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Rheological studies of polymer solutions and filled polymer melts

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Rheological studies of polymer solutions and filled polymer melts

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Content RHEOLOGICAL STUDIES OF POLYMER SOLUTIONS AND FILLED POLYMER MELTS by Khushroo H. Lakdawala A Thesis Presented to the FACULTY OF THE SCHOOL OF ENGINEERING UNIVERSITY OF SOUTHERN CALIFORNIA In P artial F u lfillm en t of the Requirements for the Degree MASTER OF SCIENCE IN CHEMICAL ENGINEERING July 1934 UMI Number: EP41815 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI EP41815 Published by ProQuest LLC (2014). Copyright in the Dissertation held by the Author. Microform Edition © ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml 48106-1346 c h I I f 3 ^ This thesis, written by Khushroo H. Lakdawala under the guidance op i s Faculty Committee and approved by a ll its members, has been presented to and accepted by the School of Engineering in pa rtia l fu lfillm e n t of the re quirements fo r the degree of Master of Science in Chemical Engineering D a te O A . / j i I ' M . Faculty Committee fair m m Dedicated to my parents and my beloved wife. ACKNOWLEDGEMENTS The author wishes to thank Professor Ronald Salovey for his advice and guidance during the course of this investigation. The author is also grateful to other members of the faculty and would especially to thank Professor John Aklonis for his helpful suggestions and discussions. Furthermore, he owes a great deal to a ll his friends and would like to express special gratitude to Mr. E. D. Chikhliwala and Mr. Murzi H. Kay. He would like to thank his typist Ms. Binh K. Ly for her cooperation and help in preparing this manuscript. F in a lly , the author sincerely appreciates the financial support of IBM Corporation and the Los Angeles Rubber Group. Special thanks to Mr. Akbar Naderi of Paker-Hannifin Co. (Seal Group) for generously providing laboratory f a c i l i t i e s . TABLE OF CONTENTS PAGE DEDICATION ---------------------------------------------------; — - ------------ ii ACKNOWLEDGEMENTS — - -------------- - ............- i [ i LIST OF FIGURES - Solution rheology - - ------------------— ■ --------------- v ii LIST OF TABLES - Solution rheology----------------- —---------- Jx LIST OF FIGURES - Melt rheology ------------------------•---------- x LIST OF TABLES - Melt rheology ------------------------------------ xi i i SOLUTION RHEOLOGY - SECTION A ABSTRACT — — — ----------------------- xIv CHAPTER I. INTRODUCTION .................. — — — ........ 1 A. Electrophotographic process ---------------- 1 B. Solution rheology --------------- — 4 C. Film formation ------------ 15 D. Optical microscopy ---------- 16 I I , EXPERIMENTAL ----------------- 19 A, Material t - “------— -------- 19 B, Film formation - - - - - - — - — - - 19 C, Testing ----------------- : ------------------------------------ 19 ( i) Solution rheology - Weissenberg rheogoniometer t - - — ----- ■ — — 19 i V TABLE OF CONTENTS PAGE ( 11) Optical thickness and refractive index - Interferometer and el 1ipsometer ----------------- 20 ( i i i ) Surface tension of binders --------------------------- 29 (iv ) Compatibility of films from blend solution ------ — -------------------- 29 I I I . RESULTS --------------- 32 A. Solution rheology ---------------------- 32 B. Film formation — ---------------------------------------------------- 42 C. Surface tension ----------------------------------------- 45 D. Compatibility ----- 45 IV. DISCUSSION ~ — --------- 53 A. Solution rheology --------------------------- 53 B. Film formation and com patibility of blends --------- 58 V. CONCLUSION 64 LIST OF SYMBOLS ------- 67 REFERENCES — --------- 70 MELT RHEOLOGY - SECTION B ABSTRACT --------------------------------------------- — — ------- 73 CHAPTER I. INTRODUCTION -------------------------------------------- 75 A. Melt viscosity ----------------------------- 75 B. Rheological concepts ---------- ^2 C. Effect of molecular weight ------------------------- 87 y TABLE OF CONTENTS PAGE D. Temperature effects — -------------------------------------------- 89 E. F ille d polymeric systems ------------------------------------------ 90 I I . EXPERIMENTAL -----------:----------------------- - .............. 94 A. Material ----------------------- — --------------------------------- 94 B. Melt mixing -------------------------------------------------------------------- 94 C. Testing --------- : ------------- 96 ( i) Molecular weight of copolymers ------------ 96 ( i i ) Composition of copolymers ------- 97 ( i i i ) Rheological behavior ------------------------------------ 98 I I I . RESULTS --------------------— -------------------------------------------------------- 104 A. Melt mixing ---------------- -------------------------------------------------- 104 B. Molecular weitht and molecular weight d istrib u tio n ------- 104 C. Composition — -------■ ------- — -------------------------------------- 108 D. Rheological behavior ----------- 108 IV. DISCUSSION ------ 125 A. Melt mixing — ---------- 125 B. Rheological behavior ----- 125 V. CONCLUSION ---------------- 150 LIST OF SYMBOLS ----------- 153 REFERENCES ------------------- 155 BIBLIOGRAPHY ---------- — ....................... 159 vi LIST OF FIGURES - SOLUTION RHEOLOGY FIGURE PAGE 1. Electrophotographic printing process ------------------------------- 2 2. Design of the dry release hot ro ll fuser ------------------ 3 3a. Flow phenotypes ---------------------------------------------------------- — ------ - 7 3b. Representative rheograms ----------■--------------- --------- ---------■ — 7 h. Generalized flow curve ^--------------;--------------------------- 9 5- Shear thinning behavior ------------------------------: - - - - ------------- 10 6. Boundaries for Couette flow --------- ------------------------------—----- 11 7. Coaxial cylinder and its characteristics ---------------------- 13 8. Light path in a Michelson Interferometer ----------------------- 22 9. Schematic interferogram of films --------------------------------------- 23 10. Reflection from a film covered interface ----------------------- 27 11. Contact angle measurement -v— ------------------------------------------- 30 12. Solution viscosity of V itel PE-200 and Acryloid A-10 resin as a function of shear' rate. Solvent - 1 ,1 ,2-trichloroethane ------ •— ----- 33 13. Solution viscosity of V itel PE-200 and Acryloid A-10 as a function of shear rate. Solvent - chloroform - - 3^ 14. Solution viscosity of V itel PE-200 and Acryloid A-10 resin as function of shear rate. Solvent - MEK ----- 35 15. Suspension viscosity of V itel PE-200 and Acryloid A-10 resin as function of shear rate --------- ■ ------- ■- 38 16. Temperature e ffe c t on viscosity of solutions and : suspensions of V itel PE-200 and Acryloid A-10 resin. Solvent - 1 ,1 , 2 - t r i chlo roe thane - - — ■ ------------------------------- 37 vi i LIST OF FIGURES - SOLUTION RHEOLOGY FIGURE PAGE 17. Temperature e ffe c t on viscosity of solutions and suspensions V itel PE-200 and Acryloid A-10 resin. Solvent - chloroform ----------------------------------------- 38 18. Temperature e ffe c t on viscosity of solutions and suspensions of V itel PE-200 and Acryloid A-10 resin. Solvent - MEK ------------------- : - — - 39 19. Flow curve for PMMA Col = 0.4 40 20. Flow curve for PMMA [ri] = 1 .4 41 21. DSC thermograms ------------------------------------------------------ 46 22a. Optical micrographs (varying w t. % PMMA) ------ 47 22b. Optical micrographs (etching) ------------------------------------- 63 vi i i LIST OF TABLES - SOLUTION RHEOLOGY TABLE PAGE 1 . Instrument constants for different.geometry -------------------- 14 2. Non-uniformity and optical thickness of films form polyester V itel PE-200, Acryloid A-10 resin and PVB resin -------------------- — ----------------------- 43 3. Optical thickness o f films from blends ----------------------------- 44 4. Optical thickness and non-uniformity of PMMA films ------ 48 5. Optical thickness and non-uniformity of PVB films -------- 49 6 . Refractive index and extinction coeficient for various resins — ---------:------ — ; ----------------- 50 7. Contact angle and surface tension of PMMA solution — 51 8 . Contact angle and surface tension of PVB solution -------- 52 9. S o lu b ility parameters for resins and solvents ---------------- 54 10, Effect of a suspension of glass beads on zero shear vi soci ty -------------------—------------- 56 11, Activation energy for d iffe re n t resins ----------------------- 57 12, Flow index ‘n 1 and consistency factor ‘ K1 for PMMA of varying--------------------------------------— — ---------------- 59 ix LIST OF FIGURES'- MELT RHEOLOGY FIGURE PAGE 1. Schematic representation of interrelationships among processing variables flow properties and chemical structure - — - - - - — ----------------- ■ ------------------------------------------- 76 2. Material behavior at d iffe re n t temperatures ----------------- 77 3- Representation of intermolecular chain entanglements 80 4. Representation of shearing action on molecular coil 80 5. Non-Newtonian viscosity model — - ----------------------------------- 84 6 . Two possible ways of variation of melt viscosity with molecular weight - — -----------—----- ;------- 88 7. Cone and plate geometry and corresponding flow character i.st ics -■— — ------------------- 1 00 8 . Capillary rheometer and its flow characteristics -------- 102 9a. Location of sampling points within chamber of an internal mixer ------------ — - — ----------- — - — ,------------------------ 105 9b. Optical micrographs showing carbon black dispersion 105 10. Vis.cosity-s.hear rate curves for PT-1200 as a function of temperature 111 11. Viscosity-shear rate curves for X-231 as a function of temperature -----— ---------------„------------------------------- 112 12. Effect of molecular weight of copolymer on viscosity 113 13. Effect of copolymer composition on viscosity (.XRP-70 and X-230) — t — — — — — ------------ --------------- 11 k 14. Effect of copolymer composition on viscosity (X— 211 and X-242) 115 15. Influence of carbon black loading on viscosity n of PT-1200 melt at 150°C (C-Black, SA-24 m2/gm). log n v/s log y --------------;-------------------------------------------------------- 117 x LIST OF FIGURES - MELT RHEOLOGY FIGURE PAGE 16. Influence of carbon black loading on viscosity n of PT-1200 melt at 150°C (C-B.lack, SA-95 m 2/gm ). log n v/s log y ----------------- — — --------------------------------------------- 118 17. Influence of carbon black loading on viscosity ri of PT-1200 melt at 150°C (C-Black, SA-525 m 2/gm ). log ri v/s log y ----------1 ------ 119 18. Influence of carbon black loading on viscosity r) of PT-1200 melt at 150°C (C-Black, SA-625 m2/gm ). log r) v/s log — -------------------------------------------------------------------- 120 19. Effect of carbon black surface area on melt viscosity of PT-1200 at 150°C (C-Black loading 5% by w eig h t). log n v/s log y ------------— -------------1 . —■------------------------ 121 20. Effect of carbon black surface area on melt viscosity of PT-1200 at 150°C (C-Black loading 10% by weight). log n v/s log y ----------------- 122 21. Effect of carbon black surface area on melt viscosity of PT-1200 at 1500C (C-Black loading 20% by weight). log r) v/s log y ----------- 123 22. Effect of carbon black surface area on melt viscosity of PT-1200 at 150°C (C-Black loading 30% by weight). log n v/s log t ----------------------------------------------------------------------- 124 23. Temperature dependence of PT-1200. log ri v/s 1/T 126 24. Temperature dependence of X-231. log ri v/s 1/T 127 25. log aT v/s T-Tq for PT-1200 131 26. log aT v/s T-T for X-231 — 132 I o 27. Master curve for PT-1200. log (a^h) v/s log (a^t) 133 28. Master curve for X-231 . log (a^ri) v/s log (a^f) 134 29. Reduced variable master curve log n/T| v/s log ri't for PT-1200 — - 138 x i LIST OF FIGURES - MELT RHEOLOGY FIGURE PAGE 30. Reduced variable master curve log (n/o ) v/s log (r) t) o o for X-231 ------------------------------------------------------- ------------------------- 139 31. Yield stress for varying carbon black loading. 2 (C-Black SA-24 m /gm). log n v/s log T --------------------- 140 32. Yield stress for varying carbon black loading. o (C-Black SA-95 m /gm ). log ri v/s log x -------------------------- 141 33. Yield stress for varying carbon black loading. (C-Black SA-525 m^/gm) . log ri v/s log T' ------------------------ 1 ^2 31 *. Yield stress for varying carbon black loading. 2 (C-Black SA-625 m /gm) . log ri v/s log x ------------------------- 1^3 35. Effect of surface area of carbon black on yield stress (C-Black loading 10%). log r) v/s log T ------------------------ 1^4 36. Effect of surface area o f carbon black on yie ld stress (C-Black loading 20%) . log r) v/s log x ------------------------ 1^5 37. Effect of surface area of carbon black on y ie ld stress (C-Black loading 30%). log rj v/s log x ------------------------ 1^6 x i i L i ST OF TABLES - MELT RHEOLOGY TABLE PAGE 1. Characteristics of carbon black -------- 9 5 2 . Molecular weight of copolymers ------ — ---------------------- 106 3. In trin s ic 'v is c o s ity o f copolymers - - ------------------------------------ 107 b. Composition of copolymers from elemental analysis -------- 109 5. Glass tran sitio n temperatures of copolymers by DSC — 110 6 . Activation energy for PT-1200 and X-231 129 7. Free volume parameters for PT-1200 and X-231 ----------------- 135 8 . S h ift factors for PT-1200 - - - — ------- 137 3, S h ift factors for X-231 — -------— ------------------------------- 137 10. Yield stress values for varying carbon black loading and surface area -— ------<— --------- ^ 7 x i i i SECTION A ABSTRACT (SOLUTION RHEOLOGY) We have studied the nature of polymer solutions, the effects of composition molecular weight and com patibility on film formation. This has involved measurements of the flow behavior of polymer solu tions and the development of optical techniques for determining the thickness and uniformity of films cast from solutions. Solution and suspension viscosities of polyester and acryloid in solvents such as 1 ,1 ,2-trichloroethane, chloroform and MEK revealed Newtonian behavior up to concentrations of 250 grams per l i t r e . Poly ester was more viscous than acryloid. Furthermore adding glass bub bles produced higher viscosity suspensions than solutions at the same concentrations whose activation energies were solely affected by the polymer species. The optical thickness of cast films from the polyester was more than that of acryloid film s. The power law equation was applicable to solutions of pure PMMA or PVB. The solution viscosity increased with molecular weight and the optical thickness of film s from PMMA or PVB solutions increased with the concentration and molecular weight. Surface tension effects on optical thickness were neg lig ib le. The com patibility of films from PMMA/PVB blend solutions were studied by d iffe r e n tia l scanning calorimetry and optical microscopy. The blends form an incompatible system above a concentration of 10% for e ith er component and phase inversion takes place at the blend ra tio 40/60 (PMMA/PVB). x i v I. INTRODUCTION (SOLUTION RHEOLOGY) A. Electrophotographic Process: The research described in this report is basic to an understanding of the commercial electrophotographic process with a high speed p rin te r (1,2) (Fig. 1). This process uses a photo conductor in the form of a fle x ib le film wrapped around a drum which rotates at a constant speed. The photoconductor is renewed by replenishing the film from a supply reel containing a solution of the photoconductor. The exposure of the photoconductor is performed by a laser beam which scans the original document and whose intensity can be modulated by an electro-acoustical modulator producing a latent image on the photoconductor. This image is developed by contacting a black polymeric powder (toner) in the p rin te r using a p arallel flow, dry toner, magnetic brush developer. The charged toner is transported to the image development zone and the developed image on the photoconductor is transferred onto the paper. This toned image is loosely held to the paper and permanent fusing is accomplished by applying the proper amount pressure and heat (F ig .2 ). We have studied the properties of the photo conductor and the fusion behavior of the toner. This involves examining the solution rheology of various binders used to carry the photoconductor and re la ting i t to film formation. The fusion process is studied by measuring the melt rheology of various toners. Subsequent chapters have there fore examined two basic aspects: The polymer solution coating process and melt rheology of toners. 1 Fuser ro ll Paper lo o p lensioner P o st-transfer , co ro n a t f T ra n s fe r 4 .. £ _ corona Erase P rrc lc a n Lamp corona V a cuum cham ber Preheat platen corona R o ta tio n Dev eloper assem blj Form s overlay u, P C supply P C taVc up Beam control StacVer H o pper (p a p e r s u p p ly) Laser M ir ro r Figure 1. Configuration of the electrophotographic p rinting process. 2 H o t r o ll T h in m M w r m a t tn j A lu m in u m tu h c o o S o fi ru b b c t c o a lin g Figure 2. Basic design of the dry release hot ro il fuser. 3 B. Solution Rheology (Couette): The behavior of polymer solutions can be considered according to the degree of interaction of the polymer with its enviroment (3). ( i) In f in it e d ilu tio n lim it . This is an ideal condition where the movement of polymer chains is analysed in terms of the superposi tion of a number of c o lle c tiv e motions of polymer molecules. The hydrodynamic flow fie ld is localized w ithin the region near the molecules and intermolecular interactions are ignored. Accord ing to Frisch and Simha (4 ), the in fin ite d ilu tio n lim it exists for concentrations, c, below which c (n )~1> where (ri) is the in t rinsic viscosity of polymer solution. The importance of in te r action between polymer and solvent at low polymer concentrations is well established. The impenetrable sphere form: "■ - % <r2 >3/2 (tl) . ^ < i ^ _ (,: c-*0 s relates in trin s ic viscosity, molecular dimensions and molecular weight for a wide varie ty of polymer/solvent systems. In theta 2 3/2 h solvents (ri)M/<r > remains constant (up to M~10 ). In good solvents it decreases as the molecular weight f a lls below the range M~103 ( 5 , 6) . ( i i ) Hydrodynamic screening l imit at in fin ite d ilu tio n : A polymer subunit experiences the presence of other subunits in the same chain through hydrodynamic interactions with solvents. With further increase in concentration the subunit experiences as well the hydrodynamic effects of neighboring macromolecules. This ; mechanism is expected to occur above a concentration defined by c[n] ^ 1. The exact value of concentration depends on the f l e x i b i l i t y of the polymer and the nature of the solvent. This effect is quite prominent until we reach a concentration corresponding to the lim it of close-packing of polymer c o ils , c [ (3) | The Huggins constant K was introduced to describe the e ffect of j interaction between polymer molecules on the zero shear viscosity. 1 2 2 1 no " ( 1 + y i] c + k [n] C + ............) Experimentally, K is essentially independent of molecular weight for long chain. * Values of K approximate 0.3-0.** in good solvents and 0 .5 -0 .8 in theta solvents (5.) . ( i i i ) Polymer-polymer contact region. The shear viscosity increases considerably once the c r it ic a l packing concentration has been exceeded. The motion of the polymer is dominated mainly by polymer c o i1-polymer c o i1 interactions. (iv) Polymer chain entanglement regions (5). Direct pol ymer-pol ymer interactions are observed in region ( i i i ) and entanglement | effects are extremely prominent above concentrations of the order of c t n l ^ l O . This is manifested due to interpenetration of the polymer coils and is associated with chain entanglements. For entanglement to occur the polymer must posses a molecular weight which is greater than a c r it ic a l value. Me. The precise value of Me is a function of the chemical nature of polymer chain and p a rtic u la rly of its f l e x i b i l i t y . (3 ) A variety of models: Necklace models (7,8) spring-bead 5 models and modifications of these have been empolyed to represent polymer chains and th e ir interactions with the surroundings. Equilibrium properties and certain very simple transport proper ties depend mainly on the radial d is trib u tio n of segments about the centre of gravity of the molecule. The p a rtic le cloud model was used to calculate the thermodynamic properties of random coils in d ilu te solution (9). When considering flow characterization it is necessary to examine a number of variables. The most general rheological equation is ri = F( y , T, t , P, c .........................) Additional factors include molecular parameters such as molecular weight (MW). Molecular weight d is trib u tio n (MWD), compositional variables and factors which relate to the processing history ( 10). The simplest relationship between viscosity and shear rate is im p lic it in defination of viscosity i t s e l f . T (2) “ T " Flow characterization involves measurement of T at various a rb i- tary values of y ■(or vice versa). Graphical representations of rheological behavior based on i/y curves are shown in Fig. 3a and 3b. These phenotypes are named Newtonian, pseudoplastic, d ila ta n t, p la s tic , Bingham and Ostwald. In pseudoplastic and d ila ta n t liquids the viscosity is no longer constant. In the former it decreases and in the la tte r i t increases with increasing shear rates. (10,11) . These two flows can be described by a S H EAS CflT£ i T Figure 3a Flow phenotypes S hear rafe q Figure 3b. Representative ( x , q) rheograms 7 power law equation T = K y n (3) The exponent n is greater than unity for d ila ta n t and less than unity for a pseudoplastic. A Bingham body is described by the equat ion x - t = nt • • •....................................... (*0 y' Below x " the material w ill not flow at a l l , hence f = 0 and y q = o o . All flow phenotypes form part of a general response pattern which may be summarized in a general flow curve (Fig k) . This flow curve can be derived in tu tiv e ly from the structural changes which may be assumed to occur in laminar flow with increasing shear rate. Most rheologically complex materials without a yield stress show shear thinning type of behavior (Fig. 3b) which is also called "pseudo-plastic" (12) . The viscosity decreases from zero shear viscosity n- to lower values with increase in shear rate 7 o Fig 5. The main fundamental flow patterns are couette flow and Poiseui11e flow. The former type is generated by the action of boundaries in re la tiv e motion. Typical examples of commonly used boundaries is shown in Fig. 6 (13). Plain couette flow is never f u lly realised in practice. Couette flow with c u rvilin ear flow lines becomes less appropriate for viscometric or rheometric work as the speed of rotation increases. This is because the pressure 8 t u r b u l e n c e / m e l t r c fic T TL’kE X*!LA1 a n t re g io n -£r X S £cu ^tgiO N A frV.'TlAL N'CWTONtAM L -' ceooN S H E A R C A T E — • ■ B U P T U 2 E S TR A 'IV -H A R D E N IN G ^ REGION t / " " V St CO N 'D CE&ION (- J>6A «V |M<) INITIAL HOO^EAN •DEGtON STCAIN • Figure k. Left: Generalised flow curve; Right: Typical fu lly developed stress-strain curve as found in tough plastics under appropriate conditions!. The conventional stress has been converted to the true stress. 9 Figure 5. Schematic diagram of typical shear-thinning behaviour. 10 s'* i-" \ / (a> ( b ) (c) Figure 6. Boundaries for Couette flow (a) PIane (b) Cylindrical (c) Spherical (cone and plate) 11 fie ld due to centripetal accelaration becomes important and also because secondary flows and, in the end, turbulence sets in. Therefore for high shear rate work use is generally made of Poi seui11e flow. Couette flow in curvi 11 inear geometry is frequently used for steady-state and dynamic experiments. I f T is the drive torque on the instrument and r is the re la tiv e rate of rotation of the solid boundaries, the shear rate and viscosity are given by the following formulae properties of polymer solutions is the couette, or concentric cylinder viscometer. This consists of a pair of coaxial cylinders arranged so that one of the cylinders can be rotated whereas the other is held fixed . The flu id to be tested is sheared in the gap between the cylinders. I f the ra tio of the radii of the two cylinders is very near unity the shear stress and shear rate are nearly uniform throughout the flu id 0 4 ) . . The characteristics of a couette or coaxialcylinder yisometer are seen i n F i g 7 0 1 ) . The physical components of velocity in the couette instru ment are assumed to be y = A Q(t) (5) n ( 6) Where A and B are instrument constants given in Table 1. A common viscometric instrument used to measure rheological v v 0 (7) r z 12 N \\\W \S R J i | COAXIAL CYLINDER o cr «r Ui Figure 7- Coaxial cylinder and it 's characteri sties 13 Table 1. Instrum ent co n sta nts A and B Constant Cone and plate Ring and plate Parallel plate Concentric cylinder (Cone angle, a 0 radius R) (Ring radii Ra>, 2 > , gap h) (Radius R , gap h) (Annulus radii 0(1). fl«>) (Liquid height hE) A 1 n/(Ra)R m) — (perimeter) h a o 2h (Geom. mean rad.) (g<2)~ g< d) (Geom etric mean) B 3 a 0 2 h 2 h (a a) — flfn) 2 7rR% 7T(K}-Ra>) 7rR4 (Newtonian only) 4rrofi)Q a)h£ Remarks Shear stress and shear rate approximately constant within the fluid sample Shear stress and shear rate approximately constant within the fluid sample Shear rate distribution known Shear stress distribution known 14 V e rw(r) (8 ) Where w is the angular velo city of the flu id about the instru ment axis. Assuming that the radius is small compared to the length, the rate of shear tensor has only r0 and 0r components, and these are rw1 (prime denotes d iffe re n tia tio n with respect to r ) . The stress system w ill in general be of the form The equations relating shear rate to experimentally measured quantities are valid when the inner and outer cylinders are concentric so that flow is a x ia lly symmetric. (15) . I f the inner cylinder is rotated, then secondary flow occurs e a r lie r as compared to outer cylinder being rotated for which the flow is stable up to very high speeds. Film Formation: The molecular weight and concentration of polymer solutions have noticeable effe c t on film formation and rheological properties. The demands on polymeric material for optimum performance is very pronounced in the area of protective coatings. I t is widely recognized that the solvent quality determines the chain configuration of macromolecules in solution. A considerable e f f o r t , both theoretical and experimental, has been directed toward the understanding of the adsorption of polymer films from solution onto a solid substrate. According to Silberberg (16) the thickness of a surface - p + p K Krr 0 (9) 0 0 "P phase is determined by the size of the molecules which constitute it and the range of forces between them. In macromolecular surface phases, therefore, the thickness is much larger than that for low molecular weight materials of sim ilar chemical consti tution . The adsorption of polymer molecules from solution onto a surface depends on two processes: the i n it ia l attachment of at least one segment to .the surface and susequent attachment of additional segments of the adsorbing molecule. The rate of in it ia l attachment depends upon the solution concentration and amount of unocccupied surface ( 17) . Cohen and Reich (18) have studied the orien tation of polymers cast from solution onto a glass substrate. The degree of ordering of chain elements is deduced from measurements of film b ire fringence, between the normal and p arallal directions to the film surface, as a function of film thickness. Examining the mole cular, as opposed to macroscopic, aspects of macromolecular adsorption onto surfaces we have three d is tin c t features playing an important role. These are: 1. Substrate properties; 2. Solution organization; and 3. In te rfa c ia l behavior of macro-j i molecules. In a review a r t ic le , in addition to the above three features, Hopfinger et al (19) gave a comprehensive summary of theoretical treatments for macromolecular adsorption. Optical Microscopy (20) : Optical, transmission and scanning(21 ,22) electron microscopy have played very prominent roles in charac te rizin g the morphology of polymers. In many cases successful microscopic analyses have depended on the use of specialized 16 sample preparation and observation techniques. The usual v a ria tions of optical microscopy are summarized below: (a) Transmitted lig h t: In transmitted 1ight microscopy, a collimated beam passes d ire c tly through the sample into the objective lens of the microscope. The magnified image, which may be further enlarged or inverted by intermediate optics, is viewed through the microscope eyepiece. Morphological features which scatter lig h t or give rise to optical density variations are v is ib le . The specimen should be appreciably thin so that an adequate amount of 1ight is transmitted. Surface, irre g u la ritie s and bulk features are usually observed due to the scattering of exiting beam. The basic disadvantage of th is method is that a very small depth, of fie ld is available when using higher powered objectives. Resolution is 1 united'by' the wavelength of the lig h t source. (b) Reflected lig h t. This is used to examine variations, in surface structure for opaque or thick specimens,. Illum ination is provided through the objective and only specularly reflected lig h t is allowed to reenter the o bjective. Contrast arises from variations in surface r e f l e c t i v i t y . To prevent excessive pene tra tio n of the surface by the incident beam and increase re fle c t i v i t y of the surfaces, it is advisable to sputter or vapour deposit a thin film of metal on the specimen. (c) Dark fie ld : I t can be carried out using e ith er transmitted or reflected lig h t. D irectly transmitted or reflected lig h t is prevented from entering the objective. Objects which re fle c t 17 ' or scatter lig h t are v is ib le against a dark background and marked gains in contrast are often obtainable. (d) Polarized lig h t. In this case the illum inating source is plane polarized before it impinges on the sample and a second polarizer is inserted in the reflected or transmitted beam. In most cases the two polarizers are crossed at 90° to each other and only those m aterials which cause a p a rtia l depolarization of the lig h t are v is ib le . Since c ry s ta llin e and oriented polymers are b ire frin g e n t, polarized lig h t microscopy is an important tool for examining such m aterials. (e) Phase Contrast: This has been most e ffe c tiv e ly applied in transmission. This technique depends on the fact that d i f - ferences in the re fra c tiv e indices of two transparent regions produce small phase sh ifts in the lig h t exiting from each com ponent. These phase differences are converted to intensity variations in the observed image. The intensity variations are propotional to optical path variations in the object. Trans parent two-phase systems whose components have s ig n ific a n tly d iffe re n t re fra c tiv e index are most suited for this technique. (f) Interference Contrast: Monochromatic.1i g h t ’from-a single source is divided by use of a beam s p lit t e r . One beam is re flected or transmitted through, the sample and then recombined with the reference beam. Contrast results d ire c tly from in te r ference of the two beams. Quantitative measurements of path length, differences are possible. 18 CHAPTER I I EXPERIMENTAL DETAILS A. M aterial: Solution Rheology and film formation of polyester resin Vitel PE 200 and Acryloid A-10 resin was examined. Further more, poly (methylmethacrylate) (PMMA) ( (r|] = 0.4 and 1.4, poly sciences, Inc.) and poly (vinyl b u tyral) (PVB)(MW = 225,000, s c ie n tific polymer products, Inc.) with d iffe re n t molecular weights were examined since the base polymer of Acryloid A-10 resin was PMMA. Three d iffe re n t solvents v iz . 1 ,1 ,2 -tric h lo ro e - thane, chloroform and methyl ethyl ketone were used for Acryloid A-10 and Polyester resin. However, for PMMA and PVB, 1 ,1 , 2 - t r i - chloroethane and tetrahydrofuran (THF) were used as solvents. Glass suspensions in polyester resin V itel PE 200 and Acry loid A-10 resin solutions were prepared by adding 38-43 y sized glass bubbles to each polymer solution by 15 vol. %. B. Film Formation: Films of various polymers were obtained by a slow solvent-evaporation casting technique. Thin films were cast onto glass slides from d ilu te homogenous solutions, and then c arefu lly dried under a steady stream of a ir at room temperature. Film thickness was controlled by varying the concentration of solution and inclination angle of the microslides. C. Testing: (|) Solution Rheology: (Couette Viscometry) the Weissenberg 19 Rheogoniometer (Model R19D, Sangamo Weston Controls, Ltd.) was used to measure the viscosity. Proper alignment of the inner and outer cylinders is important in order to have a uniform shear rate throughout the entire volume of f lu id . The radial gap is 10% of the radius of the platen. The p a rticu la r advantage of the "couette" cylinders is that they can produce a greater torque in the torsion head, for a given shear rate in the sample and this can be p a rtic u la rly useful when working with thin flu id s . A further advantage is that the centrifugal force may be less troublesome at the higher rotational speeds. The equations for the couette viscometer geometry are as follows (23): ft R, Shear r a t e , f = .........-............ (10) 2 " " 1 kt AT Shear Stress, T = ----------- 5----------- 2 it R j h (11) Kt AT (R„ - R.) Viscosity, ri = ------------= —--------------------— .(12) 2 tt R^ h Q The same "Couette" cylinders were used to measure viscosity of suspensions of glass bubbles. (38-A3]i) in polyester resin v ite l PE. 200 and Acryloid A-10 resin. i i ) Optical thickness and re fra c tiv e index - Interferom etry; The uniformity and optical thickness can be measured with a Michelson Interferometer. Light from the source L (see Fig, 8) , incident on the plane p aralle l p late, divided into two beams, the axis of which fa ll normally on the mirror A^ and The re- 20 fleeted beams are reunited at the semi ref 1ecting surface of p. The Interference pattern can be viewed d ire c tly on the screen (18,24), When the mirrors A.j and A£ are perpendicular and A^ is slig h t ly closer than the image of A^ w ill fa ll in front of at I position A j , and a series of interference rings w ill be seen. When the mirrors are equidistant and perpendicular, no in te r fe r ence w ill take place. When the surfaces A^ and A2 are not exactly parallel and the difference in th e ir distance from P is very small, a series of fringes, which are almost straight lines w ill be seen. He-Ne laser (A ■ = 6238A) is used as a lig h t source, L. When a film coated on the microslide is placed normal to the lig h t between the beam s p lit t e r P and mirror A^ and a sim ilar microslide without film is placed between P and mirror A2 as a compensator (Fig. 8) an interference pattern of coated films can be seen on the screen. Mirror A2 can be moved back and forth by adjusting the micro meter attached to i t . Thus, by adjusting the notch on the micro meter, the shifted fringes representing the film surface can be moved to coincide with the base line (Fig. 9 ). The optical path difference due to the film can be obtained d ire c tly by reading the movement of the notch (1 division movement of notch corres- h 0 \ ponds to 2x10 A movement of mirror A-^) consequently optical thickness can be obtained by dividing optical path difference, 2n'd, by two. 21 SCREEN Figure 8 . Light path in Michelson interferometer. 22 Base fine Figure 9. Schematic interferogram of films i 23 The sh ifts of interference fringes are due to the coated film s, and the shifted fringes represent the state of the film surface. The maximum nonuniformity of the film is defined as El 1ipsometry: Ellipsometry involves the re fle c tio n of mono chromatic, collimated polarized lig h t. The state of polarization is defined by the phase and amplitude relationships between the two perpendicular components of plane waves. I f P and S compo nents are in phase, the resultant wave is plane polarized. A difference in phase other than 1800 corresponds to e llip t ic a l polarization. In general, re flec tio n causes a change in the re la tiv e phases of the P and S waves and a change in the ra tio of th eir amplitudes. Thus the e ffe c t of re fle c tio n is characterized by the angle A , the change in phase, and the angle ip, the arctang ent of the factor by which the amplitude ra tio changes. I f the amplitude of the incident and reflected beams are designated E and R, respectively and the phase angle, & ellipsometry involves the measurement of A and ip. The relationship between A and \p, is expressed by Fresnel re flec tio n c o efficie n ts . The Fresnel re flec tio n c o e ffic ie n t, r, of an interface is the ra tio of the e le c tric fie ld vector, R1, of the reflected wave to that, E ', of incident wave; in terms of Y/X (Fig. 9). (13) (14) the amplitudes of the incident and reflected waves. E and R, res pectively, and the phase change, B , accompanying re fle c tio n (25, 26) the relationshep is given by; Rl _ R e ' P tic \ r “ g | “ ' £ i I I « < I • I ( I t r « f * ! . * \ „ l P / Reflection of a wave of ahy p o larization is described by the two co efficien ts r and r , so that the ra tio of these re flec tio n 5 P co efficien t is r R E i( B - B) - E = _ £ • _1 . • e P 5 . . . . . . . . . . . . . . . . . . . . . ( 16) r R t. s s . p By use of equation .(.13) and (14), equation (.16) can he sim plified to r s The Fresnel c o efficie n t of a substrate with a surface film can be derived by considering the interference between the beams resulting from re flec tio n in the film . Figure 10 shows the f i r s t three of the in f in it e number of reflected beams. Beam 1 is d i r ectly reflected . Beam 11 is transmitted through the ambi.ent- film interface. Each of these reflections and refractions a ffect the re la tiv e amplitude and phase of the beams, arid in addition, a phase change -2 6, re la tiv e to beam 1, results from double t r a versal of the film of thickness d, where 6 = 2 S i.n<(>j) 2 degree .., . . . . , , ,, (18) for an o p tic a lly isotropic film , the Fresnel re flec tio n c q e ffi- 25 c ie n t are p n^Cos4>2 " n2C os<J)1 r 12 rijCos.(^2 + n2Cos(j)j s rijCos^ - n2Cos(()2 ........................... ^20^ r 12 n^os^-j + n2Cos$ 2 The subscripts 1 and 2 refer to the media bounding the reflectin g interface;'(f)^ is the incidence angle and < j>2 is the refraction angle. For an o p tic a lly absorbing medium, the complex index of refract ion, n-1 = n1 - ik ......... . . ( 21) is substituted for n in equation ( 19) and ( 20) . k is the extinc tion c o e ffic ie n t, for an o p tic a lly non absorbing medium k becomes zero. For the film covered substrate (Fig. 10), the fundamental equation of ellipsometry is: ./ P P -21 §1 /. A s s - 2 i & ^ , iA 12 r 23 6 ^ 12 23 6 ■ . . . . . . ( 22) tanij;e = ----------- ■ -------------------------> ------; — --------------------- ' ■ /1 P P -2 i & ( s ^ s - 2 i 6\ 12 r 23 6 12 r 23 8 ! Thus, for an o p tic a lly absorbing film covered substrate, four Fresnel co efficien ts, r^* rj2 ’ r23* rT2 anc* ^ can * 3e exPressed as follow: s (n2 - ik2)Cos^ 2 - (n^ - ik ^ C o s ^ (23) r 23 (n2 - ik^C os1 ^ + (n^ - ik ^ C o s ^ m M ed iu m z f(LKl Figure 10. Representation of re flec tio n from a film covered interface. (rtj - ik 1)Cos< |)1 - (n2 - ik2)Cos<J> 2 r 12 ~ ( n 1 - i k ^ C o s ^ + (n 2 - i k 2 ) C o s f 2 (24) J 3 (n0 - ik-JCos^., - (n, - ik,)Cos(f> 0 oo — , ^ * _____ri— (n2 - ik 2)Cosv^ + (n^ - ik ^ C o s ^ p (n, - Ik 1)Cos< } )0 - (n0 - j'iLHos'K I I C m ' C m C m I / A / \ r 12 (rij - Ik 1)Cos4>2 + ("n2 - ik 2)Cos<f>1 6 = d ((n 2 - ik2) - (n2 Sin2^^)5) -....................... (27) By substituting equation (23), (24), (25), (26) and (27) into equation (22), A and ip can be obtained e x p lic it ly as functions of the angle of incidence, vacuum wave length of lig h t, optical con stants of film and substrate and thickness of the film . Since angles of incidence and refraction are related by S n ell's law, Cos^ 2 and Coscj> 3 are: C o s 2 = (1 - C ^ y - .^ 2 ) ~2 Sin2^ ) 4 . ( 28) C oscJ)3 = (1 - ( n" '— i k3- ') " 2 ....................................(29) The A and ^ measurements for each polymer film on the micro slides was carried out by use of a Rudolph Research Model RR 2000 automatic el 1ipsometer. Equation (22) can be resolved into real and imaginery parts giving us two d is tin c t equation. However, we have 3 unknowns, n2 , k2 and geometrical thickness d2> The thickness (n2d) is obtained by interferom etry. The two d is tin c t equations obtained from equation (22) when augmented with interferometry results 28 w ill enable us to compute numerical values of n2? k2 and d^. ( i i i ) Surface tension: To elucidate the effe c t of the surface tension and contact angle of polymer solutions on the thickness of film s, the surface tension of solutions was determined by use of de Nuvy tensionmeter (Fisher Co.) and the contact angle, was measured by use of pendant drop method (Cenco Instrument Co.). in applications where printing or imaging is performed by depositing drops or pools on papers or other substrates, it is important to know how the liq u id interacts with the paper. I f a small drop of polymer solution is placed on a microslide, i t w ill not spread completely over the surface, but its edge w ill make an angle with the microslide (Fig. 11), The contact angle is mea sured as the tangent of the angle formed between the liquid drop and its supporting surface (27). The formulae' used in calcula ting in te rfa cia l tension components are based on the equation of thermodynamic wetting of a solid by a liq u id , as described by the wellknown Young's equation (neglecting the equilibrium pressure of the adsorbed vapour of the liquid on the sol i d ) . y 7 Cos© = y " Y ................................................................... (30) 1 I v 1sv 1S| Now y - Y and y ~ Y 1 sv 1 s i v ■ 1 , Now equation (.30) reduces to: Y = Y + T Cos0 , . . . , . , . . . . , , . . , , . , , , , , . , , . , , . , , , . , ( 3 1 ) S S q ‘ t (iv ) Compatibi1ity of films from PMMA/PVB blend solutions: Films of blends of PMMA ((n)=1.^) and PVB (MW-32k) of varying compositions were obtained by a slow solvent-evaporation techni- Figure 11. Drop of polymer solution resting on microslide que. The thin film s were cast onto glass slides from d ilu te homogeneous solutions (cone, 5gm/1). in 1, 1 , 2-trich lo reth an e. Glass tran sitio n temperatures of the resulting films was measured by using a d iffe r e n tia l scanning calorimeter (Model DSC2, Perkin Elmer Company). Furthermore, optical micrographs were taken by use of a Unitron polarizing optical microscope. 31 CHAPTER 11 I RESULTS A. Solution Rheology. 1. Solution Viscosity for PE Resin V ite l PE 200 and Acryloid A-10 Resin: Shear rate effects on viscosity of PE resin and Acryloid A-10 resin in 1 ,1 ,2-trichloroethane, chloroform and MEK at constant temperature is shown in Fig. (12), Fig. (13) and Fig. (1*0 respectively. Concentrations of 250 g/1 and 500 g/1 were examined. The maximum shear rate attained was 22 sec 2. Suspensions: The e ffe c t of shear rate on viscosity for a suspensions of glass beads (38-43u) in solutions of concentration 250 g/1 of PE and Acryloid A-10 resins in 1 ,1 ,2-trich lo ro eth an e , chloroform and MEK can be seen in Fig. (15). 3. Temperature dependence of viscosity for PE Resin V ite l PE 200 and Acryloid A-10 resin: The e ffe c t of temperature on the viscosity of solutions and suspension in 1, 1,2-trich io ro e th an e, chloroform and MEK is manifested in Fig. (16) , Fig. (17) and Fig. (18) respec tiv e ly . The viscosities are measured at a constant shear rate 4.1 sec ^. 4. Viscosity of Pure PMMA: The flow behavior, log shear stress (t ) against log shear rate (y ), for solutions of d iffe re n t concen trations of PMMA-[ri]= 0.4 and [n] = 1.4 (varying molecular weight) in 1 ,1 ,2-trichioroethane is depicted in Fig. (19) and Fig. (20) respectively, 32 10 - o < L > c n < u Q_ >. < /) O u t f ) o - -© - £ r A A & - --------- j^T------ A — 4&r A i o ' A * Figure 12. lc f Shear rate y(sec l o 1 Solution viscosity as a function of shear rate at 22°C.(— ) Polyester V ite l PE-200; (----- ) Acryloid A-10 resin. Solvent Concentration: o - 5 0 0 g /l; A - 250g/l 1,1,2 •trIchloroethane. i 0Q © - © - ■ O 0 ■ —" 0 — — — -0 —- — - _ — Q — - - - - a — o 0) (/) ro C L >- 4 - J (/) O o tn a . A A A- A - A A . A . A A l o 1 r l 10 Figure 13. 10’ Shear rate t (sec VjO -t- Solution viscosity as a function of shear rate at 22°C. (■ — ) polyester v it e l PE 200; (— -) Acryloid A 10 resin. Concentration: ® - 500g/l; A - 250g/l. Solvent: Chloroform. -e © o a ) in in O U in > ■ * - -£s---------■ & — A - A - - A - - Concentration © - 500 g/1 A - 250 g/1 10; 1 ° Shear rate t (sec ) Figure 14. Solution viscosity as a function of shear rate at 22°C. v ite l PE 200; ( - - - ) Acryloid A 10 resin. Solvent: MEK. (— ) Polyeste Viscosity r| (Pas.sec) 10° io -1 ©---------------- - e — ■ — ©--------------- — e - -------- 0 ------------ — © — ------© © - — - - - o — — O--------------- —© - - - ^ ---------- — n □ .._ *c a ------------ ------ g — — a 3 ---------------- H ---------------- h ____a,— ------ A A --------------- - A - - — A -------------- - A - — a ------------------A --- — -A 1 0 '2 Solvent o - 1 , 1, 2-trichloroethane; © - Chloroform; e - Methyl ethyl ketone. _L 10 -i ) io 1 O ' 10° Shear rate t (sec Figure 15. Suspension viscosity as a function of shear rate at 20°C. v ite l PE 200; (----- ) Acryloid A 10 resin. Concentration: (— ) Polyester 250g/l. Q _ > ' -€)■ © - Polyester resin v ite l PE-200; • - Acryloid A-10 resin. io 1 3*3 3 5 Figure 16. Temperature effects on viscosity. (— ) Suspension; ( — ) Solution; Solvent: 1 ,1 ,2-trichloroethane. © - Polyester resin v ite l PE-200; CL. > Figure 17. Temperature effects on viscosity. Tempe rat U J CO (— ) Suspension; ( — ) Solution; Solvent: Chloroform. V a J U > Polyester resin v it e l PE-200; Acryloid A-10 resin. (S ) ~ -Q •M 3 - 5 0 Figure 18. Temperature effects on viscosity. (— ). Suspension; ( — ) Solution; Solvent: MEK. 350 g/1 250 g/1 m C L 150 g/1 e in u < 0 < U JC co * ° Shear rate Figure 19. Flow curve for PMMA ( [ril = O.k) . sec Solvent: 1 ,1 ,2-trich lo ro eth an e. Temperature: 17.8 0 C. 350 g/1 150 g/1 250 g/1 H IS ) (/> < U J - fl3 a ) JZ C O 10 - — - JqT Shear rate Figure 20. Flow curve for PMHA (£n 3 = 1 . 4 ) . Solvent: 1 ,1 ,2-trich lo ro eth an e. Temperature: B. Film Formation. 1. Optical thickness and non uniformity of films of Polyester Resin V itel PE-200, Acryloid A-10 resin PVB resin and th e ir blends: The e ffe c t of concentration on optical thickness, of films cast on microslides by the solvent evaporation technique, is shown in Table 2. Very concentrated solutions were not used because they produced non-uniform film s. Table 3 gives the optical thickness as measured by in te rfe ro - metry of films obtained from blends of PE resin with Acryloid A-10 resin, Acryloid A-10 resin with PVB and PVB with Polyester Resin V itel PE 200. The concentration of blend solutions was 25 g / 1 . Various blend ratios were examined and f in a lly the film thickness of pure homepolymers at the same concentration (25 g /l) and i n c li nation angle ( 17.92 degrees) was also obtained. 2. Optical Thickness and Non Uniformity of Pure PMMA and PVB: Table (A) and (5) manifest the combined e ffe c t of Molecular weight and concentration on the optical thickness as measured by films of PMMA (1 ,1 ,2-trichloroethane-solvent) and PVB (Tetrahydrafuran- solvent) respectively. 3. Optical Constants and Geometrical Thickness of Films, from Poly ester Resin V itel PE-200, Acryloid A-10 resin and Poly Vinyl Butyral Resin: The extinction c o e ffic ie n t, re frac tiv e index and geometrical thickness from ed1ipsometry are calculated in Table (6). The el 1i psometry results when combined with the i nterferometry data (Table (2.)_) enabled us to calculate the optical constants and geometrical thickness. kl TABLE 2 Non-Uniformity and Optical Thickness of Films from Polyester V itel PE 200*, Acryloid A-10 resin* and PVB resin** (Samples sent by 1BM) . Resin Concentrat ion (g /1) Optical Thickness d ) Max imum Non-Un i formi ty (%) Polyester Resin V itel PE 200 6.125 12.5 25.0 50.0 2,000 ± 200 4,000 ± 200 7,500 ± 500 12,500 ± 500 30 ± 5 27.5 ± 2.5 10 ± 2.5 15 ± 5 Acryloid A-10 Resin 6.125 12.5 25.0 50.0 1,500 ± 500 2,250 ± 250 4,750 ± 750 10,500 ± 500 35 ± 5 30 ± 5 17.5 ± 7.5 30 ± 5 PVB Resin 6.125 12.5 25.0 50.0 1.750 ± 250 2.750 ± 750 4,500 ± 500 9,000 ± 1 ,000 30 ± 5 25 ± 5 20 ± 5 35 ± 7.5 Solvent: 1 ,1 ,2 - t r ichloroethane * Inclination Angle: 8.85 degrees * * Inclination Angle: 21.5 degrees 43 TABLE 3 Optical Thickness of Films from Blend Solutions.* Blend Blend Ratio Optical Thickness Solut ion (by weight) (A) Polyester Resin 20/80 ! 3,500 ± 500 V itel PE 200 40/60 4,670 ± 440n Acryloid A-10 60/40 5,250 ± 750 Res i n 80/20 5,750 ± 380 Acryloid A-10 20/80 5,830 ± 390 Resin/Polyvinyl 40/60 4,930 ± 90 Butyral 6o/4o 4,330 ± 220 80/20 3,830 ± 220 Polyvinyl 20/80 5,800 + 20.0 Butyral/Polyester 40/60 5,850 + 850 Resin V itel PE 200 60/40 6,000 ± 750 80/20 6,500+500 Polyester Resin V itel PE 200 5,800 + 300. Acryloid A-10 Res i n 3,670 ± 220 Polyvinyl Butyral -■ 7 ,8 3 0 + 5 6 0 * Solvent: 1 ,1 ,2-trichloroethane Concentration: 25.0. g/1 lnclination Angle: 17.92 degrees C. Surface Tension: The variation of surface tension with molecular weight and concentration for PMMA ( 1 ,1 ,2-trichloroethane solvent) and PVB (Tetrahydrofuran-s.ol vent) solutions can be infered from Tables (.7) and (8) respectively. D . . Compatibility: The com patibility of films of Pure PMMA/PVB blend solutions can be seen in the DSC Thermograms Fig (21). A single glass tran sitio n temperature (Tg) gives us an indication of a homogenous compatible blend. Incompatible blends manifest two ig 's . Phase separation or heterogenity in PMMA/PVB, blend system as examined by optical microscopic technique. Optical (at a magni ficatio n of lQx) micrographs of thin films of PMMA/PVB blends casted from d ilu te solutions in 1 ,1 ,2-trichloroethane of the com positions 10., AO, 70 and 90 PMMA weight percent are shown in Fig 22. i ^5 u SO/40 °Oo D\ ~9JiCe 4 o ^ -^ - U ^ D S C 60 80- '* _ [ B m /s n l ^ f ° ^ > 5 ' 120 Uo Uo 180 | i n ! ] n i i j j | i i i i j n i i | n n | ; l u j n Y j i l M j l ' i ’j Figure 22a. Optical micrographs of PMMA/PVB blends (wt. kl TABLE 4. OPTICAL THICKNESS AND NON-UNIFORMITY OF PMMA FILMS* V In trin s ic \ Viscosity 0.2 0.4 1.4 Concentrat ion (g /1) Opt ical thickness 0 (A) Maximum non-un i - formity (%) Opt ical th ickness 0 (A) Maximum non-un i - formi ty (%) Opt ical th ickness 0 (A) Max imum non-un i - formity U ) 12.5 25.0 50.0 1 ,200±230 2,5001250 4,0001100 10 +2.5 15 +5 17.517.5 1,600+270 4,700+150 1512.5 20+5 1,8001350 4,5001500 9,000+500 17.5+5 ■ 20 12.5 27.512.5 * Solvent: 1 ,1 ,2-trichloroethane Inclination angle: 17.92 degrees 48 TABLE 5. OPTICAL THICKNESS (A) AND NON-UNIFORMITY (%) OF PVB FILMS* \ Molecular \ weight 32,000 125,000 225,000 c _ - \ tr a t ion \ ( g / 0 \ Optical thickness (A) Maximum non-un i - formi ty {%) Opt i cal thickness (A) Maximum non-un i - formity a ) Opt ical thickness 0 (A) Maximum non-un i - form i ty (*) 6.25 12.50 25.0 1,500±250 2 , 000±50 3,200±230 15 ±2.5 17.5±2.5 20 ±5 1 ,800±230 ^,7001230 a 17.5 ±5 30 ±7.5 3,100±300 5,000±330 a 20±5 35±5 Solvent: tetrahydrofuran Inclination angle: 17.92 degrees a: film formation is too bad to measure TABLE 6 Refractive Index, Extinction Coefficient and Geometrical Thickness of Films from Polyester Resin V itel PE 200*, Acryloid A-10 Resin* and PVB Resins.** i Res i n Concentration n2 k2 d2 (0/ 1) (fo Polyester 6.125 1.53 .0.00 1,310 Resin 12.5 1.51 0.02 2,660 V itel PE 200 25.0 1.50 0.00 5,000 50.0 1.58 0.00 7,920 Acryloid 6.125 1.47 0.00 1 ,020 A-10 Resin 12.5 1.46 0.03 1,540 25.0 1.47 0.00 3,230 50.0 1.48 0.00 7,070 Polyvinyl 6.125 1.50 0.015 1 ,170 Butyral 12.5 1.51 0.0106 1 ,820 25.0 1.51 0.00 2,980 50.0 1.48 0.0075 6,060 Solvent: 1 ,1 ,2-trichloroethane * Inclination Angle: 8.85 degrees **ln c lin a tio n Angle: 21.5 degrees 50 TABLE 7. CONTACT ANGLE(DEGREE) AT THE INTERFACE OF PMMA SOLUTION DROPLET* AND GLASS, AND SURFACE TENSION (dynes/cm)**OF PMMA SOLUTION In trin s ic Vi scos ity Surface tens ion Surface tens ion Contact angle Contact ang le Surface tension Contact angl e Concen- t r a t ion (g /1 ) (degrees) (dynes/cm) (dynes/cm) (degrees) (dynes/cm) (degrees) 6.25 35.1 35.0 9.25 35.20 35.0 10.05 10.25 25.0 50.0 * Solvent: 1 ,1 ,2-trichloroethane * * Surface tension of 1 , 1 ,2-trichloroethane solvent: 35.0 dynes/cm 51 ! TABLE 3. CONTACT ANGLE(DEGREE).AT THE INTERFACE OF PVB SOLUTION ! DROPLET* AND GLASS, AND SURFACE TENS I ON(dynes/cm)**OF PVB ! SOLUTION Molecular we ight 32 ,000 125, 000 225,000 Contact Surface Contact Surface Contact Surface Concen- angl e tens ion angle tension angl e tens ion tratIon Yi ^1 (g/1) (degrees) (dynes/cm) (degrees) (dynes/cm) (degrees) (dynes/cm) 6.25 8,75 22.8 9.5 23.0 11 .0 22.8 12.5 1A. 0 23.0 14.5 23.2 15.5 22.8 25.0 17.0 22.8 19.75 23.0 21 .5 22.8 50.0 22.0 23.8 — 23.1 — 23.0 • * Solvent: tetrahydrofuran * * Surface tension of tetrahydrofurn solvent: 22.0 dynes/cm I ! 52 CHAPTER IV DISCUSSION Solution Rheology: from F ig .12, 13 and lA it is evident that the non-Newtonian e ffe c t is prominent only when the concentration is as high as 500 grams per l i t r e . The inception of shear thining in a ll the cases is between shear rates of 2.5 to 2.8 sec Solu tions with concentration 250 grams per l i t r e are Newtonian fluids i.e . no change in viscosity with increase in shear rate. The viscosity of polyester resin V itel PE 200 solution is always greater than that of Acryloid A-10 resin. Futhermore solu tion dissolved in 1 ,1 ,2-trichioroethane solvent are the most viscous, while solutions dissolved in MEK solvent show lowest v is cosity. The s o lu b ility parameters of polyester V itel PE 200 [28] and Acryloid A-10 resin along with the three solvents used is given in Table (9 ). MEK which has moderately H-bounded group [29.j seems to be the least compatible solvent. For concentrated solutions, the intermolecular chain entangle- I rnents which control the magnitude of the viscosity undergo shear- induced changes which causes, a decrease in viscosity with increa sing shear rate. Graessley has proposed a scheme which makes it possible to represent the e ffe c t of entanglements by having an ad ditional term in the segmental fr ic tio n c o e ffic ie n t, and to pro perly incorporate the effects of polymer concentration, molecular weight d is trib u tio n , and shear rate in the fin a l result (30). 53 TABLE 9. S o lu b ility Parameters ( 6 ) For Polyester, Acryloid 1,1, 2-Trichloroethane, Chloroform and MEK Solvent S o lu b ility Parameter 6 Hydrogen Bounded 1,1,2 Tr ichloroethane 9.6 Poor Chioroform 9.3 Poor MEK 9.3 Moderate S o lu b ility Parameter Range Polymer Poor Hydrogen Moderate Hydrogen Bounded Solvents Bounded Solvents Polyester 9.2 - 11.1 8.5 - 11.1 Acryloid 8.7 - 9.9 8.9 - 12.1 5k The increase in viscosity by incorporating glass beads (15? volume) in polymeric solutions of Polyester resin V itel PE-200 and Acryloid A-10 resin in d iffe re n t solvents as infered from Table 10 is very sim ilar to the general behavior of suspensions. The addi tion o f glass beads to the polymer solutions has not introduced any non-Newtonian e ffe c ts . The viscosity of a suspension of spherical particles* has been investigated in great d etail by Goldsmith and Mason (31). and several other authors have trie d to develop models based on the Einstien equation (32-35). The temperature dependence of Viscosity as shown in Fig 16, 17 and 18 follows the Arrhenius equation, q = A exp (-E/RT) . . . . . . . . . . . . . . . . . . . . . (*t3) The activation energy at constant shear rate, E ^ , can be obtained from the slope of each curve. From the values of E . Y from table 11, it seems that the activation energy was not affected by solvents in solution or suspensions but solely by the polymer species. Furthermore, the temperature dependence of poly ester resin v ite l PE-200 is much greater than that of Acryloid A-10 resin (higher E ^ values). The flow curve for pure PMMA (log t v / s log y - Fig 19 and 20) is 1 inear and obeys the power law equation. t = K y n (kb1 The n and K values along with zero shear viscosities are tabula ted in Table (12). PMMA with, in trin s ic viscosity of Q.*t exhibits Newtonian behavior (n. - l) for a ll concentrations since flow index is between 0.95 and 0.99. For the case of PMMA with in trin s ic 55 TABLE 10. Ratio of zero shear viscosity of Suspension ( r i ) and solution ( n ) o Sol vent n . / n o suspension o solution Polyester V itel PE-200 Acryloid A-10 1 ,1 ,2-Trichloroethane 1 .48 1.46 Chloroform 1 .26 1 .20 MEK -cr C M 1.18 56 TABLE 11 Activation Energies (J/mol) j . . _ ------------------------------------------------- ... ^ S sns^ State P o lym e r\. Species SOLUTION SUSPENSION 1,1,2 Tr i ch loroethane Chioro- form MEK 1,1,2 Tr ich 1oroethane Chloro form MEK Polyester Resin V itel PE 200 32.4 27.1 28.0 32.1 30.6 26.9 Acryloid A-10 Res i n 13.1 13.7 10.9 10.7 15.8 12.5 57 viscosity 1.4 and concentration 250 and 150 grams per l i t r e , the behavior is nearly Newtonian (n = 0.95 and 0.972). However, for low shear rates the solution with concentration of 350 grams per l i t r e does exh ib it Newtonian behavior, but for shear rates exceed ing 0.41 sec ^ we have non-Newtonian behavior and the flow index | is 0.78. For PVB of high molecular weight (225 K) the non-Newtonian behavior is manifested for a concentration of 100 grams per l i t r e . The zero shear viscosity of PVB is 10.1 pa sec as compared to 20.1 pa sec for PMMA Cnl = with a concentration of 350 grams per 1i t r e . B. Film Formation: The optical thickness of film increases with an increase in concentration at a constant inclination angle, the optical thickness of polyester resin V itel PE-200 is greater than that of Acryloid A-10 (Table 2 ). Solution rheometry results show that polyester resin is more viscous than Acryloid A-10 resin hence it is appropriate for it to have greater thickness. Solutions with a concentration of 25 grams per l i t r e produce uniform film s. Thus at a concentration Of 25 grams per l i t r e , the optical thickness of the blend solutions was measured (Table 3K PVB solutions were very viscous and did not flow eas ily, hence, the angle of inclinp- I tion of the, micros 1 ides was changed from 8.85 degrees to 21 .5 i degrees. For the blend solution of polyester Vi tel PE-200 and Acryloid A-10 resin, the optical thickness increased with increase in con- 58 TABLE 12 Values of flow index, n (dimension 1 ess) and consistency n-2- index, K(-2—1 —------) for PMMA solution in 1,1 ,2-Trichloroe- , cm ’ thane solvent at 17.8°C. \ Concentration \ ( g / i ) \ 150 250 .350 In trin s ic \ viscosity [ n } \ n k n k n k 0.4 0.99 0.582 0.975 1.718 0.95 4.519 \.k 0.972 6.76 0.95 46.77 0.78 154.88 \ Concentration \ (g /D In trin s ic \ viscosity [n ] \ 150 Zero Shear Viscosity ri (Pas.sec) 250 Zero Shear Vi scosi ty ri (Pas.sec) 350 Zero Shear Viscos ity n (Pas.sec) 0.4 0.0637 0.130 0.5025 1 .4 0.747 6.210 18.874 59 tent of polyester resin v ite l PE-200. Furthermore, at the blend ra tio of 20/80 and 80/20 the optical thickness for each of the blend solution almost approaches that of pure Acryloid A-10 resin and pure polyester V itel PE-200 resin (Table 3). A sim ilar tendency was observed for Acryloid A-10 resin/PVB blend solutions and PVB/Polyester V itel PE-200 resin blend solu tions, PVB is more viscous than the other two polymers ie. Poly ester and Acryloid. When the inclination angle is increased, the optical thickness decreases because the solution flows more rapidly. The optical thickness for pure PMMA and PVB increases with increase in concentration of the solution and increase in Molecu lar Weight of the polymer. However, the e ffec t due to increase in Molecular Weight is considerably less as compared to that due to increase in concentration (Table k and Table 5 resp ectively). Unlike the case for polyester resin and Acryloid resin, the films for pure PMMA and PVB become more uniform with decrease in concen tratio n at constant molecular weight and decrease of molecular weight at constant concentration. Film formation from PVB was not satisfactory and it was d i f f i c u l t to measure uniformity and optical thickness at concentrations higher than 50 grams per l i t r e . The amalgamation of ellipsometry and interferometry results enabled us to calculate the geometrical thickness of films and it was found that geometrical thickness increases with increase in concentration (Table 6 ). Polyester resin whick is more viscous than Acryloid resin has a greater geometrical thickness. The extinction c o efficien t for each polymer is zero, which implies that 60 resulting films are non-absorbing. The refractiv e index of films for each is constant (no effect of concentration). Tables 7 and Table 8 suggest that the variation of surface tension, of PMMA and PVB solution, with molecular weight and con centration is almost n e g lig ib le . However, the contact angle increases with concentration and molecular weight, sim ilar to the optical thickness of film s (Table and 5 ). Since y s is constant, can be estimated to be constant within the concentration and molecular weight range, and Gos0 decreases with concentration and molecular weight. This implies that the force at the interface of the polymer solution and micro slides is increased with concentration and molecular weight, and, in turn, the polymer solution sticks more to the m icroslide. This implies that the f lu i d i t y of polymer solution becomes less with concentration and molecular weight. As a resu lt, i t could be speculated that the thickness of films increases with concentration and molecular weight. The glass tran sitio n temperature is determined from the mid point of the tran sitio n in the heat capacity of the sample. The DSC thermograms of Fig. 22 indicate that the compatible blend sys tem exists for blend ra tio 10/90 and 90/10 of PMMA and PVB. The single Tg obtained in the case of compatible blends comply to the Fox expression for random copolymers. 1 W 1 W 9 + (*5) Tg Tg j Tg2 Tg^ and Tg2 are glass tran s itio n temperatures for the pure 61 homopolymers which are the constituents of the copolymer. and are the corresponding weight fractions. The Tg calculated from equation kS for 10% PMMA is 70°C which is in agreement with the measured Tg of 68°C. Optical micrographs of thin films of PMMA/PVB blends reveal that phase separation occurs in the composition range 10 to 90 weight percent of PMMA at room temperature. It was found that phase inversion occurs when we have 40 weight percent of PMMA con te n t. This observation was confirmed by solvent etching technique (Fig. 22b). The blend samples containing between 30 to 60 weight percent of PMMA were subjected to solvent etching by dipping for 1 minute into benzene, which is a solvent for PMMA only. From the damage caused onto the PMMA portion we can infer that at 30/70 ra tio PMMA is the dispersed phase where as at 60/^0 ra tio PVB i s the dispersed phase. For 10 to kO weight percent PMMA the domain size of the dispersed phase increases with increase in PMMA con tent. However, a fte r phase inversion, the domain size of the dispersed phase, PVB phase, decreases with increase in PMMA con tent . 62 UNETCHED ETCHED PMMA/PVB 30/70 (wt. % ) 'p J fC lr PMMA/PVB t ^ l G t » * i w * : .. ' • -vnr; Figure 22b. Optical micrographs of PMMA/PVB blends etched and unetched in benzene 63 CHAPTER V CONCLUSIONS The properties of commercial samples such as polyester resin i V itel PE-200, Acryloid A-10 resin, polyvinyl butyral (PVB) as well as pure polymethyl methacrylate (in tr in s ic viscosities = 0.2, 0.4 and 1 .4) and pure PVB (molecular weights = 32,000, 125,000 and 225,000)) were examined. A Weissenberg Rheogoniometer with couette viscometer geometry was used to measure the rheological behavior of the solutions of these polymers in 1 ,1 ,2-tric h lo ro e th a n e , MEK, chloroform and tetrahydrofuran (for PVB only). The uniform ity, thickness and optical constants (extinction co efficie n t and re frac tiv e index) of films cast from polymer solutions were measured with an el 1ipsometer and a Michel son interferometer. Solutions of polyester resin V itel PE-200 were more viscous than those of Acryloid A-10 resin. Solutions with 1 ,1 ,2-trichloroethane I had the highest viscosity. All solutions with concentration 250 grams per l i t r e were Newtonian. Films cast form the polyester resin V itel PE-200 had a higher optical thickness than those of Acryloid A-10 resin. Furthemore, solutions at a concentration of 25 grams per l i t r e produced the most uniform film s. Ellipsometry showed that such films were non-absorbing because the extinction coefficients were zero and re fra c tiv e indices were constant for each polymer. The temperature dependence of Polyester resin v ite l PE-200 was (E^=f30J/mole) greater 64 than that of Acryloid A-10 resin (E.y = 13-0 J/mole). Furthermore the activation energy was not affected by solvents in solution or suspensions but solely by the polymer species. j As expected, the solution viscosities of pure PMMA and PVB incr ease with the reported in trin s ic viscosity or molecular weight. These solutions seem to follow a power law equation t = kf . The flow index (n) was approximately 1 for PMMA, indicating almost Newtonian beha v io r, whereas for PVB, the flow index varied with concentration and molecular weight from 0.818 to 0.987. The optical thickness of cast films increased with in trin s ic viscosity (or molecular weight) of the polymer and concentration of the solution. The e ffe c t of concentra tion was more prominent. The surface tension of the polymer solution on glass was exam ined. The contact angle increased with concentration and molecular I weight (or in trin s ic v is c o s ity ). The measured contact angle for PMMA varied from 8.5 to 16.5 degrees, and for PVB from 8.75 to 22.0 degrees. However, the corresponding change in surface tension was not appreciable. Thus, the effects of surface tension on optical thickness were negligible compared to changes in concentration and molecular weight. Films resulting from PMMA/PVB blend solutions often formed an incompatible system showing phase seperation. For blend ratios less than 1*0 weight percent PMMA, PVB. was the continuous phase and PMMA the dispersed phase, whereas for blend ratios greater than 40 weight percent of PMMA, PMMA forms the continuous phase. The compatibi1ity of films was ascertained by calorim etric detection of glass tra n s i- 65 I tion temperature (Tg). It was found that films containing less than I I 10 percent of e ith er component yield compatible systems showing a single Tg. Other compositions usually show two Tg's ch aracteristic I of each of the pure components. The calorim etric studies revealed a sim ilar behavior as the one obtained from optical microcopy. 66 LI ST OF SYMBOLS (SOLUTION RHEOLOGY) c - concentration to ] - in trin s ic vi scos i ty 0 - viscosity of solvent 2 < r > - mean square and to end distance of Polymer chain $ - vol. fraction of polymer $ - flo ry constant f - shear rate T - temperature t - t i me p - pressure t - shear stress K - consi stency factor n - flow index x - yield stress y T ) - zero shear-viscosity o vr, v0, vz - Physical components of velocity in cylindrical polar coordinates Rj - radius of inner cylinder - radius of outer cylinder h - height of inner cylinder Ky - torsion bar constant 67 AT - torque, reading in microns - angular velocity n 1 - refractive index of film d - geometrical thickness of film Y - maximum width of fringe X - minimum width of fringe p - e le c tr ic f ie ld vector, p arallel to incident plane s - e le c tr ic fie ld vector, normal to incident plane A - change in phase (el 1ipsometry) ip - arc tangent of the factor by which amplitude ra tio changes ( e l l i psometry). E - amplitude of incident beam R - amplitude of reflected beam 6 - phase angle (ellipsometry) r - fresuel reflectio n c o efficie n t 2 6 - phase change due to double traversal of film thickness - incidence angle §2 ~ refraction angle k - extinction c o efficien t Yj - free energy of liquid against its saturated vapour Y s^ - free energy of solid against i t s saturated vapour Y sj - free energy of interface between solid and liquid Y - surface tension of solid s Yi - surface tension of polymer solution 68. E - a c tiv a tio n energy at co nsta n t shear ra te R - universal gas constant Tg - glass tran sitio n temperature W - weight fraction I REFERENCES (SECTION A) j J 1. Brooms, K.D., IBM J. Res. Develop., Vol 22 No 1 (1978). 2. Vahtra, U., Wolter, R.F., IBM J. Res. Develop., Vol 22, No 1 1978. 3. Bailey, R., North, A.M., Pethrick, R.A., Molecular Motion in High i Polymers, Clarendon Press: Oxford (1981). b. Frisch and Simha R. Iri Rheology (ed. F.R. Eirich) vols. I and I I , Accademic press: New York (1956). 5. Graessley, W.W. Adv. Polym. Sci. J_6_, 1.(197*0. 6. Florry, P.J. S ta tis tic a l mechanics of chain molecules. New York: Wiley Interscience (1969). 7. Iwata, 1., Kurate, M J. Chem. Phys 50,4008 ( 1969) . I 8. Orwol1, R.A., Stockmayer, W.H. : Stochastic medels for chain dynamics. Advan. Chem. Phys. 15, 305 (1969). 9. Onogi, S. et a l : Viscoelastic properties of concentrated solu tions of PMMA in diethyl phthalate. Polymer J. (Japan) 3» 315 (1972). 10. Lenk, R.S. & Polymer Rheology. Applied Science publishers Ltd. London (1978). 11. Nielson, L. E. : Polymer Rheology. Marcel Dekker Inc.: New York (1977). 12. Walters, K .: Rheometry: Industrial Applications. Research studies Press: New York (1980). 13. H arris,J. Rheology and Non Newtonian flow. Longman group Ltd: London (1977). 7r I 14. Fredrickson, A.G: Principles and application of Rheology. I Prentice Hall Inc.: New Jersey (1964). 15. Dealy, J.M. Rheometers for Molten P lastics. Van Nostrand Reinhold Company: New York (1982). 16. Silberberg, A ., Discuss. Faraday Soc., 59, 203 (1976). 17. Grant, W. H., Smith, L .E ., and Stromberg, R.R, Discuss. Faraday Soc. 59, 209 (1976). 18. Cohen, Y. and Reich. S.J. of Poly. S c i., Polymer Phys. Edition, ! J9., 599-608 ( 1981). 19. Rickert, S.E., B alik, C.M., Hopfinger, A . J . , Adv. in Colloid and Interface Science J_1_, 149-191 (1979). 20. Hobbs, S.Y., J. macromol, Sci. -Rev. Macromol. Chem C(.19)2, 221-265 (1980). 21. Kruse, J ., Rubber Chem. Technol., 40, 653 (1973). 22. Thomas, D. A., J. Polym. S c i., Poly. Symp., 60, 189 (1977). 23. Bird, R.B., Armstrong, R.C., and' Hass iager., 0. Dynamics of Poly meric liquid vol. 1 and vol 2.,. New York: Wiley (1977). 24. Universal Interferom etry. An exprimental Handbook the Ealing Corporation (1979). 25. Archer. R .J., Manual on el 1ipsometry. Gaertuer S c e in tific Corpo- rat ion (1978), 26. Ditchburn, R.W. J. of the Optical Society of America vol. 45_ Number 9 _ (1955). 27. Agbezuge, L ., Wieloch, F ., Journal of Applied Poly. Sc. TJ _ , 271 (1982) . 28. Description and Physical properties of V itel Polyester Solution 71 resins. Good year Chemicals. 29. Brandup, J. and Immergut, E. H., Polymer Handbook. Second edition ( 197* 0 . 30. Graessley, W.W., Journal of Chemical Physics bj_, Number 6, 19*t2- 1953 (1967). 31. Goldsmith H .L ., and Mason S.G., in Rheology, F.R. Eirich Ed., vol *t, Accademic Press: New York (1967). 32. Mooney, M., J. Colloid Sci J_6, 162 (1951). I 33. Thomas D.G., Journal of Colloid Sci. 2jD, 267-277 (1965). 3*K Parkinson, C., Matsumoto, S. and Sherman, P., Journal of Colloid and interface Sci, 33, No. 1, 150-160 (1970). 35. Nicodemo, L ., Nicolais, L ., Journal of Applied Polymer S c i., J[8, 2809-2818 ( 197*0 . 72 j SECTION B i ABSTRACT (MELT RHEOLOGY) i i ■ The melt rheology of pure and f i l l e d copolymers was studied. As a basis for this emphasis, copolymers of styrene and butylmethacry1 la te , the major component of electrophotographic toners, were charac terized . The chemical composition was determined by elemental analy sis for carbon and hydrogen and by correlation to glass transitio n temperatures determined by d iffe r e n tia l scanning calorim etry. The copolymers vary in weight percent styrene from 50 to 11%. Molecular weights were determined by gel permeation chromatography fractionation and in trin s ic viscosity measurements. The weight average molecular weights approximate 57,000 to 85,000 with a poly-dispersity index (Mw/Mn) about two. The flow behavior of the copolymers has investigated by a com bination of rheological techniques such as cone and plate and c a p il lary rheometry atvarious temperatures. Measurements of the dependence of viscosity on shear rate and temperature indicate the flow and fusion behavior of toners which a ffe c t the q uality of p rin tin g . The activation energy for viscous flow reduced with an increase in shear i rate. The zero shear viscosity was propotional to 3.0 power of mo lecular weight and increased by increasing the styrene content within | the copolymer. Toner copolymers containing carbon black were prepared by melt j mixing and the uniformity of mixing assessed by optical microscopy. Rheometric studies illu s t r a t e the altered flow properties. The v is 73 cosity was increased with f i l l e r content depending on the surface area of carbon black. A markedly enhanced shear rate dependence of viscosity and a yield phenomenon were observed that depend on the surface area of the carbon black. Using a low surface area carbon black, it was possible to incorporate 20 weight percent of the f i l l e and s t i l l approximate the viscosity of the pure copolymer at modera tely low shear rates. The e ffe c t of molecular weight, composition and f i l l e r content tend to wear o ff at high shear rates. I CHAPTER I [ I | I. INTRODUCTION '(MELT RHEOLOGY) A. Melt Viscosity: A study of polymer processing explores the re la tionships that exist between mechanical flow properties, and chem ical characteristics. Fig. 1 shows schematic of such in te r r e la tionships. Among the various types of polymeric m aterials, it is advantageous to clas sify thermosetting, thermoplastic or elasto- meric polymers. The material behavior at d iffe re n t temperatures is shown in Fig. 2 (1 ,2 ). Essentially a ll thermoplastic resins, and many thermosetting resins in th e ir more flu id state, are required to undergo flow in the molten state during the course of manufacture and fabrication into products. S tr ic tly speaking the term "melt" flow should apply only to semi c ry s ta llin e polymers. However, since non-cross 1inked amor- | phous polymers above th e ir glass tra n sitio n temperatures soften and I exhibit flow behavior sim ilar to melted semi crystal 1ine polymers, it is convenient to speak of the melt flow and melt viscosity of poly meric materials, in the region in which they behave as viscoelastic fluids, rather than solids. The above statement underlines the importance of melt viscosity as a necessary material parameter, the knowledge of which is essential to control flow behavior under d iffe re n t circumstances. Such know ledge may relate e ith er to the phenomenon of melt v isco sity, or to — «<- PROCESSING EQUIPMENT (D IE MOLD, MIXING DEVICE ETC ,) PROCESSING CONDITION (TEMPERATURE FLOW RATE, ETC ,) ■MECHANICAL PROPERTY (TENSILE STRENGTH IMPACT STRENGTH, E TC ,) MOLECULAR PARAMETER BRANCHING) SIDE CHAIN (VISC O SITY, ELA STICITY) FLOW PROPERTY Figure 1. Representing the existing interrelationships among processing variables, flow properties, and chemical structure. LOG E (MODULUS) F^TTRTSTA'nrrN'E- b = AMORPHOUS c = ELASTOMER d = CROSS LINKED O j J Material behavior at d iffe re n t temperatures Figure 2. its molecular o rig in . Understanding the dependence of melt viscosity on variables such as temperature, pressure, rate of flow, and polymer molecular weight and structure is very important (3). Molecular Theories of Melt Viscosity. Several theoretical approaches have been developed to relate both the Newtonian lim iting viscosity and shear-dependant viscosity to polymer structure. The flow process for a long-chain molecule in an environment of sim ilar molecules involves visualizing the motion of chain segments, rather than whole molecules, from one position to another in the liq u id . Such segmental motion, w ill have a preferred direction in the presence of an external stress. The individual chain segments are not independent of neighboring chain segments e ith e r d ire c tly connected to the same polymer chain or temporarily connected by v irtu e of intermolecular entanglements. A cooperative motion of many such segments is involved in the viscous flow of the polymer molecules,. Erying Segmental Jump Concept (4) Beginning with the absolute theory of rate process and a s ta tis tic a l mechanical theory of liquids based on a free-volume model, Erying developed the concept of the flow mechanism of a simple flu id . According to him, a molecule jumps from .its minimum potential energy "well" Into a neighboring hole. Such a jump requires passage over a potential energy b a rrie r, i.e.. through an "activated" or transition state of higher free energy, with this activation energy barrier giving ri.se to flow resistance or viscosity. 78 Segmental Friction Factions: Bueche (5) has shown the equivalence of the segmental jumping concept to one which u tiliz e s a segmental fr ic tio n factor for polymer i melts in the same way that i t had previously been used to calculate the viscosity of d ilu te polymer solutions. In order to account for the fact that the e ffe c t of entangled molecules Fig. 3 varies from the extremes of chemically crosslinked systems (permanent entangle ment) to no e ffe c t at a ll , Bueche introduced a variable "Slippage factor" s. I f N is the e ffe c tiv e number of chain segments involved in the motion and M& is the molecular weight between entanglements then the molecular fric tio n factor " f" is given by equations 1 and 2. In these equations N f ™ Nf for H ^ 2M » .« « « .« « ..... . . . . . . . . . . . . . . . . . ( l ) e N*f = (Nf)(p,'N/48) (M/H ) Z M* (R2/M )3/Z S. Sn (2n -1)3/2 e n= I for M>2M . . . . . . . . . . . . . . . . . . (2) e p is the polymer density and N is Avogadro's number. The Newtonian lim iting viscosity for a polymer melt in a shearing medium is given by equation 3. n = ( p N /36 ) ( r 2 /m ) N*fn ____. . . . . . . . . . . . . . . . --------.....(3) 0 u Figure 4 can be used to consider the non-Newtonian region of flow. Bueche (6-9) claims that the segments rotate with an angular velocity y /2 , furthermore, in the shear f ie ld the segments of the molecule are pulled away from the center of mass, in one direction and pushed towards the. center of mass along the other direct ion shown by 79 Figure 3. Representation of .intermolecular chain entanglements. I Figure k. Shearing action on molecular coil 80 dotted arrows. This alternating compression and d ila tio n leads to viscous energy loss which is a maximum at low shear rates, and becomes less with increasing shear rates. Bueche arrived at the following expression for the reduced apparent viscosity: N = 1 , 2 .2 *1 * where 2 n=l 2( h 2 72* m n in + A.| y ' 12n H 2 - , 2 .2 Ai T 2 ,2,2 n + X] y (*0 A1 = tt2P RT ,(5) Equation h predicts that melt viscosity of any polymer may be expre ssed as a unique function of X ff, * *e * a single master curve can be. obtained i f lo g C n /n ) is plotted against lo g (X .y ). Greassley1 s (.10). a 0 J model predicts the shear dependance of viscosity by making the entan- ! glement density a function of shear rate, rather than adopting the compress io n -d i1 at ion c o i1-d isto rtio n concept.of Bueche. Free Volume: Several d efin itio n s of free volume, (v^.) , e x is t, the most f r e quently used is v = v - v f o (6) where v is the specific volume, and vq is the specific volume of the liquid extrapolated to 0°K without any phase change. D o o little proposed an expression for the viscosity of a system in terms of free volume. H = A exp(BvQ/ v f ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (7) Where A and B are constants. Equation 7 suggests that as the free 81 | volume Increases, the viscosity rapidly decreases. Rearrangement of I : equation 7 gives I n n = In A + B ( i - 1) (8) Where f is the fractional free volume v^/v. It is assumed that above the glass transitio n temperature, the fractional free volume incre ases lin e a rly with temperature, that is: f = f + < x f (T - T ) g f g (9) where f is fractional free volume at T, any temperature above Tg, f is fractional free volume at Tg, and is the c o e fficie n t of thermal expansion of fractional free volume above Tg. In terms of equation 9, the Dooli t t l e equat ion becomes: 1 1n n^y) = 1nA + B( f g + af (T-Tg) 1 - 1) at T>Tg ____ (10) ln t1('T„\= 1 nA + B(^— - 1) at T g ( 11 ) Subtraction yields: log n (T )/n (T j B 2.303f g T - T V “f > + " - Tg (12) B. Rheological Concepts: The most important relationship in the rheology of a flu id is that between shear stress (force) and rate of shear (deformation). The "equations of . . . change", which describe the conservation of mass, momentum and energy are impor tant when we discuss the rheology of polymeric flu id s . For an incompressible flu id these are Continuity, (V.v) = 0 (13) 82 Motion, p v = - (V.S) + pg Energy, p u = -(V .q ) - (S:Vv) ( H ) (15) in which p, v and u are the flu id density, local velocity and internal energy per unit mass, g the g ravitatio n al acceleration, q the heat flu x vector, and S the stress tensor. Note that (n.q)dS gives heat flow from negative side of dS to the positive side; S im ilarly [ n . Tr]dS is the force exerted by the negative-side flu id on the positive-side flu id (12,13). The total stress can be s p lit into two parts: an isotropic part containing the pressure p, and t, which is that part of S that is zero at equilibrium where u is the viscosity and f is the rate of shear tensor. The I "rheological equation of state" or a "constitutive equation esta-' blishes a relationship between Tandy. Bird has given a review of of accuracy and complexity of calculations, a d iffe re n t model can be used. In Fig. 5 curve 1 represents the power law viscosity model S - p 6 + t .......................................................... For an incompressible Newtonian f lu id , one has ( 16) t - -y [Vv + (Vv)T] = -<yy (17) various useful non-Newtonian models (1^,15). Depending on the degree n = Kt n-1 (18) and curve 2 represents the Carreau model (19) where r i ^ is referred to as zero shear rate viscosity, and r i ^ 83 ( PASCAL - SEC) ( I ) POWE RL AW MODEL r \ = K T n"' oo T ( l/SEC) Figure 5. Non-Newtonian viscosity model (2) CARREAU MODEL + ( A T ) (I). 2 .. in - 1) ,2 represents the constant v is c o s ity at high shear ra tes. Lodge (16) has proposed some rheological methods for polymer characterization. Bird et al have worked on the k in e tic theory for polymer melts and developed a Curtiss-Bird constitutive equation. Rheological properties for shear flows (17) and experimental compari sons for shear flow rheological properties (l8) have been explored in great depth. Many rheological formulae have been published with a view to describing one or more features of non-Newtonian behavior. For simple shearing motion some of the better known formulae are: (i) Ostwalde-de Waele (power-law) Model T = Ky'1 " 1 (20) to avoid taking roots of negative quantities it is often given by T - K|t | n V ........................................ ............................................(21) where x is the shear stress and t the corresponding shear rate, n is the flow index and K the consistency factor. For n=1 i t reverts to Newtonian expression. For n<l i t is used to describe pseudoplastic behavior and for n>1 it describes d ila ta n t behavior. ( ii) Viscoplastic-generalised Bingham Model x - x = K|t! n 1f ..................................... (22) y where x^ represents f i n i t e yield stress to in it ia t e flow. ( i i i ) Power Series Model: The relationship between shear stress and shear rate for a non linear flu id without a yield stress can be represented by a power series containing only odd powers of shear rate. 85 t = Cjt + C2i 3 + C3y 5 + ................................................... (23) A truncated version of this formulae is useful to examine behavior of simple non-Newtonian flu id s . (iv) Ree-Eyring Model It is considered that there are M d iffe re n t flow species within the flu id per unit of shear plane area, each contributing to the stress on the shear plane. The shear stress is given by a summation over a ll flow species, N=M n£i CNSinh V ..............................................................................m is the relaxation time of the rate process of the Nth u n it. is the Nth c o e ffic ie n t. (v) Casson Model (20) / t " = + r J f ....................................... ( 25) y where is viscosity at high shear rates. (vi) Ellis Model (21) 1 -n TT I " 1 + ( T / T i ) 0 1 (26) n n - 2 0 where T j l is the shear stress at which the v is c is ity has fa llen to 2 in . o (vii) Oldroyd Model (22) n (i + i A.X9t 2) n ■ ^ (27) 1 + 3 X1 Y where X j , X^ are constants. 86 C. Effect of Molecular Weight: ;i The effect of molecular weight on the melt visco s ity, and other rheological parameters, of a large number of polymeric systems has been studied in detail (23-26), Below a c r it ic a l molecular weight.M, the viscosity of a molten polymer is roughly propotional to the weight average molecular weight M . n = k.m ........... (28) I w At molecular weights above Mc , the viscosity at low rates of shear depends upon M to a power equal to about 3.^ or 3.5 w log n = 3 . ^ logM + K„ fo r M>M . . . . . . . . . . . . . . . . (29) ■ o *■ c The solid lines in Figure 6 show the dependence of viscosity on molecular weight at very low shear rates. The dependence at high shear rates is d i f f i c u l t to comprehend. The dashed lines in figures 6a and 6B indicate two p o s s ib ilitie s with the arrows indicating the direction of s h ift as shear stress increases. In Fig. 6a the slope gradually decreases from the 3.^ power dependence at low shear rates to almost a linear dependence on molecular weight at high shear rates. This type of q-M dependence, is expected i f shearing destroys the w entanglements much faster than they can reform. The behavior i l l u s trated in Fig. 6B is possible i f M increases as shear rate 0 • increases (27). The d is trib u tio n of molecular weight affects the value of the shear rate at which non-Newtonian behavior becomes apparent. A polymer with a broad d is trib u tio n exhibits non-Newtonian flow at a lower rate of shear than a polymer with same zero shear viscosity but 87 LO G O F VISCOSITY A B LO G M w LOG Figure 6. Dependence of viscosity on molecular weight. 88_ which has a narrow d is trib u tio n in molecular weights. The s h ift to non-Newtonian behavior at lower shear rates as the d istrib u tio n broadens makes it possible to extrude or mold a polymer with a broad d is trib u tio n of molecular weights much more easily than a polymer with narrow d istrib u tio n ( 28). D. Temperature effects: The viscosity/temperature function can be studied at constant shear stress or at constant shear rate. The changes in viscosity with temperature at constant shear rate and at constant shear stress are not equal (29). The total d iffe re n tia l of viscosity as a function of shear stress and temperature can be w ritten as the sum of two p a rtia l d iffe re n tia ls dn = (|£)t dT + (|I1)T d t ....................................................... .(30) Furthermore, i t can be shown that (3n/9t). T - t - t ( | ? ) T (31) (3n/3T)t " Y 3 t ; T Since viscous flow is a rate process it is possible to express the temperature dependence of viscous flow by an Arrhenius-type equation involving the activation energies at constant shear rate (E^) or at constant shear stress (E ) . For a power law flu id ( t =. SSfn) i t can be shown that C ' - 4 ................................................................... <3*> Y The knowledge of the variation of melt viscosity of thermoplastic polymers with both shear rate and temperature is very important. However actual measurements at a large number of temperatures is a 89 time consuming and tedious task. Mendelson has developed a technique for predicting flow curves of a number of o le fin polymers and copoly mers at various temperatures from experimental data for those polymers at one temperature (30-33). The specific s h ift factors were obtained by choosing a p a rticu la r shear rate at the reference temperature and then observing shear rates at the other temperatures which corresponded to the same shear stress. The s h ift factor, a^., was defined by aT “ W ^ w (T) < constant t ) (33) This d e fin itio n of a^ is equivalent to aT = n (T )/n (T R) (constant t ) (3^) The general viscoelastic expression corresponds to the s h ift factor obtained by taking ratios of the zero-shear viscosity (31 *) • aT = n0TpTR TR/ t1 0TRPTT \ ................................................................ E. F ille d polymeric systems: Reinforcement in elastomers, as well as in glassy polymers, has been the subject of intensive study for a very long time. The most highly reinforcing f ille r s , namely carbon blacks and silicas, consist of aggregates of quasi-spherical par tic le s fused together (35). When carbon black is mixed with a polymer, some breakdown of the aggregates occurs. The extent of this breakdown depends on loading and mixing procedure. The research on f i l l e r reinforcement has been pursued along two d is tin c t lines. The f i r s t is basically physical. It seeks physical and phenomenological descriptions of reinforcement e ffe c ts . It assumes that some sort of bonding exists between the f i l l e r and the polymer m atrix. The second approach to reinforcement is chemical. It concen- 90 trates on the surface chemistry of the f i l l e r and its interactions with the polymer (36). Janzen has given a detailed review on the physicochemical charac- i te riza tio n of carbon black (37). Usually when use of fille rs is con sidered, a compromise has to be made between improved mechanical properties in the solid state, the increased d if f ic u lt y of melt pro cessing and the problem of dispersing the f i l l e r in the polymer. Theoretical correspondence between slow viscous flow of a liquid and the infinitesim al strain e la s t ic it y of a solid has been established. For some cases the viscosity (q) of a liquid and the shear modulus of a solid containing an identical d is trib u tio n of rigid f i l l e r were related to the quantities for the u n fille d matrix (q ) , G by ( 38) 0 o q/q = G/G ............................................................................................(36) 0 o The flow behavior and viscosity of mica f la k e - f ille d polypropylene melts and the mechanical properties of mica-polypropylene composites were investigated. The properties of the moiil ded.compos i tes exhibit moduli which were higher than most filled polymers (39). It was found j j that t a l c - f i 1 led polypropylene melts have the same viscosity as the homopolymer for shear rates greater than 1.0 sec however, for shear -1 rates lower than 1.0 sec there was a sharp increase in viscosity (^0). Calcium Carbonate-filled polyropylene melts follow a power law in viscous behavior over a limited shear-rate range. The viscosity increases and e la s tic it y decreases as the f i l l e r concentration is increased (4l). The inorganic f ille rs have l i t t l e in te rfa c ia l in te r action- with the resin, so, the introduction of coupling agents, which 91 provide a molecular bridge between the interface of an inorganic f i l l e r and an organic polymer m atrix, enhances the reinforcement e ffe c t. The effects of these coupling agents on the rheological and mechanical properties of filled polymer melts has also been in vesti gated. Studies on the rheological properties of fibre - filled polymer melts are made at high shear rates (43,44). The shear viscosity of suspensions of glass fib re is independent of the type of measurement. Extrudate swell was found to be suppressed by the presence of fibres. The addition of glass microspheres to polystyrene melt does not delay the onset of extrudate d is to rtio n . Experiments were done to determine re la tiv e importance of p a rticle size and the type of f i l l e r on the reduction in and delay o f extrudate d is t o r t io n .(45). Crawson et al (46) have studied the rheology of short glass fib e r - f i l l e d thermoplastics. The effects of fib e r length, temperature and fib e r concentration on the viscous and elastic properties of polypro pylene and nylon 66 has also been examined (47). During processing, the fibers adopt complex patterns of orientation and this produces sig n ifican t anisotropy. Furthermore, it was found that converging flow produces high alignment of fibers along the direction of flow, shear flows have an e ffe c t of partially disorienting the fibers, whereas, diverging flow causes a ninety degree rotation of the previ ously aligned fib e rs. Experimental study of the influence of carbon black loading, p a rtic le size and structure on the extrusion characteristies. of poly- butadiene and butadiene-styrene copolymer synthetic rubber has been done by White and Crowder (48). The cause for increase in viscosity 92 and decrease in die swell and extrudate d is to rtio n , with an increase in carbon black loading or decrease in p a rtic le size or increase in structure, can be explained e ith er by the concept of suspension of particles in a viscoelastic flu id , or can be based on the idea of the interaction of an entanglement network with carbon black surface (49). 93 CHAPTER I I EXPERIMENTAL A. M aterial: The materials selected for studying the viscous response were copolymers procured from Sybron (Chemical Division) and were standard lonac Toner polymers: XRP-70, X-21 1 , X-230, X-231 and X-242. Another copolymer PT-1200 was procured from Hercules Incorporated. All the toners are copolymers of styrene and butyl - methacrylate varying in e ith e r composition and/or molecular weight. The carbon-black was obtained from City Services-Columbia chemicals and were furnace blacks Raven AlO, Raven 1020 Raven 5250 and Raven 7000. THe complete characteristics of these carbon-blacks is given in Table 1. B. Melt Mixing: The C-BlaCk and copolymer in powder form were first dry mixed for about 30 min. Subsequently the homogenous mixture was added to an internal mixer (Brabender PIasticorder) where i t was melt-mixed at about 1300C. The twin blades rotated at 100 revolutions per minute and the mixing was done for about 20 min. In order to test the homogeniety of the mixing process in the chamber of the internal mixer, three samples were examined. The firs t one was near the outer wall of the chamber. The second was from the middle of the chamber between the walls and the blade. The last one was from the inner part of the chamber very close to the blade as shown in Fig. 9. 3k Table 1. C h a ra c te ris tic s o f C-Black Raven Surface Area Blackness P article Dia. my Oil DBP cc/1OOgm Absorpt ion S tiff Paste cc/gm CTAB BET 7000 350 625 170 15 105 15.7 5250 250 525 170 20 95 12.5 1020 102 95 155 27 57 CO CO k\0 27 2k 65 70 65 8.2 95 These samples were compression moulded in hydraulic press (PRECO) j at 1500C under 16,000 lbs platen pressure. A 1x£ inch rectangular mould about 1/8 inch thick was used. Thin films of ^,000 R thickness were cut, from the compression moulded p late, by a Ultramicrotome Sorval MT2-B. These films were observed under an optical microscope (Unitron ME^l449). Optical micrographs were taken with a polaroid camera mounted on the micro scope. The samples were magnified 800 times in order to observe the dispersion of carbon black in the copolymer matrix. C. TESTING: (i) Molecular weight of Copolymers: The molecular weight and mole cular weight d is trib u tio n were determined using gel permeation chro matography. The instrument used was a Waters; model R-A00 which had fiv e columns - 500 R, 10^ R, 10^ R, 1C T* R and 10^ R. The columns were filled with, micro styragel and the volumetric flow rate was maintained at 2 cc per minute. The series, combination of the above mentioned columns,; gave good resolution. The experiments were done at room temperature 25°C ± 1 °C. Tetrahydrofuran (THF) was used as the solvent. S en s itivity was set at 8X, and chart speed was 0.1 inch per minute. Intrinsic Viscosity of Copolymers: The in trin s ic viscosity of a ll the copolymers of styrene and butyl methacrylate was measured with an Ubelhode-Cannon VIscometer - The apparatus; consisted of a viscometer connected to a reservoi r containing tetrahydrofuran (.THF) to maintain an atmosphere of THF and prevent evaporation of the spiv6*1*1' Solutions of d iffe re n t toners were prepared in THF at four d iffe re n t concentrations, 0.625%, 1.25%, 2.5% and 5% (weight/volume). The elution time for a fixed volume of pure solvent and for solutions of d iffe re n t concentration was mea sured. In trin s ic viscosity [r|] can be obtained as follow (50): 0_ rnl = Lim (37) o o %=[n] + k-c ....................................................................(38) Where, r| is the specific viscosity given by o = n . - 1 (39) sp rel Where, hre j is the re la tiv e viscosity given by elution time of solution -v ^rel elution time of pure solvent ••••* .............. (ii) Composition of Copolymers: Elemental Analysis: The copolymer was dissolved in THF (2% weight/volume) and p re ci pitated in a large excess of methanol (non solvent) to eliminate impurities (or a d d itive s ). The precipitates were dried in vaccum at 60°C for a week. Carbon and hydrogen contents of a ll the purified toners was determined by elemental analysis at Galbraith Laboratories, Inc. (Knoxv?lie, TN). From the amounts (%) of Carbon and hydrogen in the copolymer the percent styrene in each of the copolymers can be evaluated as follows: * Carbon - x ’ 00 m X + Y = 1 (*»2) 97 Here, X and Y denote the mole fraction of styrene and butyl methacry late in copolymer respectively. Therefore l A i i V Weight % Styrene = ^■ q ^ - - X 100 (43) D iffe re n tia l Scanning Calorimetry (DSC): The glass tran sitio n temperature of pure copolymer was measured by the use of a D iffe re n tia l Scanning Calorimeter (Model DSC 2C, Perkin Elmer Co.). The glass tran sitio n temperature (Tg) of these copolymers was measured at a heating rate of 20°C/min and 1Q°C/min. The copolymer composition can be obtained from the Tg's of pure toners by using the Flory-Fox empirical equation (34) 1 W1 W2 =1-+.=3- ............ '....(M ) Tg t9| t 92 Where, W ^ and W ^ are weight fraction of styrene and butyl methacrylate within the copolymer. Tg^ is the glass tran sitio n temperature of a ta ctic polystyrene and T.g^ fs the glass tran sitio n temperature n-butyl methacrylate. Tg is the glass tran sitio n temperature of the copolymer. ( i i i ) Rheological Behavior: The viscosity of the pure copolymers was determined using a Weissenberg Rheogon i.©meter model R-19 and Monsanto processabi1ity tester (Capillary rheometer). The filled system was investigated at low shear rates using the Weissenberg Rheogoniometer. A cone and plate geometry with platen diameter 7.5 cms and a cone angle of .0.9877 degrees was used in the Rheogoniometer. Compres sion moulded disks of thickness 1/8 inches were prepared in a "PRECO" 98 hydraulic press at 150°C for 15 minutes under a platen pressure of 14,000 lbs. The viscosity was measured at 130°C, 140°C, 150°C and 160°C. The processabi1ity testing machine is based on the concept of a constant rate c a p illa ry rheometer enables us to obtain viscosity of the copolymer at high shear rates. The copolymer is placed in an e le c tr ic a lly heated extrusion barrel and tested at pre-selected dwell times (pre heating) under conditions of known temperature, shear rate and o rific e geometry. The flow that is most used to measure viscometric and linear viscoelastic material functions is the flow between a cone and a p late, one of which is rotating. A sketch of this geometry and its flow characteristics are shown in Fig. 7. The main advantages are that loading and cleaning are re la tiv e ly easy and the shear rate is uniform, so that d iffe re n tia tio n of data is not necessary to compute values of the material functions. Due to the flow irre g u la ritie s at the air-1iquid interface, the use of cone and plate geometry for the study of molten polymers is limited to a maximum shear rate in the range 0.1 to 10 sec ^ (51). To derive an expression relating the shear rate in the space between the cone and the plate to rotational speed and cone angle, the following assumptions are made: (i) At s u ffic ie n tly low rotational speeds, the " in e rtia " or accelera tion terms of the equation of motion can be neglected. (ii) The cone angle is very small so that certain approximate trigno- metric relationshiips can be used. ( i i i ) The edge effects are neglected. 99 U J to {RAD/SEC.) R Figure 7. Characteristics of flow in a cone and plate. 100 (iv) The surface tension acting on the free surface has no e ffe c t on the fluid motion. The shear rate is given by (52): y = sln0 = r_ (M 5) Y r 39 1 Sin6 1 6 0........................................................ Since the shear rate is nearly uniform, the shear stress will also be uniform arid the torque required to rotate the cone or to hold the plate stationary is given by: M ' C 2lTr2 dr " f * r 3 t04, (,|6) In our set up, the torque is obtained d ire c tly M = ICj-AT ............ (47) Where is the torsion bar constant given in dyne cm per micron and AT is the deflection reading (microns). It is possible to compute the value of the viscosity at one shear rate from the results of a single experiment M 3M6» 3- - . . . . m Y 2 7 T The processability te s te r, which operates like a cap illary rheometer, and its flow characteristics are shown in Fig. 8. Tijie shear rate at the wall was obtained using the Weissenberg equation, (incorporation of Rabmowitsch correction) (.21) y = ( AHJL ,'L.) . (In9) T V 1 / > * 1 • « s « « a e 0 c « » e * e « B « « a » 9 * B e « « e « 0 e e \ ' ^ / w 4n -3 IT D Where, Q . is the extrusion rate or volumetric flow rate under a pressure drop P, D is the diameter of the c a p illa ry and n is given by 101 1 ' A TEST MATERIAL. CAPILLARY Figure 8. Flow characteristics in a capillary rheometer. 102 d l o g T ' f r n \ n = *7 * 1 • ■ ■ ■ . ■ (50) d 1 og 'f ■ and t the wall shear stress is given by w a 7 : - ?r .............................. ( S ' ) The end correction used by Bagley has been neglected in calcula ting the wall shear stress because c a p illa ry with large L/D ratio was used in this study. The viscosity was determined using the express i on ................................................................... (52} w 103 CHAPTER I ] I RESULTS A. Melt Mixing: A proper uniform dispersion of carbon black within the copolymer matrix was necessary in order to examine the e ffe c t of f i l l e r loading and surface area on viscosity. The optical micrographs of thin films from piccotoner-1200 with 10 and 15 2 weight percent carbon black (surface area 525 m /gm) are shown in Fig. 9b. B. Molecular Weight and Molecular Weight D istribution: A calibration curve for polystyrene standards (Pressure Chemical Company, Pittsburgh, PA) was obtained by taking the elution volume corres ponding to the maximum peak of the chromatogram. The a sterik in Table 2 indicates that the molecular weight was obtained from universal cal ibration curve (. p M v/s Ve) by taking the reported K -4. and c c values (K = 1.6x10 and « = 0.706) for polystyrene in THF at 25°C (53). The rest of the molecular weight data (Mw, Mn and Mw/Mn) given in Table 2, along with the corresponding equations, assumes the copolymers to be homopolystyrene. GPC studies on fractionated samples of piccotoner-1200 were also done. Intrinsic Viscosity: A least square f i t is done on the data on n /c v/s c and the intrinsic viscosity obtained is given in Table sp 3. The correlation factor for a ll the toners was about 0.998. 10A H i D D L E INNER Figure 9A. ‘O U T E R ' s ‘3 £ . = n i a 3 C T 9 *~~F ^ ■ * r ” F * T > « . - -■:£*£. V "7 * w * \ / .' / 7 \ J ' . - . f*s.;% Sample points within chamber of the Internal mixer. f , - ^ r - f & f.^'-‘ v » * • V ’ 1 * V > , - > A i V V V, % ' i *s ^ ■ r*.^' v i *■£.-' • 1 V.‘7 ' T - V * *«~ *s £ £ * o r ' - - * 7 ✓ ^ # *t 10% f i 1ler loading r £ r ^ - -s iS&. ^ r j . .^ . w r s , .--3 ~ y j & S l igure 9B. Carbon black dispersion (SA: 525 m 2/gm) . £ * -'• § * £ . ^** ■>^r. 15% f i l l e r 1 oad i ng f r i Table 2. M olecular Weight o f Various Toners Toner Mw x 10~3 < v\ 1 O > < 1^ Mw/Mn Picco-toner-1200 85.10 47.75 1.78 XRP-70 78.65 45.00 1.77 X-230 75.60 42.85 1.76 X-231 68.40 38.30 1.79 X-211 62.50 33-25 1.88 X-242 60.30 34.80 1.73 sp2 50/50 124.00 70.00 1.77 Picco toner-1200 63.00 30.00 2.10 Universal c alib ratio n curve: -q.2466V. (n.')M. - 1.256 x 10 . 10 1 Calibration curve: 1n -0.14V. M. = 2.386 x 10 . 10 1 In trin s ic viscdsity of fractionated sample vs. elution volume: -0.084v. (n.) = 89651 x 10 ' 106 In trin s ic Viscosity of various copolymers (toners) Toner [n ]d l/g m . Picco toner-1200 0.3341 XRP-70 0.3005 X-231 0.2164 X-211 0.2455 X-242 0.2606 X-230 0.1924 sp2 50/50 0.4368 107 C. Composition. Elemental Analysis: A determination of amount Carbon and Hydrogen (wt. %) in the copolymer ebables us to calculate the percent styrene (by weight) in each of these copolymers. The analysis given in Table b indicate that the amount of styrene varies from 50% to 76%. The copolymer composition can also be obtained from the Tg of pure copolymer by using the flory-Fox equation. The Tg of a ta c tic polystyrene and n-butyl methacrylate were 373 K and 293 K respectively (5*0. The Tg's and composition of toners are given in Table 5. D. Rheological Behavior. Pure Copolymers: In Fig. 10 and Fig. 11 we combine cone and plate (low shear rates) and c a p illa ry viscometer (high shear rates) steady state viscosity ^ (o ^ /? ) data for PT-1200 and X-231 at four d iffe re n t temperatures (130°C to 160°C). At low shear rates both the copolymers (toners) have a plateau corres ponding to the zero shear viscosity. However, as the shear rate increases we observe shear thinning behavior. The remaining copo lymers were characterized at 150°C. The e ffe c t of Molecular weight on viscosity can be seen in Fig. 12, It was observed that the zero shear viscosity was propor tional to (Mw)^"^ and furthermore the zero shear viscosity was effected by the copolymer composition Fig. 13 and Fig. \b . F ille d Copolymer: The e ffe c t of carbon black'concent ration (5%, 10%, 20% and 30% by w t.) on the viscosity of the copolymer at 1500C can be s e e n in Figs. 15 to 18. Q u alita tiv ely it can be seen that carbon black increases the level of viscosity especially in the low shear rate range. Even for 5% loading we do not observe a zero 108 Table 4. Elemental Analysis and Composition o f copolymers Toner % Carbon % Hydrogen Weight % of styrene Pi ccotoner-1200 83.88 8.94 66.52 XRP-70 85.00 8.56 70.97 X-230 81.86 9.10 58.49 X-231 83.78 8.77 66.12 X-211 86.34 8.30 76.30 X-242 84.75 8.92 69.98 sp2 50/50 79.67 9.20 49.80 109 Table 5. Tg's and composition of toners Toner Tg (°C) Weight % of styrene Picco Toner-1200 71 69.10 X-RP-70 73 71.1 X-230 63 59.7 X— 231 68 65.6 X-211 78 77.0 X-2b2 72 70.3 sp2 50/50 57 52.3 Viscosity n (Pa.sec) WElSSEN8€ReRu£OfrONtOM£TER c a p i l l a r y Rh e o m e t e r Shear rate y (sec ) Figure 10. Steady shear viscosity of PT-1200 at various shear rates and temperatures. Viscosity ri (Pa.sec) V s IEiS S £N 0£R <3 RheO G O N IO C A £ T £ R 1 0 * O ttU A R Y R«€QM £T£R Shear rate y (sec — * Figure 11. Steady shear v is c o s ity of copolymer X— 231 at various shear rates and m temperatures. A - 130°C; B - 1^0°C; C - 150°C; D - 160°C. Viscosity r) (Pa.sec i o 4 1 0 icr 10 io' io 1 10 lo2 io 3 Shear rate i (sec ) Figure 12, Effect of molecular weight on steady shear viscosity of copolymers at 150 C, Composition of copolymer - ST/BMA-70/30, A - XRP-70; B - X-2A2„ Viscosity n (Pa.sec) . 4 10 l o 2 lo 1 Shear rate f (sec 1 0 lo' Figure 13. Steady shear v is c o s itie s o f copolymers varying in styrene content at 1500C. _ A - X-211; B - X-2kZ. .c- id 1 10a i o 1 10C 1 0 1 - 1 Shear rate y (sec ) lo * , .. ± — 10* Figure 12 *. Steady shear viscosities of copolymers varying in styrene content at 1500C A - XRP-70; B - X-230. shear viscosity. At high carbon black levels the non-Newtonian behavior was prominent and the viscous response becomes increas- ingly non-linear and unbounded at low shear rates. 2 Fig. 19 to 22 shows the e ffe c t of surface area (2b m /gm, 2 2 2 95 m /gm, 525 m /gm, 625 m /gm) of carbon black on viscosity of the f i l l e d system at constant carbon black loadings. Carbon black with highest surface area has the maximum viscosity. 116 Viscosity n (Pa.sec) 10 10 1 C ? 10 10 3 io 1 Shear rate y 10° (sec 10‘ 10* ) tL Figure 15. E ffe c t o f carbon black (Raven 410, surface area 2h m /gm) loading on the v is c o s ity o f copolymer PT-1200 at 1500C at various shear ra tes. Viscosity ri (Pa.sec) -a Shear rate y (sec ^) 2 Figure 16. E ffe c t o f carbon black (Raven 1020, surface area 95 m /gm) loading on the v is c o s ity o f copolymer PT-1200 at 150°C at various shear stresses. Shear rate y (sec ) 2 Figure 17. E ffe c t o f carbon black (Raven 5250, surface area 525 m /gm) loading on the v is c o s ity of copolymer PT-1200 a t 150°C at various shear ra tes. Viscosity n (Pa.sec) 3 i f f Shear rate y (sec ) 2 Figure 18. Effect of carbon black (Raven 7000, surface area 625 m /gm) loading on the _ viscosity of copolymer PT-1200 at 1500C at various shear rates. M O Viscosity r| (Pa.sec) . 4 10 Shear rate t (sec Figure 19. E ffe c t o f carbon surface area on the v is c o s ity o f PT-1200 at 150°C containing m 5% carbon black at various shear rates. Vi scosi ty ri (P a .sec tt? 103 lo* - 1 Shear rate t (sec ) Figure 20. E ffe c t o f carbon black surface area on the v is c o s ity o f PT-1200 at 150°C c o ntaining 10% carbon black at various shear rates Vi scos i ty n (Pa.sec) i o 5 , 3 10 Shear rate y (sec ) Figure 21. E ffe c t o f carbon black surface area on the v is c o s ity o f PT-1200 at 1500C co ntaining 20% carbon black at various shear rates. h o IO* 10 3 Figure 22 101 icr io1 io 2 Shear rate t (sec ^) Effect of carbon black surface area on the viscosity of PT-1200 at 1500C containing 30% carbon black at various shear rates. CHAPTER IV DISCUSSION A. Melt Mixing: We obtain uniform mixing in a ll the locations within the chamber of the internal mixer. For 10% carbon black loading the agglomerates range from 1.2 microns to 12.5 microns in diameter with an average separation of about 20 microns. However, for 15% carbon black loading the average diameter of the agglomerates range from 10 microns to kO microns. This suggests that there was a decrease in the dispersion o f carbon black with an increase in concentrat ion. 2 For carbon black with surface area 625 m /gm (high structure) it was necessary to break the secondary aggregates in order to establish uniform mixing. During mixing the shearing and compression tends to compact the polymer with the carbon black and along the border the polymer penetrates into the interstices between powder p a rtic le s . The rate of penetration of polymer depends on the depth of the layer of carbon black, in contact with the polymer as well as the size and structure of carbon black p a rticle s . B. Rheologlcal Behavior. Pure Copolymer: The data for Fig. 10 and Fig. 11 was, continuous and this shows the consistency of the results for d iffe re n t instruments (cone and plate and c ap illary viscometer). Figs. 23 and 2k indicate that melt viscosity of the copolymer can 125 Viscosity ri (Pa.sec) ^ i x 103 (" k‘ V * Figure 23. Arrheneus type dependence of viscosity on temperature for PT-1200. •-shear rate 0.1 sec • o-shear rate ^.0 sec ©-shear rate ^0.0 sec -1 A-shear rate 600.0 sec 126 Q_ •to Figure 24. Arrheneus type dependence of viscosity on temperature for X-231. •-shear rate 0.1 sec e-shear rate 40.0 sec o-shear rate 4.0 sec A-shear rate 600.0 sec 127 be represented by an Arrhen i us^-type equation E. X ] = A exp(— r— ) (53) It was observed that E ^ , decreases with increase in shear rate. Table 6 gives the values of (kcal/mole) for PT-1200 and X-231. Comparing the values of E^ for both the copolymers suggests that energy for activation for flow at constant shear rate does not depend steeply on the molecular weight of the copolymer and this is understandable because for the molecular weights we are considering we have already exceeded the c r it ic a l entanglement density. It has been shown (Ferry) that the W /LF equation for the tempera ture dependance of viscoelastic response can be obtained from the Dooli t t l e equat i on. 1 nri.. = In A + B(— ^----1) .. . . .. . .. .... ... ... .... ... ( . 5 * 0 . f ( v f /v) is the fractional free volume. Above the glass transitio n temperature f = f + a ,(T - Tg) -------. . . . . . . . . . . . . . . . . . . . . . . . . . . (55) i 9 r i The s h ift factor for viscosity can be given by n x t p j . n T a - o J ref ref o.,T T V l r e f T p n0,Tref i I ! Where r\^ is zero shear viscosity at some a rb itary temperature (T) I and r | _ r is the zero shear viscosity at a reference temperature o.Tref (Tref = Tq = 150°C). Equations 5^, 55 and 5b simplify to give 128 Table 6. Effect of shear rate on Activation Energy for PT-1200 i and X-231 Shear Rate Sec ^ Activation energy for flow Ey'-kcal/gm mole PT-1200 X-231 0.1 27.50 27/66 4.0 26.36 27.02 40.0 25.64 25.47 600.0 20.66 20.84 I 129 log T 1 0 T 1 ,T _ ,T = log aT = B T 2.303f T - T o f — + T - T O tj. o (57) Generalized WLF equation is given by log aT = c1° < T - T0> (58) C^° and C^0 can be determined from the least-square slope and intercept of the data plotted as log ay versus log ay/T-TQ. The parameters obtained are very sensitive to experimental errors. Subsequently c | , Cg , f and can be determined Cg = C f / 1 - (Jo - Tg)/C 2° C2 = C2° “ (To " Tg) f =--------*.. ................................... ° 2.303 C,0 .. .. (59) ....( 60) ....( 61) ( 6 2 ) A plot of log ay v/s T-Tq is shown in Fig. 25 and 26 for PT-1200 and X-231 respectively. Table 7 gives the free volume parameters: the co efficie n t of expansion, f , the free volume at glass tra n s i tion, Cg and C2 , the WLF constants. We have developed a phenonmenological master curve for the copolymers at a reference temperature of 150°C in Figs. 27 and 28. A best f i t curve was obtained by using proper vertic a l (a ) and horizontal (a.) s h ift factors. The s h ift factors for both the Y 130 ■icr -Zo -30 - l o 30 Figure 25. WLF equation for PT-1200. 0 ^ = 5 . 06°C; C2°=157.37°C •-Experimental; ©-extrapolated. .131 ■ 1 0 -2 0 -40 Figure 26. WLF equation for X-231, C^°=5.46°C; C2°=167.67°C •-Experim ental; ©-Extrapolated 132 Viscosity an (Pa.sec) 1(? 1 < ? • x id Shear rate a .f (sec Figure 27. Master curve o f v is c o s ity versus shear rate fo r PT-1200 at a reference temperature o f 150°C. From data at 130°C ,D ; 140°C, A; 150°C, • ; 160°C, x. Viscosity an (Pa.sec) 1<? A * 0 • O A0 z 1 0 Shear rate a.y (sec M Figure 28, O O - P- Master curve of viscosity versus shear rate for X-231 at a refe of 150°C. From data at 130°C,O; H 0°C , A; 150°C, • ; 160°C, x. Table 7. Free Volume Parameters Tg (°C) C9 U1 C9 2 a f -1 Degree f 9 PT-1200 71.00 10.56 75.37 5.5x10'** 0.041 X-231 68.00 10. 3b 83.67 it.7x10_if 0.039 135 copolymers are given in table 8 and 9. In our case the activation energy for flow was high and the dependence of viscosity on tempera ture at low shear rates was much greater than its dependence on temperature at high shear rates. A general method of obtaining master curve at d iffe re n t tempera tures is a double logarithmic delineation of reduced viscosity (n/r| ) o against r r y . This approach seems to be true for blends (55,56) and other polymers (57). A sim ilar approach for our system, Fig. 29 and 30, reveals some descrepancy with the proposed method. Mendel son (58-60) has proposed a method of obtaining master curves at a p a r t i cular reference temperature by applying suitable horizontal s h ifts to shear stress shear rate data. However, he assumes the flow-index "n" at d iffe re n t temperatures to be the same. FILLED COPOLYMER: The experimental results cited in the previous section are in agreement with those described by several investigators (61-64). The viscosity shear rate behavior Figs. 15-18 showing a negative slope of (-1) indicates a yield value. This may be seen in Figs. (31-34) where we plot the shear viscosity v/s shear stress. The values of yield stress depend on carbon-black loading and the surface area of the carbon black, Fig. (35— 37). For a 10% f i l l e r loading we observe 2 a yie ld value only for f i l l e r with surface area 625 m /gm. The yield values for constant f i l l e r loading but of f i l l e r varying in surface area are given in Table 10. The c r it ic a l shear rate was the minimum shear rate required to produce: a stress greater than the yield stress (material ju s t begins to flow ). 136 Table 8 . S h ift fa c to rs fo r PT-1200 Temp. °C Vertival Shift factor (a^) Horizontal Shift factor (a^) WLF S hift factor (aT=n T/n T r) I o,T o,Tref 130 0.183 2.55 5.37 140 0.444 1 .55 2.22 150 1 .000 1 .00 1 .00 160 2.000 0.68 0.50 Table 9. S h ift factors for X-231 Temp. °C Vertical Shift factor (a ) n Horizontal S hift factor v WLF S hift factor 1 1 T T ° ’T C J T * B l < 1 T n T r o,Tref 130 0.187 2.45 5.43 140 0.444 1.55 2.23 150 1.000 1.00 1 .00 160 2.000 0.68 0.49 137 z 1 0 1 0 * 10° oft 1 0 ■ z 1 0 ' n t Q Figure 29. Reduced v a ria b le master curve fo r PT-1200. 0 -1 30°C; A-140°C; •-150°C; x-160°C. I0a 0 1 0 10 id1 10 8 n t Figure 30. Reduced variable master curve for X-231• 0-1 30°C ; A-1 i40°C ; •-150°C; x-160°C Viscosity r) (Pa.sec 1 0 i i i > > _ _ - p . _ Shear stress (Pa.) 2 Figure 31. E ffe c t o f carbon black (Raven 410, surface area 24 m /gm) loading on the v is c o s ity o f copolymer PT-1200 at 150°C at various shear stresses. -t- Viscosity n (Pa.sec) I v y 105 1 0 to*' _j_ _ 10® Figure 32. 1 0 J iO1 10? Shear stress (Pa.) E ffe c t o f carbon black (Raven 1020, surface area 95 m2 /gm) loading on the v is c o s ity o f copolymer PT-1200 at 1500C at various shear stresses. Viscosity n (Pa.sec) -e- N > 10 10 K f 10 1 0° 10 _L « r io- 4 Shear stress (Pa.) 10 10* Figure 33 E ffe c t of carbon black (Raven 5250, surface area 525 m /gm) loading on the v is c o s ity o f copolymer PT-1200 at 150°C at various shear stresses. Viscosity n (Pa.sec) 4^ L a ) io5 1 0 10 10° Figure 3^. 10x 1 C T 10s Shear stress (Pa.) 10' 10- E ffe c t o f carbon black (Raven 7000, surface area 625 m /gm) loading on the v is c o s ity of copolymer PT-1200 at 150°C at various shear stresses. Viscosity n (Pa.sec) \ Shear Figure 35 - c - -C- stress E ffe c t o f carbon black surface area on the v is c o s ity o f PT-1200 at 150°C contain ing 10? carbon black a t various shear stresses. Viscosity r) (Pa.sec) Figure 36 Shear stress (Pa.) E ffe c t o f carbon black surface area on the v is c o s ity o f PT-1200 at 1500C c o ntaining 20 % carbon black at various shear stresses. Viscosity n (Pa.sec) I Figure 37. 105 1 0* Shear stress (Pa.) E ffe c t o f carbon black surface area on the v is c o s ity of PT-1200 at 150°C c o ntaining 30% carbon black at various shear stresses. -C - O N Table 10. E ffe c t o f surface area o f f i l l e r on y ie ld values C-BLACK LOADING: 30% (wtl) Surface Area m2/gm Yield Stress Dyne/cm2 C ritic a l Shear Rate -1 sec 625 1 .7x105 2.4x10_1 525 k 3.0x10 1.8x10-1 95 7.0x103 6.6x10-2 24 1 .7x103 1 .8x1 O'2 C-BLACK LOADING: 2-0% (wt.) Surface Area m 2/gm Yield Stress 2 Dyne/cm C ritic a l Shear Rate - 1 sec 625 9.0x103 7.0x10-2 L A CM L A 4.3x103 6.6x10-2 95 9.2x102 1 .3x10“2 2k - - 147 C-BLACK LOADING: 10% (wt.) C ritic a l Shear Rate Yield Stress Dyne/cm^ Surface Area m /gm sec 1 .85x10 625 9.2x10 NOT OBSERVED 1A8 It would appear from a ll 't h e experimental data that at high levels the carbon black was able to interact or aggregate in such a way as to produce g e l-lik e structure or apparent gel-1 ike structure which must be disrupted by high stress levels before flow can begin. The gel easily reforms when stressed are removed. The carbon black cab assumed to form pseudo-crosslinks within the copolymer matrix and i the a b ilit y to form these pseudo-crosslinks depends on the surface area of the carbon black. These pseudo-cross links are extremely shear sensitive. The decrease in viscosity with an increase in shear rate was maximum for carbon black having highest surface area for a fixed f i l l e r loading. An examination of the experimental data reveals that there were two d is tin c t ways in which the viscosity of the f i l l e d system decreases with an increase in shear rate, i n i t i a l l y , at low shear rates the decreases was much greater, at some shear rate the decrease was not so intense. The steepness of the in i t i a l decrease of viscosity depends on f i l l e r concentration and surface area. The effe c t of f i l l e r depends on the experimental time scale, i t wears o ff at high shear rates. We propose that the f i l l e r concentration (for a fixed surface area) and experimental time scale (shear rate) are analogous. Based on this assumption we plan to obtain a master curve at some f i l l e r loading as our reference. We need to have a horizontal s h ift facter "a M which w ill enable us to superpose the flow p ro file of d iffe re n t y carbon black loading onto the reference curve. 1 ks CHAPTER V CONCLUSION Copolymers of styrene and butymethacrylate, the major polymeric component of electrophotographic toners, have been characterized. The chemical composition was determined by elemental analysis for carbon and hydrogen and by correlation to glass transition tempera-* tures determined by d iffe re n tia l scanning calorim etry. The copolymers vary in weight percent styrene from 50 to 70%. Molecular weights were determined by gel permeation chromatography, fractionation and in trin s ic viscosity measurements. The weight average molecular weights approximate 60,000 with a polydispersity (Mw/Mn) about two. The flow behavior of the copolymers was investigated by a com bination of rheological techniques such as cone and plate and c a p il lary rheometry at various temperatures. Measurements of the depen dence of viscosity on shear rate indicate the flow and fusion behavior of toners which a ffe c t the q u ality of p rin tin g . The activation energy for viscous flow reduced s lig h tly with shear rate and was not depen dent on the molecular weight of the copolymer. The zero shear viscosity increases with molecular weight and/or styrene content within the copolymer. The temperature e ffe c t on viscosity was eliminated by preparing a master curve at a reference temperature of 150°C. The v e rtic a l s h ift factor a^ was proportional to (a-j.) ^ and the horizontal s h ift factor was proportional to ( a j ) ^ ' ^ ” • 150 Toner copolymers containing carbon black were prepared by melt mixing, and the uniformity of mixing assessed by optical microscopy of thin film s. Rheometric studies illu s t r a t e the altered flow properties of f i l l e d toners. Addition of carbon black results in the viscosity being increased especially at low y and t ^ ie ^evel of carbon black increases, the viscosity at low shear rates becomes increasingly unbounded and eventually appears to go to in fin ity at a value c r.|2 equal to the yie ld stress for the system. The increase of viscosity and a markedly enhanced shear rate dependence were observed for carbon black with high surface area. Using a low surface area carbon black, i t was possible to incorporate at least 20 weight percent of the f i l l e r and s t i l l approximate the viscosity of the pure copolymer, even at moderately low shear rates. It would be important to minimize the surface area of carbon black consistent with main taining a good dispersion, reduce molecular weight and styrene content in order to enhance flow during printing. Future plans call for further rheological characterization of the copolymer and f i l l e d systems by performing transient and dynamic measurements to supplement the s ta tic data already obtained. The ! dependence of modulus on time and temperature fo r specific copolymers | I containing f i l l e r s of varied type and surface area can be determined, I In addition to the loss modulus and viscosity we can determine the storage modulus and e la s t ic it y . I t is very important to examine the interaction of the f i l l e r with the individual constituents of the copolymer. This requires synthesising pure polystyrene (currently under progress) and poly 151 Butyl methacrylate of controlled molecular weights. I n i t i a l l y the rheological behavior of pure and f i l l e d homopolymers has to be examined in order to predict the behavior of f i l l e r within the copolymer. It would be very interesting to examine blends of homopolymers of sim ilar composition and molecular weight to those of the copolymer in order to more precisely control the dispersion of f i l l e r and the flow behavior. The study of blends would enable us to examine the e ffe c t of a macroscopicly incompatible matrix on the location and adhesion of f i l l e r p a rticle s . S im ilarly blending random copolymers with homopolymer may allow control led enhancement of flow. 152 LIST OF SYMBOLS (MELT RHEOLOGY) p - flu id density V - local v elo city U - internal energy per unit mass g - g ravitatio n al acceleration q - heat flu x vector s - stress tensor u - vi scosi ty Y — rate of shear s - slippage factor N* - e ffe c tiv e no. of chain segments N - number of chain segments in the i Me - Molecular weight between entangli M - Molecular weight f - fr ic tio n factor H - Avogadro's Number Vf - free volume 0 - viscosity V - specific volume A, B - constants in D o o little equation f - fractional free volume v^/v f g - fractional free volume at Tg a^. - c o efficie n t of thermal expansion t , - a 12 - shear stress 153 K - consistency fa c to r n - flow index - s h ift factor riSp - specific viscosity [ n] - In trin s ic viscosity ri^ j - re la tiv e viscosity C - concentration K‘ - constant - rotational speed 9 - cone angle M - Torque Ky - torsion bar constant AT - deflection due to torque D - diameter of c ap illary L - length of c a p illa ry Q . - volumetric flow rate P - pressure drop t - shear stress at the wall w C.0 - WLF constant at T = 150°C • o C„° - WLF constant at T = 150°C i- o C? - WLF constant at Tg Cf - WLF constant at Tg a^ - vertic a l s h ift factor - horizontal s h ift factor a_ - s h ift factor for various carbon black loading 15A REFERENCES (MELT RHEOLOGY) 1. 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Creator Lakdawala, Khushroo H. (author)

Core Title Rheological studies of polymer solutions and filled polymer melts

Degree Master of Science

Degree Program Chemical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag chemistry, polymer,engineering, chemical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Salovey, Ronald (committee chair), Chang, Wenji Victor (committee member), Yortsos, Yanis C. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c20-314112

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