymer and break up larger structures formed by interchain self-association between hydroxyl groups. Whereas more compact polymer coils due to intrachain H- bonding association would be expanded upon the addition of pyridine. A change in the size of poly(p-t-butyl styrene-4-hydroxyl styrene) copolymer in toluene is expected in either case when pyridine is added. Thus, intensity measurements and dynamic light scattering experiments both suggest that the donor copolymers do not self-associate either intermolecularly or intramolecularly. Effect of Donor to Acceptor Ratio The scattering intensity and the relaxation times of the aggregates are measured by dynamic light scattering at 40° scattering angle upon 208 100 < /5 =L 0.2 0.4 0.6 0.8 m olar fraction of pyridine Figure VIII-7. The relaxation time vs. molar fraction of added pyridine in toluene at 40° scattering angle. 209 mixing a solution of donor polymer with a solution of acceptor polymer of the same mass concentration. For donor and acceptor copolymers composed of 25% donor and 22% acceptor groups, the solution concentrations were kept below 0.2 mg mL' 1 because above this concentration, the mixture solutions turned turbid suggestive of phase separation. [29] Figure VIII- 8 and VIII-9 show that the scattering intensities and relaxation times of the mixture at mass concentration of 0.075 mg mL' 1 against the molar fraction of the acceptor copolymer which is denoted as Fa- The molar fraction Fa is calculated as the molar concentration of acceptor copolymer over the total polymer molar concentration. The dramatic increases of intensity (Figure VIII-8 ) and relaxation time (Figure VIII-9) demonstrate the apparent formation of large aggregate particles in the mixture solution. The copolymer alone at this low concentration of 0.075 mg mL"1 does not display significant correlation functions at 40° scattering angle after 30 minutes averaging. The solution scattering intensity is almost the same as the solvent scattering as seen at two ends of Figure VIII-9. Therefore all the excess scattering for the mixtures can be presumed to arise from the complexes formed by two copolymers. Measurable correlation functions are obtained from mixtures with Fa as high as 0.97 or as low as 0.03. Figure VIII-10 is an example of typical dynamic light scattering data obtained at a total concentration of 0.075 m g mL' 1 and a F a of 0.70. The g^Ht) autocorrelation function is plotted against the log of the decay time with the nearly single peak of the relaxation spectrum s r l * 210 10000 8000 6000 4000 2000 1 1 1 “ 1 ------------- ocP o ° o ° o o - o ° o o o o o o CP o 1 -§ o o CQo °o . * o o ________ 1 ________ 1 ________ I ________ 0.8 1.0 Fa Figure VIII-8. The relaxation times of the aggregates formed by poly(p-t-butyl styrene-25% 4-hydroxyl styrene) and poly(styrene- 22% 4-vinyl pyridine) in toluene at c = 0.075 mg m L'1. Intensity, kcps 211 600 O dSP Figure VIII-9. The intensity profile of the mixture of poly(p-t- butyl styrene-25% 4-hydroxyl styrene) and poly(styrene-22% 4- vinyl pyridine) in toluene at c = 0.075 mg mL*1. 212 0.4 0.8 0.3 0.6 0.2 0.4 o> 0.2 0.1 0.0 0.0 2 2 3 0 1 4 1 0 ) 3 - o Q . C D pT C t , ms Figure VIII-10. The dynamic light scattering results of a mixture of poly(p-t-butyl styrene-25% 4-hydroxyl styrene) and poly(styrene- 22% 4-vinyl pyridine) in toluene at 0.075 mg m L'1 and Fa = 0.70. 213 extracted from CONTIN superimposed on it. The relative amplitude of the slow mode representing the aggregates is around or above 90% for all ratios of mixture solutions. Thus, the aggregate is the dominant form in solution and the absolute intensity and decay time directly correspond to the scattering and relaxation of aggregates. The intensity and relaxation curves displayed in Figure VIII- 8 and VIII-9 are interesting. The hydrodynamic size of the aggregates (i.e. relaxation time) changes as Fa varies. Over the Fa range of 0.15-0.8, the relaxation time, i.e., the hydrodynamic radii, Rh, varies by approximately a factor of three while at the two extremes the relaxation times increase by an order of magnitude. The relaxation time reaches a maximum as Fa approaches 0.16 from both sides suggesting that the maximum complexing between the donor and acceptor copolymers is achieved at this certain donor to acceptor ratio. At high Fa value (the right end of Figure VIII-8 ), each phenol group in the donor copolymer chain is paired up with one pyridine group in the acceptor copolymer. Whereas at the other end of Figure VIII- 8 (low Fa value), the aggregate consists of more donor copolymer chains than stoichiometrically required w ith unbonded hydroxyl groups. For this particular pair, the acceptor copolymer possesses approximately 3480 pyridine functional groups per chain while the donor copolymer contains approximately 1270 phenol groups per chain. The maximum size of complexes is expected to form at Fa = 0.27 if 214 donor and acceptor copolymers form exact equimolar complexes. In Figure VIII-8 , the maximum x value occurs at Fa =0.16 meaning that excess phenol units are required to achieve maximum interaction. The formation of non-equimolar interpolymer complex via hydrogen bonding has been observed for many systems in water and polar organic solvents.[12] The same phenomenon has also been seen for the maximum glass transition temperature Tg of poly(4-vinyl phenol)/poly(styrene-co-50% 4-vinyl phenol) blend systems.[26] It has been explained that not all phenol groups are able to complex with the pyridine groups. In addition to the bulkiness of the copolymer backbones and steric hindrance of adjacent aromatic side groups, copolymer chain conformations in solution can also affect the activity of donor and acceptor groups. The complexing strength of phenol group may be even weaker in solutions due to the expanded chain conformation. This speculation provides a possible explanation for the asymmetric feature of the relaxation time plot. The most possible scenario of the aggregation is that there are many small aggregates at either end of Figure VIII- 8 and the small aggregates combine to form larger clusters when the ratio of donor to acceptor approaches the maximum complexing ratio. It is puzzling at first sight that the intensity curve in Figure VIII-9 does not have the same shape and maximum position as the relaxation time plot. In a semi-quantitative consideration, the second virial coefficient term in equation 11-16 can be neglected since the solution 215 concentration is very dilute. An expression for scattering intensity is then obtained as follows I ~ cMwP' 1 (0)(dn/ dc)2 (VIII-1) where c, Mw, P(0) and d n /d c are the mass concentration, weight- averaged molecular weight, particle scattering factor and refractive index increment of the aggregates. The mass concentration of aggregates is determined by the mass concentration of limiting reagent, the composition and the molecular weight of aggregate as well as the equilibrium constant of the phenol-pyridine complex. We attem pted to use the apparent hydrodynamic radius Rh to estimate the scattering factor P(0 ) by considering the R g /R h ratio for different sizes of aggregates. Theoretically, a = Rg/R h ranges from 1 .8 6 to 0.775 but experiments find values as low as 0.5 for soft spheres and as high as 2.0 for highly branched latexes.[28] According to Burchard,[28] P(0) for polydisperse randomly branched structures takes the formula of (l+q 2Rg2 /3). We assume that toluene is a good solvent for all species in the mixture solution and thus radius of gyration scales as M ^ -6 in good solvent,[29] the following expression can relate the scattering intensity to the m easured relaxation time t, I ~ c(aRh)1/°-6(l+ a 2q2Rh2 /3)-1(d n /d c ) 2 (VIII-2) where c is the aggregate concentration and can be calculated from the mixture constitution. This relationship shows that intensity is not simply proportional to hydrodynamic radius (i.e. relaxation time). This 216 may account for the difference in the shape and the maximum value of intensity and relaxation time curve. We would like to fit the intensity data numerically by choosing d n /d c and a values for the mixture with different donor to acceptor ratio. However, comprehensive information regarding the aggregate structure (P(9)), density of the aggregates (Rg/Rh) and d n /d c for the different size of aggregates as well as the equilibrium of the aggregate formation is needed to verify the intensity data from relaxation times. Unfortunately, it is difficult to determine these variables from the experimental data available. Concentration Effect The influence of polymer concentration on the formation of aggregates is shown in Figure VIII-11. The titration experiments between poly(p-t-butyl styrene-25% 4-vinyl phenol) and poly(styrene- 22% 4-vinyl pyridine) were performed at different concentrations. We mixed this pair of donor and acceptor copolymer solutions at concentrations of 0.075 and 0.017 mg mL*1. The relaxation times, x, measured by dynamic light scattering at 40°, are plotted against the molar fraction of acceptor copolymer, Fa (Figure VIII-11). The two relaxation time curves overlap perfectly over the entire Fa range and each curve appears to have a maximum at nearly the same Fa values. The low value of Fa at which the maximum hydrodynamic Sri ‘ 217 10000 8000 - 6000 4000 2000 o p o & Figure VIII-11. The relaxation times of the aggregates formed by poly(p-t-butyl styrene-25% 4-hydroxyl styrene) and polyfstyrene- 22% 4-vinyl pyridine) in toluene at concentrations of 0.075 (O) and 0.017 mg mL' 1 (O). 218 size of aggregates is formed again suggest that donor copolymer chains may have a weaker complexing ability to neutralize the acceptor copolymers. The relaxation time measured at any given Fa (Figure VIII- 11) does not seem to depend on the total polymer concentration. The independence of molecular weight and concentration has been observed in other cases of associations through hydrogen bonding and also oppositely charged polyelectrolyte systems. [11,12] This has been attributed to a high degree of long range coupling for these types of interactions (hydrogen bonding and electrostatic) between two complementary polymers. Figure VIII-12 is a plot of the scattering intensity versus Fa for the same titrations at the above concentrations. The two curves both have the same shape and the same maximum near 0.5 Fa- The difference in the amplitude of the intensities is approximately proportional to the total polymer concentration of each titration. As discussed before, the intensity is predominant by the scattering of aggregates. Therefore, at these low concentrations, the scattering intensity is determined by the mass concentration c, molecular weight Mw , structure factor p l(0 ) and refractive index increment d n /d c of the aggregates as stated in equation VIII-1. The concentration independence of the relaxation times of the aggregates strongly indicated that the molecular weight Mw , structure factor P'^G) and refractive index increment d n /d c of the aggregates also do not change with , kcps 219 500 400 - 300 - — 200 - 100 - a ssf O ^ n Figure VIII-12. The scattering intensities of the aggregates formed by poly(p-t-butyl styrene-25% 4-hydroxyl styrene) and poly(styrene- 22% 4-vinyl pyridine) in toluene at concentrations of 0.075 (O) and 0.017 mg mL-1 (O). 220 concentration. This means the intensity should be directly proportional to the total polymer concentration. In order to investigate the hydrodynamic behavior of the aggregates, dynamic light scattering data was acquired at several angles for an 0.14 mg mL' 1 mixture of poly(p-t-butyl styrene-25% 4-hydroxyl styrene) and polyfstyrene- 22% 4-vinyl pyridine) at Fa = 0.57. Figure VIII-13 shows that the plot of inverse relaxation time versus scattering vector squared is linear with a zero intercept. This result confirms the diffusive nature of the aggregates. The hydrodynamic radius and diffusion coefficient computed from the slope of the line in Figure VIII- 13 are 390 nm and 1.04 x 10"8 cm2 s' 1 respectively. Effect of Acceptor Comonomer Content For the same donor copolymer, poly(styrene-25% 4-vinyl phenol), complexation with acceptor copolymer of various comonomer content was also monitored by dynamic light scattering. Three acceptor copolymers consisting of 22,14 and 6 mol% of 4-vinyl pyridine comonomer units, respectively, were chosen for titration experiments. Intensity and relaxation time plots of the complex formation between poly(p-t-butyl styrene-25% 4-vinyl phenol) and poly(styrene-22% 4-vinyl pyridine) are shown in Figure VIII-11 and VIII-12. Dynamic light scattering data was taken at a concentration of 0.75 mg mL*1 for the pair of poly(p-t-butyl styrene-25% 4-vinyl phenol) and poly(styrene-14% 4- vinyl pyridine) (Figure VIII-14) while the total polymer concentration 4 1000 (0 500 0.0 0.2 0.4 0.6 0.8 1.0 1.4x10 2 -2 q ,cm Figure VIII-13. The inverse relaxation time vs. the square of the scattering vector for the aggregates formed by poly(p-t-butyl styrene-25% 4-hydroxyl styrene) and poly(styrene- 22% 4-vinyl pyridine) in toluene at concentration of 0.14 mg mL*1 and Fa = 0.57. , K cps T > M ^ s Jtr& 222 10000 8000 6000 / y % — • 4000 2000 0 100 50 0L - 0.0 0.2 0.4 0.6 0.8 1.0 Fa Figure VIII-14. The relaxation times (upper) and intensities of the aggregates formed by poly(p-t-butyl styrene-25% 4-hydroxyl styrene) and poly(styrene-14% 4-vinyl pyridine) in toluene at concentration of 0.75 mg mL*1. , Kcps x » M s 223 1000 ~ * s Figure VIII-15. The relaxation times (upper) and intensities of the aggregates formed by poly(p-t-butyl styrene-25% 4-hydroxyl styrene) and poly(styrene- 6 % 4-vinyl pyridine) in toluene at concentration of 1.0 mg m L'1. 224 for the mixture of poly(p-t-butyl styrene-25% 4-vinyl phenol) and poly(styrene-6 % 4-vinyl pyridine) was 1.0 mg mL-1 (Figure VIII-15). The intensity and relaxation time are combined in Figure VIII-14 and VIII-15 for these two pairs. Direct comparisons for the intensity magnitude are not possible because the concentration and the instrument settings were chosen differently for these titration experiments to obtain the optim um scattering intensity. However, the relaxation times or hydrodynamic radii provide more im portant information. When the acceptor P4VP comonomer content decreases from 25% to 14%, the changes in hydrodynamic size of the aggregates are not significant. Two relaxation time curves possess almost the same shape and the maximum value of x occurs at the similar donor to acceptor ratio. Even though 14% P4VP copolymer contains a lower mole percent of functional comonomer, it has a longer chain (larger molecular w eig h t). The absolute number of accepting comonomers per chain of 14% P4VP copolymer (2840) does not differ much from that of the 22% P4VP copolymer sample (3480). This small difference in the number of pyridine units per chain could account for the small decrease in the relaxation time curves for these two titrations. A dramatic decrease is observed for the pair of poly(p-t- butyl styrene-25% 4-vinyl phenol) and poly(styrene-6 % 4-vinyl pyridine) because the 6 % P4VP copolymer contains only 1330 pyridine groups per chain. The hydrodynamic size of the aggregates formed through hydrogen bonding interactions decreases with a decreasing accepting 225 comonomer content in the copolymers. For the mixture solutions of 25% P40H and 2% P4VP, increases in the scattering intensities and hydrodynamic radii were not observed. This suggests there exists a critical comonomer content below which complexation does not take place in solution. This critical comonomer content should lie between 6 % and 2 % because the weak aggregation was still measurable for the titration of 25% P40H with 6 % P4VP. Such a critical composition has been found for interpolymer complexation in solution[30] and for polymer blends in bulk state. [31] The stoichiometric complexes should be formed at 0.27, 0.31 and 0.49 Fa for 25% P40H mixing with 22% P4VP, 14% P4VP and 6 % P4VP, respectively. The observed maxima, 0.16, 0.20, 0.05, of all three relaxation time curves are shifted to lower Fa values compared to the stoichiometry of equimolar complexes. This is probably due to the weak complexing strength of the phenol group as the hydrogen bonding donor in an aprotic and nonpolar solvent. The fact that the donating copolymer has a much shorter chain length yet high density of associating units may be another factor resulting in maximum interactions at low acceptor to donor ratio. Since the acceptor copolymer is much longer than the donor copolymer, some donor groups are probably buried inside the initial small aggregates and become less accessible to further complexation. Therefore, complexation requires more and more 4-vinyl phenol comonomer than required by stoichiometric coupling as the accepting copolymer chain becomes 226 longer and the total number of complexing sites decreases. More studies, including spectral analysis are needed to better understand this phenom enon. The intensity curves for the titrations with 22% and 14% P4VP copolymers, like the relaxation time curves, displayed nearly the same shape, with the maximum intensity occurring at a lower Fa than for the complexes formed by 22% P4VP and 25% P40H. Since the hydrodynamic radii of the aggregates in these two cases are insignificantly different, according to equation VIII-2, the aggregates formed in these two titrations must possess the same structure factor P(0) and d n /d c to give the same shape of intensity curves. For the same reason, the intensity curve in Figure VIII-15 suggested that the aggregates formed by 6 % P4VP and 25% P40H copolymers have different structure factor P(0) and d n /d c along with smaller hydrodynamic size. Solvent Effect The solvent effect has been demonstrated in Figure VIII-16 which shows the titration results of poly(p-t-butyl styrene-31 % 4-vinyl phenol) with poly(styrene-14% 4-vinyl pyridine) in tetrahydrofuran (THF). In THF the aggregation is barely visible with light scattering because the hydrodynamic radii are remarkably smaller even though the polymer concentration was much higher in THF than in toluene. The hydrodynamic radius at a given donor to acceptor ratio is approximately the z-average of the hydrodynamic size of donor and acceptor , kcps 227 600 500 i c o = 1 - 400 300 200 25 20 0.2 0.4 0.6 0.8 0 Figure VIII-16. The relaxation times (upper) and intensities (bottom) of the aggregates formed by poly(p-t-butyl styrene-31 % 4- hydroxyl styrene) and poly(styrene-14% 4-vinyl pyridine) in THF at concentration of 19.0 mg m L'1. 228 copolymers, indicative of the complete destruction of the aggregates in THF. When THF is used as a polar and hydrogen accepting solvent, combining the donor and acceptor polymers only gives a binary mixture with no aggregation. Therefore, the aggregation did not happen because polar THF can interact with the donor copolymers preferentially. V. Conclusions The proton-donating copolymer poly(p-t-butyl styrene-co-4-vinyl phenol) and proton-accepting copolymer poly(styrene-co-4-vinyl pyridine) of varying comonomer compositions are characterized thoroughly by static and dynamic light scattering measurements. The characteristics of the copolymers remain nearly the same as polystyrene homopolymers of similar degree of polymerization. Titration experiments of poly(p-t-butyl styrene-co-31 % 4-vinyl phenol) are performed by adding pyridine solution. The fact that the radius of gyration and hydrodynamic radii do not change with the addition of the proton-accepting agent pyridine indicates no self hydrogen bonding interactions are present in the donor copolymers. When the donor and acceptor copolymers are mixed in a nonpolar aprotic solvent toluene, the aggregation results in a tremendous enhancement in scattering intensity and hydrodynamic radii compared to the individual copolymer components. Dynamic light scattering results demonstrate that the aggregates formed through 229 hydrogen bonding interactions is predominant and diffusive in solution. At different ratio of donor to acceptor polymers, the aggregates possess different compositions and thus different hydrodynamic sizes. The hydrodynamic size of the aggregates is nearly independent of the polymer concentrations. However the hydrodynamic size of the aggregates decreases as the 4-vinyl pyridine comonomer content in accepting copolymers decreases. With THF used as a polar and proton accepting solvent, the aggregates formed via hydrogen bonding interaction are broken. Therefore, the aggregation phenomenon is not observed for the mixture solution of poly(styrene-4-vinyl pyridine) and poly(p-t-butyl styrene-4- vinyl-phenol) in THF. 230 VI. References 1. X. Zhang, K. Takegoshi, and K. Hikichi, Macromolecules 24, 5756 (1991). 2. Y. Wang and H. Morawetz, Macromolecules 22, 164 (1989). 3. Polymers in Aqueous Media: Performance through Association; E.J. Glass, Ed.; Advances in Chemistry 223, American Chemical Society: Washington, D.C., (1989). 4. E. Tsuchida and K. Abe, Adv. Polym. Sci. 45, 47 (1982). 5. D.F. Hodgson and E.J. Amis, J. Non-Cryst. Solids 131-133, 913 (1991). 6 . H. Ringsdorf, J. Venzmar, and F.M. Winnik, Macromlecules 24, 1678 (1991). 7. I. Iliopoulos, J.L. Halary, and R. Audebert, }. Polym. Sci. A26, 275 (1988). 8 . G. Straikos and C.J. Tsitsilianis, J. Appl. Polym. Sci. 42, 867 (1991). 9. I. Iliopoulos and R. Audebert, Polym. Bull. 13, 17 (1985). 10. D.J. Eustace, D.B. Siano, and E.N. Drake, /. Appl. Polym. Sci. 35, 707 (1988). 11. S.K. Chatterjee, D. Yadav, S. Ghosh, and A.M. Khan, J. Polym. Sci., Part A: Polym. Chem. 27, 3855 (1989). 12. E.A. Bekturov and L.A. Bimendina, Adv. Polym. Sci. 41, 2 (1981). 231 13. A. Polderman, Biopolymers 14, 2181 (1975). 14. Y. Wang and H. Morawetz, Macromolecules 22, 164 (1989). 15. K. Abe and S.J. Seoh, /. Polym. Sci., Part A: Polym. Chem. 24, 3461 (1986). 16. L.A. Bimendina, E.A. Bekturov, G.S. Tleubaeva, and V.A. Frolova, }. Polym. Sci., Polym. Symp. 6 6 , 9 (1979). 17. E.A. Bekturov, V.V. Roganov, and E.A. Bekturov, ]. Polym. Sci., Polym. Symp. 44, 65 (1974). 18. H. Ohno, K. Abe, and E. Tsuchida, Makromol. Chem. 179, 755 (1978). 19. S. Malik, P. Joshi, S.N. Shitre, and R.A. Mashelkar, /. Polym. Sci., Polym. Phys. Ed. 30, 299 (1992). 20. D.N. Schultz, K. Kitano, I. Duvdevani, R.M. Kowalik, and J.A. Eckert, in Polymers as Rheology Modifiers; D.N. Schultz and E.J. Glass, Ed.; American Chemical Society Symposium Series 462, Washington, D.C. (1991). 21. T.A.P. Seery, M. Yassini, T.E. Hogen-Esch, and E.J. Amis, Macromolecules 25, 4784 (1992). 22. T.A.P. Seery, Ph.D. Thesis, University of Southern California, Los Angeles, CA (1992). 23. G.C. Beery, J. Chem. Phys. 44, 4550 (1960). 24. T.A.P. Seery, J.A. Shorter, and E.J. Amis, Polymer 30,1197 (1989). 232 25. E.J. Mosakala, D.F. Varnell, and M.M. Coleman, Polymer 26, 228 (1985). 26. M. Meftahi, M.V. Frechet, and M.J. Jean, Polymer 29, 159 (1989). 27. C.T. Chen and H. Morawetz, Macromolecules 22, 159 (1989). 28. W. Burchard, Adv. Polym. Sci. 48, 1 (1983). 29. P.G. De Gennes, Phys. Lett. 38A, 339 (1972). 30. K. Abe, M. Hasegawa, and S. Senoh, Makromol. Chem. 187, 967 (1986). 31. C.J. Serman, Y. Xu, P.C. Painter, and M.M. Coleman, Macromolecules 2 2 , 2015 (1989). 233 Chapter 9. Future Work We have used laser light scattering and viscometry to study the polymer associations driven by specific interactions in solution. The specific interactions involved in this dissertation encompassed dipolar, hydrophobic, and hydrogen-bonding interactions. By choosing unique polymer systems and carefully designing experiments, we were able to provide some new experimental observations on associating polymers of different topology (aggregation of ring diblock) or thermodynamic origin (fluorocarbon association). The results described in the preceding chapters have illuminated a number of interesting features for each associating system. Many exciting opportunities for future investigations on associating polymers still remain. Discussions of some new experiments are given below. I. Matched Linear Triblock and Cyclic Diblock In direct relation to the experiments presented in Chapters 4 and 5, matched linear and cyclic block copolymers with larger molecular weights and varying relative block length are needed for a complete study of dilute solution properties. The most basic observation about a ring homopolymer compared to its linear counterparts is that the ratio 234 of the mean-square radius of gyration /(R g )j a cyclic polymer to linear homologue of identical molecular weight is 0.5 under 0- conditions and 0.56 in good solvents, respectively. [1-4] The molecular weights of our block copolymer samples in Chapter 4 are too small to obtain the accurate radii of gyration by light scattering for comparisons to the theoretical predictions. Since cyclohexane is an index-matching solvent for PDMS blocks, the scattering intensity from the PDMS blocks was masked by the solvent. This substantially increased the time needed for correlation in the dynamic light scattering experiments. Thus, it would be worthwhile to perform measurements on the same pair of PDMS-PS-PDMS linear and ring copolymers in another theta solvent for the PS block or by neutron scattering. Also, confirmation from another polymer-solvent pair would allow us to draw more general conclusions in comparison w ith linear and cyclic homopolymers. In our study of ring copolymer aggregation, larger quantities of sample are needed to investigate the structures of aggregates formed by the linear triblocks and cyclic diblocks and therefore gain some insights into block copolymer aggregation from a thermodynamic viewpoint. The average aggregation number and packing density of aggregates are also expected to be different for the linear and cyclic block copolymers because of the fundamental difference in chain topology. While no readily usable theoretical model exists, experiments on samples of various molecular weights and block length can enable us to establish scaling relations for the aggregation of cyclic diblocks. 235 The reverse solvent effect on the diblock ring aggregation is definitely an experiment that clearly must be conducted. A theta solvent for the outer PDMS blocks of the linear triblock is desirable to clarify the debate over the occurrence and the structures of block copolymer micelles in selective solvents for the middle block. [5-11] Since ring molecules do not have chain ends, the reversed solvent should not affect the aggregation except that the cores and shells of aggregates will be reversed exactly as in the micellization of linear diblocks. Future successes in cyclization of other triblock copolymers[12-13] would provide us alternative sample pairs for investigations of the micellization of diblock rings. For instance, poly(2-vinyl pyridine)- polystyrene-poly(2 -vinyl pyridine) triblocks and polystyrene-poly(2 -vinyl pyridine) diblock rings could make an interesting pair for studies of micellization. Measurements on molecular weight matched linear and cyclic poly(2 -vinyl pyridine) polyelectrolytes have been conducted in our lab and interesting results have been obtained. [14] Poly(2-vinyl pyridine) block in triblock linear and diblock ring copolymers could be charged by protonation or quaternization to form polyelectrolyte blocks or ionomers. Therefore, in addition to neutral parent copolymers, ionic block copolymers can also associate in selective solvents via electrostatic interactions. Apart from their intrinsic interest as new materials, these block ionomers provide model compounds to investigate both the importance of molecular architecture on ionic aggregation and the effect of 236 electrostatic interactions on the final structure of aggregates in comparison with nonionic triblock and cyclic diblock copolymers. Copolymer aggregation driven by electrostatic interaction would be a significant addition to the current dissertation covering hydrophobic, dipolar, and H-bonding driven associations. It has been reported that lightly sulfonated PS-poly(t-butyl styrene) diblock copolymers exhibit polyelectrolyte behavior in polar solvent N,N-dimethylacetamide (DMA),[15] whereas in nonpolar organic solvents, block ionomers form reverse micelles.[16] The importance of a reverse micelle lies in its ability to solubilize hydrophilic compounds in a water pool inside the micelle. Thus, reverse micelles can serve as hosts for proteins and small hydrophilic molecules, and many reactions can be carried out in these "microreactors" with adjustable sizes.[17-19] For example, in the nonpolar solvent cumene, a lightly sulfonated PS- poly(t-butyl styrene) diblock ionomer forms reverse aggregates with the salt groups in the interior. [20] For highly charged diblock ionomers or single end-capped PS in the selective solvent toluene, various experiments have shown that the ionic block (or end group) assembles in spherical microdomains surrounded by a solvated corona, as seen in nonionic diblock copolymers. [21-23] The aggregation number and hydrodynamic size of the aggregates were found to depend on the chain length, the size of the counterion, and the dielectric constant of the solvent. [23] Comparisons with theoretical predictions show that the aggregation of diblock ionomers is best described by Halperin's star 237 model for nonionic diblock micelles.[21, 22] Experiments on linear triblock ionomers have been concentrated on dual end-functionalized (charged) polymers. No work on linear triblocks with longer polyelectrolyte end blocks or ring diblock ionomers has been reported so far. Therefore, charged poly(2-vinyl pyridine)-PS-poly(2-vinyl pyridine) linear triblock and ring diblock would open a new avenue for the investigation of reverse micelles. However, it has to be recognized that the above suggestions all rely on success in the synthesis lab to provide macrocyclic block copolymers in sufficient quantity. This is not a trivial task. II. Fluorocarbon End-Capped PEOs Spectroscopic methods would be complimentary techniques to explore the association process of fluorocarbon telechelic polymers. Fluorescence probe and quenching experiments have been performed by Winnik et al. on hydrocarbon telechelic PEO's. [24-27] The same technique could be employed to study fluorocarbon telechelic PEO's. Also, for fluorocarbon modified water soluble copolymers, 19F NMR has been extensively used to characterize the disappearance of fluorine containing comonomers and the reaction kinetics. [28] The chemical shift of 19F NMR should, in principle, be also useful to probe association equilibrium and aggregate structures. The end fluorocarbon groups in the unassociated form are most likely surrounded with hydrophilic 238 backbone and those in aggregates are shielded by other end groups in the same association junction. Since the chemical shift is sensitive to the chemical environment, fluorocarbons (especially CF3) in associated and unassociated forms should have different chemical shifts.[29] However, samples specifically for 19F NMR measurements would be required to maintain a balance between the fluorocarbon density and the hydrophilic chain length. To obtain reasonable signal to noise ratio, long perfluoroalkyl groups and short PEO chains are desired. At the same time, long fluorocarbon end groups and short backbones may result in associations too strong for the polymer to be soluble in water (or D2O). Despite the structural differences in associating polymers, some rheological characteristics are common among many associating polymer solutions. It is thus clear that rheology is necessary for studying fluorocarbon telechelic PEOs in semi-concentrated or concentrated regimes. Viscoelastic experiments should provide information about the Theological properties of polymer solutions resulted from the dynamics of association structures under shear. The results of model fluorocarbon PEO's can be compared to experimental and theoretical studies of hydrocarbon telechelic PEOs. [30-35] At the same time, a relevant experiment would be to observe the viscoelastic relaxation modes of a mixtures of telechelic polymers of different fluorocarbon lengths. Distinct relaxation times instead of simply an intermediate relaxation time have been observed for mixtures 239 of two hydrocarbon telechelic polymers with different hydrophobe length.[31] This type of rheological experiment would distinguish the Tanaka-Edwards’ model[35] from the reptation model.[36] When reptation has no influence on the relaxation dynamics of telechelic associating polymers, each disengaged single chain would relax independently and the spectrum should show a num ber of sharp peaks corresponding to the number of components.[35] It has been observed that the fluorocarbon telechelic PEO's form physical gels as the solution reaches a certain high concentration depending on the lengths of polymer chain and the fluorocarbon end groups. Thus, it is of great interest to investigate the gelation dynamics of hydrophobic associating polymers in aqueous media. The dynamic mechanic measurements on a chemical gel, tetraethoxysilane, and a physical gel, gelatin, yielded static scaling exponents for networks held together by covalent[37,38] and H-bonding forces,[39] respectively. The complex shear modulus showed that a power law relation G' - G" - governs the gelation dynamics of this chemical gel and of gelatin. The critical exponents are predicted to be 0.67 and 0.73 based on concepts of fractal dynamics and percolation calculations, respectively. [40-43] In the case of fluorocarbon modified water soluble polymers, the underlying physics controlling the gelation process is the hydrophobic association. Therefore, dynamic viscoelastic measurements revealing gel formation of hydrophobic associating polymers will allow a convenient comparison with the previously studied gelation systems. 240 In parallel to the rheological measurements, dynamic light scattering and pulsed field gradient NMR can also be utilized to monitor diffusion behavior and thus investigate the dynamics of fluorocarbon association in solutions and gels. It has been found that the concentration dependence of the self-diffusion coefficients of such association systems can be well described with a stretched exponential function.[39, 44, 45] The field correlation function g^Kt) measured from DLS is described by an initial single exponential decay followed by a nonexponential relaxation function. [45] These results can be rationalized in terms of fractal structure [40, 41] and the coupling model. 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