. 'o\s ”4.3. ‘e w; 3‘. ' ,9. g C)- ‘m a: 4‘ ‘t ‘ . .y&u’5,{[¥”‘.x. a Evin. 9‘1 4‘ 9.1% . ,1“ {ukziy :03” , 4. “102:: ”55/“: 1 {*fl' ~ -. "Vt-1 u¢ru ,{un ‘ u l. ”< THESiS This is to certify that the dissertation entitled Studies on the Grafting Reaction Between Polymers Having a Large Number of Reactive Groups and the Formation of Compatibilized Blends presented by Li Nie has been accepted towards fulfillment of the requirements for Ph.D. degree in Chemical Engr. J (EMMA/(1W A [My (14W ‘ x Major professor U Date 31011/79 ' l MS U is an Affirmative Action/Equal Opportunity Institution 0 12771 “ ulmmmmmi 1293 3 1 91 LIBRARY Michigan State Unlverslty PLACE ll RETURN BOX to romovo thi- ohockout from your record. TO A ID FINES return on or More am duo. DATE DUE DATE DUE DATE DUE STUDIES ON THE GRAFTING REACTION BETWEEN POLYMERS HAVING A LARGE NUMBER OF REACTIVE GROUPS AND THE FORMATION OF COMPATIBILIZED BLENDS By Li Nie A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Chemical Engineering 1994 ABSTRACT STUDIES ON THE GRAFTING REACTION BETWEEN POLYMERS HAVING A LARGE NUMBER OF REACTIVE GROUPS AND THE FORMATION OF COMPATIBILIZED BLENDS By Li Nie The formation of graft copolymers in the course of grafting reactions between two polymers each having a large number of reactive groups can result in compatibilized blends. Cellulose acetate (CA) and styrene maleic anhydride random c0polymers (SMA) were selected in this study. The inclusion of SMA into CA can improve the dimensional stability of CA, one of the major shortcomings of CA. Grafting reaction happens in solution between the hydroxyls of CA and the anhydrides of SMA. The grafting process was studied in detail to understand the various parameters that are important to the rate of SMA grafting conversion. The compatibilized blends have greatly improved dimensional stability in comparison to CA while maintaining good mechanical properties. Phase size and homogeneity in ternary blends depend on the structures of graft copolymers and the amount of graft copolymers in the mixtures. Studies based on transmission electron microscopy showed that uniform phase size distribution appears when there are substantial amounts of graft copolymers. Polydispersity in reactive polymers was found to be desirable for free chain solubilization based on the current understanding on the solubilization phenomena. A thorough theoretical analysis based on a kinetic approach was done to look into the various parameters that are important for the build up of graft copolymers up to the point of gelation. The grafting system is defined as two reactive polymers A and B having a large number of reactive groups a and b, where a react irreversibly with b in a homogeneous state. The grafting reaction of CA with SMA falls into this system. It was found that the percentage conversion of the reactive polymers is quite limited in order to avoid too high a system's weight-average molecular weight. The presence of high molecular weight tail in the polydisperse reactive polymers will reduce the extent of graft conversion of the reactive polymers. A self-consistent kinetic theory was developed and a general procedure was provided to look into the extent and the effect of intramolecular reaction in the defined grafting system. The self-consistency is satisfied via a normalization procedure that reflects the hidden redistribution of polymer species away from the complete randomness due to differences in volume exclusion for different species. The self-consistency in past gelation theories as a whole was not adequately addressed in incorporating the presence of intramolecular reaction. This part of the work makes an important contribution to the completeness of the gelation theory. Copyright by LI NIE 1994 to my parents, my wife and my beloved son ACKNOWLEDGEMENTS I would first and foremost like to thank my thesis advisor, Prof. Ramani Narayan, whose guidance, dedication and optimistic thinking steered me in the right direction whenever I wavered. I would like to thank the members of my committee, Prof. Eric A. Grulke, Prof. Lawrence Drzal, and Prof. James Jackson for their helpful suggestions. Special thanks are to Prof. Grulke for reminding me some of the theoretical work about molecular weight, molecular weight distribution and a lot of discussion during the course of my research. I would also like to thank Prof. Dale J. Meier at Michigan Molecular Institute for patiently answering my questions about the current theoretical understanding on microphase separation in block copolymer systems. I thank all the peoples in Prof. Narayan's group for their helps in various ways. They are: Dr. Zhongxiao Chen, Dr. Steven Bloembergen, Mr. Dimitri C. Argyropolus, Mr. Ajay Gupta, Mr. Steve Hull, Mr. Amit Lathia, Mr. Mohan Krishnan, Mr. Rick Rizzo, Mr. Dave Witzke, Mr. Mark Benedict, Mr. Joe Snook, Ms. Julie David, Ms. Amy Gustafson, Mz. Dea Ann Nicholes. I'would like to thank Mr. Michael Rich in the Composite Materials and Structures Center for the access of various instruments, Dr. Stan Flegler, Dr. John Heckman and Dr. Karen Klomparen in the Center of Electron Optics for helps in TEM work. I thank Michigan Biotechnology Institute for providing generously the lab space and computers for most of my work. I thank the Department of Chemical Engineering, Coultaulds plc. and ARCO Chemical Comp. INC. for financial supports. Last, and certainly not least, I thank the support of my wife Weixuan for never complaining about the long hours in the lab. TABLE OF CONTENTS LIST OF TABLES - - - - ....... LIST OF FIGURES NOMENCLATURE CHAPTER 1. INTRODUCTION 1.1 1.2 1.3 1.4 1.5 gate. TRUST FIELD OF THE WORK THERMODYNAMICS OF POLYMER BLENDING MISCIBLE BLENDS - IMMISCIBLE BLENDS COMPATIBILIZED BLENDS 1.5.1 Graft copolymer as compatibilizer AQUNNHHu—A 1.5.2 Synthesis of graft copolymers 1.6 IN SI TU GENERATION OF GRAFT COPOLYMERS TO FORM 1.7 1.8 1.9 1.10 OBJECTIVES OF THE RESEARCH COMPATIBILIZED BLENDS CLASSIFICATION OF GRAFTING SYSTEM VIA GRAFT COUPLING CELLULOSE ACETATE/ POLY(STYRENE-co-MALEIC ANHYDRIDE) TWO IMPORTANT ISSUES -10 10 1.11 ORGANIZATION OF THE THESIS 1.12 TERMINOLOGY. ...... 11 -- 12 2. EXPERIMENTAL - - -- - - - - - 2.1 MATERIALS 2.2 CONSTRUCTION OF PHASE DIAGRAM...-. ................... 2.3 GRAFTING REACTION...-.. - - 2.4 CHARACTERIZATION ............................................................................. 2.4.1 Extraction separation 2.4.2 Analysis by gel permeation chromatography (GPC) ...................... 2.4.3 Sample preparation - -- ..................... 2.4.5 Differential scanning calorimetry (DSC)- - - ......... 2.4.6 Electron microscopy--- ----- 2.5 PROPERTY EVALUATION - ----- . 2.5.1 Tensile property 2.5.2 Moisture adsorption - - 2.5.3 Dimensional stability ------------ ....-_- - -- - -- . GRAFTING REACTION AND THE PROPERTIES OF THE GRAFTING REACTION PRODUCTS- -- _- -_ _- - - _ - - -- 3.1 PHASE DIAGRAM OF TERNARY MIXTURE 3.2 GRAFTING REACTION . 3.2.1 Description of the rate of SMA grafting conversion in the absence of water 3.2.1.1 Effect of polydispersity on the change of E: III: with grafting conversion 3.2.1.2 Effect of stirring speed on grafting reaction 3.2.1.3 Effect of polymer concentration 3.2.1.4 Effect of catalyst concentration 3.2.1.5 Effect of reaction temperature 13 13 15 15 16 16 21 21 21 21 22 22 -31 35 3.2..16 EffectofMAlevelofSMA ontherateofgrafting 118060“ ----. -. -- ----- 3.2.2 Effect of small amount water on grafting reaction 3.3 PROPERTIES OF THE GRAFTING REACTION PRODUCTS............. 3.3.1 DEP as plasticizer- - -- - - 3.3.2 Tensile properties - - - ----- 3.3.3 Moisture adsorption -- - -- 3.3.4 Dimensional stability- -- - -- -- -- -- - -- 3.4 SUMMARY - - - -- - 4.1 BACKGROUND LITERATURE 4.2 GRAFTING CONVERSION OF CA VERSUS SMA 4.3 SELECTIVE GRAFTING CONVERSION OF THE HIGH MOLECULAR WEIGHT CHAINS OF THE REACTIVE POLYMERS 4.4 PHASE SIZE AND HOMOGENEITY 4.5 PHASE SIZE AND STABILITY ------ - - - 4.6 SUMMARY . THEORETICAL ANALYSIS OF THE BRANCHING PROCESS OF GRAFTING REACTION BETWEEN TWO REACTIVE POLYMERS........ 5.1 BACKGROUND LITERATURE - 5.2 THEORETICAL DEVELOPMENT - 5.2.1 Monodisperse reactive polymers 5.2.1.1 Balance equation- -- 5.2.1.2 Concentrations of polymer species 5.2.1.3 Molecular weight averages and gel point 5.2.2 Polydisperse reactive polymers - 5.2.2.1 Balance equation 35 37 41 43 - 47 . PHASE BEHAVIORS OF GRAFTING REACTION PRODUCTS................. 49 49 55 69 69 73 74 74 76 79 -79 5.2.2.2 Concentrations of polymer species 5.2.2.3 Molecular weight averages and gel point - 82 5.2.3 Average numbers of graft linkages on each polymer A segment of the graft copolymers 5.3 DISCUSSION - 5.3.1 Monodisperse reactive polymers- ------------------ SEES 5.3.2 Effect of polydispersity - - 5.3.3 Average numbers of graft linkages on each polymer A segment of the graft copolymers 94 5.4 CA-SMA GRAFTING SYSTEM - - 96 5.5 SUMMARY - 98 . EFFECT OF INTRAMOLECULAR REACTION ON THE BRANCHIN G PROCESS OF GRAFTING REACTION BETWEEN TWO REACTIVE POLYMERS - - _- 100 6.1 BACKGROUND LITERATURE_ - - -- 101 6.2 THEORETICAL DEVELOPMENTS -- - 105 6.2.1 Probability of intramolecular reaction - - 105 6.2.1.1 Intrinsic probabilities of intramolecular reaction for the chain segments of A and B of a simple graft copolymer......... 108 6.2.1.2 Average intrinsic probabilities of intramolecular reaction of the chain segments of A and B of any graft copolymer............ 110 6.2.1.3 Probabilities of intramolecular reaction of the graft copolymers and system's probability of intramolecular reaction...............111 6.2.2 Kinetic formulation..- - - - -_ - - 112 6.2.3 Weight average molecular weight (WAMW) and gel point.......... 113 6. 2. 4 Effect of chain characteristics and dilution on the model parameter ------ . - - 119 6.3 DISCUSSION-.. - -- - - -- - - 122 6.3.1 Order of magnitude of 6, . 122 6.3.1.1 A special case: N. = N” v. =v,--- 6.3.2 System's probability of intramolecular reaction - 6. 3. 3 Gel point and system's weight-average molecular weight (WAMW)- - -- - 6.4 EFFECT OF POLYDISPERSITY 6.5 EFFECT OF INTRAMOLECULAR REACTION IN CA-SMA GRAFTING REACTION 6.6 SUMMARY 7. CONCLUSIONS AND SUGGESTION FOR FURTHER WORK 7.1 CONCLUSIONS 7.2 SUGGESTION FOR FURTHER WORK - -- 123 - 127 127 -130 130 132 134 134 139 APPENDICES -- Appendix A: Solution by the method of characteristics Appendix B: Serial solution of the characteristic equatiom considering intramolecular reaction -- _ BIBLIOGRAPHY . -- - - - - ------ 140 140 144 LIST OF TABLES Table 3-1 3-2 3-3 3-4 3-5 3-6 3-7 3-8 3-9 3-10 Tensile properties of the east films with/without plasticizer 5-1 5-2 5-3 6-1 6-2 Effect of stirring speed on grafting rate.‘ f; .vs. reaction time at different polymer concentrations.* 31 Film clarity of reaction products prepared at three polymer concentration! 34 Effect of reaction temperature on the grafting conversion of SMA.‘.......... Effect of MA level on the grafting conversion of SMA *- - Weight change of the reaction products at three water content and reaction times * Weight change of CA at two degrees of substitution Effect of small amount water on the grafting conversion of SMA '....... Glass transition temperature of SMA in the presence of DEP Critical grafting conversion .vs. molar ratio Effect of polydispersity of the reactive polymers on critical grafting conversion at various molar ratios - Effect of PDI of A on the critical grafting conversion at various molar ratios Effect of 8 on the critical grafting conversion at two molar ratios.............. Probability of Intramolecular Reaction it at f A“ 35 36 36 37 37 38 42 85 92 92 128 128 LIST OF FIGURES Figure Page 1-1 SEM picture of the melt blend of CA-SMA showing macrophase separation and interfacial debonding (SMA being the dispersed phase) ............................... 3 2-1 Structures of CA and SMA .............................................................................. 14 2-2 Molecular weight distribution of CA and SMA from GPC analysis ................... 14 2-3 Structure of DMAP .......................................................................................... 15 2-4 GPC evolution showing association of CA and SMA in DMF ........................... 18 2-5 GPC evolution showing reasonable molecular distributions of CA and SMA in THF .............................................................................................. 18 2-6 GPC evolution showing association in grafting reaction products ...................... 19 2-7 GPC evolution showing the shift of molecular weight distribution toward higher molecular weight .................................................................................... 19 2-8 GPC evolution showing association for CA and SMA when small amount of water is added to THE ...................................................................................... 20 3-1 Phase diagram of DMF-CA-SMA at 110°C (weight percentage basis) .............. 24 3-2 Reduced weight-average molecular weight of free SMA versus grafting conversion at two values of PDI for two types of distribution ........................... 29 3-3 Molecular weight distribution of SMA fitted with Schulz function ...................... 29 34 Linear fitting for homogeneous grafting reaction showing constant reaction rate 33 3-5 Change of -1n(1- f3“) with reaction time at three concentrations ..................... 33 3-6 First order dependence of reaction rate on the concentration of DMAP catalyst. 34 3-7 DSC scan of CA films with different amount of DEP cast at room temperature 39 3-8 DSC scan of CA films with different amount of DEP cast at 80°C ..................... 40 3-9 DSC scan of CA-SMA grafting product at different DEP content cast at 80°C.. 40 3-10 DSC scan of film samples with/without isothermal at 190°C for 15 minutes ....... 41 3-11 Moisture adsorption of CA, CTA and the alloy ................................................. 43 3-12 Comparison of dimensional changes at 25°C ..................................................... 45 3-13 Comparison of dimensional changes at 51°C ..................................................... 45 3-14 Comparison of dimensional changes at 66°C ..................................................... 46 3-15 Comparison of dimensional changes at 95°C ..................................................... 46 4-1 Idealized morphologies and the effect of solvent. .............................................. 50 4-2 Grafting conversion of CA versus that of SMA ................................................. 55 4-3 Change of the number-average molecular weights for the grafted and ungrafted SMA chains and the ratio of the two with grafting conversion ........... 57 44 Change of the ratio of the effective number-average molecular weight of the grafted SMA chains to the number-average molecular weight of the free SMA chains with grafting conversion ......................................................... 58 4-5 TEM micrographs of films cast from acetone-water mixture solvent (96:4) at 70°C with 25% SMA in the alloy. f3“: (a)=0.26, (b)=0.39, (c)=0.51, (d)=0.74 ............................................................. 60 4-6 TEM micrographs of films cast from acetone-water mixture solvent (96:4) at 70°C with 50% SMA in the alloy. 3}“: (a)=0.30, (b)=0.45, (c)=0.56, (d)=0.66 ............................................................. 61 4-7 TEM micrographs of films cast from THF-water mixture solvent (96:4) at room temperature with 25% SMA in the alloy. fsfiuz (a)=0.26, (b)=0.39, (c)=0.51, (d)=0.74 ............................................................................ 62 4-8 TEM micrographs of films cast from THF-water mixture solvent (96:4) at room temperature with 50% SMA in the alloy. fSL: (a) =0.30, (b)=0.45, (c)=0.56, (d)=0.66 ............................................................................ 63 4-9 Change of domain size with conversion ............................................................ 66 4-10 TEM micrographs of cast films from TI-lF-Water mixture solvent cast with a film applicator and dried at 50°C. 33,: (a)=0.30, (b)=0.45, (c)=0.56, (d)=0.66 ............................................................................ 67 5-1 Illustration of the branching process after transformation of the molecular forest of trees into a forest of rooted trees (with permissions from Richard F. Voss and Elsevier Science Publishers B. V.) ...................................................... 70 xiv 5-2 System's reduced graft copolymer concentration in relation to grafting conversion and molar ratio ............................................................................... 5-3 Reduced concentration of the simplest graft copolymer in relation to grafting conversion and molar ratio ............................................................................... 5-4 Reduced system number-average molecular weight in relation to grafting conversion and molar ratio .................................................. 5-5 Reduced system weight-average molecular weight in relation to grafting conversion and molar ratio ............................................................................... 5-6 Weight fraction molecular weight distributions of Schulz and Wesslau functions at two P.D.I. values ........................................................................... 5-7 Reduced system weight-average molecular weight of Schulz and Wesslau distribution functions with P.D.I. of 2 in relation to grafting conversion and molar ratio ....................................................................................................... 5-8 Average numbers of linkages of A chain of the graft copolymers versus grafting conversion .......................................................................................... 5-9 Comparison of the amount of reactive groups of A consumed in polydisperse case to monodisperse case .......................................................... 5-10 Change of WAMW with SMA grafting conversion at two compositions ......... 6-1 Definitions for primary cyclization and secondary cyclization .......................... 6-2 2-d Model representation of the local environment of a simple graft copolymer ..................................................................................... 6-3 Naming for the chain segments of a graft copolymer ....................................... 6-4 Structure of one isomer of a simple graft copolymer ..................................... 6-5 Illustrations for block and star linkage ............................................................. 6-6 Fractional summation S(N)/ S(oo) .vs. the numbers of reactive groups on chain A and B ............................................................................................. 6—7 Average summation S(N,,N,,, 1) .vs. numbers of reactive groups on chain A and B ............................................................................................. 6-8 Model parameter 9 in relation to the numbers of reactive groups on chain A and B ............................................................................................. 6-9 System's probability of intramolecular reaction in relation to grafting conversion of polymer A and molar ratio ........................................................ XV 85 86 87 87 90 93 95 96 97 103 107 107 108 121 124 125 126 127 6-10 Reduced WAMW in relation to grafting conversion at different 9 with equal molar amount A and B ................................................................... 129 6-11 Reduced WAMW in relation to grafting conversion at different 9 with x of 2.0 .................................................................................................... 129 xvi .9 9| .5), I), a?“ 3’ €- 53 or ,on '...;j'f.... ....-.j'f’... OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO NOMENCLATURE storage index of the generating function for monodisperse polymer A storage index of the generating function for polydisperse polymer A model parameter in Schulz distribution reflecting polydispersity storage index of the generating function for monodisperse polymer B storage index of the generating function for polydisperse polymer B binary interaction energy density (energy/unit volume) initial molar concentration of polymer A initial molar concentration of polymer B reduced concentration of graft copolymers molar concentration of polymer species containing i A chains and J B chains reduced molar concentration of polymer species having i A chains and J B chains reduced concentration of all polymer species concentration of polymer species having i,i ',«- numbers of polymer A of different molecular weight and j,j',~-- numbers of polymer A of different molecular weight reduced concentration of polymer species having i,i numbers of polymer A of different molecular weight and j,j numbers of polymer A of different molecular weight variable relating to grafting conversion of polydisperse polymer A xvii G(A,B, Z) ......................... G, (I=A, 3, Am, Bu, Z) ...... OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 000000000000000000000000000000 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO .............................. OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 000000000000000000000000000000 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO fraction of polymer A found in graft copolymers (molar basis) grafting conversion of an arbitrary chosen chain fraction grafting conversion of A at gel point (molar basis) grafting conversion of polymer A (weight basis) grafting conversion of the reference free chain component of polymer A having a molecular weight equivalent to the number-average molecular weight of the initial A generating function in case of polydisperse A and B generating function in case of monodisperse A and B partial derivative of the generating function free energy of mixing length of the statistically equivalent unit molecular weight of monodisperse polymer A molecular weight of monodisperse polymer B reduced molecular weight of free chain component of polymer A reduced molecular weight of free chain component of polymer B number-average molecular weight of reaction mixture initial number-average molecular weight of reaction mixture weight-average molecular weight of reaction mixture initial weight-average molecular weight of reaction mixture weight average molecular weight of free chains number of dispersed SMA phase per unit volume average numbers of linkages of polymer A segment of the graft copolymers r.r”':jrj‘r"' ....;j’j"... OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO 000000000000000000000000000000 OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOO 000000000000000000000000000000 total numbers of isomers that can be constructed out of the simplest graft copolymer numbers of reactive groups i in polymer chain constitutional units of polymer I numbers of statistical equivalent units between two reactive groups with coarse-grained gaussian distribution numbers of structural units of the coordination ball molar fraction of chain component of the initial polymer A having molecular weight of 117% molar fraction of chain component of the initial polymer A having molecular weight of 117,. mean probability of {a,} reactive groups meeting with {b j} reactive groups of the simplest graft copolymer mean probability of {b1} reactive groups meeting with {a,} reactive groups of the simplest graft c0polymer probability of a, reactive group meets with b} reactive group fraction of grafting reaction for the generation of polymer species having i A chains and j B chains fraction of grafting reaction for the consumption of polymer species having i A chains and j B chains probability of grafting reaction for the generation of species having i,i numbers of polymer A of different molecular weight and jj ',--- numbers of polymer A of different molecular weight probability of grafting reaction for the consumption of species having i,i ',--° numbers of polymer A of different molecular weight and jj ',--° numbers of polymer A of different molecular weight grafting reaction rate of the system ratio of the numbers of reactive groups consumed in the polydisperse case to that of monodisperse case at the same weight basis grafting conversion of polymer A R .............................. ratio of the numbers of reactive group a of polymer A consumed in the polydisperse case to the monodisperse case at the same molar concentration and percentage conversion of polymer A Rwhm, .............................. radius of the coordination ball S .............................. number-average interfacial area of the two phases T8 .............................. glass transition temperature VA .............................. numbers of constitutional units carried by each reactive group of polymer A v, .............................. numbers of constitutional units carried by each reactive group of polymer B 11,. .............................. total volume of component i V“, .............................. volume of coordination ball 7; .............................. molar volume of component i w, .............................. weight fraction of component i in bulk W( M) .............................. weight fraction molecular weight distribution function x .............................. molar ratio of polymer A to polymer B Z .............................. variable relating to grafting conversion of monodisperse polymer A up .............................. fraction of u grafted SMA having the same chance of collision for reaction as the grafted SMA chain [3 .............................. normalization factor 0 .............................. model parameter in log-normal distribution reflecting polydispersity 9.- .............................. volume fraction of component i qt} .............................. volume fraction of polymer i in the bulk q): .............................. volume fraction of structural units i in the copolymer (P, .............................. number fraction of constitutional units containing reactive group a of chain A in the reaction system excluding solvent (p b .............................. number fraction of constitutional units containing reactive group b of chain B in the reaction system excluding solvent C.n,§,,n, ...................... F(b+2) ............................. 9(or 94 or 9,) ................ interfacial penetration depth solubility parameter (cal/cm3)°-s implicit variables bond angle between two constitutional units system's probability of intramolecular reaction probability of intramolecular reaction from species having i polymer A chain and j polymer B chains mean intrinsic probability of intramolecular reaction for reactive groups on chain A of the simplest graft copolymer mean probability of intramolecular reaction for reactive groups on chain B of the simplest graft copolymer mean intrinsic probability of intramolecular reaction for reactive groups on chain A of the graft copolymer having i A chains and j B chains mean probability of intramolecular reaction for reactive groups on chain B of the graft copolymer having i A chains and j B chains Garma function contribution to the probability of intramolecular reaction from the ith neighbor model parameter rotational angle Chapter 1. INTRODUCTION 1.1 TRUST FIELD OF THE WORK This work falls in the fields of polymer blends/alloys and block/graft copolymers. It is about the compatibilization of one reactive polymer with another reactive polymer each having large numbers of reactive groups. The two reactive polymers are immiscible. Control on the phase size and homogeneity of the compatibilized blends and the potential of gelation during the course of grafting reaction are two important characteristics of such system. 1.2 THERMODYNAMICS OF POLYMER BLENDING Blending two or more polymeric materials provides a simple way for tailoring the properties of the available materials, i.e., performance of materials (mechanical properties, impact properties, optical properties, solvent resistance and heat distortion temperature), processability, and cost effectiveness. The new material often exhibits combined properties when the blending components are miscible. Whether or not the two polymers are miscible depends on the free energy of mixing. According to Flory-Higgins's theory, the free energy of mixing for two polymers A and B in the assumed homogeneous state satisfies TV—f hinder—wee] an A B A B where 9.- is the volume fraction of component i , Bus is the binary interaction energy density, 17, is the molar volume of component i and V, is the actual volume of the l components comprising the mixture. For high molecular weight polymers, the entropy of mixing diminishes and the free energy of mixing is determined mainly by the enthalpy of ..g. 1.3 MISCIBLE BLENDS Polymers can be miscible when there are some kinds of specific intermolecular interactions ($11) so that the enthalpy of mixing is negative (exothermal). The $11 [cowie, 1985] may include acid-base interaction, hydrogen bonding, n-bonding etc. Chemical modification can lead to favorable interactions in some blend systems. In recent years, there have been increasing activities in finding miscible blends involving random copolymers. Many miscible systems were found with copolymers at a certain copolymer composition for the given blending pair. What has been found theoretically is that the unfavorable interactions within the random copolymer itself can be diluted by the presence of a proper polymer. It, therefore, provides opportunities for miscibility at a certain composition range, the so called miscibility window [Alexandrovich et al., 1977; Aptel and Cabasso, 1980; Eisenberg et al., 1982; Vukovic et al., 1983; Brinke et al., 1983; Kambour et al., 1983; Paul and Barlow, 1984; Liberman and Gomes, 1984; Pearce et al., 1984; Balazs et al., 1985; Shiomi et al., 1986; Bourland and Braunstein, (a)1986, (b) 1986; Gardiner and Cabasso, 1987; Aoki, 1988; Kim et al., 1989; Defieuw et al., 1989; Zhu et al., 1990; Jo and Lee, 1990; Brannock and Paul, 1990; Sun and Cabasso, 1991; Krause, 1991]. Current practice in miscible systems has been on the finding of new miscible blends under the guidance of this established theory. Nevertheless, among the vast variety of polymers commercially available nowadays the majority are still immiscible, even though more and more miscible blends have been found and will certainly continue to be found. 1.4 IMMISCIBLE BLENDS Unfavorable interactions between the structural units of two polymers cause immiscible blends. Irnmiscible blends are characterized by the presence of macrophase separations. Figure 1-1 shows an example of macroscopic phase separation of the blend of cellulose acetate/poly(styrene-co-maleic anhydride) (CA/SMA) prepared by extrusion process (typical of immiscible blends). There is complete demixing at the interface. The poor control on phase sizes and the lack of interfacial mixing lead to poor material properties, i.e., tensile strength, elongation, impact strength, and optical properties. The original meaning of blending is often lost because of this. Figure 1-1 SEM picture of the melt blend of CA-SMA showing macro- phase separation and interfacial debonding (SMA being the dispersed phase) 1.5 COMPATIBILIZED BLENDS 1.5.1 Graft copolymer as compatibilizer The presence of graft copolymers (I avoid mentioning block copolymers for the sake of coherence for my system) in the blends often helps make a better dispersion of the phase size and improves interfacial bonding [Paul, (a) 1978]. The ultimate performance of the material depends on the phase size and phase structure [Noshay and McGrath, 1977; 4 Bucknall, 1977]. The control on the phase size and morphology depends very much on the structures and the amount of the graft copolymers in addition to processing conditions. The amount of graft copolymers can vary from a few percent to nearly pure graft copolymers. Pure graft copolymers exhibit the limiting phase size (microdomain) and morphological behaviors. Commercial products are often characterized as ternary mixtures. This is particularly true for systems involving graft copolymers, i.e., high impact polystyrene (HIPS), acrylonitrile-butadiene-styrene (ABS). The most exciting discovery has been the extraordinary improvement of the impact properties of glassy polymers with the inclusion of rubbery materials. Optimum properties are obtained through careful design of the architecture of graft copolymers as and careful control on the content of graft copolymers so as to have the desired phase sizes and phase structures in the allolys [Echte, 1989]. To achieve this one needs to go back to the basics as to how the grafting scheme is selected to give the best process in the first place. 1.5.2 Synthesis of graft copolymers There is, perhaps, no particular reason to synthesize graft copolymers instead of block copolymers. The route for the formation of graft copolymers comes from the fact that active sites or reactive groups are more likely to be generated or present on the chain backbone in a random manner. There are basically two ways to synthesize graft copolymers: (a) graft copolymerization of monomers onto the polymer backbone (b) graft coupling between two reactive polymers In case of graft copolymerization the active or reactive sites on the polymer backbone initiate the polymerization of monomers to form graft copolymers. The active or reactive sites on the polymer backbone can be part of the polymer structure, they can also be generated right before graft copolymerization or during graft copolymerization by some initiating methods. The synthesis of graft copolymer both past and present adopts mostly graft polymerization via a free radical reaction, because of the availability of large numbers of vinyl monomers. Free radicals are generated on the polymer backbone by redox, UV irradiation and high energy radiation [Ceresa, 1976; Stannett and hopfenberg, 1971; Stannett, 1982, 1985; Mukherjee and Goel, 1985; Samal et al., 1986]. The radicals initiate the polymerization of monomers to form graft copolymers. Extensive studies have been conducted on the graft polymerizations of vinyl monomers onto cellulose and its derivatives [Stannett, 1982, 1985; Samal etal., 1986], nylons [Mukherjee and Goel, 1985] and poly(vinyl chloride) [Ceresa, 197 6]. Most of the studies were focused on surface modification to alter the surface properties of the materials. One of the major problems in graft polymerization has been the poor control of the amount of homopolymer production, the structures of the graft copolymers, and the chain lengths of the grafted chains and homopolymer chains. Graft polymerizations through ring-opening, condensation and ionic methods have been studied very little compared to free radical graft polymerizaitons. Ring-opening graft copolymerization of ethylene oxide with cellulose forming hydroxylethylcellulose is well- known. Sundet and Thamm [1977] reported studies on the synthesis and properties of the graft copolymers of pivalolactone with carboxylated polymers by ring-opening polymerization. Kobayashi et al. [198 8] reported ring-opening graft polymerization of 2- Oxazolines onto cellulose and cellulose diacetate with the hydroxyls being tosylated. Ring-opening polymerization is perhaps not a good route for the synthesis of graft copolymers since the initiating groups on the backbone are often numerous, and chain transfer could lead to poor control of molecular weight of the polymerized chain (low degree of polymerization). * Ionic graft polymerization includes cationic and anionic processes, the advantages of ionic graft polymerization come from the fact that the molecular weight and molecular weight distribution can be well controlled. Nevertheless, ionic graft polymerization is little studied. Kennedy et a1. [1974] studied aluminum alkyl-initiated cationic grafting of isobutylene onto the alylic and/or tertiary chloride sites present in poly(viny1 chloride). However, chain transfer to monomer limits the efficiency of this process. Falk et al. [1973] studied initiation of styrene by metallated polybutadiene. Ionic copolymerizations are more useful for the synthesis of block copolymers. The disadvantage of ionic reaction is the stringent requirement on impurities. Coupling reaction requires the matching of reactive groups on two reactive polymers. Rempp [1968] reported studies on backbone coupling by the interaction of a living polystyrene anion with macromolecules bearing ester side groups, e. g., poly(methyl methacrylate), the interaction results in the displacement of a methoxyl group and formation of a ketone graft linkage. Narayan [1990] developed a new synthetic approach to tailor-made cellulose-polystyrene graft copolymers with precise control over molecular weights, degree of substitution and backbone-graft linkage via displacement reaction of polystyrylcarboxylate anion with the mesylate groups on the cellulose backbone. The polystyrylcarboxylate anion was prepared by anionic polymerization. In a different reaction route, Holohan et al. [1991] prepared polydimethylsiloxane graft copolymers via the coupling reaction of bisphenol-A-based polyhydmxyether (phenoxy) with chlorosilyl- terminated polydimethylsiloxane (PDMS). The monofunctional PDMS oligomers were prepared by anionic polymerization of hexamethylcyclotrisiloxane using BuLi as initiator and chlorodimethylsilane or dichlorodimethylsilane as the terminating agent. 1.6 IN SI TU GENERATION OF GRAFT COPOLYMERS TO FORM COMPATIBILIZED BLENDS Compatibilized blend can be prepared with the addition of graft copolymer to function as a compatibilizer. It can also be prepared by reactive processing such as reactive extrusion where the graft copolymers are generated in situ. The most common way to make compatibilized blends is by reactive processing [Dean, 1985; Angola et al., 1988; Chen et al., 1988; Perron and Bourbonais, 1988; Kim and Park, 1991]. Solution or bulk grafting can be employed depending on the nature of the given system. In recent years, there have been increasing activities in the area of reactive polymers and reactive processing. The variety of functionalized polymers has grown, both in the nature of polymer backbone and in the array of functional groups [Benham and Kinstle, 1986]. This provides opportunities for the synthesis of graft copolymers and the development of new compatibilized blens and alloys. For example, one series of reactive polymers are the maleic anhydride based reactive polymers, the most important and celebrated family of reactive polymers [Sweeney, 1988]. Maleic anhydride is unique because of its reluctance to homopolymerization and its double functionalities: double bond and anhydride. The first successful commercial development was based on reactive blending of polyamide and ethylene-propylene modified rubbers containing grafted carboxylated or anhydride groups. Approximately 1 wt% of carboxyl or anhydride groups was sufficient to create a graft product by condensation reaction with the amino terminated polyamide, as described by Cirnmino and coworkers [1984] and others [Flexman, 1979; Wu, 1983, Chen and Kennedy, 1987]. There have been many studies utilizing the fast reaction between anhydride (or carboxylic acid) and amino groups on the polymer chain ends [Venkatesh et al., 1983; Dean, 1985; Chen et al., 1988; Angola et al., 1988; Perron and Bourbonais, 1988; Campbell et al., 1990; Chang and ku, 1991; Kim and Park, 1991]. A similar idea of simple grafting was also applied by DOW Chemicals in a system based on styrenic copolymers containing oxazoline groups. These resins were mixed reactively with carboxylated polyolefins [Sneller 1985; Baker and Saleem, 1987]. MA modified polymers such as Polypropylene [Gaylord et al., 1980], rubbery ethylene-propylene copolymer (EPDM), polyethylene (PE), Polystyrene (PS), etc., provide opportunities for the production of graft copolymers and its alloys. In a closely related field, extensive studies have been done on reactive filler-matrix blends and composites [Broutrnan and Sahu, 1971; Scott et al., 1987; Takase and Shiraishi, 1989; Tsubokawa and Kogure, 1991]. 1.7 CLASSIFICATION OF GRAFTING SYSTEM VIA COUPLING REACTION Coupling reactions between two reactive polymers can be classified into three categories according to the numbers of reactive groups on the backbones of the two reactive polymers: (a) one or two reactive groups on both polymers; (b) one or two reactive groups on one polymer and a large number of reactive groups on another polymer; (0) a large number of reactive groups on both polymers. The first category is often seen in block copolymer systems. C0polymerization and chemical modifications of homopolymers often result in a large number of reactive groups on the polymer backbones. Most condensation polymers bear reactive groups on the chain ends. There are, therefore, many combinations that fall into the last two categories. The most complicated graft copolymers in terms of structure will be produced in systems of the third category, and gelation occurs at a certain extent of a grafting reaction. 1.8 CELLULOSE ACETATE/POLY(STYRENE-CO-MALEIC ANHYDRIDE) GRAFTING SYSTEM Cellulose esters are one important family of modified natural polymers. They are prepared in multiton quantities with degrees of substitution (D.S.) ranging from that needed for hydrolyzed, water-soluble monoacetate (biodegradable), plastic secondary diacetate (DS=2.45, films, fibers, molding articles, filters) to those of fully substituted triacetate (photographic films, textile fibers) and specialty mixed esters (cellulose acetate propionate, cellulose acetate butyrate). Although cellulose ester plastics is noted for their toughness, face gloss, smoothness, and excellent optical clarity, its usefulness is restricted by many unfavorable factors. It is well known that cellulose diacetate has a dimensional stability problem when exposed to a high humidity environment. This is one of the biggest problems for applications in fibers and films. The other shortcomings are its high cost, high processing temperature and very limited compatibility with other synthetic resins [Brewer and Bogan, 1985]. So far only poly(4wvinyl pyridine) [Aptel and Cabasso, 1980] and poly(styrenephosphonate ester) at certain degree of phosphorylation [Gardiner and Cabasso, 1987; Sun and Cabasso, 1991] were reported to be miscible with cellulose acetate. These weak points hamper its competitiveness with most synthetic polymers, and there has been a declining demand in the market since 1965. Combining Cellulose acetate with other synthetic polymers can result in new functionalities and is one of the ways to combat these shortcomings. Styrene maleic anhydride random copolymers (SMA) with different maleic anhydride (MA) levels are commercially available. These resins are characterized by: excellent melt flow properties that provide ease of injection molding and extrusion; retention of stiffness under exposure to high heat and stress loading; inherent low moisture absorption which results in negligible change in dimension under high humidity; low thermal expansion coefficients over a broad range of temperatures and low mold shrinkage. The reaction between the anhydrides on the SMA backbone with the hydroxyls on the CA backbone provides a synthetic scheme for the production of graft copolymers. Compatibilized blends can be produced through such grafting reactions. The use of the grafting reaction between hydroxyl and anhydride is rarely seen in the open literature. Part of the reason could be for the relatively low reaction rate between the anhydride and the hydmxyl. One report utilizing such a reaction was given by Lambla et al. [1988] on the crosslinking of styrene maleic anhydride copolymer with dihydroxyloligostyrene in the molten state. It is important to point out here that the grafting reaction between hydroxyl and anhydride is of potential interest, given the fact that a vast number of natural polymers have hydroxyl groups. Combining natural polymers with synthetic polymers using such a grafting scheme could lead to important commercial development in the future even though the chemistry is not new. 10 The compatibilized blends are expected to have improved dimensional stability because of the inclusion of hydrophobic SMA. It is important that the optical clarity of CA be retained after the inclusion of SMA, since it is one of the most important selling points for CA. The potential application for such compatibilized blends could be in fibers and films for the replacement of cellulose triacetate (better dimensional stability). The problem with cellulose triacetate is the use of methylene chloride in fiber spinning and film casting. Concerns over the environment lend such a solvent unfavorable. Another potential application of the new alloys is new membrane material for ultrafiltration and reverse osmosis where the inclusion of SMA might help improve the compaction problem of CA membrane in the skin layer during operation. Compaction in the skin layer over the operation time reduces the flux of water permeation [Baayens and Rosen, 1972; Ohya et al., 1981; Funk et al., 1986]. 1.9 TWO IMPORTANT ISSUES There are two important issues that are general for the grafting systems of the third category: (a) when to stop the grafting reaction so that the system's weight-average molecular weight (W AMW ) is kept at a reasonable value from a processing point of view; (b) how the structures of the graft copolymers and the free chains, namely the effective chain length of the grafted chains and the ungrafted chains, differ, and what the effect of polydispersity is in promoting homogeneous phase size. Heterogeneity is often not good in terms of properties. The presence of macroscopic phase size results in a loss of optical clarity that could be crucial for some applications. 1.10 OBJECTIVES OF THE RESEARCH The combination of CA and SMA belongs to the third category as was classified above due to the large numbers of reactive groups on both CA and SMA. In this study, the grafting reaction between CA and SMA was canied out in solution. A thorough study on the compatibilization of CA with SMA covers many subjects: (a) the study on the grafting 11 reaction itself; (b) the development of graft copolymers; (c) characterization of the structures of the graft copolymers; ((1) phase size and phase homogeneity of the reaction products; and (e) evaluation of some of the properties of the new materials. A detailed study is not only important for the case of CA-SMA itself but also important in unveiling some points that are common to the system represented by this particular CA-SMA combination. The objectives of this research were three folds: 1. to examine the compatibilization of CA with SMA: the grafting reaction; the characterization of the reaction products; and the evaluation of some of the properties of the new blends. 2. to look at the phase size and phase homogeneity in relation to the structures of the graft copolymers and the content of graft copolymers in this particular grafting system. The results from this study shall apply to other cases under similar conditions. 3. to look in detail into the buildup of the graft copolymers of the grafting system, namely the branching process of the grafting reaction. Such an analysis is extremely important not only from the standpoint of understanding the complex system better but also from a control point of view in terms of processing. 1.11 ORGANIZATION OF THE THESIS Chapter 1 covers a general background of the field and the work as is shown above. Chapter 2 gives the experimental methods employed. Chapter 3 covers studies on the grafting reaction, the characterization of the reaction products and the evaluation of some properties of the reaction products. Chapter 4 gives experimental studies on the phase behaviors of the grafting reaction products. Chapter 5 covers theoretical analysis of the branching process of grafting reaction between two reactive polymers each having a large number of reactive groups (without the consideration of intramolecular reaction). Chapter 12 6 covers analysis of the effect of intramolecular reaction on the branching process of the grafting system. Conclusions and suggestion for further work were given in chapter 7. 1.12 TERMINOLOGY The term "polymer blends and alloys" is widely used in the open literature and industry. However, until now there has been no precise definition for "polymer blends" and "alloys". In the recently published superb and fundamental book by Utracki et al. [1989], "polymer blend (PB)" was defined as the "the all-encompassing term for any mixture of homopolymers or copolymers", "polymer alloys" was defined as "a sub-class of PB reserved for polymeric mixtures with stabilized morphologies", "compatible polymer blends" was defined as "a utilitarian term, indicating commercially useful materials, a mixture of polymers without strong repulsive forces that is homogeneous to the eye". There is no distinction between the terms "Alloys" and "compatibilized blends" according to above definitions. Alloys and compatibilized blends were used in the thesis for blends showing desirable properties. No attempt was made to clarify the definitions of "alloys" and "compatibilized blends". Chapter 2. EXPERIMENTAL 2.1 MATERIALS Cellulose acetate (CA, D.S.=2.45, Mw=103,000, Mn=46,000) was provided by Courtaulds plc. Styrene maleic anhydride random copolymers (SMA132: 4.75% maleic anhydride, Mw=274k, Mn=136k; SMA232: 7.08 wt% maleic anhydride, Mw=249k, Mn=126k; SMA332: 12.2% maleic anhydride, Mw=l93k, Mn=100k) were provided by ARCO Chemical Company. The content of anhydride in SMAs was determined by back titration in xylene with sulfuric acid (dissolved in ethanol), the anhydride was neutralized with potassium hydroxide for 24 hours, phenolphthalein was used as an indicator. SMA stands for SMA232 through out the thesis if not specified. Figure 2-1 shows the structural units of CA and SMA. There are, on the average, 85 hydroxyls per CA chain and 90 anhydrides per SMA chain from the number-average molecular weight. Gel permeation chromatography (GPC) analyses for the four samples were provided by Viscotek Corporation. Figure 2-2 shows the molecular weight distributions of CA and SMA. 4-Dimethylaminopyridine (DMAP) and anhydrous grade NN-Dimethylfonnamide (DMF, 99%) were purchased from Aldrich Chemical Company, INC. Figure 2-3 shows the structure of DMAP. 13 SMA (the distribution of MA is random) Figure 2] Structures of CA and SMA 120 O SMA A CA A o o A A at) F o O A A A o 2 co - ° v a A O A o o 40 . A A A o o o A o A A A 20 _ A 00 A ° A g 00° A A 3 4 s 6 7 Log(M) Figure 2-2 Molecular weight distribution of CA and SMA from GPC analysis 15 Mew/Me Figure 2-3 Structure of DMAP 2.2 CONSTRUCTION OF PHASE DIAGRAM Irnmiscibility between CA and SMA resins persists in the presence of a common solvent, even though the unfavorable contact between CA and SMA is much reduced by the solvent. The phase diagrams were constructed by visual observation on the cloudy point with successive addition of a small amount of solvent at a fixed polymer composition, the same method used by Dobry and Boyer-Kawennoki [1947]. The tie line was obtained by measuring the volume changes after equilibrating the CA solution with SMA solution for three days. The SMA solution of lower density was carefully transferred onto the surface of the CA solution in a tube with volume ticks. The tube was capped with a serum stop and heated gradually to 110°C for equilibration (little head space, excess pressure from air was released with needle). 2.3 GRAFTING REACTION Grafting reaction happens between the hydroxyl and anhydride to form a half ester with the aid of a catalyst. In the absence of water, the grafting reaction proceeds by ”Drew mag The complexity of the graft c0polymers keeps growing because of the large numbers of reactive groups on the chain segments of the graft copolymers. Above reaction route 16 gives the simplest graft copolymer. The grafting reactions were carried out in DMF solution at increased temperature and with stirring. DMAP was used as the catalyst~ The cellulose acetate was vacuum dried overnight at 80-100°C and kept under dry nitrogen before anhydrous DMF was transferred to the reactor through the transferring line. Water was added to the reactor through serum stop after the transfer of DMF in looking at the effect of water on the grafting process. DMAP was added after the polymer solution reached to a stable temperature. The reaction temperature was controlled within 02°C deviation. After reaction, the solution was cooled down immediately to room temperature, and was precipitated right away with three-time volume of water. Precipitate in the form of porous pulp (low grafting conversion) and porous string (high grafting conversion) was washed with excess amount of hot water every two hours for three times, it was soaked overnight with excess amount of water, further wash was done with methanol for three times. Extensive wash is for the removal of the residual DMF and catalyst. The samples were dried at room temperature to a dry state, and were dried further at 50°C under full vacuum. The amount of sample was weighted under dry condition since CA picks up moisture easily. 2.4 CHARACTERIZATION 2.4.1 Extraction separation Information on grafting conversion of SMA (wt%) was obtained by Soxhlet extraction with toluene for two days. Carbon-Hydrogen—Nitmgen (CI-IN) analysis (C%: CA=48.4%, SMA=89.7%) showed less than 3% of CA in the extractable. 80 only free SMA is extracted. The percentage conversion of SMA is obtained from mass balance. Extraction efficiency depends on the form of sample to be extracted. Precipitates obtained by slowly adding polymer solution (controlled to the concentration of 8g (CA+SMA)I100 ml DMF) into large volume of water is satisfactory for extraction separation. Extraction 17 on the precipitates of simple blends at two compositions (10%SMA, 50%SMA) gave 100% extraction of SMA. No appropriate solvent was found which extracts free CA only. 2.4.2 Amlysis by gel permeation chromatography (GPC) Studies on the molecular weights and molecular weight distributions of the grafting reaction products were attempted using GPC. The column for separation was a Plgel 20m m mixed-A column with a separation capacity ranging from 1k to 40M. Monodisperse polystyrene standards were used for calibration. The analyses were performed on a Viscotek 200 at a flow rate of 1.0 mein. with THF and 0.7 mein at 50°C with DMF. It was found that there are associations for both CA and SMA in DMF (see Figure 2-4). THF is a good solvent for both CA and SMA (Figure 2-5), the problem came from the grafting reaction products where GPC analyses showed unlikely high molecular weight averages, i.e., the weight-average molecular weight for the half hour reaction sample is more than two millions (see Figure 2-7, Table 3-2 and also theoretical analysis in section 5.4 of chapter 5). It can be explained by the association of SMA chains, free or grafted because of ionic association: grafting reaction with the formation of half-esters and the inevitable hydrolysis of a small amount of anhydrides due to the presence of trace amount of water. A few numbers of carboxylic acid groups on the SMA chain are enough for a substantial ionic association since THF is a non-ionizing solvent [Utracki et al., 1989]. Without theoretical analysis, it could have been taken as the true molecular characteristics of the grafting products since the molecular weight distributions of the grafting reaction products did shift with grafting conversion (Figure 2—7). Adding a small amount of water (2.5 v%) to THF resulted in the associations for both CA and SMA (Figure 2-8). No further attempt was made with GPC analysis. 18 4.66 195: nanourmandmd 3 . 00 6M: M-=6.000.000 A f: Snazaz O r v—t - '-, 35 2.06 ~~ ’1 l '. > .i ' E '. \l N86" '3 I \ fig 1 ea —— f x; i3 1 ‘2' \. \ .l 1"“. / \_ I - “Ce—L .1 .2/ V S .660 —e " ‘ "‘ couccuraarrou canonarocean _ 1 l 1 l L J J I l l _1 I 1.0q'30 ‘ 4.ba ‘ ' 7fbe ' ' rake ‘ ‘ 13’s I Retention volume Figure 2-4 GPC evolution showing association of CA and SMA in DMF Signal mv (x10+l) 4.60 ~~ sanzaz [\ uszou - I J.60 j— {I \ lcni ussn ' 2.oo-—_ {I i l ,n l '. r.aa-— ' t! / l. I : Li I at H—_‘__ — '.‘ 4’ .000 -— .__ :====a~—~' '— CONCENTRATION cuaonarocaan -:.00 . . J t I r L 1 n J u r r J i.ea ' ‘ 4.bo ‘ ‘ 7.bo ‘ ‘ rake ‘ I rake ‘ r47 Retention volume Figure 2-5 GPC evolution showing reasonable molecular distributions of CA and SMA in THF Signal mv (x10+l) Signal mv (x10+1) 4.00 .00 L) 24.00 1.00 .906 19 119 (cnosmtnruent our nszur [fl 6 . S It r I l 4- a I] :' 't .a' 1 I N S 6 t‘. .. I‘ l "a I: l-‘ '| I f .0- 1 ' l ‘1 ‘H I '1' ‘1. l: I" m I ‘ ti ' .l 1:1". (.1. I I l l I‘ZBrs H ll 1' ' I l T” i ("-‘u' I Vii j’}ii \ i ll ’ l l \ l l' -/ f t i \4 t f5 We- “-v-P'lzh‘z N —\ __1—'.:‘- -. —=:.__‘—‘_v— "_- _" .— V’ 1 w . ____ ‘h— I \~___—___ 5! \\ coucrnrnarlou cuaonarocana V J l A 1 l I an r l l '90 I i 4 b0 ‘ ‘ 7‘ba ‘ ‘ re‘o ' ‘ rahe ' I Retention volume Figure 2-6 GPC evolution showing association in grafting reaction products .808 '1Ji'10 Oucatcvs CONCENTRATION CHRONATOCRAH (lSOu) {1. 1.0 (hr) IF':|_ (h rs __ j .1 ‘v, a 2.0 (hrs) / If“; .. If. 1" I“. l I . I ’ ..y/ .‘l r. u l— "a: .1! 9“ 423' I, l ,5: 1 ti 369' r' a .. /. 5:! / '.'- in. ‘ .._._¥ r“ - ff it‘s A's-‘3“,- - -\ t: —'.=.—__—:..—_= "-3 ..i A! r r r r . 4 r r ; 4‘ 1;: r . i no I ‘ 4.ba ‘ T"thee I - rage ' ’ rifle ‘ ' Retention volume Figure 2-7 GPC evolution showing the shift of molecular weight distribution toward higher molecular weight 20 coucnnrnarrou cunonarocnnn 4.001—L l SHAZ32 curators 3 . 00 -— ca245 2 sna232 + :3 Fl 35’ 2.00.4; > 8 ca '3 l .g 1 e 00 —”" I \\ no i a, / /‘ \k 1"" 0000 q — --.\-"~_.’.‘:=‘_-iF—!~ _1 00 I I I .L I I I I I I I I L ' r. a ’l ‘ 4.ba P ' 7.ba ‘ I rate - rake ' ' Retention volume Figure 2-8 GPC evolution showing association for CA and SMA when small amount of water is added to THF 2.4.3 Sample preparation Films of the grafting reaction products were cast with a film applicator onto clean glass plate and dried at oven temperature of 80°C for 15 minutes. Films for DSC and TEM studies were cast from both acetone/water and THF/water mixture solvents (96v% organic solvent) at a polymer concentration of 0.8-1.0g/10ml. Films for moisture adsorption, tensile properties and dimensional stability were cast from acetone/water mixture solvent (96v% acetone), the polymer concentration was adjusted to proper viscosity for making nice films, it ranged fmm 0.8g/ml to 1.4g/ml. The solutions were stirred for two days before casting. Small amount of water was added to reduce the solution viscosity. Acetone and THF containing 4 v% water are very effective in reducing 21 the solution viscosity. GPC analyses showed that there are associations for both CA and SMA in the presence of water. 2.4.4 Differential scanning calorimetry (DSC) DSC studies were conducted to get the glass transition temperature (T3) of SMA, the glass transition temperatures and the melting temperatures of CA and grafting reaction products (cast films). T3 was taken as the midpoint of a step transition. 2.4.5 Electron microscopy Transmission electron microscopy (TEM): Phase size and phase homogeneity (homopolymer solubilization) of the film samples were studied by TEM. The phase contrast develops after the ultrathin sections were exposed to the electron beam for a few seconds. This can be attributed to the loss of material from the CA phase (which was appearing lighter) under the electron beam [Thomas and Talrnon, 1978]. Staining is not required for this system. Sections of silver color (60-90nm) were ultramicrotomed at room temperature. The TEM studies were performed on a JEOL IOOCX transmission electron microscope at an accerating voltage of 80 kV. Scanning electron microscopy (SEM): Blends of CA-SMA prepared by extrusion process (Baker-Perkins co-rotating interrneshing twin-screw extruder) were studied briefly using SEM to observe the macroscopic phase separation. The SEM studies were performed on a JEOL 35 CF scanning electron microscope at an accerating voltage of 10 kv. The samples were coated with a thin layer of gold. 2.5 PROPERTY EVALUATION 2.5.1 Temile pmperty The tensile properties of the cast films were tested according to ASTM D882-83. The tests were performed on a united tensile tester with a crosshead movement at a testing speed of 2%lmin. The test samples were cut into dimensions of 4 x 5/16" with a thickness 22 around 0.04". The thickness of a sarnpls was measured with a caliper having a precision of 0.0005". Before testing, the samples were dried overnight at 60°C and were conditioned at room temperature and also a relative humidity of 60%. All test samples were bubble free. The test results were reported by averaging 10 useful tests. 2.5.2 Moisture adsorption The moisture adsorptions of the cast films were tested according to ASTM D570- 81 at a relative humidity of 95%. 2.5.3 Dimensional stability The dimensional stabilities (moisture sensitivity) of the films were tested by soaking the films in water for 30 hours at different temperatures. The dimensional changes of the lengths of the films were measured after the film samples were dried naturally for one day. The initial dimensions of the films were taken as the dimensions cut from the glass plates. All samples have a dimension of 8 x 2". Chapter 3. GRAFTING REACTION AND THE PROPERTIES OF THE GRAFTING REACTION PRODUCTS 3.1 PHASE DIAGRAM OF THE TERNARY MIXTURE CA is immiscible with SMA (SMA132, SMA232, SMA332). Phase separation happens in solutions even though the presence of a large amount of solvent dilutes greatly the unfavorable interaction between CA and SMA. The phase diagram can be constructed according to the Flory-Higgins theory if the three phenomenological interaction parameters among CA, SMAs and the solvent are available. Scott's [1949] analysis shows semi-quantitatively the important feature of phase behavior in the ternary solution of polymer] + polymer’Z + solvent. For CA and SMA dissolved in DMF, no interaction parameters are available. The phase diagram was constructed by observing the cloudy point experimentally. Figure 3-1 shows the phase diagram of DMF-CA-SMA at 110°C on a weight percentage basis, the tie line is for CA—SMA232 only. Three important things are noted for grafting reaction from the phase diagram: (1) the shape of phase separation curve is very flat, therefore, a few percentage increase in the polymer concentration from the apex point will cause a drastic phase separation; (2) DMF partitions more in the CA phase than in the SMA phase, the SMA phase will be the dispersed phase if the amount of SMA is less than CA; and (3) the unfavorable interaction between CA and SMA decreases with the content of maleic anhydride in SMA. 23 24 DMF 2 + SMA13Z 6‘: SMA232 . SMA332 Figure 3-1 Phase diagram of DMF-CA-SMA at 110°C (weight- percentage basis) To have a better appreciation of the presence of solvent in diluting the unfavorable contact and the content of maleic anhydride of SMA resins in reducing the irnmiscibility between CA and SMA, one can do a qualitative analysis for the free energy of mixing of the ternary mixture. According to Flory-Higgins's theory, the free energy of mixing in the assumed homogeneous state satisfies AG," FT? = EVLL: 1“ (pom? T ¢DMF¢SMABDMr-sm (3_1) + ¢DMF¢CABDMF—CA + ¢CA¢SMABC4-SMA where the combinatorial entropies of CA and SMA have been neglected. Bi}- is the binary interaction energy density, for non-polar or slightly polar system it is related to the solubility parameters by 25 =1. .. 2 - B, ”(8.. 5,.) (3 2) Since DMF is a good solvent for both CA and SMA, the driving force for phase separation comes from the unfavorable interaction between CA and SMA (last term of equation 3-1). Let pa, be the volume fraction of CA in the absence of solvent, it's,“ be the volume fraction of SMA in the absence of solvent (to, +63,“ =1), the last term of equation 3-1 becomes ¢ca¢smBa-sm = ‘l’tx‘l’smBa-sm (1 — (four )2 (3‘3) One see from equation 3-3 that the dilution of the unfavorable interaction is quite sensitive to the amount of solvent in solution, especially at low polymer concentrations. The solutions are often prepared at a concentration of less than 20 wt% polymers due to a high solution viscosity. At this low end, the dilution for the unfavorable interaction between CA and SMA is very sensitive to the change of polymer concentration. As a result, the grafting process is expected to be much affected by the change of polymer concentrations. SMA resins are commercially available with several maleic anhydride (MA) contents. One can look at the effect of maleic anhydride content of the SMAs on the CA- SMA binary interaction energy density by decomposing the interaction between CA and SMA into the interaction among CA and the monomer units of SMA. Let 4):", be the volume fraction of maleic anhydride in SMA, 4);, be the volume fraction of styrene in SMA (62,, +4);’ =1), the binary interaction energy density between CA and SMA, following Paul and Barlow's generalization [1984], becomes BOA-SMA = Bro-64¢; + Barn-(14¢; — Buy-ara¢:ry¢:t¢ .. .. .. (3'4) = cry-Gt (1 - ¢ma ) + Bard-64¢“ — Bay-m (1 - ¢rna )¢m The presence of a minus term is due to the unfavorable interaction within the structural units of SMA. It is the presence of such unfavorable interaction within the copolymer 26 itself that leads to the potential of miscibility window in polymer blends involving random copolymers [Brinke et al., 1983; Kambour et al., 1983; Paul and Barlow, 1984]. To fix the idea, let us assume that the binary interaction energy density of 8W0, is zero (it is supposedly to have a small negative value for the possible weak hydrogen bonding between the hydroxyl of CA and the anhydride), and BM“ equals to 3...... (5“,:93, 50:12.7, 5m=13.6, 8,515.4, (cal/cm3)°5, sa stands for succinic anhydride, [Grulke, 1989]). It is conservative to have BCA-SMA = Buy-c140 _ ¢m )2 (3'5) We see from equation 3-5 that the unfavorable interaction between CA and SMA reduces with increasing MA content in SMA. This explains the shifting of the phase diagram as the MA content of SMA changes. However, the sensitivity of the MA content in reducing the unfavorable interaction is less than the solvent since the important commercial resins have the MA content of less than 25%. 3.2 GRAFTING REACTION 3.2.1 Description of the rate of SMA grafting conversion in the absence of water Grafting reaction will happen in the diffusive interface when each phase contains only one polymer (the following discussion is for CA—SMA232 only, SMA is meant for SMA232 in rest of the discussion). The phase size decreases as the grafting conversion of SMA increases. This is due to the dispersing power of the graft copolymers once they are formed in the reaction system. Experimentally it was observed that the clarity of the reaction solution changed gradually from opaque to clear. To understand the grafting process, we need to relate the grafting reaction to the percentage conversion of SMA, the only information we can obtain from extraction. The percentage grafting conversion of SMA is defined as 3* I 1h 27 . _1 [Mac 1_ (L—MdC) fm— —(IMdC°)m=( M°=,_C_°)”'" (3-6) The rate of disappearance for the concentration of free (ungrafted) SMA chain of a certain molecular weight satisfies ctMC 2MC°- (1— (1)2MC)” 81151“ dc, _ —(_Zt—)m=( (3 7) wherer Mis the rate of MA consumption. a MC /(2Mc° -(1- a M)2MC) is the statistical weight of the reaction used for the consumption of the chain species of that particular molecular weight (the numbers of MA reacted on the graft copolymers were neglected in the statistical weight due to the large numbers of MA on the SMA chains). or, is the fraction of ungrafted SMA chains that have the same chance of collision for reaction as the grafted chains. It is a function of phase size and phase size distribution. Its value should increase with grafting conversion if there were no blocking effect by the graft copolymers. 8 is the equivalent interfacial penetration depth for reaction. It should be relatively constant under given conditions. it is the total numbers of the dispersed SMA phase per unit volume. S is the number-average interfacial area of the two phases for the given size distribution of the dispersed SMA. Multiplying both side of equation 3-7 by M, and summing for all the i gives M dC. or M 2 - 42 ‘ -———'),,,, 0 Z L... 5’1er (3-8) dt =(2MHC -(1— a )EMC.” By substituting equation 3-6 into equation 3-8 and rearranging, we have df" M5 PD] 1 — -—""—"" 1— 8nS 3-9 dt =( f‘“ )(M °C° W1+f;m(1/ot,-1) r” ( ) M5 / M3 is the reduced weight-average molecular weight of the free SMA chains. PD] is the polydispersity index of the starting SMA. 28 Among several parameters of equation 3-9, only rm does not change with grafting conversion since the numbers of reactive groups consumed are negligible when the grafting conversion of SMA is less than 80%. The phase sizes and distribution are difficult to quantify since a number of factors contribute it: the extent of irnmiscibility between CA and SMA; the change of phase size and distribution with grafting conversion; and the stirring strength. As a result, the initial values of and the change of 01,, n, S" with grafting reaction are not readily available. Actual modeling of the rate of SMA grafting conversion is not attempted in looking at some parameters of equation 3-9. 3.2.1.1 Effect of polydispersity on the change of M: / M: with grafting conversion The change of 117: / M3 in equation 3—9 depends on the molecular weight distribution of the starting SMA. It satisfies 17.5 j M/ M'£(1— f”: )“m W(M)dM 17.? " [ (14,7, W”: wdM (3-10) where fm is the grafting conversion of the reference SMA chain having a molecular weight of the weight-average molecular weight of the starting SMA. In case of Schulz distribution we have 1 (17,: IE3)... =(1-f.'.'..)"*° (341) b is the model parameter characterizing the polydispersity of the sample. Figure 3-2 shows the change of 117: [MS with grafting conversion at two values of polydispersity for two typical distributions: Schulz and log-normal. We see from Figure 3-2 that the effect of polydispersity on M: Ill—If is quite substantial. The reduction of M1 [M3 is nearly linear with the percentage conversion of the polymer. 29 0 \~ ~\‘ ~ h \~. ~ 0.8 w- \“~ ‘ \‘ ~ - \ ‘ ~ . \ - log: 0.6 1- \ . ‘ \ \ "H g ‘ .4 -- , I: 0 ----- Schulz.PDl=2.0 \ ‘ -— - — Schulz. PDI=2.5 0.2 L Log-Nor...PDI=2.0 Log-Nor..PDI=2.5 0 i i i .L o 0.2 0.4 0.6 0.8 1 Percentage conversion Figure 3-2 Reduced weight—average molecular weight of the free. chains of a polymer versus the grafting conversion of the polymer at two values of PDI for two types of distributions The polydispersity of SMA is 1.98 from GPC analysis. Its molecular weight distribution can be modeled very closely by the Schulz function. Figure 3-3 shows the curve fitting for the molecular weight distribution of SMA using Schulz function. 0.7 0,6 41- 0.5 .1. 0.4 .. 0.3 4» W(M)M 0.2 4» 0.1 6 8 10 I2 14 16 ln(M) Figure 3-3 Molecular weight distribution of SMA fitted with Schulz function 30 3.2.1.2 Effect of stirring speed on grafting reaction The complexity involved in or, and n5 comes from both the extent of mixing and the dispersing power of the graft copolymers. The polymer solution is very viscous at a concentration of around 10 wt%. The dispersing force from the stirrer is of viscous shear. The low interfacial tension (diluted in the presence of solvent) at the diffusive interface will result in micron/submicron dispersion for the dispersed SMA phase (indicated by later TEM studies). The high solution viscosity slows down the merging of the dispersed phase to form dispersion of larger size. The formation of graft copolymers during the reaction provides a dispersing force for the dispersed phase to stabilize the dispersion (similar to the role of surfactant). The low interfacial tension and high solution viscosity, plus the stabilizing force from the graft copolymers formed more and more during the reaction, tend to reduce the effect of stirring intensity on the grafting reaction. Table 3—1 shows the effect of stirring speeds on the rate of grafting reaction. It can be seen that the grafting reaction rate increased slightly as the stining speed increased from 200 rpm to 600 rpm. Therefore the speed of stirring in that range is not particular important for the grafting reaction. A stirring speed of 400 rpm was selected in the rest of the studies. Table 3-1 Effect of stirring speed on grafting rate" Speed (rpm) 200 425 600 f " 0.41 0.43 0.44 SMA r CA:SMA=1:1, 14g polmelOOrnl DMF, 0.5g cat/100ml DMF, 2hrs., 110°C 31 3.2.1.3 Effect of polymer concentration The effect of polymer concentration on the rate of SMA grafting conversion was conducted at three concentrations. Table 3-2 lists the change of SMA grafting conversion with time at three polymer concentrations. Table 3-2 129;, vs. reaction time at different polymer concentrations“ 8g/100ml DMF 11 £00m] DMF 14g/100ml DMF Time (hrs) 1;}, Time (hrs) f5}, Time (hrs) f3“ 0.5 0.27 0.5 0.30 1.0 0.33 1.0 0.40 1.0 0.45 2.0 0.46 1.5 0.51 1.5 0.56 3.0 0.54 2.0 0.58 2.0 0.66 4.5 0.63 2.5 0.64 2.5 0.74 5.9 0.72 3.0 0.69 * CA:SMA=1:1, 0.5g DMAP/100ml DMF, 110°C We saw from Table 3-2 that the grafting conversion of SMA is very sensitive to polymer concentration. At a concentration of 8g/ 100ml DMF, the grafting process was very close to homogeneous (the solution turned to clear in less than 10 minutes). A plot of 2[1/(1—f&,)°‘5 -l] versus time is shown in Figure 3—4. The factor 2 is the value of denominator of the power term in equation 3-11 since b equals to zero for a polydispersity of 2. Constant reaction rate rm is shown from the linear curve fitting. We can probe somewhat into the effect of phase separation on the grafting process by plotting -ln(1-f) versus reaction time (see Figure 3-5). It happened that at the concentration of 11 g(CA+SMA)/ 100ml DMF the curve is nearly linear. The production of graft copolymer, therefore, helps disperse the homopolymers so to give higher reaction area. This is supported by the gradual transition of the solution clarity from opaque to clear. There is about one fold increase in the reaction area from the beginning to the grafting conversion of 75% since the reduction of M: lit—{,3 in equation 4-9 is close to half 32 at that conversion. However, such dispersion power from the graft copolymers seems to disappear at higher polymer concentration. There is an obvious deviation from the linear relationship at a concentration of 14g/100 ml. The grafting reaction solution never turned clear. The or, factor in equation 3—9 could be responsible for such behavior. The explanation is that the graft copolymer present at the interface may block somehow the chance of free chains to react. Such blocking action should increase with polymer concentration. As a result, more reaction is given to the graft copolymers at the same grafting conversion as compared to the situation of lower polymer concentration. It is to point out here that the presence of blocking effect by the graft copolymers is unfavorable for homopolymer solubilization since the effective chain length of the graft copolymer is reduced (see more detailed discussion in chapter 4). As a result, there is a reduction on the solubilization ability of graft copolymers for the free polymers. Tests of free SMA solubilization by comparing the optical clarity of cast film from acetone-water mixture solvent (96% acetone) are shown in Table 3-3. The transparency of the films comes from the homogeneous solubilization of the fiee SMA into the domains of the grafted SMA Only if the size of domains is well below the wavelength of visible light (see more detailed discussion in chapter 4). We saw from Table 3-3 that the solubilization power of the graft copolymers produced at the highest polymer concentration is less than the other two. Too high a polymer concentration, therefore, is not favorable for producing compatibilized blends with homogeneous phase size. 33 1.8 1.6 i / a :1 1.4 1' / I /' v1 L2 "' / "A 3’ is: l T / / I 0.0 4- /' S 0-6 1* I/ / a 0.4 ,_ ./ / .1 / 0.2 / 0 i i t i . . 0 0.5 l 1.5 2 2.5 3 3.5 Time (hrs) Figure 3-4 Linear fitting for homogeneous grafting reaction showing constant reaction rate 1.4 ~1- l.2 4- w) ma d k 0.8 «- -ln(l—-f, 0.6 ~- _._ 8g/100ml —+— rig/100ml —-4— 14g/lOOrnl 0.4 0.2 0 1 2 3 4 5 6 Time (hrs) Figure 3-5 Change of — ln(l — a“) with reaction time at three concentrations 34 Table 3-3 Film clarity of reaction products prepared at three polymer concentratiom“ 8g/100 ml f_,‘;“ 0.27 0.40 0.51 0.58 clarity opaque translucent transparent transparent l l g/ 100 ml 13;, 0.30 0.45 0.56 0.66 clarity opaque translucent transparent transparent 14g/ 100 ml 1;}, 0.33 0.46 0.54 0.63 clarity opaque opaque translucent transparent * Films cast onto glass plate at 80°C, all transparent films have blue tint 1.6 1.4 «- T=110’ C ,1" ‘2 .. 2hrs ' ) W ma 0.8 4 0.6 .. 0.4 - 0.2 i 0 t i a 4 . O 0. l 0.2 0.3 0.4 0.5 0.6 —ln(l—f ‘- r \ . I \ Concentration of catalyst (g/ ml solution) Figure 3-6 First order dependence of reaction rate on the concentration of DMAP catalyst 3.2.1.4 Effect of catalyst concentration Changing the concentration of the catalyst has little effect on the phase separation of CA and SMA. At a polymer concentration of 11 g/ 100 ml DMF, the increase of SMA grafting conversion is very close to first order with the concentration of free SMA. We can use the same kind of plot as in Figure 3-5 to see the dependence of reaction rate on 35 the concentration of the catalyst. Figure 3-6 shows a first order dependence of the reaction rate on the concentration of DMAP catalyst The reaction rate, therefore, is directly proportional to the concentration of the catalyst. 3.2.1.5 Effect of reaction temperature The effect of reaction temperature on the grafting reaction comes from two factors: reaction kinetics and phase heterogeneity. The change of grafting conversion with temperature is shown in table 3-4 for a polymer concentration of 11g/100ml DMF. There is quite an influence of the reaction temperature on the rate of SMA grafting conversion. Table 3—4 Effect of reaction temperature on the grafting conversion of SMA“ Temp. (° C) 91 100 110 125 f;;,, 0.43 0.58 0.66 0.73 * CA:SMA=1:1, reaction time=2.0 (hrs), 05.g DMAP/100 ml DMF 3.2.1.6 Effect of MA content in SMA on the rate of grafting reaction Irnmiscibility between CA and SMA reduces with the content of MA in SMA resins. The grafting reaction between CA and SMA132/SMA332 can be analyzed the same way as in the case of CA-SMA232. The overall feature should be the same except that in case of CA-SMA132 the concentration dependence will shift to lower polymer concentration, and in case of CA-SMA332 the concentration dependence will shift to higher polymer concentration. Increased MA content in SMA and the resultant reduction on the irnmiscibility between CA and SMA will lead to increased rate of grafting reaction. Table 3-5 shows the grafting conversion of CA with three SMAs at the same polymer concentration. The rate of SMA332 grafting conversion is much faster than SMA232, so does SMA232 to SMA132. Table 3-5 Effect of MA level on the grafting conversion of SMA * 36 Sample MA wt % (g) DMAP/ Reaction Grafting 100ml DMF time (Hrs) conversion SMA132 4.74% 0.5/ 100 2.0 0.56 SMA232 7.08% 0.5/ 100 2.0 0.66 SMa332 12.20% 0.2/ 100 1.0 0.61 * CA:SMA=1:1, T=1100C, llg (CA+SMA)/100 ml DMF 3.2.2 Effect of small amount water on grafting reaction Water is an important factor in this grafting reaction system. The presence of water can result in the hydrolysis of anhydride and the ester groups of cellulose acetate. It will also limit the equilibrium grafting conversion of SMA. Table 3-6 shows the loss of the total amount of polymer mass at three water levels. Both the hydrolysis of the anhydride and the hydrolysis of CA are seen from material balance. The partial hydrolysis of the anhydride caused a slight gain in weight for the polymers (compared to anhydrous case). The hydrolysis of CA resulted in a loss of the polymer mass, it is severe at a water/MA molar ratio of 12. Table 3-7 shows the weight loss of CA at two degrees of substitution, remember there is only half amount of CA for the polymer composition shown in Table 3-6. So only a small amount water can be tolerated in this grafting reaction system. Table 3-6 Weight change of the reaction products at three water levels and reaction times" Total weight change (%) 1 hr 2 hrs 4 hrs H20/MA 0 -1.0 -1.1 -1.1 (mole/mole) 6 -0.71 -0.73 -0.80 12 -1.9 -3.7 -7.7 * T=110°C, (SMA+CA+DMAP)/DMF=(5+5+0.5)IIOO (g/ml) 37 Table 3-7 Weight change of CA at two degrees of substitution D. S. unit weight unit wt. Chang; 1.0 202 -23.8% 2.0 244 -7.9 % 2.5 265 basis Table 3-8 shows the effect of small amount water on the grafting conversion of SMA. The addition of small amount water caused steady increase on the grafting conversion of SMA. It is, therefore, necessary to control the amount of water in the reaction system even though it is only a small amount The highest water amount in Table 3-8 corresponds to a water content of 0.45 wt% in DMF. Fortunately, the amount of water in DMF can be readily controlled below 0.5%. Table 3-8 Effect of small amount water on the grafting conversion of SMA“ H,O/MA (molar) 0.0 4.0 6.0 12;“ (1 hour) 0.45 0.48 0.50 f5“ (2 hours) 0.66 0.70 0.71 * T=110°C, 5.5+5.5+0.5 (CA+SMA+DMAP)/100 ml DMF 3.3 PROPERTIES OF THE GRAFTING REACTION PRODUCTS The properties of the grafting products depend on the phase size and phase arrangement of CA and SMA in the final products. The inclusion of SMA is meant to improve the performance of CA. It is therefore necessary to disperse SMA into the CA matrix and to have fine dispersion. Acetone is the most common solvent used for CA in film casting and fiber spinning, it is fortunate that SMA is also soluble in acetone. As were shown in chapter 4 films cast from acetone-water mixture solvent gave the desirable matrix phase of CA. A fine and uniform solubilization of ungrafted SMA into the domain of the grafted 38 SMA chain segments were obtained when the grafting conversion of SMA is above a value of around 50%. Under such conditions, cast films retained optical clarity (with blue tint) since the domain size of the SMA phase is well below 0.1 micron. Property evaluations in the form of cast films were done with such pre-requirements. 3.3.1 DEP as plasticizer Diethyl phthalate (DEP) is a good plasticizer for CA. The presence of DEP helps increase the toughness of CA films or molding parts. It is essential to have plasticizer in molding formulations for better processability and thermal stability. In this CA—SMA system, DEP is found to be a good plasticizer for both CA and SMA. The effect of DEP is therefore also considered in property evaluation. Table 3-9 shows the reduction of the glass transition temperature (T.) of SMA with DEP. Table 3-9 Glass transition temperature of SMA in the presence of DEP DEP/SMA (g_/_gL 0.0/1.0 0.1/1.0 0.2/1.0 0.3/1.0 0.4/1.0 T. (°C) 118 86 65 56 51 Figure 3-7 shows the DSC scan of the CA films cast at room temperature with different amount of DEP. There is no obvious glass transition for CA under such casting conditions. In the presence of DEP the melting temperature of CA decreases with increasing amount of plasticizer. The crystallinity of CA is completely suppressed at a DEP level of 0.4/1.0 (DEP/CA). Figure 3-8 shows the DSC scan of CA films with different amount of DEP cast at 80°C. Under such casting conditions, there is no time for CA to crystallize. It is interesting to observe the appearance of the glass transition temperature of CA. Figure 3-9 shows the DSC scan of a CA-SMA (1:1) grafting product at different DEP content cast at 80°C. The glass transition temperature of SMA is much reduced as the amount of DEP increases. There is quite a amount of DEP partitioned in 39 the SMA phase. It is, however, difficult to tell exactly how much DEP is in the SMA phase since the glass transition temperature of CA is not clearly seen and the exact amount of DEP is not known for the isothermal step needed in the DSC scan in order to remove the moisture. It is also interesting to see the melting like endotherrn at a temperature of around 160°C that falls between the T. of SMA and the T. of CA. It is not clear what causes such melting like behavior in the alloy films. Conditioning the sample at 190°C for 15 minutes followed by a cooling rate of 20°C/min removes such endotherrn for the unplasticized sample (see Figure 3-10). DEP/CA (g/g) r I a 0.4/1.0 fl 'fi—n g f 0.3/1.0 ‘5 A 0 2/1 0 3 [T -—— . . II: A 0.1/1.0 rfi, 0.0/1.0 I I l I 50.0 100.0 150.0 200.0 250.0 300.0 Temperature ( °C ) Figure 3-7 DSC scan of the CA films cast at room temperature with different amount of DEP 40 DEP/CA (g/g) 0.4/1.0 r f f / 0.3/1.0 3 h 0.2/1.0 O 4/ r: / "‘ F g 0.1/1.0 #/-——/\_ /— 0.0/1.0 l I I l T 50.0 100.0 150.0 200.0 250.0 300.0 Temperature ( °C ) Figure 3-8 DSC scan of CA films with different amount of DEP cast at 80°C . DEP/reaction product (g/g) 0-3/1-0 0.2/1.0 :/ . 0.1/1.0 _.,z/f—_'IIIIIII’”———‘—_-_"”'_—_—“I‘\ ‘__"/,,””/’_\\“\-2__,_,__—/'\\‘.0.0/1.0 Heat flow _—" “'l I I 50.0 100.0 150.0 200.0 250.0 300.0 Temperature ( °C ) Figure 3-9 DSC scan of CA-SMA grafting product at different DEP content cast at 80°C 41 iso therm. Heat flow I #1 7 t ' 'T 50.0 100.0 150.0 200.0 250.0 300.0 Temperature ( °C ) Figure 3-10 DSC scan of film samples with/without isothermal at 190°C for 15 minutes 3.3.2 Tensile properties One of the most important measures for the compatibilized blends is of tensile properties. According to current understanding, there is a certain degree of demixing between the uniformly solubilized free chains and the corresponding chain segments of the graft copolymers in the microdomains (see background literature of chapter 4). The direct consequence of such demixing could be the loss of tensile strength. The seemingly compatibilized blends, i.e., through the observation of optical clarity, does not necessary possess desirable tensile properties. Tensile properties of the reaction products (CA:SMA=1:1) in the form of cast films were measured with the SMA grafting conversions of 56% and 66% at equal amount of CA and SMA. Cast films of CA were tested for comparison. Since the presence of non—equilibrium factor is always there in the 42 fast casting process, no attempt was made to look into the equilibrium properties. Table 3-10 shows the test results with/without plasticizer. It can be seen that there is basically no difference for the two alloy films at two SMA grafting conversion, therefore, there seems to be no reason to pursue higher grafting conversion from the point of view of mechanical properties whence the films exhibit uniform and microscopic phase size. The alloy films show slightly increased tensile strength in contrast to the most dramatic drop in simple blends under such composition, much increased tensile modulus, but of reduced elongation at break. The difference in those properties between the alloy films and the CA films widens as the amount of DEP increases. The most likely explanation is that DEP partitions more into the SMA phase than the CA phase, this seems to be supported by the results of moisture adsorption. Increased tensile modulus and decreased elongation at break are all good for improving the dimensional stability of the new materials. Table 3-10 Tensile properties of the cast films with/without DEP DEP/ tensile modu. elon.% S.D.% S.D.% S.D.% sample sample break break tensile modu. elon. (glg) x 103 psi x103 psi CA:SMA 0.0 7.5 0.39 3.1 8.6 3.6 15.2 (1:1) 0.1 6.1 0.36 3.2 7.8 3.2 12.6 fJ..=0-56 0.2 5.4 0.34 3.5 7.1 3.3 9.6 CA:SMA 0.0 7.7 0.38 3.3 9.2 3.4 14.4 (1:1) 0.1 6.2 0.35 3.5 6.3 3.3 13.3 f3..=0-66 0.2 5.7 0.34 3.9 7.6 4.1 10.6 0.0 7.1 0.35 5.4 6.0 3.0 11.3 CA 0.1 6.3 0.29 8.7 4.8 2.9 10.8 0.2 6.1 0.27 10.1 5.1 2.3 13.1 43 3.3.3 Moisture adsorption CA is moisture sensitive. Substantial amount of moisture adsorption causes dimensional stability problem in film and fiber applications. It is therefore important to look at the moisture adsorption of the grafting products. Figure 3-11 shows the moisture adsorption of CA, cellulose triacetate (CTA), and one reaction product containing 50% SMA, with/without plasticizer. The moisture adsorption of CTA is measured for comparison. As can be seen the presence of 50% SMA in the new product reduce the moisture adsorption nearly by half. The moisture adsorption is lower than CTA. However, there is apparently no synergistic effect on the reduction of moisture adsorption. This is expected since SMA is immiscible with CA. The presence of DEP helps reduce further the moisture adsorption for all three samples. 14 - 12 - I CA(2.45) CTA 10 - 50%SMA % moist. ads. Gram DEP/gram unplasticized sample Figure 3-11 Comparison of moisture adsorption for CA, CTA and the alloy 3.3.4 Dimensional stability The dimensional stability of CA is shown by its dimensional change (contraction) in contact with water. In case of film sample, uneven exposure of film surface to water, i.e., water drop on the surface, can destroy the smoothness of the film. For potential applications in textile fibers, the dimensional stability at increased temperature is extremely important. One of the driving forces in this study is to improve the dimensional stability of CA so that it can have the performance comparable to CI‘A. The commercial casting process for CTA fiber involves the use of methylene chloride which is environmentally unfriend. Acetone used for CA is a much better solvent in that regard. The change of the dimension of film samples under water soaking condition at various temperatures can be used as a measure of the dimensional stability of the new materials. Figure 3-12 to Figure 3-15 show the percentage contraction of film samples of different DEP levels under different water soaking temperatures. It can be seen that the inclusion of SMA substantially improves the dimensional stability of the CA based alloys, i.e., at 50% SMA, the reduction of the dimensional contraction is more than 50% in comparison to CA. The dimensional stability of the alloys is better or comparable to CTA at various conditions. There is, therefore, a big potential in finding the new grafting products for applications in films and fibers. Another interesting thing that can be looked at is in new membranes where the improved dimensional stability could reduce the skin layer compaction problem in conventional CA based membranes. 45 25°C I CA(2.45) CTA 50%SMA owcazo EcoicoEmEe 0.3 0.2 Gram DEP/gram polymers Figure 3-12 Comparison of dimensional changes at 25°C 51°C I CA(2.45) CTA m A. S % 0 5 omSEo Ecommcofi€§ Gram DEP/gram polymers Figure 3-13 Comparison of dimensional changes at 51°C 46 ..e mm. .......... /////////////o owcfio ficoicofimgs Gram DEP/gram polymers Figure 3-14 Comparison of dimensional changes at 66°C I CA(2.45) omcmfi Enema—08%....» Gram DEP/gram polymers Figure 3-15 Comparison of dimensional changes at 95°C 3.4 In 1 pm “'1‘ iii 47 3.4 SUMMARY In this chapter, the grafting reaction and some properties of the CA-SMA grafting reaction products were studied in detail. The phase diagram of the CA-SMA-DMF ternary mixture was constructed first. The dilution of the unfavorable contact between CA and SMA is very sensitive to the amount of polymers dissolved in DMF. Increasing the MA level in SMA reduces the irnmiscibility between CA and SMA. The analysis on the free energy of mixing by a mean field approach shows qualitatively the order of sensitivity. The grafting reaction between CA and SMA was carried out successfully in the presence of the DMAP catalyst. The rate of grafting conversion can be described by taking into account the effect of phase separation and the effect of polydispersity of the reactive polymers. While the effect of polydispersity on the rate of SMA grafting conversion can be analyzed exactly, the rate of SMA grafting conversion cannot be described in a simple manner since information on the phase sizes and phase size distribution is not readily available. The complexity of the grafting process is also shown by the dispersion power of the graft copolymers whence they are produced during the course of grafting reactions. Several parameters involved in the rate expression of SMA grafting conversion were looked separately. (a) The stirring intensity indicated by the stirring speed in the range of 200-600 (rpm) has little effect on the rate of SMA grafting conversion. This is explained by the low interfacial tension and high solution viscosity, these two important factors tend to smear out the effect of mixing intensity. (b) The grafting reaction is very sensitive to the concentration of polymers in solution. The concentration of the polymers in a solution is rather limited in order to avoid too much a reduction on the compatibilizing ability of the graft copolymers, since the net effect of phase heterogeneity is to reduce the effective chain length of the chain segments of the graft copolymers. (c) There is a first order relationship on the intrinsic kinetics between the reaction rate and the concentration of the catalyst. (d) The grafting reaction is very sensitive to the reaction temperature, so is 48 the MA level in SMA. (e) Only a small amount of water is allowed in this grafting reaction system in order to avoid the excess hydrolysis of CA. The presence of a small amount of water promotes grafting reaction. Tensile properties, moisture adsorption and the dimensional stability were measured for some grafting reaction products in the form of cast films. The film alloys exhibit slightly improved tensile strength, greater tensile modulus and lower elongation at break in comparison to CA, with/without plasticizer. Such tensile properties together with reduced moisture adsorptions are good for improving the dimensional stabilities of the grafting products, i.e., in the presence of 50 % SMA in the alloys, there is more than 50% reduction on the dimensional changes as compared to CA from tests in the form of cast films under various water soaking conditions. The dimensional stabilities of the film alloys are better or comparable to CI‘A. There is a good potential to find applications for the grafting reaction products in films, textile fibers and separation membranes. Chapter 4. PHASE BEHAVIORS OF GRAFTING REACTION PRODUCTS The generation of graft copolymers changes the phase behavior of the ternary mixtures of the grafting reaction products. Controlling the phase size and phase homogeneity of a reaction product is necessary for obtaining many of the desirable performances of the material. It is extremely important to look at that particular aspect of the CA-SMA grafting system. The unique feature of the particular CA-SMA grafting system in terms of phase size and homogeneity shall also be a reflection of the grafting system as was defined in the first chapter. So far no work has been done to look at the phase size and homogeneity in such practical system. 4.1 BACKGROUND LITERATURE Ternary blends (A+A—g-B+B) are bounded by two extremes of A+B and A-g-B. For immiscible blends, the addition of a small amount of (<10%) block or graft copolymers to the binary blends helps reduce the size of the dispersed phase substantially on the macroscopic scale and improve the mechanical properties of the blends [Locke and Paul, 1973; Meier, 1991]. There is a large body of experimental evidence supporting the interfacial activity of block (or graft) copolymers in mixtures with homopolymer. For example, Gaines and Bender [197 2] have demonstrated a lowering of polymer melt surface tension on addition of a styrene/dimethylsiloxane copolymer to polystyrene. Addition of only ~0.2% of the copolymer was shown to give a surface tension close to that of polymethylsiloxane. Reactive extrusion has been the dominant way of making various compatibilized blends. 49 50 Pure Block/graft copolymers composed of immiscible chain segments form microphase separation (less than 100 1110). There are interesting morphological behaviors associating with pure block/graft copolymers. It has been established that segregated microphases can be sphere, cylinder, larnellae for pure block copolymers. The type of morphology adopted by the copolymer essentially depends on its composition [Gallon 1978]. Recently, a new morphology named "ordered bicontinuous double diamond (OBDD)" structures were found in starpolymers [Aggarwal, 1976; Alward et al., 1986; Thomas et al., 1986; Kinning et al., 1986], three~component pentablock copolymer [Hasegawa et al., 1983], and linear diblock copolymer [Hasegawa et al., 1987]. The OBDD phase appeared to be the equilibrium morphology existing between cylinders and lamellae [Hasegawa et al., 1987; Herman et al., 1987]. The equilibrium morphologies in the bulk state can be shifted in the presence of a selective solvent as was shown by Inoue et al. [1970], Shibayarna et al. [1983] and Hashimoto et al. [1983]. Cowie [1982] gave a review on the effect of solvent on block copolymer system. Figure 41 illustrates three morphologies (OBDD not listed) as well as the effect of selective solvent. B-selective solvent 1W A-sphere A—cylinder A-lamellae A—selective solvent Figure 4-1. Idealized morphologies and the effect of solvent 51 Meier [1967, 1969, 1973], Helfand [1976, 1978, 1980] and Leibler [1980] have developed statistical mechanics theories to explain quantitatively the equilibrium forces for the three idealized morphologies of block copolymers. The presence of various equilibrium morphologies is associated with the conformational entropy of the chain segments of the block copolymers. Both theoretical prediction and experimental evidences (small-angle neutron scattering) indicated that the chain segments of the block in the bulk are stretched away from the unperturbed state [Meier, 1969; Helfand, 1980; DiMarzio, 1988; Hasegawa et al., 1985; Matsushita et al., 1990]. When homopolymers are admixed with block/graft copolymers (A+A-b/g-B or B+B-b/g-A or A+A-g-B+B), the hom0polymers may or may not be solubilized uniformly into the microdomains of the block/graft copolymers, the so called solubilization phenomena. Solubilization phenomena were studied mostly with block copolymers of a narrow molecular weight distribution made by anionic polymerization. Solubilization of A by A-b-B was reported in an early work by Inoue et al. [1970], in which mixtures of styrene/isoprene diblock copolymer with polystyrene and/or polyisoprene were examined for optical clarity of toluene-cast films and for the microstructure by electron microscopy. The results, though not quantitative, suggest that the amount of solubilized homopolymer could be 2-3 times the volume of the like copolymer block when the corresponding molecular weight ratio was around unity, while films containing a much higher molecular weight homopolymer were invariably opaque. Skoulios et al. [1971] used small angle x- ray scattering (SAXS) and visual observation to determine the solubility of polystyrene of different molecular weights in the styrene domains of a styrene/(vinyl-2-pyridine) diblock copolymer, the vinyl-2-pyridine block was swollen with octanol. On addition of the polystyrene with a molecular weight equal to the copolymer styrene block, the solubility limit was reached when the volume ratio of the polystyrene to the styrene block was roughly unity, while cloudy macrophase separated mixtures resulted when the polystyrene molecular weight was higher. Ptaszynski et al. [1975] also used SAXS to study mixtures 52 of polystyrene of varying molecular weight with a styrene/isoprene diblock copolymer with block molecular weights 40000 and 50000, respectively. Essentially corroborating the above results, they found that at a fixed homopolymer concentration (15% w/w) the mixtures were transparent until a homopolymer molecular weight of 60000 (i.e., 1.5 times the styrene block length) was reached and thereafter the mixtures were visibly cloudy. With polystyrene of molecular weight 10000, the solubility limit was reached when the polystyrene content was around 30%. Thus it was concluded that the statement that the homopolymer molecular weight must be less than or equal to that of the corresponding copolymer block for solubilization to occur represents a good rule of thumb, but that a certain amount of solubilization occurs even at higher molecular weights. Roe and Rigby [1987] has given an excellent review on the studies of solubilization phenomena of homopolymer-block copolymer systems. Recently, Kinning et al. [198 8] pointed out the importance of TEM study on the judgment of solubility limit, since homogeneous solubilization does not necessary lead to transparent films. The theory on homopolymer solubilization is much less studied as compared to the theories on equilibrium morphologies. Meier's theory [1977] on homopolymer-block copolymer system showed general agreement with experiments, that is the length of the homopolymer has to be of the same order of magnitude or smaller in comparison to the corresponding block length for it be soluble in the microdomains of the copolymers, the solubility limit would decrease with increasing homopolymer molecular weight. There is, however, about an order of magnitude difference on the solubility between Meier's prediction and experimental observations. Roe and Zin [1984] argued that the underestimation by Meier's theory arises because the theory assumes a model in which the hom0polymer is uniformly distributed within the microdomain, where in practice it is more likely that the homopolymer will concentrate more toward the center of the microdomain to avoid overly stretching the block chains. Xie et al. [1986] did some work to calculate theoretically the free energy of mixing in case of the localized concentration distribution of 53 the homopolymer. Their studies, though not rigorous because of the self-claimed density profile used in their calculations, showed that the amount of homopolymer solubilization is greatly increased in accordance with Roe and Zin's argument [1984]. They suggested further that there is no solubilization limit if the homopolymer can be solubilized into the domain of the copolymer. Shall and Winey's analysis [1992] showed a more detailed density profile in the extreme case of adsorbing layer of the block junction. Recent experimental studies seem to conform the non-uniform distribution of the homopolymers inside the microdomains of the copolymers [Bemey et al., 1988; Winey et al., 1991; Hashimoto et al., 1990]. It is apparent that the study on the solubilization phenomena is far from being complete, both‘theoretically and experimentally, even for the ideal case of block copolymer systems. The chain length of the copolymer depends on the structure of the copolymer. For homopolymers and complex copolymer system, particularly graft copolymers of complex structures, there is no theoretical prediction on the extent of homopolymer solubilization. Jiang et al. [1986] reported their studies on the effect of molecular architectures of copolymers on the solubilization of polyisoprene, their study showed clearly that the power of solubilization of copolymers for homopolymers has the sequence of diblock>triblock>four-arm block when the molecular weights of the chain segments of the copolymers are close to each other. Eastmond [1979] and Jiang [1985] studied AB- crosslinked copolymers (ABCP) of relatively complicated structures (somehow similar to graft copolymers of this study). They found that the miscibility between ABCP and homopolymer A is rather limited, macrophase separation occurred. Graft copolymers formed between two reactive polymers each having large numbers of reactive groups will react further to form new graft copolymers during the course of grafting reaction. The net result is the reduction of the effective chain length of the chain segments of the graft copolymers as grafting reaction continues. On the other hand, the reactive polymers are often highly polydisperse. Polydispersity can cause 54 differences in the average chain lengths between the grafted chains and the ungrafted chains. In chapter 5 it will be shown that there is an upper limit on the extent of grafting conversion for the reactive polymers in order to avoid too high a system's weight-average molecular weight (high viscosity). It is, therefore, very important to know in such a practical system how phase size and phase homogeneity changes with grafting reaction, at what extent of grafting reaction there is homogeneous solubilization in the reaction products. TEM was used as a tool to look at these aspects. The studies on the CA-SMA system shall have general implication for the defined grafting system. 4.2 GRAFTING CONVERSION OF CA VERSUS SMA The grafting conversion of CA is intemally related to the grafting conversion of SMA at given compositions. In the assumed state of homogeneous grafting reaction, we can connect the grafting conversion of CA to the grafting conversion of SMA by .. 1—[0”(1-f,,)”’*wa(M)dM f» = (41) CA SMA co 7 1-[0 (1—f,,,) wMtMMM M: MIME (42) where W(M) is the weight fraction density function of a molecular weight distribution, x is the molar ratio of the molar concentration of CA divided by that of SMA, f“, is the grafting conversion of the reference SMA chains having a molecular weight of the number-average molecular weight of the starting SMA. Figure 4—2 shows that the percentage conversion of CA is much less than the percentage conversion of SMA for a composition of 0-50% SMA. The grafting reaction products used in this part of the study were made at a concentration of 11g/100ml (polymers/DMF). Phase hetemgeneity during the early stage of grafting reaction will affect the actual relationship between the grafting conversion of CA and the grafting conversion of SMA. However, it is believed that such 1! 55 effect is minor even though there is no way to characterize experimentally the grafting conversion of CA. 0.9 ’ / r 0.8 > ‘ / / 0.7 - . 50%SMA 0.6 - 0.4 t 0.3 ~ 0.2 — 0.] ~ 0 0.] 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 I Figure 4-2. Grafting conversion of CA versus that of SMA 4.3 SELECTIVE GRAFTING CONVERSION OF THE HIGH MOLECULAR WEIGHT CHAINS OF THE REACTIVE POLYMERS The formation of complex graft copolymers in this grafting reaction system has a net effect of reducing the effective chain length of the grafted chain segments. On the other hand, the grafting reaction happens with more grafting conversion of higher molecular weight chain fraction of the reactive polymers. The importance of polydispersity shall not be overlooked in this grafting system. In a homogeneous state, the grafting conversions between two chain fractions having molecular weights of M, and M 1 (CA or SMA) satisfy l—fM, =<1-f,.,.)”*’“’ (43) 56 This is because the numbers of reactive groups on the chain species are proportional to molecular weight We can look at the effect of polydispersity in increasing the effective chain length of the chain segments of the graft copolymers by comparing the number- average molecular weight of the free (ungrafted) chains with that of the grafted chain segments. The number-average molecular weights for free SMA and grafted SMA are calculatedby 1— “WMdM (m )3... = I; ( f"’_) ( ) (44) f<1-f,,,)"W(M)/Mdu _ 1-1- IT'WMdM (Mi),,.,= m ( fwl ( ) (4—5) [0' [1-(1— f", )7]W(M)/MdM The ratio of the number-average molecular weight of the grafted SMA chains to that of the free SMA chains is defined as = (If? )m R _ (M1 )5,“ (4—6) Figure 4-3 shows that the number-average molecular weight of the grafted SMA chains is more than twice that of the free chains. The selectivity of the grafting process is quite substantial. If we divide R by the average numbers of linkages per grafted SMA chain we have a rough sense of effective chain length (number average) for the grafted and the ungrafted. The average numbers of linkages per grafted SMA chain is defined as -... cf“ 1,, (4.7) nsm = (:3me It is related to the molecular weight distribution as well as the grafting conversion of the reference chain species by 57 ‘VM ‘1“ 1- m..- = _0 ,, ( f") (4—8) 1—M,.J'0 (l—f,4)MW(M)/MdM 2.0 3.8 grafted ‘ 1.6 — > ~ 3.3 E 1'2 _ “ 2-8 CC 3‘ rm 0.8 — —.2.3 l 0.4 a J 4 r 4 I r r I l I - - I r 4 1.8 o 02 0.4 06 08 1 fs‘ia Figure 4-3 Change of the number-average molecular weights for the grafted and ungrafted SMA chains and the ratio of the two with grafting conversion Figure 44 shows the ratio of the effective number-average molecular weight of the grafted chains to the number-average molecular weight of the free chains. We see that such ratio decreases with grafting conversion but is still greater than one (the actual ratio shall be smaller since graft linkage reduces the effective chain length as compared to block linkage). Polydispersity, therefore, shall have a significant effect in the solubilization of free chains into the microdomains of the chain segments of the graft copolymers. 58 2.0 3-0 1.9 e < " 2.5 1.8 r > ff- 1.7 ~ E ‘ 2-0 .5. e: 1.6 ~ It." 1.5 e ‘ 1.5 1.4 ~ 1.3 * * 1 1 4 1 1 f 1.0 O 02 0.4 06 08 1 1?er Figure 4-4 Changes of the ratio of the effective number-average molecular weight of the grafted SMA chains to the number-average molecular weight of the free SMA chains and the average numbers of linkages per grafted SMA chain with grafting conversion 4.4 PHASE SIZE AND HOMOGENEITY Figure 4-5 and Figure 4-6 show two sets of TEM micrographs of the reaction products at different grafting conversions (50% SMA for the first set, 25%SMA for the second set). SMA is the dispersed phase. The films were cast from an acetone-water mixture solvent (96 v% acetone, SMA is swelled only in this mixture solvent). The matrix phase looked homogeneous in the long range. The overall feature of the two sets of micrographs is very similar. Homogeneous solubilization occurs when the grafting conversion of SMA is above a value of around 50%. The composition of SMA has minor effect. At low 59 grafting conversion of SMA (26%, 39%, and 51% of Figure 4-5, 31% and 44% of Figure 4-6), macrOphase separation and microphase separation coexist. Films with such phase heterogeneity are not transparent while the others are transparent but with a blue tint. A close inspection on the phase sizes at lower SMA conversions shows a distribution of phase sizes. There is no clear cut of two sizes with order of magnitude difference. The presence of such characteristics cannot be explained simply by the insolubilization of the free chains. Figure 4-7 and Figure 4-8 show two sets of micrographs of the corresponding reaction products cast from THF-water mixture solvent (96 v% THF). The THF-water mixture solvent is close to be non-selective. The SMA phase becomes continuous except for the case of 26% SMA conversion (Figure 4-7). At higher grafting conversion, the phase structures become homogeneous, co-continuous phases were observed. The SMA phase in its matrix state was homogeneous at lower grafting conversion as compared to the case of the dispersed state. There is no separated microphase of SMA. The dispersed CA phase appeared less homogeneous. This is because the grafting conversion of CA is less than the grafting conversion of SMA. Apparently, solubilization of SMA free chain happens at the lowest grafting conversion of SMA. It seems to suggest that there is no solubilization limit when SMA is in its matrix state. From the four sets of micrographs, we found that phase size homogeneity increases with the grafting conversion of SMA. The homogeneity of SMA was observed at lower conversion in the continuous state than in the dispersed state. The formation of more and more complex graft copolymers causes a net reduction of the chain segments of the graft copolymers as was discussed earlier. Such a reduction of the block length of the graft copolymers does not reverse phase homogeneity with grafting conversion. The desirable feature of this grafting reaction system is explained by the grafting conversion of more high molecular weight chain fractions of the reactive polymers. To illustrate the importance of the selectivity of grafting reaction because of polydispersity, the free SMA . l I ’ u. 12:... I '1' ’ n ("4131 1';- '- .. ‘ "-'l I " &. 's ‘r. ’ ‘0. ”'1 a .- r! Figure 4-5 TEM micrographs of films cast from acetone-water mixture solvent (96:4) at 70°C with 25% SMA in the alloy. f5“: (a) = 0.26, (b) = 0.39, (c) = 0.51, (d) = 0.74. (bar length = one micron). 61 hs of films cast from acetone-water mixture solvent nucrograp Figure 4-6 TEM (96 = 0.45, (c) f5“: (a) = 0.30, (b) 4) at 70°C with 50% SMA in the alloy. one micron). 0.66. (bar length = 0.56, (d) 62 Figure 4-7 TEM micrographs of films cast from THF-water mixture solvent (96:4) at room temperature with 25% SMA in the alloy. firm: (a) = 0.26, (b) = 0.39, (c) = 0.51, (d) = 0.74. (bar length = one micron). 63 Figure 4-8 TEM micrographs of films cast from THF-water mixture solvent (96:4) at room temperature with 50% SMA in the alloy. fs‘LA: (a) = 0.30, (b) = 0.45, (c) = 0.56, (d) = 0.66. (bar length = one micron). 64 in one reaction product (Figure 4»6 (d)) was extracted and the remaining was mixed with free SMA without going through grafting reaction (The SMA was treated the same way as in the grafting reaction of the reaction product except for the absence of CA so to eliminate the possible change of SMA) to arrive at the same composition. The cast film from acetone-water mixture solvent at the same condition (Figure 4—6(d)) was no longer transparent. Insolubilization or less solubilization of the high molecular weight chains of SMA is seen from such a test. This simple test tells the importance of the effective chain length of the free chains and that of the chain segments of the graft copolymers. It also tells that adding small amount reaction products of high graft copolymer content to the blend of CAISMA may not provide the same kind of compatibilzing effect by the graft copolymers as the one produced by a reactive extrusion process. Homogeneous solubilization happened at relatively high grafting conversion. Given the results on the change of system's weight-average molecular weight (W AMW) with grafting conversion, there is, therefore, at equal amount of CA and SMA only a narrow range of SMA grafting conversion from a Practical point of view, so that homogeneous phase size is obtained while the WAMW of the reaction product is still kept at a reasonable value. 4.5 PHASE SIZE AND STABILITY The appearance of macrophase separation from visual observation of optical clarity and electron microscopy is often used as evidence of the insolubilization of homopolymers or of solubility limit on the amount of homopolymer that can be solubilized if the homopolymers are initially solubilized. The unfavorable enthalpic interaction between basic structural units of chain A and chain B of the block copolymer results in microphase separation and the growth of domain size. The loss of conformational entropy of the confined chains exerts an opposing force for the growth of domain size. Morphological behaviors of block copolymers result from the minimization of the conformational entropy 65 of the confined chain through spatial arrangements [Meier, 1967; Helfand, 1976]. In the presence of homopolymers, the driving force for homopolymer solubilization has to do with the conformational entropy of both confined and fiee chains. It is the relaxation of the confined chains in the presence of homopolymers that results in homopolymer solubilization. Relaxation because of the presence of homopolymers causes more freedom of spatial arrangement. The homopolymer chains have to be disturbed at the same time, and therefore has less degree of freedom as compared to the undisturbed state. There is a net increase of the combined conformational entropy for the confined chains and the homopolymer chains. The system takes the form of uniform phase size so to have a free energy minimum if the reduction of free energy is more than linear to the amount of solubilized homopolymers. However the reduction of free energy may not be necessary more than linear since the relaxation comes from both phases. Therefore heterogeneous phase size is not necessary an indication of homopolymer insolubilization. On the other hand, as more and more homopolymers are solubilized into the domains of graft copolymers, the driving force for homopolymer solubilization may become so small from a relaxation point of view that dynamic force can easily distort the equilibrium phase structure. Let us take a look at the dispersed spheres (chain A) in the case of slow relaxation of the confined chains. Let VA be the volume of the confined A chain in its compacted state, 3A be the interfacial area per confined chain. We have from material balance 1 chA —m13 = .. (4.9) 6 f, The surface area of the sphere becomes: M2 = nCSA (440) Dividing equation 4-9 by equation 4-10, we have 66 =£Y¢ f: 3‘ (4-11) If the interfacial area per confined chain does not change with the solubilization of homopolymers, the diameter is reversibly proportional to the fraction of the copolymer. Figure 4—9 shows the change of domain size with the content of copolymer. It is important to point out that the change of phase size is the most drastic at low copolymer content. Therefore the phase heterogeneity on the order of a few time differences in sizes does not necessary mean that the homopolymer is not solubilized in the copolymers. It does tell that the driving force for solubilization is weak if there is no solubility limit for the given system at low graft copolymer content §§§ d=50 run at f=l.0 §§ Diameter of sphere § 0 0.2 0.4 0.6 0.8 l Grafting conversion Figure 4-9 Phase size .vs. copolymer content 67 Figure 4-10 TEM micrographs of cast films from THF-Water mixture solvent cast with a film applicator and dried at 50°C. f;: (a) = 0.30, (b) = 0.45, (c) = 0.56, (d) = 0.66. (bar length = one micron). 68 Figure 4—10 shows a set of TEM micrographs for films cast from THF-water mixture solvent with a film applicator. The solvent was evaporated in less than 10 minutes at 50°C. The external force from the film applicator caused drastic change for the samples with macrophase separation. The phase homogeneity at higher grafting conversion was preserved even though the microphases are stretched along the moving direction of the applicator. This set of experiments shows clearly the weak driving force in maintaining the phase structures at low grafting conversion of SMA. 4.6 SUMMARY Homogeneous phase structures appear in the grafting reaction product of CA-SMA as the grafting conversion of SMA increases. There is a substantial amount of free chain solubilization into the microdomains of the graft copolymers. The formation of complex graft copolymers at high grafting conversion does not lead to the insolubilization of free chains. Such a desirable property is explained from the more grafting conversion of the high molecular weight chain fraction of the reactive polymers, a unique feature for synthesizing graft copolymers in the defined grafting system. While the driving force for homogeneous solubilization at low content of graft copolymers is not clearly understood, the dynamic force can be important in causing the phase size distribution of the dispersed phase. This part of the study shows the importance of polydispersity in promoting homogeneous phase size of the grafting reaction system. Chapter 5. THEORETICAL ANALYSIS OF THE BRANCHING PROCESS OF GRAFTING REACTION BETWEEN TWO REACTIVE POLYMERS Graft copolymers formed during the grafting reaction of CA-SMA are capable of grafting further due to the large numbers of reactive groups on the backbones of both CA and SMA. The buildup of the complexity of the graft copolymer structures during the grafting process raises an immediate concern as to how far the grafting reaction can be carried out, since too high a molecular weight average is generally undesirable from a processing point of view. It is important to know theoretically how the system's molecular characteristics changes with grafting reaction, at what extent of grafting reaction the system starts to gel. One of the difficulties in understanding such complex system is the lack of adequate techniques to characterize the grafting reaction products. In case of CA- SMA, the association behavior of the grafting products caused difliculty doing GPC analysis. Theoretical analysis of the CA-SMA system can be done on a more general basis, in which the nature of the grafting chemistry is less important as long as it provides grafting linkages irreversibly. 5.1 BACKGROUND LITERATURE The term branching process was used by Gordon to describe the development of polymer species in systems capable of gelation. Figure 5-1 is an illustration of branching process of an aggregation system from computer simulation. The grafting process of this grafting system can best be described as a branching process when we neglect the presence of rings. 69 Figure 5-1. Illustration of the branching process after transformation of the molecular forest of trees into a forest of rooted trees (with permission from Richard F. Voss and Elsevier Science Publishers B. V.) Theoretical works on the branching process of network forming systems have been done extensively over the past decades. The works are exclusively on the polymerization of monomers to form a three dimensional network at the end of the polymerization. The important things for the characterization of the polymerization system are the content of polymer species of different sizes, molecular weight distribution, molecular weight averages, gel point, sol-gel relationship, and finally the crosslinking density of the network. Theoretical analyses can be classified into: statistical, percolation, and kinetic. The statistical approach can be classified further into four techniques: (1) Flory and Stockmayer's classic combinatorial method [Flory, 1941, 1953; Stockmayer, 1943, 1944, 1952, 1953]; (2) Gordon's cascade theory [1962]; (3) Macosko and Miller's recursive method [1976]; (4) Durand and Brumeau's approach [1982]. These methods differ in their language and power. Gordon's theory used abstract vectorial probability generating 71 functions. The method is powerful but difficult like the combinatorial method. Macosko and Miller’s method uses conditional probability. It is mainly useful for deriving the molecular weight averages and the gel point of the polymerization process. Extension to the consideration of unequal reactivity, intrinsic [Case, 1957; Miller and Macosko, 197 8] and/or induced such as the first-shell substitution effect [Grodon and Scantlebury, 1964, 1966; Sarmoria and Miller, 1991; Dotson, 1992], is readily made from above theories since unequal reactivity affects the equivalent reactive groups as a whole. The consideration of unequal reactivity and substitution effect narrow the gap between theory and many actual polymerization systems. The most important assumption made in the statistical approaches is of random mixing with reaction control, that is the probability of reaction between two reactive species is weighted according to the equivalent numbers of reactive sites on the two species. The equal accessibility of space (any lattice site) by any species represents one extreme case, another extreme case is represented by fixed lattice sites where the species is stuck to it. Simulations on the branching process using a computer on the constructed lattice sites, namely the percolational analyses were developed by Staufeer et. al. [1982], Boots et al. [1985] and Herrmann et al. [1982, 1983]. Difference between the classical theory and the percolation model on the scaling behavior near the critical point was observed. Since the motion of chain segment is so restricted, such simulations are perhaps applicable to the situation when a system starts to gel or after the system has already gelled, i.e., some curing system [Dusek, 1986]. Nevertheless, present percolation models are far from simulating actual network formation, since the bonds are too rigid, the movement of molecules is too suppressed and the chemical rules of bond formation are quite often ignored. The kinetic approach involves the solution of the differential equations which describe the rate of change of individual species. It is always possible to describe the system based on first principle (material balance) no matter how complex the system is. 72 The complexity of the problem is embodied in the form of the differential equations, i.e., linear or nonlinear. In the latter case, numerical method is often used to solve the equations. The power of the kinetic approach is best shown in the studies of free radical polymerization of linear chains where complex situations such as the change of kinetic rate coefficients during the course of polymerization, the presence of several mechanisms during the course of polymerization (chain transfer, different ways of termination), changing monomer concentration, reactor selection (PFR, CSTR), can be readily considered in the differential equations [Hamielec and MacGregor, 1983]. The equal reactivity assumption in the statistical derivation is simply a special case. A large number of ingenious methods, i.e., generating functions, transformations and continuous variable approximations [Ray, 197 2], have been applied to the solution of the batch, free radical polymerization kinetics for relatively simple system. Numerical method is possible for complex system since the advent of stiff ODE codes [I-Iindmarsh, 1974]. Skeirik and Grulke [1985] developed a calculation scheme to reduce the extremely large number of differential equations by grouping chain lengths into equal sized groups and still retain the flexibility of the initial kinetic formulations. Kinetic formulation of nonlinear condensation system was referred to briefly without details or development by Stockmayer [1943]. Stafford [1981] derived a distribution function for a self condensing Al + A2 + A; + system by a kinetic approach and extended to several cases including a stoichiometric mixture of A1 + A, + A,.+ + Bl + B2 + B]. + In a closely related field on cluster formation or aggregation process, Smoluchowski's coagulation equation (kinetic approach) has been used to study the formation of clusters in the coaggregation process of particles. Computer programs based on kinetic aggregation process (including many of the percolational models) have been developed to study the scaling exponent of the mass versus the mean length of the cluster, the so called fractal [Stanley, 1984]. Ziff [1984] gave a broad discussion on the aggregation kinetics via Smoluchowski's equation. Recently, Tobita and Harnielec [1989, 73 1991] proposed pseudokinetic rate constant method to simulate network formation in free radical polymerization. Tobita [1992] applied their kinetic theory to emulsion copolymerization of vinyl and divinyl monomers and found highly heterogeneous network structure. A kinetic approach is developed in this part of the study for the grafu'ng reaction system of two reactive polymers each having large numbers of reactive groups. General discussions were given of the effect of various parameters on the branching process. A limiting case of infinite numbers of reactive groups on both reactive polymers is the defined system in this part of the work, practically the number of reactive groups on both polymers can be considered as infinite when the numbers of reactive groups are large, say, more than 50 (see discussion section) so far as grafting reaction is concerned. No theoretical analysis has been given to such system. CA and SMA is one particular case that falls to such system. 5.2 THEORETICAL DEVELOPMENT Grafting reactions are generally heterogeneous since most polymers are immiscible. Heterogeneity complicates the analysis. Theoretical Analysis assuming a homogeneous grafting process represents the limiting case, homogeneous grafting can be found in solution processes. Since the numbers of reactive groups on the polymer chains are so large, the substitution effect can be neglected. A homogeneous, kinetically controlled, irreversible grafting reaction is considered. Two assumptions are made in the kinetic approach: (1) equal reactivity of the reactive groups on the polymer backbones; (2) no intramolecular reaction. Neglecting temporarily the effect of intramolecular reaction does not affect us in finding out the main features of the grafting process. The importance of intramolecular reaction will be discussed in chapter 6. All discussions are made in respect to the percentage (weight basis) conversion of one reactive polymer to graft copolymers 74 since that information can be obtained by extraction study, it is perhaps the only information one can obtain in grafting system. 5.2.1 Monodisperse reactive polymers 5.2.1.1 Balance equation Let A and B represents the two reactive polymers having large numbers of reactive groups a and b respectively. With the assumptions mentioned above, the kinetic equations which describe the rate of change of the concentration of individual species are generalized by . ~ .. .. %=%§§’ummo-I> +éré—i-té—é “raw 'gg’bm (5'1) where subscript notation ij+pq means grafting reaction of component ij with component pq. Subscript on the left side is assigned for polymer A. Subscript on the right side is assigned for polymer B. rnflmfl appears when i and j are both even since there is no component with non-integer index, extra rm term is counted because self grafting reaction kills two species simultaneously compared to reaction with other components. The rate expression of equation 5-1 can also be written as dC.. -—d-;’— = (P; - E; )r (5’2) where R} is the fraction of the total reaction rate r for the generation of graft copolymer ij. P; is the fraction of the total reaction rate for the consumption of graft copolymer ij. Since the polymers have infinite numbers of reactive groups, the rate of grafting conversion for polymer A satisfies C0£1f_a A dt =(l-fA)r (5’3) 75 where (l - ft.) is the fraction of the total reaction rate for the consumption of A in case of infinite reactive groups. Combining equation 5-2 with equation 53 gives div/«If. =03; —P..;)/(1-f,.) (5-4) where the reduced concentration Eg’ is defined by E-fi- (5 5) U_CA0 - The reduced initial concentration of B becomes —0 —o C a C = — = x 5'6 8 C2 ( ) where x is the molar ratio of the two reactive polymers. The grafting reaction environment is the sarrre for any particular reaction. The chance for a particular reaction of component ij with component kl to forru component (i+k)(j+l) is proportional to (il+ jk)C.-,~ Cu. The chance for all reactions to occur at any moment is proportional to (“:3 Ci: . The fraction of the total reaction rate for the formation of any particular component is the summation of all the chances for the formation of that component divided by the chance of all reactions. The expression for I}; is generalized as r j _ _ Pi; = 5%{221/(0 — l) + [(i - k)]Cu C(i—ka-D} (5'7) k=0 [=0 where the separated plus term in equation 5-1 is adsorbed to give equation 5-7. Accordingly, the expression for B; is generalized as . 1 . .— . . PU. =;—[(rx+})C.-j] (r=O,l,---n,j=0,1,--~m) (5-8) where the separated minus term in equation 5-1 is adsorbed to give equation 5-8. 76 5.2.1.2 Concentratiom of polymer species From expressions of Pi and Pf of equation 5-7 and equation 5- 8, we can solve equation 5-4 analytically with the initial conditions f,=0, 53:1, 62:; Eli-=0 07:10:01) (5-9) The solution is generalized as i+j-l l Ca-‘gij(1-fr)+%[-ln(1-fr)] x,_-—1- (5-10) where mg§[k(j— l)+l(i- k)]€u8(r—k)u—I) (5-11) (i- — 1,2,---m+l; j = l,2,---n+1) 81,-: 310 =gor =1, 8m =80; =0 . . (5-12) (I = 0,2,3,4,-~m+1;1 =O,2,3,4,~-n+1) Since there is no intramolecular reaction, the total reduced concentration of all species satisfies _ d ., dC (22C ) i=0 j==0 rm = = —— 5- 13 (It dt C2 ( ) by combining equation 5-13 with equation 5-3 and integrating, we have Cr=x+l+ln(l—fA) (5-14) The total reduced concentration of the graft copolymers C, becomes ‘C’, = CT -E. -EB = x+1+ln(l-fA)-(1-.fA)—x(1—fA)”‘ (5-15) 77 Equations 5-13, 5-14, 5-15 are valid only for grafting conversions before the onset of gelation. Equation 5-10 is valid for post-gel grafting conversion according to Flory's argument This is obvious since equation 5-1 describes species of finite size. Intramolecular reaction happens only to the single gel of infinite size. The presence of gel does not change the expression for P. C lj. 5.2.1.3 Molecular weight averages and gel point The reduced number-average molecular weight (N AMW ) and weigh-average molecular weight (WAMW) of all species are calculated by Mn 1+x 37° =“ET (5'16) _ 22(i+jM,/M,)’E., ”1;” = “° j‘° , (517) M. 1+(MBIMA) x Equation 5-17 can be easily programmed to get the reduced WAMW in relation to molar ratio , molecular weight ratio of the reactive polymers and grafting conversion. A more compact forru can be sought by seeking the generating function of equation 5-1 or equation 5-4. The various molecular weight averages can be obtained from the moments of the generating function. Let us define the generating function as G(A,B, Z) =22A“BIE,(Z) (5-18) i=0 j=0 where z=—ma-L) 64% By multiplying equation 54 by A‘B’ and summing for all the i and j, we have 1 GI =—ABGAGB -AGA Jae, (5-20) x x 78 The initial condition becomes G(A,B,0) = A+Bx (5-21) 0,, GB, and 02 are the partial derivatives. Equation 5-20 belongs to a nonlinear first order partial differential equation with three independent variables. We can solve it using the method of characteristics [Rhee et al., 1986] with the initial condition of equation 5-21 (see Appendix A). The results are: G(A, B, Z) = §+ xn - gnz (5-22) A =CEXP[(1—n)Z] (5-23) B = nEXP[(1 — 1;)2] (5-24) 0,, = CIA (5-25) G, = xn / B (5-26) ApparentlyC=n=1 when A=B=1. The WAMW is related to the generating function by M2 i(AG,)+2M,M,GM +M§%(BGB)I _ A M. = 3" g, (5-27) MAGA +MBGB 8:] By manipulation of equations 5-23, 5-24, 5-25, 5-26, we have for the reduced WAMW (see Appendix A): A7. _1+2ZMBIMA+x(M,/MA)2 M3. [1+x(M, /M,)2](1—z2 Ix) (5-28) From equation 5-28, we have at the critical point of gelation 22 = x (5-29) 79 Substituting expression for Z, we have —ln(1—fj”)= x05 (5-30) 5.2.2 Polydisperse reactive polymers 5.2.2.1 Balance equation Polymers can be highly polydisperse when they are made by condensation polymerization, free radical polymerization, and ring-opening polymerization with chain transfer. For polydisperse reactive polymers, it is necessary to relate the grafting conversion to weight-base grafting conversion. The new kinetic description has to reflect the grafting history of each individual species of a particular molecular weight when the individual component of certain molecular weight of the polymers is labelled individually. The kinetic expression of equation 5-1 can be readily extended to accommodate the situation with polydisperse reactive polymers. Let us designate the species concentration by C. ,.,‘"...;j'j'.... where i,i’,--- stand for numbers of chains of polymer A of different molecular weight j, j ’,-~- stands for numbers of chains of polymer B of different molecular weight The kinetic expression of equation 5-4 becomes _ 8 _ c dc,,,.,...,,,,-5... = 125.5... ,5 , P555}, , dfmg l'ffi.: (5-31) where H3. is the reference fiee chain component of polymer A having molecular weight of the number-average molecular weight of initial polymer. _C-i,r",....j,1 is defined as _ C. ., ,. ., c =—C-,-— (5-32) A 80 With such identification, we can extend 1355...,“ and 13.35%]. into W0 Md) HM{ZZH][Z=(1+Zai.-E‘)c. +n.2b..-E‘ i=1 i=1 535030,) = x(1+ 2b,}? m, + xCBZauE‘ i=1 i=1 (6-43-g) (6-43-h) (6-43-i) (6-44-a) (6—44-b) (6-44~c) (6-44-(1) (6—44-e) (6444) (6-44—g) (6-44-h) (6-44-i) (6-44-j) (6—45) (6-46) 119 a a CAB = 55(AGA ) = 5X(BGB) = (1+:auEi)CB +n,:b,,z‘ = x(1+:buE‘)nA ”giant (6-47) i=1 i=1 i=1 i=1 at A = B = t; = n =1. The reduced WAMW of equation 6-27 is calculated with the results of equations 6-39, 6-40, 6-41, 6-42, 6-43, 6-44, 6-45, 6-46, 6-47. There is a common denominator associated with the WAMW. This leads to the condition for the critical point of gelation AE-Féw (M) We have thus obtained the expressions for the gel point, the system's WAMW and the probability of intramolecular reaction at any instant of grafting conversion. The statistically equivalent number 8 B of chain B, free and confined in the local environment of the simplest graft copolymer, is the model parameter. It is a function of chain characteristics and dilution. The results reduce to the situation of grafting with no intramolecular reaction when 9,, (or 94 ) goes to infinity. 6.2.4 Effects of chain characteristics and dilution on the model parameter Before looking at the effect of intramolecular reaction on the WAMW and the grafting conversion at the gel point, we need to estimate the range of 9, (or 8‘ ) value. 8 B is related to chain characteristics and dilution by (from equation 6-7 and equation 6- 11) xNMNaanEOO—tp) a“, N, N (N, + NBx)22 2 1:, k=l i=1 j=l e, = (6-48) For chains of gaussian distribution, we have 3/2 3 Pf _ = ——-— V (6-49) 120 Where N Zr, are the numbers of statistical equivalent units between the two reactive groups a, and b}. for k isomer, 1 is the length of the statistically equivalent unit, V“, is the volume of the coordination sphere. The exponential term is omitted since it is very close to one for large Naibj . Let the radius of the coordination sphere KW", be expressed by R here! =kl (6-50) 3p The volume of the coordination sphere becomes V =1nk’z3 (6-51) sphere 3 By substituting equation 6—51 into equation 6-49, we have 3'; ..~. 1.38k3(N:'_,,’_ )‘3’2 (6-52) We see from equation 6-52 that the effect of chain flexibility is reflected in k. k equals to one for random flight chain, normally k is less than one. It is related to the fixed bond angle and rotational potential barrier (no consideration of steric interactions resulting in the interdependence of rotations about neighboring bonds) by [Benoit, 1947; Kuhn, 1943; Freed, 1987] _1+cosO-(cosv) -1-cose+(cosw) (6-53) where 9 is the fixed bond angle, \y is the rotational angle, and the azimuthal averages < cosw > are defined by KCOSW expl-wm/ (mm < COSV >= ‘ J_,exp[-w(v) I (may (6—54) The summation in equation 6-48 is over all the reactive groups and all the isomers that can be constructed of a simple graft copolymer. Block and symmetric four-arm star copolymers are two extreme cases. Their structures are sketched in Figure 6-5. 121 block star Figure 6-5 Sketches of block and star linkage The statistically equivalent numbers of structural units satisfy Nab; = k(iva + jvb) (6-55) In case of block linkage, the double summation of equation 6—48 becomes N N, 22133:“ =1. 38k1'v‘ 352204:— —:j)"5 (6-56) i=1 i=1 i=1 is] In case of symmetric star linkage, the double summation of equation 6-48 becomes N, N, N /2N,/2 22103;“: 5. 52kl'v5 ;‘5 2 2a +-‘-’-j)-‘5 (6-57) i=1 j=l i=1 i=1 Va Here the reactive groups are taken to be even. The uneven situation shall be very close to the even case for large numbers of Na and Nb. It is assumed here that the gaussian distribution of two structural units is not affected by the presence of two extra branches as was mentioned earlier. We see from equation 6-56 and equation 6-57 that the summations in the two extreme cases differ by a factor of nearly four fold. It is, therefore, necessary to do a detailed calculation to get the average from all isomers. Let §(N,,N,,,v,, Iv.) be the average of the double summation taken over all the isomers. We have §(N H,Nb,vb/v )_—222(z+—,)55 (6-58) ".50 k=1 181 1‘2] By counting the numbers of isomers, we have 122 n,” = (N, / 2+1)(N,, /2+1) (6-59) for even numbers of N, , Nb. Equation 6-48 becomes bea_ll(l " ‘1’.)ng o = (6-60) 5 1 v 1 - 1.38k‘5(—+ x—"— )S(N,, N,,v, I V“) Nb Va Na 6.3 DISCUSSION 6.3.1 Order of magnitude of 9, The system's WAMW and gel point are related to the model parameter 9,. Several qualitative conclusions are deduced about the effects of chain characteristics and dilution on 9, based on equation 6-60. (a) 9, is directly proportional to dilution in a theta solvent. A good solvent expends the coil and results in smaller k value and therefore higher 9,; (b) 6, is very sensitive to the flexibility of the chain, this is shown by the 1.5 powers dependence on k; (c) 9, increases with the numbers of inert units on the chain (v4), but the influence of inert spacing on 9 B is much less sensitive than chain flexibility; (d) the change in molar ratio also affects 9, value. 9, increases with increasing; (e) the numbers of reactive groups on chain A and chain B affect 6, value. The numbers of reactive groups on chain A and chain B are perhaps the most important since they connect to the dimensions of chain A and chain B at fixed numbers of inert spacing. Apparently, many factors contribute to 9, value. A complete discussion on the various factors and their combinations is cumbersome. The important thing from equation 6-60 is to estimate the order of magnitude of 9, given the assumptions made in deriving equation 6-60. 123 6.3.1.1 Special ease: N, = N” v. = v, Let us look at a special case when the numbers of reactive groups on chain A and chain B are equal, so do the numbers of inert spacing. Let O=OA+OB (6-61) One sees from equation 6-11 and equation 6-60 that 6 is independent of x. The meaning of statistically equivalent mean volume is seen more physically in this special case, it is the equivalent volume where the whole simple graft copolymer is contained in it. We can, therefore, choose 9 as the model parameter and see the effect of molar ratio on a common basis. The mean double summation S(Na , N b , v, / v“) is for the first neighbor contribution only. The contributions from the second neighbor, the third neighbor, so on so forth, can be included by adding additional summations. The asymptotic behavior of the double summation is similar to the single summation (Truesdell summation). S(N) =23“ (6—62) i=1 Figure 6-6 shows the fractional increase of S(N)] S(oo) ( S(oo) =2.612) with increasing numbers of reactive groups. Major contribution to S(N) comes from the first 50-150 reactive groups. If the reactive polymers bear that many of reactive groups, then, the first neighbor contribution to intramolecular reaction is indeed a major part. This serves as a justification for the assumption (first neighbor contribution) made in the derivation of the expressions for the system's WAMW and gel point. A particular set of parameters is chosen for an estimation of the change of 9 value with the numbers of reactive groups. The parameters are: v =v, =10;3l n13) for several polymers in the unperturbed state following his complete theory of chain configuration [Flory,l969], i.e., 6 for polyethylene, 8 for syndiotactic poly(methyl methacr'ylate) (PMMA) and 10 for isotactic PMMA in the asymptotic limit of coarse-grained gaussian chain [Flory, 1975], with the corresponding k of 1/6, 118 and 1/10. 9 increases to 370- 2350 if we choose k of 1/6. It drops back in the range of 40-235 for a ten-fold dilution in solution grafting reaction and 20-120 for a twenty-fold dilution (the equivalent number 126 fraction can be considered to be equal to volume fraction in the mean field approach as a first order approximation). Above arguments are based purely on the assumptions of long chain gaussian distribution. Such an analysis is good at least for estimating the order of magnitude of 9. In a broader sense, we select 9 in the range of 10-100 for a discussion of its effect on the WAMW and gel point. It is very important to point out that the mean probability of intramolecular reaction decreases with chain length. 200 180- 160. l 1 0 50 1(1) 150 2(1) N (Na=N,,=N) Figure 6-8 Model parameter 9 in relation to the numbers of reactive groups on chain A and B It was shown in a chapter 5 that the growth of WAMW of the grafting reaction process is the fastest with grafting conversion when there are equal moles of A and B (grafting conversion is based on A when B is to be modified by A). By increasing the molar ratio x, we slow down the growth of weight average molecular weight and the onset of gelation. 9,, increases with x at fixed 8 value. We choose x values of 1 and 2 for a discussion. 127 6.3.2 System's probability of intramolecular reaction The extent of intramolecular reaction in the grafting system is looked also with a special case as was selected above. Figure 6-9 shows that the system's probability of intramolecular reactions increases exponentially with grafting conversion and it decreases with increase of x. The curves stop at the gel point. Such self-accelerating characteristics for intramolecular reactions is expected intuitively. 0.4 0.35 0.3 . 0.25 . Figure 6-9 System's probability of intramolecular reaction in relation to grafting conversion of polymer A and molar ratio. 6.3.2 Gel point and system's weight-average molecular weight (WAMW) The expressions for the gel point (equation 6-47) and the WAMW (equation 6-26) contain serial terms with coefficients {an }, { b“ }. The calculations were made in which terms with coefficients {an }, { bu} were dropped except for those with coefficients a“, a ,2, b, 1, b”. This is a good approximation for the range of 98, E, and x values chosen in the calculations. 128 Table 6-1 Effect of 9 on the Critical Grafting Converm'on at Two Molar Ratios :5 9:... 9:50 9=20|9=10 x=l.0 0.63 0.67 0.73 | 0.82 =20 0.76 0.80 0.85 I 0.93 NA = N8 Table 6-2 Probability of Intramolecular Reaction 1. at ff” x 9=oo 9:50 9:20 | 9:10 x=1.0 0.0 0.039 0.123 H.290 x=2.0 0.0 0.047 0.132 J 0.328 NA = N B Tables 6-1, 6-2 list the grafting conversion and the system's probability of intramolecular reaction at gel point. We see that the critical grafting conversion is fairly sensitive to intramolecular reaction even though the system's probability of intramolecular reaction is relatively small at the gel point We are more concerned with the sensitivity of intramolecular reaction in delaying the take off of the system's WAMW for the purpose of grafting reaction. Figures 6-10, 6-11 show the effect of 9 on the reduced WAMW at two molar ratios of the two reactive polymers (x). The plots are for the relatively small values of reduced WAMW since our grafting system starts with long chain polymers. The effect of intramolecular reaction gradually shows up with grafting conversion. At fixed grafting conversion, the WAMW can be much different once it is in the region of take off. For example, a few percentage changes in grafting conversion means substantially different WAMW with or without the presence of intramolecular reaction at a 9 value of 50 when the desirable reduced WAMW is 4.0. 129 8 7* MA=NB 6_ x=l.0 @=°°.50.20,10 '0: 1:3 0 0.2 0.4 0.6 0.3 1 f4 Figure 6-10 Reduced WAMW in relation to grafting conversion at different 9 with equal molar amount A and B. x=2.0 ®=°° , 50. 20, 10 Figure 6-11 Reduced WAMW in relation to grafting conversion at different 8 with xof 2.0. 130 6.4 EFFECT OF POLYDISPERSITY Effect of polydispersity on the system's probability of intramolecular reaction and the grafting process can be readily extended into the kinetic formulation. However, the gel point and molecular weight averages can not be calculated easily since the change of the probability of intramolecular reaction with length of the chain segment of a graft copolymer is not linear. Implementing the effect of polydispersity directly means the presence of more than first order partial differential equation of the generating equation (equation 6-24), a vast increase in the complexity of the generating equation. No direct numerical simulation was attempted, however we can still tell the importance of polydispersity in terms of intramolecular reaction by comparing to the case of monodisperse reactive polymers at the same number-average molecular weights of polydisperse reactive polymers. Under such consideration, the presence of polydispersity is to reduce the extent of intramolecular reaction at the same percentage conversion of a refrence reactive polymer, since increasing the chain length results in lower probability of intramolecular reaction (see Figure 6—8). Selective grafting conversion of higher molecular weight reactive polymers also results in less extent of intramolecular reactions. Since gel point and weight-average molecular weight of the grafting system are most sensitive to the polymer species of high molecular weight, polydispersity, therefore, will reduce the effect of intramolecular reaction on the change of the gel point and weight- average molecular weight of the grafting reaction system if we compare to the assumed monodisperse polymers having the number-average molecular weights of the polydisperse reactive polymers. 6.5 EFFECT OF INTRAMOLECULAR REACTION IN CA-SMA GRAFTING SYSTEM There are on the number-average 85 hydroxyls on the CA backbone and 90 anhydrides on the SMA232 backbone. On the average there is one hydroxyl per two modified 131 anhydroglucose units of CA and one anhydride unit per 13 styrenic units. In order to estimate the order of 9m , we can do a rough estimation starting with polystyrene chain, that is the modified anhydride glucose units, the anhydride unit are treated as styrenic unit. The parameters of equation 6-60 are: No” =85, N... =90, v0” =2, v,“ =14, x=2.95, (p, :09, 2,,” =12, k=1/10 The selection for x is with equal amount of CA and SMA. The value of k is based on the calculation by Yoon et al. [1975] where the reduced mean square end-to-end distance (< r >2 lnlz) for atactic polystyrene was reported to be 10.0. With the exclusion of small ring of less than 20 constitutional units (the smallest ring will consists of 21 constitutional units in the calculation), 9 is found to be 74.6. Therefore the probability of intramolecular reaction is very small and its influence on the grafting process is minor based on the discussion of section 6-3. The consideration of nonuniform distribution of constitutional units bearing reactive groups on the chain backbone will decrease 6," since the ring closure probability is a concave function of the numbers of statistically equivalent structure units of the coarse-grained gaussian chain, but this effect is expected to be minor since the ring closure probability decreases smoothly with the numbers of statistically equivalent units when that number is large. The more rigid chain of CA and SMA (the presence of SMA decrease the chain flexibility as is evidenced by increased Tg in the presence of MA) as compared to polystyrene will increase the estimated 6,,M value, so will the unfavorable interaction between CA and SMA. The effect of polydispersity will reduce the extent of intramolecular reactions as was discussed qualitatively in section 6-4. The consideration of all these factors can lead only to the conclusion that the probability and the extent of intramolecular reaction are minor at a polymer concentration of 10 wt% for the purpose of grafting reaction in this particular CA-SMA grafting system. 132 6.6 SUMMARY The kinetic formulation in chapter 5 has been extended to include intramolecular reactions for the grafting reaction system of reactive polymers A and B bearing large numbers of reactive groups. The importance of spatial correlation among chain species because of differences in volume exclusion is recognized and properly incorporated into the kinetic theory. Difference in the excluded volume among polymer species creates the overall redistribution away from the state of complete randomness. Such redistribution can be taken care of by introducing a normalization procedure in the kinetic formulation. The kinetic formulation is self-consistent with such normalization procedure when one considers the presence of intramolecular reaction. A general procedure was provided to look into the effect of intramolecular reaction in slowing down the growth of system's weight average molecular weight and the onset of gelation.. While the grafting system is good for the issues at hand, the importance for the consideration of spatial correlation among polymer species because of volume exclusion is believed to be universal in other polymerization systems for the correct formulation of the theory no matter how small the excluded volume effect is. A mean probability of intramolecular reaction is taken over all the isomers of the graft copolymer in the kinetic formulation. The buildup of the complexity of the structure of graft copolymers calls for a distinction for the probability of intramolecular of different graft copolymers. A generating function is introduced to derive the expressions for the system's probability of intramolecular reaction, WAMW, and gel ‘point in the approximation of only the first neighbor contribution to the probability of intramolecular reaction. Exact expressions for the system's weight-average molecular weight and gel point are obtained A semi-quantitative discussion was made on the model parameter 8 in relation to chain characteristics and dilution under the assumption of gaussian distribution. 8 is defined as the numbers of chain A and chain B (including chain A and chain B of the graft 133 copolymer) in the statistically equivalent mean volume of a simple graft copolymer. It is shown that 9 can have a broad range depending on chain characteristics and dilution. Increasing the numbers of reactive group on the chain results in increased 9 , therefore of reduced system's probability of intramolecular reactions. The effects of intramolecular reaction on the system's weight average molecular weight and gel point were discussed in terms of model parameter 9. It is found that the gel point is fairly sensitive to intramolecular reaction even though the system's probability of intramolecular reaction is relatively small at the gel point. The sensitivity of system's weight average molecular weight can be either sensitive or not depending on the value of the system's WAMW sought in the practical situation. In general, the effect of intramolecular reaction cannot be simply neglected in the defined grafting system. Even though an extension of the kinetic formulation to polydisperse reactive polymers posses no difficult, direct simulation on the effect of intramolecular reaction with polydisperse reactive polymers represents a diffith task. However, we can still tell qualitatively what the presence of polydispersities of the reactive polymers does in enhancing or reducing the extent of intramolecular reaction in the pregel region by comparing to the monodisperse case at the same percentage conversion and number- average molecular weights. Under such comparative basis, the presence of polydispersity lowers the system's probability of intramolecular reaction since the intrinsic probability of intramolecular reaction of a graft copolymer decreases with chain length and the grafting reaction weights toward more grafting conversion of the high molecular weight chain fraction of the reactive polymers. In case of CA-SMA grafting system, it is concluded that the effect of intramolecular reaction can be neglected. Chapter 7. CONCLUSIONS AND SUGGESTION FOR FURTHER WORK 7.1 CONCLUSIONS Grafting reactions between cellulose acetate (CA) and styrene maleic anhydride random copolymers (SMA) were successfully carried out in solution with the aid of a catalyst. The grafting reaction occurs in a non-homogeneous state at a polymer concentration of ~10 wt%. The dilution of unfavorable interaction between CA and SMA is very sensitive to the concentration of polymer solution. Increasing the MA level in SMA reduces the irnmiscibility between CA and SMA. Analysis of the free energy of mixing by a mean field approach shows qualitatively the order of sensitivity of the concentration of polymers and the MA content of SMAs in changing the unfavorable interaction between CA and SMAs. The rate of grafting conversion can be described by taking into account the effect of phase separation and the effect of polydispersity of the reactive polymers. While the effect of polydispersity on the rate of SMA grafting conversion can be analyzed exactly, the rate of SMA grafting conversion cannot be described in a simple manner since information on the phase size and phase size distribution is not readily available. The complexity of the grafting process is also shown by the power of dispersion of the graft copolymers whence they were produced during grafting reaction. Several parameters involved in the rate expression of SMA grafting conversion were studied separately: (a) The stirring intensity indicated by the stirring speed in the range of ZOO—600 (rpm) has little effect on the rate of grafting reaction. This is explained by the presence of low interfacial tension, high solution viscosity and the dispersion power of graft copolymers for equilibrium phase size. These important factors tend to smear out the effect of mixing intensity. (b) The grafting reaction is very sensitive to the 134 135 concentration of polymers in solution. The concentration of polymers in solution is rather limited in order to avoid the reduction of compatibilizing ability of the graft copolymers, since the net effect of phase heterogeneity is to reduce the effect chain length of the chain segments of graft copolymers. (c) There is a first order relationship on the intrinsic kinetics between reaction rate and the concentration of catalyst. (d) The grafting reaction is very sensitive to reaction temperature, so does the MA level in SMA. (e) Only small amount of water is allowed in this grafting reaction system in order to avoid excess hydrolysis of CA. The presence of small amount of water promotes grafting reaction. Tensile properties, moisture adsorption and the dimensional stability of some grafting reaction products were evaluated in the form of cast films. The film alloys show slightly improved tensile strength, appreciably increased tensile modulus and reduced elongation at break in comparison to CA, with/without plasticizer. Such tensile properties, together with reduced moisture adsorption, are good for improving dimensional stability of the grafting products. For example, in the presence of 50 % SMA in the alloys, there is more than 50% reduction on the dimensional change as compared to CA for tests in the form of cast films under various water soaking conditions. The dimensional stability of the film alloys is better or comparable to CTA. There is a good potential to find applications for the grafting reaction products in films, textile fibers and separation membranes. Phase size and homogeneity in the reaction products need to be controlled for best performance in compatibilized blends and alloys. Controlling phase size and homogeneity depends on the structures of the graft copolymers as well as the amount of graft copolymers in the ternary mixtures. It is found that homogeneous phase structures appears in the grafting reaction product as the grafting conversion of SMA increases. Substantial solubilization of homopolymers into the domains of graft copolymers is found. The formation of complex graft copolymers at high grafting conversion does not lead to the insolubilization of free chains. This desirable property is explained from the grafting 136 conversion of more high molecular weight homopolymers based on the current understanding of solubilization phenomena from block copolymer system, a unique feature for synthesizing the graft copolymers in the defined grafting system. While the driving force for homogeneous solubilization at low graft copolymer content was not clearly understood, the dynamic force could have been important in causing the size distribution of the dispersed phase. The study shows the importance of polydispersity in promoting homogeneous phase size in this grafting reaction system. For a better understanding of the molecular characteristics of the grafting reaction products from a control point of view, it is important to analyze theoretically the branching process of the CA-SMA grafting reaction system. Such an analysis can be done on a more general basis for the defined system of: (a) two reactive polymers bearing large numbers of reactive groups; and (b) homogeneous, irreversible grafting reaction. A kinetic approach is employed to arrive at various expressions for the molecular characteristics of the grafting process neglecting the presence of intramolecular reaction. Both monodisperse and polydisperse polymers are considered. The discussion made on the monodisperse reactive polymers reveals many important things on the branching process. The two most important findings are: (a) the critical grafting conversion is quite limited and changes with the composition of the two reactive polymers; and (b) the take off of the system's WAMW starts long before the onset of gelation. It, therefore, further limits the extent of grafting conversion. When the two reactive polymers are highly polydispersive, the critical grafting conversion behaves in a complicated manner depending on several factors: PDI, distribution, and composition. Increasing PDI results in lower critical grafting conversion when the polydispersities of two reactive polymers are close to each other. It is found that the presence of high molecular weight tail in the polydisperse reactive polymer reduces the critical grafting conversion of the reactive polymer, an undesirable factor for the purpose of grafting. The practical grafting conversion for a reasonable WAMW can be greatly affected when the PDIs of the reactive polymers 137 become extremely high (much more than 3). The study also shows that simulating the molecular weight distribution of the grafting process with polydisperse reactive polymers is not readily done because of long computational time, even though the concentration of each individual species is obtained analytically. For the particular case of CA-SMA grafting system, calculation based on the assume homogeneous state indicates that the grafting conversion of SMA is limited to 60: 5% at equal amount of CA and SMA, and 70:1: 5% at a quarter amount of SMA in the polymer mixture. The presence of heterogeneity at the early stage of grafting reaction will limit further the grafting conversion of SMA. The theoretical analysis is of great importance because of the difficulty in GPC analysis due to the association of the grafting reaction products in carrier solvents. Grafting reaction of the defined system starts with long chain reactive polymers. The presence of large numbers of reactive groups on the two reactive polymers calls for an analysis on the extent of intramolecular reaction of the graft copolymers during the course of grafting reaction. In the broad sense, the effect of intramolecular reaction remains to be an old problem that has not been dealt with completely from a theoretical point of view. A self-consistent kinetic theory is developed to look at the extent of intramolecular reaction in the defined grafting system. The self-consistency is satisfied via a normalization procedure that reflects the hidden redistribution of polymer species away from the complete randomness due to differences in volume exclusion for different polymer species. A general procedure is provided to look into the effect of intramolecular reaction in slowing down the growth of the system's weight average molecular weight and the onset of gelation. While the grafting system is good for the issues at hand, the consideration of spatial correlation among polymer specibs because of differences in volume exclusion effect is important, and is believed to be universal in other 138 polymerization systems for the correct formulation of the theory, no matter how small the differences in excluded volume effect is. A mean probability of intramolecular reaction is taken over all the isomers of the graft copolymer in the kinetic formulation. The buildup of the complexity of the structure of graft copolymers requires distinction for the probabilities of intramolecular reactions of different graft copolymers. A generating function is introduced to derive the expressions for the system's probability of intramolecular reaction, WAMW, and gel point using the approximation of only the first neighbor contribution to the probability of intramolecular reaction. Exact expressions for the system's weight-average molecular weight and gel point are obtained A semi-quantitative discussion is made on the model parameter 9 in relation to chain characteristics and dilution under the assumption of gaussian distribution. 9 is defined as the numbers of chain A and chain B (including chain A and chain B of the graft copolymer) in the statistically equivalent mean volume of the simplest graft copolymer. It is shown that 9 can have a broad range depending on the chain characteristics and dilution. Increasing the numbers of reactive groups on the chain results in increased 9, and therefore reduced system's probability of intramolecular reaction. The effects of intramolecular reactions on the system's weight average molecular weight and gel point are discussed in terms of model parameter 9. It is found that the gel point is fairly sensitive to the presence of intramolecular reactions even though the system's probability of intramolecular reaction is relatively small at the gel point. The sensitivity of the system's weight average molecular weight depends on the value of the system's WAMW sought in the practical situation. In general, the effect of intramolecular reaction cannot be simply overlooked in the defined grafting system. Extension of the kinetic formulation to polydisperse reactive polymers poses no difficulty, even thougu a direct simulation of the effect of intramolecular reaction in case of polydisperse reactive polymers represents a difficult task. However, one can still tell 139 qualitatively what the presence of polydispersities of the reactive polymers does in enhancing or reducing the extent of intramolecular reaction in the pregel region by comparing it to the assumed monodisperse case at the same percentage conversion and the same number-average molecular weight. Under such comparative basis, the presence of polydispersity reduces the system's probability of intramolecular reaction since the intrinsic probability of intramolecular reaction of a graft copolymer decreases with chain length and the grafting reaction weights towards more grafting conversion of the high molecular weight chain fraction of the reactive polymers. For the particular case of CA-SMA grafting system, it is concluded that the effect of intramolecular reaction can be neglected for the purpose of grafting reaction products without crosslinking. 7.2 SUGGESTION FOR FURTHER WORK There are many potentials to utilize the property of improved dimensional stability (compared to CA, d.s.=2.45) of the new compatibilized blends. It is of practical interest to look at the dimensional stability of grafting reaction products for textile fibers. Further work should include: (a) fiber spinning in acetone-water mixture solvent; and (b) testings of the dimensional stability of the fibers under water soaking condition, particularly at high temperature. The results from the above mentioned tests should then be Compared with cellulose triacetate. APPENDICES APPENDICES APPENDIX A: Solution by the method of characteristics In order to solve the first order nonlinear partial differential equation in case of monodisperse reactive polymers, let us rearrange equation 5-20 into E: Gz +AG, +130, —lABG,G, = 0 (A-l) x x The characteristic equations from equation A-l become dA —-=FG =A-ABGB/x (A-Z) ds A (18 —=FG' =(B-ABGA)/x (A-3) ds dZ E = 1v},z = 1 (A-4) 19 = 26,170} — ABGAG, / x (A-S) ds K=A.B,Z dG 719A = -F, = -(G, - BGAG, / x) (A-6) dz” = —F, = —(G, - AGAGB) / x (A-7) d —1= 0 (A-8) ds The initial conditions are: s = 0, Z=0. A =1; B =11. GA(C.n,O)=1, G,(C.n,0) = 1:. (A9) GZ(C’n90) =01 —C ‘11: C(C’WO) = C+m 140 141 We have by solving the characteristic equations G(A, B, z) =§+ xn -§nz (A-lO) A = CEXP[(1-n)Z] (A-l 1) B = nEXP[(1—§)z] (A-12) a, = g/ A (A43) G, = xn/B (A—14) By taking derivatives of equation A-11 and equation A-12 with A and solving the two resultant equations at A=B= 1, we have CA|A=B=1= x, (x-Zz) (A-15) nA|A=B=l= Z/ (x - 22) (A'16) By taking derivatives of equation A-11 and equation A-12 with B and solving the two resultant equations at A=B= l, we have CB|A=B=1= xZ/ (x-Zz) (A-l7) relax,= x/(x—Zz) (A-18) The partial derivatives in equation 5-27 contain terms of equations A-15, A-l6, A-17, and equation A-18 starting from equation A-13 and equation A-14. Equation 5-28 was obtained by further manipulation. In case of polydisperse polymers, let us rearrange the partial differential equation into 142 a, :izzm amigo, -2120“, £219,123,. (mzi,i’,...; n :j’j”...) The characteristic equations are: % = Amfig -A,'M‘A_23,fia_0,l Ix d2" =(B,m_ -B,HB_ZAMEA_GA_)Ix % = 4; ENG MB_A,B,G,_G,_ )/ x (16 _ _ __ 71?: -(Mgch -MA_GA_ZB,,MB_GB_ Ix) dG,_ _ _ _ 7: -(MB-GB. -MBnGB,ZAmMA-GA_ )lx (1G, (is =0 The initial conditions become s=0, 15:0, A, :gm, 8. =11", G,_ :N°(Tw'._), GB. =xN°(-A?a_) G=2C.N°(-M_A.)+XZII.N°(A—la.) (mzi’i”...; nzj’j”...) By solving equations A-20 to A-26, we have G=2c..~°+xzn.~°-Ezzc.n.~°