THERMODYNAMIC S OF SYSTEMS CONTAINING FLEXIBLE-CHAIN POLYME Q I C C i BY VITALY J KLENIN THERMODYNAMICS OF SYSTEMS CONTAINING FLEXIBLE-CHAIN POLYMERS Scientific edition by Professor Sergei Ya Frenkel Translated by Sergei L Shmakov and Dmitri N 'Ifichinin THERMODYNAMICS OF SYSTEMS CONTAINING FLEXIBLE-CHAIN POLYMERS Vitaly J Klenin Chair of Polymers, Chemistry Department, Saratov State University, Saratov 410071, Russia 1999 ELSEVIER Amsterdam - Lausanne - New York - Oxford - Shannon - Singapore - Tokyo ELSEVIER SCIENCE B.V Sara Burgerhartstraat 25 EO Box 211, 1000 AE Amsterdam, The Netherlands 1999 Elsevier Science B.V All rights reserved This work is protected under copyright by E l m e r Science, and the following terms and conditions apply to its usePhotocopylng Single photocopies of single chapters may be made for personal use as allowed by national copyright laws Permission of the publisher and payment of a fee is required for all other photocopying, including multiple or systematic copying, copying for advertising or promotional purposes, resale, and all forms of document delivery Special rates are available for educational institutions that wish to make photocopies for non-profit educational classroom use Permissions may be sought directly from Elsevier Science Rights & Permissions Department, PO Box 800, Oxford OX5 IDX, UK; 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I s c i e n t l f l c e d l t l o n by S e r g e i Ya F r e n k e l : t r a n s l a t e d by S e r g e i L Shmakov and D m i t r i N T y c h i n i n l s t ed p CR I n c l u d e s b l b l l o g r a p h i c a l r e f e r e n c e s and Index ISBN 0-444-82373-5 Polymers Therm1 QD381.9.TS4K57 1999 547'.70456 dc21 ISBN 444 82373 properties Thermodynarlcs I Title 99-20359 CIP The paper used in this publication meets the requirements of ANSliNISO Z j 48-1992 (Permanence of Paper) Printed in The Netherlands v Foreword There are very few serious monographs on polymer thermodynamics The problems of this science are mainly considered in the courses or monographs 011 thc physical chemistry of polymers, the statistical physics of molecular chains (conformational and configurational statistics), in books dealing with the principles of scaling, intramolecular phase or cooperative transformations, and, finally, in mini-monographs (I would refer them to the category of manuals) treating direct applications of thermodynamics to various chemical and physical polymer technologies Books dealing with either rough applications or new high technologies are most abundant, but it is difficult to find in them even a trace of thermodynamics-in the proper sense of the word Special books on the thermodynamics of polymers or, at least, on the thermodynamics of polymer solutions, at least, have not been widely scattered around the scientific world In contrast, there is a great number of large reviews or original papers on this subject in the international or Russian scientific journals Many of them are of a general character but the principle itself of writing problematic or review papers prevents a relatively complete consideration of any branch of science on the whole Therefore a possible question of the “why another book again?” type concerning the publication of V.J.Klenin’s monograph should not arise It would be wrong to consider it a textbook, although students, post-graduate students and fairly ripen researchers are recommended to study macromolecular science by it There was no such monograph before, and one must thank the author for its appearance Another question may be raised: whether it did not appear too late ? At present the school of 1.Prigogine (and his followers and proselytes) almost entirely predominated in the thermodynamics, physical and chemical kinetics and non-linear dynamics in general The answer to his question is quite definite: the author has not been too late publishing this monograph It is not possible to “jump” into the modern non-equilibrium dynamics and several more narrow and specialized sciences and theories developed from it (the theory of dissipative structures, synergetics, the theory of catastrophes, fractal “geometry” and dynamics, etc.) on the basis of “nothing” It would be the well-known attempt to jump over the precipice in two jumps However, the founders of classical statistical thermodynamics, Boltzmann and Gibbs, doubtless firmly occupy the pedestal built for them by History Any further path begins from their works Moreover, the algorithms of classical thermodynamics can be easily transformed into those of Prigogine’s one(however, the latter can already be considered to be classical also but with a new shade of meaning) To start with, it is sufficient to replace the terms “stable” (“equilibrium”), “metastablen, and “unstable” by the terms “stationary”, “metastationary”, and %on-stationary” Thus, with the aid of such a primitive glossary, a complete analogy in description of linear and non-linear phenomena may be attained including even the methods of description and the criteria of first- and second-order (in Landau’s sense) phase transitions However, this is not the only analogy There are many situations in which Gibbs’ and Prigogine’s thermodynamics are related to each other just as Newton’s and Einstein’s physics In many of these situations the New thermodynamics requires such minute corrections vi d q ) that they (in the sense of corrections of the same type as the famous root may be neglected The author of the present book bears this in mind and restricts himself essentially just to such situations that can become sufficiently complicate on the classical statistical-thermodynamic level Nevertheless, the introduction of thermokinetic corrections or properly termed Prigogine’s corrections into t he conventional thermodynamic equations changes the situation even to the first approximation and makes it possible to pass from non-realistic to realistic equations, interpretations, and, if necessary, predictions After the first approximation it is not difficult to pass to the second one and thus still to jump over the precipice dividing the two thermodynamics in two jumps! Another question may also be raised: wy did the author limit himself to systems with flexible-chain polymers ? In many publications my colleagues and myself have attempted to give quite an unequivocal answer to this question The “polymer state” may be considered to be a peculiar form of condensation of molecules, and the transition into this state may be regarded as a special fundamental phase transition’ on the background of which “usual” phase transitions take place This concept may be proven and developed just for flexible-chain polymers capable of the manifestation of rubber-like elasticity, i.e of reversible 1000-fold and greater deformations which involve forces of the entropy nature In this case it is easy to make a transition to rigid-chain or cross-linked (3D) polymers without introducing any fundamentally new factors into the equations for flexiblechain systems For example, chain rigidity may be regarded as due to an increase in internal energy or enthalpy The results of this concept become clear if an example which I have repeatedly reported is used If the melting or dissolution temperature of the polymer system is expressed not by the conventional equation but by a ratio of binomials in which subscripts Uln and “2” at the entropy and enthalpy terms refer to conformational and configurational contributions it becomes clear that upon melting or dissolution of flexiblechain polymers when great changes in both entropies occur, it is possible to increase markedly T* by simple superposition of external restrictions (e.g., tensile stress which in this case is equivalent to pressure in conventional van der Waals systems) This trick may be used in reverse transitions in technology or for the production or transformation of energy In contrast, in rigid-chain polymers the changes in both entropies are slight (a rod can be only a rod, hence, AS, + 0) and all the “load” is applied to the enthalpy terms Moreover, under the conditions of the same uniaxial stretching, the Poisson coefficient that reduces AS2 to zero and increases AH,, predominates This can also be directly ’Here I refer to my mini-tractat “Polymers:problems, prospects, and prognoses’’ in: “Physics today and tomorrow” (in Russian) Leningrad, “Nauka Press’’ 1973, p 176-270 vii used in technology in the preparation of superfibers from rigid-chain polymers, However, in this case the process occurs quite differently from that for flexible-chain polymers This is also related to a more fundamental factor: flexiblechain polymers are usually soluble and fusible, whereas rigid-chain ones are thermally stable and often neither dissolve nor melt This property involves considerable technological difficulties, although in many cases modern high technologies require the application of just rigid-chain polymers This postulate may be reinforced as follows: rigid-chain or super-oriented flexible-chain polymers lose to a considerable extent their specific “polymer nature” which combines the possibility of the coexistence of three phase and aggregate states depending on the method of treatment In many respects they cannot be distinguished from simple solid bodies (it is in this form that L.P.Myasnik0v.a has expressed this principle which is of great importance for polymer physics)2 In contrast, in flexiblechain polymers virtually any superpositions of phase, aggregate and relaxation (glass, rubber, and viscous fluid) states are possible Hence, the phase equilibria are extremely varied and complex, and phase diagrams are unusual (the author characterizes the states of the system according to Gibbs’ configurative points) and the morphological kinetics of phase transformations are also unusual Again, this situation, as well as the author’s didactics itself, may lead to some miscomprehension of his main aims which became apparently too trended forward essentials of polymers materials science and, consequently, applications However, in the same Preface V.J.Klenin points several times that the book is planned as a foundation of polymers materials science, and one can attain just nothing if the fundamentals (pure science) are omitted The epigraph from Minster (A.Minster, Chemical Thermodynamics) restarts wholly the logistics and didactic order in the book And this book just substantiates this consequence It deals with the methodology rather than with the methods This methodology is very logical but often this logic is not sufficiently apparent, and the author confidently leads the reader along the labyrinths of imaginary and real difficulties (that may result from the fact that the readers are not accustomed to the specific form of physical thinking) to indisputable and rigorously demonstrable truths In this sense the book might be called “Introduction to the thermodynamics of polymers,’ but it should be borne in mind that the term “Introduction to ” has two meanings in the scientific literature One on them is primitive The reader is provided with a certain primary information so that he can subsequently begin to study the more special literature In the German scientific literature the term “Introduction” or “Einfiihrung” has a much deeper meaning It need not be followed by a “Handbuch” or “Manual” The “Einfiihrung” gives an almost complete summary of facts, theories, and general principles that should be used by the researcher in his own work and developed not only on the “low” technical level but also on the high fundamental level Of course, I not mean to neglect the practice (as was already hinted), which would be silly, but only should ’See i “Oriented Polymer Materials”, S.Fakirov editor, Huthig and Wepf Verlag, Heidelberg-Oxford, n 1996, chapter (by V.A.Marikhin and L.P.Myasnikova: Structural basis of high strength and high modulus polymers) Index y-order critical point, 481 y-order critical state, 481 absorption index, 113 action, 212 activity, 19 affinity, 258 antigen-antibody complexes, 144 artificial blood plasma, 143 asymmetric tricritical point, 245 asymmetry ratio, 112 atomic amplitude, 123 attenuation index, 113 autocorrelation function, 154 autocorrclator, 157 bacteria, 143 binary (pair) distribution function, 166 binodal, 27 bistructural models of water, 163 blobs, 289 bond percolation, 405 bond vectors, 266 boundary of phase separation region, 308 Brownian chain, 666 chain skeleton effect, 269 cluster, 405 cluster expansion, 100 coef3i cient s activity coefficient, 19 cooperative diffusion coefficient, 364 diffusion coefficient, 3-55 effective second virial coefficient, 303 expansion factor, 272 interphase separation coefficient, 305 microscopic diffusion coefficient, 464 molecule packing coefficients, 265 Poisson’s coefficient, 389 tension coefficient, 389 thermal expansion coefficient, 472 virial coefficients, 102 cohesion energy density, 185, 264 collapse of gel, 400 compressibility isoentropic compressibility, 11 isothermal compressibility, 13 compressional modulus, 387 concentration fluctuation function, 182 configuralional quantities, 70 conjugate phase, 483 connected graph, 225 contact diameter, 185 continuous limit, 665 contour length, 268 correlation, 70 correlation function, 120 correlation length, 176 correlation point, 658 correlation volume, 122 correlators, 218 critical indices, 59 critical line, 489 critical object, 665 critical opalescence, 60, 164 critical phase, 29 critical phenomena, 60 critical space dimension, 591 cross-correlation functions, 195 crosslinked polymer, 385 crossover, 90 crossover index, 91 cumulant method, 360 curves boundary curve, 27 cloud-point curve, 309 818 precipitation curve, 317 Debye’s function, 118 Debye’s length, 176 deformation tensor, 385 deformation vector, 385 degree of phase transformation/separation, 306 depolarization coefficient, 112 depolarization factor for vertically polarized incident light, 148 diagrammatic method of approximation, 362 diagrams P-irreducible diagram, 662 P-reducible diagram, 662 connected diagrams, 583 effective r-body interacting diagram, 583 irreducible diagram, 583 locally-interacting irreducible diagram, 583 dielectric constant, 107 dielectric state equation, 158 differential optical cross-section, 114 diffusion coefficient, 189 dimensional regularization, 240 direct correlation function, 167 direct problem, 133 DNA, 143 dressed propagator, 234 dynamic correlation range of the concentration fluctuations, 198 dynamic critical phenomena, 197 dynamic form factor, 159, 355 dynamic similarity hypothesis, 197 effective field, 67 efficiency factor, 114 elementary dipole, 107 end-bend distance moment, 268 energy spectrum, 155 enthalpy, entropy entropy flux, 49 entropy production, 49 entropy of polymer disorientation, 256 equations Gibbs fundamental equation, Gibbs-Durgham generalized equation, Gibbs-Helmholtz equations, mechanical state equations, renormalization group equation, 600 state equation, state equation of an ideal dilute solution, 24 thermal state equations, virial expansion equation, 32 equilibrium, cquilibrium conditions, 21 metastable equilibrium, osmotic equilibrium, 22 stable equilibrium, equivalent sphere, 136 excluded volume, 368 external field, 214 external momentum, 230 external wavevectors, 661 extinction coefficient, 113 field mean field, 74 molecular field, 74 self-consistent field, 74 filter technique, 157 fixed point, 210 FIory’s equation, 272 form factor, 118 Fourier transform, 124 fractal principle, 573 free volume of liquid, 470 friction coefficient, 191 fugacity, 17 full optical cross-section, 114 functionality of a branch point, 390 functionality of the crosslinks, 391 functions characteristic functions, connected two-chain distribution function, 636 819 correlation function, 96 end-to-end vector distribution function, 266 normalized functions of time correlation, 359 pair correlation function, 287 partition function, 92 state function, fundamental relaxation time, 464 Gaussian distribution, 47 gel, 385 gel syneresis, 397 generating functional, 216 Gibbs canonical distribution, 92 globule, 368 globule trimming, 380 grand canonical ensemble, 94 grand statistical sum, 94 Green’s connected function, 233 Green’s functions, 216 group expansion, 100 Hamiltonian, 92 heat capacity at constant pressure, 13 heterodyne method, 157 heterogeneous double critical point, 496 homodyne correlation function, 157 homodyne method, 157 Hooke’s law, 389 horizontally polarized light, 109 hydrodynamic factor, 191 hydrodynamic mode, 162 hydrodynamic region, 198 hypothesis of static similarity, 60 hysteresis, 56 ideal fractionation, 314 incipient phase, 483 incorrect problem, 134 index of refraction, 107 induced dipole, 107 induction period, 56 infinite cluster, 405 infrared divergence, 240 integral correlation parameter of molecular orientation, 152 integrals cluster integrals, 101 configurative integral, 93 irreducible cluster integral, 591 statistical integral, 93 interaction vertex, 226, 583 interdiffusion coefficient, 191 interference function, 117 internal stress, 386 interpenetrating polymer networks, 469 inverse space, 123 isometric line, 527 Ic-tolerant walking, 593 Kuhn’s chain, 666 Lagrangian, 211, 214 Lagrangian density, 214 Lagrangian form, 211 laws fundamental scaling law, 577 law of corresponding states, 32 lines tie lines, 27 liposomes, 143 liquidus curve, 43 local equilibrium, 158 long-range correlation distance, 174 long-range interaction, 368 longitudinal functions, 519 longitudinal modulus, 393 longitudinal wave, 409 loop approximation, 240 luminous space, 110 mean range of molecular interactions between two molecules, 185 mean scale, 104 mean specific Gibbs potential of mixing, 445 mean-square end-bend distance, 270 memory factor, 395 metastable critical point, 487 microcapsuling, 140 microscopic relaxation time, 464 microsyneresis, 400 mitochondria, 143 mixtures ideal mixture, 15 real mixture, 17 regular mixture, 32 mobility, 191 models continuouti equivalent random-walk chain model, 281 Freed’s model, 265 model of potential barrier, 275 pearl necklace model, 271 mole fraction, momentum conservation, 230 near order, 70 necessary and sufficient stability condition, 15 negative deviation from ideality, 183 network polymer, 385 node percolation, 407 nodes, 27 non-interacting (free) field, 216 oneloop approximation, 240 oneparticle irreducibility, 231 one-particle reducibility, 231 optical anisotropy, 148 optical constant, 186 optical cross-section, 114 optical density, 113 optical problem, 317 Optimization diagram, 329 optimization of STT, 329 ordered Green functions, 516 osmotic pressure, 23 reduced osmotic pressure, 24 packing factor, 472 pair correlation function, 167 parameters enthalpy parameter , 259 entropy parameter, 259 excluded volume parameter, 272 extensive parameters, Flory-Huggins’ parameter, 257 Hildebrand’s solubility parameters, 264 intensive parameters, interaction parameter, 257 long-range order parameter, 69 order parameter, 52 similarity parameters, 62 particle polarizability, 107 partition function, 94 percolation problem, 405 percolation threshold, 405 phase boundary, 308 phase separation, 50 phase shift, 115 phase space, 93 phase transition, 50 continuous transition, 50 first-order phase transition, 50 high-order phase transitions, 52 photon correlation spectroscopy, 157 photon correlator, 157 plane of scattering, 108 plasticizer sweating, 397 point correlator, 219 points configurative point, 25 critical point, 27 tricritical point, 81 polar diagram of the scattered light intensity, 110 polarization vector, 115 polymers butyl rubber, 460 cellulose 2,8-acetate1 478 cellulose 3,0-acetate1 478 cellulose triacetate, 440 epoxy resin, 366 EPS rubber, 460 latices, 328 PaMS, 320, 322, 329-333, 336, 624 PaMS, 321, 329, 330, 336, 341, 478, 623 PAA, 373, 374, 379 821 PAA (network), 402, 413 PAA branched, 373 PDMS, 363, 399, 568 PDMS (network), 399, 444, 446 PEO, 568 PIB, 363 PMAA, 418 PMMA, 653, 654 poly(D-/3-hydroxybutylate), 654 poly(dimethoxy ethylene), 439 poly(ethy1ene oxide), 440, 451, 768, 770-774 poly(viny1 alcohol), 758-768 poly-P-naphthylmethacrylate, 346 poly-P-vinylnaphthalene, 346 poly-rn-phenylene isophthalamide, 438, 439 polyacrylamide, 414-417, 540 polyamidhydrazide, 440 polyamidimide, 768 polyamidoacid, 768 polybutylmethacrylate, 346, 352 polychloroprene, 613, 655 poly(D-P-hydroxybutylate),653 poly( D, L-/3-methyl-P-propiolatone), 653, 654 polyethylene, 424-427, 460, 769 polyimide, 768 polyisobutylate, 460 polyisobutylene, 294, 478, 537 polymethylsiloxane, 346 poly(para-methylstyrene), 655 polypropylene, 458, 460 polystyrene, 279, 280, 291, 294, 295, 312, 342, 344, 346, 347, 349, 350, 352, 354, 363, 366, 372-375, 378, 379, 383, 398, 418, 424, 42G428, 432-435, 449, 451, 458, 460, 477, 478, 536-540, 543-549, 563, 564, 566, 570-572, 613, 624-626, 644, 650, 653, 654 polystyrene (network), 397 polyvinylpyrrolidone, 364 PVA (network), 398, 405 rubber (natural), 478 vinyl alcohol copolymer with ethylene, 451 vinyl alcohol copolymer with vinylacetate, 451 vinyl row polymers, 346 positive deviation from ideality, 183 potentials generalized thermodynamic potential, 94 Gibbs thermodynamic potential, Helmholtz thermodynamic potential, thermodynamic potentials, precipitating titration, 317 precipitation threshold, 311 principal phase, 483 principle of the least action, 214 proteins, 143 pseudospinodal, 433 pulse-induced critical scattering, 433 quantities excess quantities, 19, 34 mean molar quantities of mixing, mean molar quantity, quantities of mixing, reduced quantities, 31 quasibinary section, 309 quasimonomers, 376 radial distribution function, 164 radiation diagram, 110 random-walk chain, 267 range of molecular interaction, 176 Rayleigh’s ratio, 112 refractive index, 107 regularization methods, 362 regularization of the reverse problem, 134 regularization procedure, 240 relationships Maxwell’s relationships, relative deformation, 390 relative particle size, 114 relative refractive index, 114 relaxation time, 56, 155 renormalization group, 210, 579 822 renormalization method, 240 renormalization transformation, 579 renormalization transformation group, 579 reptation, 463 resolution degree of fractionation, 315 retention volume, 448 reverse problem, 133 rubbers, 143 scaling hypothesis, 60 scattering angle, 108 scattering coefficient, 114 scattering index, 113 scattering space, 110 scattering wavevector, 116 screening length, 289 second-order vertex function, 237 segment, 253 segment excluded volume, 273 self-beat method, 157 self-diffusion coefficient, 192 semi interpenetrating polymer networks, 469 shadow line, 311 shear, 387 shear modulus, 387 shear modulus of the network, 392 shift effect, 303 shift vector, 385 short-range effects, 269 short-range interactions, 268, 368 short-range repulsion potential, 273 solubility, 319 solutions concentrated solution, 288 dilute solution, 287 ideal polymer solution, 260 pseudoideal polymer solution, 260 semidilute solution, 287 strictly regular solution, 258 solvents acetone, 373, 374, 379, 402, 451, 477, 478, 653, 654 alcohol, 192 alcohols, 163 amyl acetate, 769 aniline, 546 benzene, 152, 153, 163, 352, 399,418, 444, 446, 460, 478, 537, 540, 563, 564, 653 benzyl alcohol, 346 bromobenzene, 152 bromoform, 279 butanol, 192 butyl chloride, 478 CC14, 188, 279, 280, 613 chlorobenzene, 152, 397 cyclohexane, 193, 291, 294, 295, 312, 320-322, 324, 329-333, 336, 344, 346, 347, 349, 350, 352, 354, 363, 372-374, 378, 379, 383, 397, 398, 424, 426-428, 432-435, 449, 451, 478, 536-538, 546, 570-572, 653, 654 decaline, 279, 346,478,655 decanol, 192 dextrane, 568 diethyl cebacate, 772 diethyl ether, 427, 477 diethylsuccinate, 655 diisobutylketone, 294 dimethylacetamide, W , 768 dimethylformamide, 768 dioctylphthalate, 373, 378, 383 dioxane, 32k322, 329-331 diphenyl ether, 424-426, 460 ethanol, 192 ethylbenzene, 342, 478 ethylenglycol acetate, 366 glycerol, 366 heptane, 352 isobutyric acid, 546 isopropanol, 346 mesitylene, 152 methanol, 192, 374, 379, 540, 546 methylacetate, 374, 375 methylcyclohexane, 424, 478, 543549 methylethylketone, 418, 563, 564, 823 624, 625 n-butylacetate, 363 nitromethane, 440, 769 @xylene, 153 octanol, 320, 321, 329-333, 336 pbutylacetate, 613 pdichlorobenzene, 152, 153 pxylene, 152 mpentane, 478 perfluoromethylcyclohexane, 188 phenylethyl alcohol, 346 polypropyleneglycol, 366 propanol, 153, 192 propylene oxide, 478 pyridine, 152 tetrahydrofuran, 653, 654 tetraline, 324, 346 theta solvent, 260 toluene, 153, 163, 192, 341, 346, 363, 460, 539, 563, 623425 trans-decaline, 366, 613 trifluoroethanol, 653, 654 water, 163, 192, 364, 373, 374, 379, 398, 402, 405, 413417, 439, 440, 451, 540, 546, 758-768, 770-774 xyleue, 769 source, 214 spatially inhomogeneous distribution, 200 spectral density, 155 spectral density of the autocorrelation function of density fluctuations, 159 spectral power, 157 spectroturbidimetric titration, 317 spectrum analyzer, 157 spinodal, 26 isoentropic spinodal, 29 isothermal spinodal, 29 spontaneous process, stability, absolute stability, 104 diffusional stability, 11 mechanical stability, 11 stability on the whole, 21 thermal stability, 11 state diagram, 25 states absolutely unstable state, 26 metastable state, 9, 27 statistical integrals with an imposed constraint, 658 statistical sum, 92 stress tensor, 386 structural factor, 130, 159, 395 subchain, 583 short subchain, 583 substances N, N’-methylenebisacrylamide, 402 acrylamide, 402, 417 ammonium persulphate, 402 aniline, 193 bis-acrylamide, 417 helium, 447 NaCl, 374 nitrogen, 447 phenol, 192 SFe, 178 tetramethylethylenediamine,402 water, 417 surface fraction, 473 surfactants, 143 swelling curve, 395 symmetrical moment, 687 symmetry factor, 221 synaptosomes , 143 systems PDMS (network)+benzene, 444 aniline+cyclohexane, 193 butyl rubber+EPS rubber+benzene, 460 cellulose 2,&acetateSacetone, 478 cellulose 3,0-acetate+acetone, 478 cellulose triacetate+nitromethane, 440 closed system, 20 dextrane+ water, 756 3He 4He, 245 isolated system, P a M S cyclohexane+oct anol , 320, + + 824 329-333, 336 PaMS+dioxane+octanol, 320, 329331 PaMS+toluene, 624 PaMS+butyl chloride, 478 PaMS+cyclohexane, 478 PaMS+cyclohexane+octanol, 321, 329, 330,336 PaMS+dioxane+octanol, 321, 330 PaMS+methylcyclohexane, 478 PaMS+propylene oxide, 478 PaMS+toluene, 341, 623 PA A (network)+water+acet one, 402 PAA+water+acetone, 373, 379 PAA+water+methanol, 374, 379 paraffin+f&hydroxyquinoline,334 PDMS (network)+benzene, 399, 446 PDMS+benzene, 399 PDMS+toluene, 363 perfluoromethylcyclohexane+CC14, 188 phenol+water, 192 PIB+cyclohexane, 363 PMAA+methylethylketone, 418 PMMA+acetone, 653, 654 POlY(D-Phydroxybutylate)+trifluoroethanol, 654 poly( dimethoxy ethylene)+water, 439 poly(ethy1ene oxide)+diethyl cebacate, 772 poly(ethy1ene oxide)+water, 440, 451, 768, 77&774 poly(viny1 alcohol)+water, 758-768 pOly(pcSTYZmet hylstyrene)+diethylsuccinate, 655 Poly-Pnaphthylmethacrylate+ benzyl alcohol, 346 Poly-Pnapht hylmethacrylate+phenylethyl alcohol, 346 Poly-P- napht hylmet hacrylate+ tetraline, 346 Poly-Pnaphthylmethacrylate+toluene, 346 poly-,B-vinylnaphthalene+benzylalcohol, 346 Poly-Pvinylnapht halene+phenylethyl alcohol, 346 Poly-Pvinylnaphthalene+toluene+decaline, 346 poly-m-p henylene isopht halamide+dimethylacetamide, 438, 439 polyacrylamide+water, 414-4 17 polyacrylamide+water+methanol, 540 polyamidhydrazide+dimethylacetamide, 440 polyamidimide+dimethylformamide, 768 polyamidoacid+dimethylacetamide, 768 polyamidoacid+dimet hylformamide, 768 polybutylmethacrylate+benzene+heptane, 352 polybutylmethacrylate+isopropanol, 346 , poly chloroprene+ C Cl, 613 polychloroprene+decdine, 655 poly(D-P-hydroxybutylate)$ trifluomethanol, 653 poly (D,GP-methyl-Ppropiolactone)+tetrahydrofuran, 653, 654 polyethylene+amyl acetate, 769 polyethylene+diethyl ether, 427 polyethyleneSdipheny1 ether, 424426 polyethylene+nitromethane, 769 polyethyleneSxylene, 769 825 polyimide+dimethylacetamide, 768 polyimide+dimethylformamide, 768 polyisobutylene+benzene, 478, 537 polyisobutylene+cyclohexane, 478 polyisobutylene+diisobutylketone, 294 polyisobutylene+n-pentane, 478 polymethylsiloxane+tetraline, 346 PolYProPYIeneSpolyet hyleneSdipheny1 ether, 460 polystyrene (network)+chlorobenzene, 397 polystyrene (network)+cyclohexane, 397 polystyrene+CC14, 279, 280 polystyrene+n-butylacetate, 363 polystyrene+acetone, 451, 477, 478 polystyrene+benzene, 418, 478, 540, 563, 564, 653 polystyrene+ bromoform, 279 polystyrene+cyclohexane, 291, 294, 295, 312, 344, 346, 347, 349, 350, 352, 354, 363, 372-374, 378, 379, 383, 398, 424, 426-428, 432-435, 449, 451, 478, 536-538, 570-572, 653, 654 polystyrene+decaline, 279, 478 polystyrene+diethyl ether, 477 polystyrene+dioctylphthalate, 373, 378, 383 polystyrene+ethylbenzene, 342, 478 polystyrene+methylacetate, 374, 375 polystyrene+methylacetate+antioxidant , 374, 375 polystyrene+methylcyclohexane, 424, 543-549 polystyrene+methylethylketone, 563, 564, 624, 625 polystyrene+polyisobutylate+ toluene, 460 polystyrene+polypropylene+ toluene, 460 polystyreneStoluene, 539, 563, 624, 625 polystyrenetpbutylacetate, 67 polystyrene+ trans-decaline, 366, 613 polystyrene+ trunsdecaline, 366 polyvinylpyrrolidone+water, 364 PVA (network)+water, 398, 405 rubber (natmal)+ benzene, 478 toluene+an alcohol, 192 tricosane+&hydroxyquinoline, 334 vinyl alcohol copolymer with ethylene +water, 451 vinyl alcohol copolymer with vinylacetate+water, 451 temperature cloud temperature, 3I3 Curie temperature, 69 Flory’s temperature, 259 lower critical solution temperature (LCST), 38 temperature, 259 upper critical solution temperature (UCST), 38 temperature tit ration, 317 tension modulus, 389 ternary distribution function, 166 theories Flory-Huggins’ theory, 253 tweparameter theory, 277 theory of corresponding states, 469 theory of liquid state, 469 thermal diffusion ratio, 195 thermal pressure coefficient, 473 thermodynamic coordinates, thermodynamic factor, 191 thermodynamic forces, thermodynamic limit, 95 thermodynamic problem, 317 thermodynamic quality, 258 thermodynamic retardation, 466 three-phase point, 486 tie lines, 308 total propagator, 234 total square end-to-cnd distance, 688 translational wave, 409 transversal functions, 519 826 transversal waves, 409 triple point, 429, 486 truncated diagram, 236 turbidimetric titration, 317 turbidity, 112, 113 twepoint vertex function, 238 ultraviolet divergence, 240 unary function, 166 uniform compression, 387 unstable critical point, 429 vacuum graph, 221 vertex function, 237 virial expansion, 102 viruses, 143 volume factor, 395 wave number, 109 wavelength exponent, 127 Wiener’s integral, 283 Wiener’s measure, 281 Young modulus, 389 zero loop approximation, 240 ... THERMODYNAMICS OF SYSTEMS CONTAINING FLEXIBLE- CHAIN POLYMERS Scientific edition by Professor Sergei Ya Frenkel Translated by Sergei L Shmakov and Dmitri N ''Ifichinin THERMODYNAMICS OF SYSTEMS. .. SYSTEMS CONTAINING FLEXIBLE- CHAIN POLYMERS Vitaly J Klenin Chair of Polymers, Chemistry Department, Saratov State University, Saratov 410071, Russia 1999 ELSEVIER Amsterdam - Lausanne - New York -. .. technologies require the application of just rigid -chain polymers This postulate may be reinforced as follows: rigid -chain or super-oriented flexible- chain polymers lose to a considerable extent