Computational Materials Science of Polymers

COMPUTATIONAL MATERIALS SCIENCE OF POLYMERS

COMPUTATIONAL MATERIALS SCIENCE OF POLYMERS A NDREY A LEKSANDROVICH ASKADSKII

CAMBRIDGE INTERNATIONAL SCIENCE PUBLISHING

Published by Cambridge International Science Publishing 7 Meadow Walk, Great Abington, Cambridge CB1 6AZ, UK http://www.cisp-publishing.com First published January 2003 © A A Askadskii © Cambridge International Science Publishing

Conditions of sale All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library

ISBN 1 898326 6 22

Production Irina Stupak Printed by Antony Rowe Ltd, Chippenham, Wiltshire, Great Britain

About the Author Andrey Aleksandrovich Askadskii is a Professor of Chemistry at the Institute of Organo-Element Compounds of the Russian Academy of Sciences. He holds M.S. in Civil Engineering from the Moscow Civil Engineering Institute (1959), M.S. in Chemistry from the Mendeleev Institute of Chemical Technology (1962) and Ph.D. in Physics of Polymers (1968). The main scientific interests of the author are: the development of a physical approach to the quantitative evaluation of the physical properties of linear and network polymers on the basis of their chemical structure; development of computer programs for calculating the properties of polymers and low-molecular liquids and also computer synthesis of polymers with the required properties; experimental examination of the structure of properties of heat-resistant aromatic polymers of different grades; development of new methods of experimental and theoretical analysis of the relaxation properties of polymer materials; production of new types of polymers; production and examination of electrically conducting polymer materials on the basis of heat-resistant polymers and organo-element compounds; development of gradient polymer materials with a variable modulus of elasticity within the limits of the same material and retaining elastic (not viscoelastic) properties at any point of the gradient material. Prof Askadskii is the author of more than 400 scientific studies and 20 books, six of which have been published abroad.

Contents

Preface Introduction Chapter I. Brief information on types of polymes and their chemical structure Chapter II. Packing of macromolecules and polymers density II.1. Increments method and basic physical assumption Chapter III. Temperature coefficient of volumetric expansion Chapter IV. Glass transition temperature of polymers IV.I. Thermomechanical and other methods of evaluation of the glass transition temperature of polymers IV.2. Mechanism of glass transition IV.3. Calculation of the glass transition temperature of linear polymers IV.4. Influence of plasticization on the glass transition temperature of polymers IV.5. Calculation of the glass transition Chapter V. Temperature of transition into the viscous flow state for amorphous polymers V.1. Estimation of temperature of transition into the viscous flow state of polymers V.2. Dependence of Newtonian viscosity on molecular mass of polymer in a wide range of its change Chapter VI. Melting point of polymers Chapter VII. Temperature of onset of intense thermal degradation of polymers Chapter VIII. Optical and opto-mechanical properties of polymers VIII.1. Refractive index VIII. 2. Stress-optical coefficient Chapter IX. Dielectric constant of polymers and organic solvents Chapter X. Equilibrium rubber modulus for polymer networks X.1. Calculation of the equilibrium modulus X.2. Heteromodular and gradient-modulus polymers Chapter XI. Description of relaxation processes in polymers XI.1. Stress relaxation XI. 2. Sorption and swelling processes Chapter XII. Solubility of polymers XII.1. Specific cohesive energy of organic liquids and polymers. Hildebrand solubility parameter XII.2. Solubility criterion XII.3. Influence of molecular mass and degree of macromolecule orientation on solubility Chapter XIII. Surface properties of organic liquids and polymers XIII.1. Surface tension of organic liquids XIII.2. Surface tension of polymers Chapter XIV. Miscibility of polymers Chapter XV. Influence of the end groups on the properties of polymers Chapter XVI. Thermophysical properties of polymers XVI.1. Heat capacity XVI.2. Thermal diffusivity and heat conductivity

3 9 16 16 58 67 67 88 108 322 343 385 385 388 398 408 418 418 426 445 456 456 466 475 475 497 504 504 509 520 527 528 536 547 555 562 562 564

Chapter XVII. Molecular design and computer synthesis of polymers with predermined properties Appendix 1. Examples of solution of direct problems of polymers synthesis Appendix 2. Examples of solving the reverse problem of polymer synthesis Appendix 3. The example of solving the complex problem – analysis of the chemical structure of phenol formaldehyde resin Appendix 4. Application of the approach to multicomponent copolymers Appendix 5. Influence of strong intermolecular interaction occurring between two dissimilar polymers on their miscibility Appendix 6. On formation of super-molecular structure in amorphous polymers 1. Scheme of formation of the super-molecular structure 2. Calculation method of evaluation of dimensions of elements of supermolecular structure of polymers 3. Phase state of polymers as a result of formation of the super-molecular structure by one-cavity bond hyperboloids References Index

567 589 602 607 621 625 645 645

653 669 689

PREFACE Published in the journal “Chemistry and Life”, No. 2, 1981 was the article by me, titled by the editor as “Atom plus atom plus thousand atoms”. This article discussed the possibility of calculating some physical properties of polymers on the basis of the chemical structure of the repeat unit (it was then possible to calculate properties of linear polymers only). In conclusion of the article, titled “A little fantasy”, it was written: “Therefore, many properties of polymer can be predicted, if nothing except the structural formula of the appropriate monomer is known. It is a great progress: nowadays already, such calculations allow chemists to be drawn away from heavy duty to synthesize hopeless monomers. Formerly, under empirical selection of materials, many of such monomers had to be synthesized. Nevertheless, calculations are to be made manually still. Moreover, when they are translated into the machinery language, chalk and blackboard traditional for any chemical dispute can be substituted by an electronic “pencil”. A chemist will draw a formula of the suggested monomer on the screen by it, and the computer will answer immediately if it is useful or not to synthesize it. Another opposite task seems to be much more absorbing. If the computer is able to calculate properties by structural formulae, apparently, it may be taught, vice versa, to calculate the formula of a suitable monomer (or several formulae to choose) by any, even contradictory set of properties, given to it. In this case, it will be able to substitute the chemist in his most problematic part of work, one is able to succeed in on the basis of experience, intuition and luck.” That was a fantasy, and it could be hardly imagined that these ideas would be realized at any time in neat future. However, events were developing very fast, especially after appearance of high-power personal computers. Before discussing stages of this great work, methods of the quantitative estimation of polymer physical properties must be presented in brief performed on the basis of their chemical structure. At the present time, there are three main approaches to this estimation. One of them, developed by Van Krevelen [214], is based on the idea of so-called ‘group contributions’, according to which the simplest empirical expressions of the additive type are written down, the present group, existing in different polymeric units, making one and the same contribution to the calculated characteristic (for example, glass transition temperature, melting, etc.). As the author states, this is just an empirical approach, which allows the physical properties of many of linear polymers to be calculated with high accuracy. Another approach, being developed for a long time by the author of this preface in company with Yu.I. Matveev [28, 128] is semi-empirical. According to it, equations for calculation of the physical properties are deduced on the basis of ideas of physics of solids, and calibration of the method is performed with the help of physical characteristics of polymeric standards, the properties of which are studied well. Consequently, parameters of equations possess a definite physical sense (energy of dispersion interaction, energy of strong intermolecular interaction, including hydrogen bonds, Van-der-Walls volume, etc.). Application of this approach makes possible estimation with enough accuracy of many physical characteristics of polymers (about 60 up to now). Therefore, the number of polymers of various structures is unlimited. The third approach developed by J. Bicerano [133] has appeared recently. It is based on the so-called coherence indexes, reduced in practice to a search for various

2

correlations of physical properties with many rules of obtaining coefficients of correlation dependencies. Discussed in the present monograph are principles of the approach, developed by A.A. Askadskii and Yu.I. Matveev, special attention being paid particularly to computer realization of the current calculation method for physical properties of polymers. The first computer software has been composed by E.G. Galpern, I.V. Stankevich and A.L. Chistyakov - investigators of quantum chemistry laboratory of A.N. Nesmeyanov Institute of Organo-Element Compounds, RAS. Initially, computer “synthesis” of polymers by this software was performed from so-called large procurements representing residues of monomers, involved into the synthesis reaction. In the second variant, computer synthesis was performed from smallest procurements, from which the repeat unit of the polymer was constructed. This broadens significantly capabilities of the software for solving both direct (calculation of the polymer properties from its chemical structure) and reverse task (computer ‘synthesis’ of polymers with preliminarily programmed /assigned/ properties, the ranges of which were set in the computer), because the amount of ‘synthesized’ olymers has increased sharply. Then principally new software was composed by A.F. Klinskikh, in which chemical structure of the repeat unit was ‘constructed’from atoms. Thus, the user needs just to depict chemical structure of the polymer on the computer screen as chemist does it on the paper, and computer lays out all physical properties of polymers, involved in the software (all about 60). This software also provides for calculation of a sequence of properties of low-molecular weight organic compounds, as well as, which is very important, properties of polymeric networks. Solution of the reverse task is also provided. Of special importance is the possibility to calculate properties of copolymers and their mixtures, to predict solubility and compatibility of polymers, to construct dependencies of properties on temperature, molecular mass, crystallinity degree, microtacticity (of special importance are dependences of glass transition temperature and temperature of transition into the viscous flow state on molecular mass). It stands to reason that not all the problems are solved. Accuracy of the calculation and various predictions of polymers behavior at dissolution and mixing with each other must be increased, calculation schemes to estimate new properties of polymers must be developed, and their computer realization must be performed, etc. It is obvious that the present monograph possesses some drawbacks. The authors will be thankful for any notes on the point of the book.

3

INTRODUCTION As mentioned above, the approach to estimation of the physical properties of polymers, discussed in the monograph, is semi-empirical. When estimating the thermal characteristics of polymers, such as glass transition temperature, melting point, it is supposed that the repeat unit is composed of a set of anharmonic oscillators representing atomic pairs, linked by intermolecular physical bonds. The critical temperature of this set of anharmonic oscillators is that determines the abovementioned two transition temperatures. The thermal expansion coefficient is also closely related to these characteristics. In the case of a characteristic as the temperature of the onset of intensive thermal degradation, the polymeric unit is considered as a set of anharmonic oscillators representing atomic pairs, linked by chemical bonds. The critical temperature of such a set of oscillators characterizes the temperature of the onset of intensive thermal degradation at the given rate of heating (clearly at a different rate of heating, the temperature of the onset of intensive thermal degradation will be different, i.e. kinetic effects play a significant role in this case). At first glance, it may seem strange that thermal degradation is considered here not as a kinetic, which is conventional, but as an original phase transition, at which, however, the initial substance cannot be obtained from the products of thermal decomposition by simple cooling down. Equations for calculating other physical characteristics are based on physical approaches, discussed in detail below, and we will not consider them in this part. Common for all these equations is summarizing the sequence of atomic constants, which characterize contributions to the energy of intermolecular interaction, chemical bonds energy, Van-der-Waals volume, etc. Strictly speaking, the present approach cannot be named additive in the common sense of the word, because the calculated properties are not additive in relation to atoms and groups, which compose the repeat unit of polymer. Here additivity is applied to the characteristics which are really additive (Vander-Waals volume, molecular mass, intermolecular interaction energy, etc.). The approach being described allows calculation of their properties of the unlimited number of polymers and conduction of the computer synthesis of polymers with assigned properties with the help of software created and described in the monograph that is not possible using other existing programs. As mentioned above, the approach discussed in the monograph is semiempirical, calibration of the method being based on the so-called polymeric standards, the properties of which are studied in detail and common. Let us consider the essence of calibration on an example of the equation calculating glass transition temperature of a linear polymer, Tg:

Tg =

∑ ∆Vi i

∑ ai ∆Vi + ∑ b j i

j

,

4

where ai are atomic constants; bj are constants bound to the energy of strong intermolecular interaction (dipole-dipole, hydrogen bonds), occurred between polymeric chains at the sacrifice of polar groups existing in them; ∑ ∆Vi is the Vani

der-Waals volume of the polymer repeat unit, summarized from Van-der-Waals volumes of atoms participating in the composition of the unit. Reduce the equation to the following view: 1

∑ ai ∆Vi + ∑ b j = T ∑ ∆Vi . i

g i

j

Basing on this equation, the excessive system of linear equations is composed as follows:   1   a1∆V1,1 + a2 ∆V1,2 + ... + an ∆V1, n + α1b1 + β1b2 + ... + γ1bk = ∆Vi  ; ∑   Tg ,1  i  1   1   ∆Vi  ; a1∆V2,1 + a2 ∆V2,2 + ... + an ∆V2, n + α 2b1 + β 2b2 + ... + γ 2bk = ∑   Tg ,1  i 2   .......... .................... .................... .................... .................... .................... ...........   1  ∆Vi  . a1∆Vm,1 + a2 ∆Vm,2 + ... + an ∆Vm, n + α m b1 + β m b2 + ... + γ m bk = ∑  Tg ,1  i  m Then the matrix of coefficients at the unknowns of this excessive system of equations:  ∆'  ∆'  =    ∆'P



 



∆' ∆'

 

 



∆'P



∆' Q ∆' Q













α α







∆'P Q α P





β β





 





βP



γ  γ     γ P  



and the column matrix of free terms of these equations       ∑ ∆'L       %J  L       ∑ ∆'L     =  %J  L            ∑ ∆'L     %J P  L  P  









are composed. Further on, a transposed matrix à is composed and multiplied by the initial one – ÃA, as well as by the column matrix – ÃB. All this results in obtaining a

5

canonic system of equations. This canonic system is solved, for example, by the Gauss method. The whole procedure of calibration is performed by standard software. Without considering features of such regressive analysis, let us note only that polymers, selected for calibrating the method, must possess experimental values of analyzed physical characteristics in broadest range, and the chemical structure of polymeric standards must be sufficiently different. Usually, an excessive system composed of 30–0 equations is to be solved, which corresponds to 30–40 polymers. Next, the properties of other polymers are calculated from the coefficients obtained. In this case, the energy of weak dispersion interaction, strong dipole–dipole interactions and hydrogen bonds, their relative part and many other physical parameters of the system are determined. We are coming now to a brief description of the contents of individual chapters of the monographs. The first chapter discusses the data of modern classification of polymers and their chemical structure. Of the outstanding importance, induced by the features of the chemical structure and the application field, are interpolymers, dendric and staircase (ladder) polymers. The second chapter discusses the approach to computerized materials technology of polymers on the atomic–olecular level, based on the method of increments. The increments of various atoms and main groups of them are calculated. The main physical ideas about structure of macromolecules of polymers and parameters determining it are displayed. The method for calculating such an important characteristic of the polymer structure, as the coefficient of molecular packing, is given. A connection between the free volume of the polymer, the coefficient of molecular packing and parameters of its porous structures is established. For experimental determination of characteristics of the microporous structure of polymers, the method of positron annihilation, the application of which indicated structural changes in polymers in their relaxation, is used. With consideration of weak dispersion and strong (dipole–dipole and hydrogen bonds), the third chapter gives formulae for calculating the thermal coefficient of the volume expansion in dependence on the chemical structure of the polymer. In this case, the type of atoms in the polymeric chain and type of the intermolecular interaction are estimated by a limited number of corresponding increments, numerical values of which are determined. The fourth chapter describes in detail the thermomechanical method of determination of the glass transition temperature and fluidity of polymers, features of interpreting thermomechanical curves for amorphous and crystalline polymers are analyzed, the calculation method of determination of the mechanical segment from the chemical structure of the polymer is displayed. Two main concepts of the mechanism of vitrification processes of polymers, relaxation and intermolecular, are discussed. The ‘atomistic approach’ which is more universal than the widespread socalled ‘group contributions method’ to calculation of polymer properties from their chemical structure, is considered. This approach was used for deriving an analytical expression to calculate the glass transition temperature of linear and network polymers from their chemical structure. The influence of types of linear polymers branching and the number of units between cross-link points, type and structure of these points, existence and type of the network defects for network polymers on the glass transition temperature of the polymers is analyzed. Given in the fifth chapter is the method for calculating the fluidity temperature of amorphous polymers and the temperature range of the rubbery state of polymers

6

from their chemical structure, and conditions of appearance of the rubbery state in a polymer depending on its molecular mass, as well, which is important for processing of polymers. The sixth chapter describes two approaches to calculating the melting point of polymers from the chemical structure of the repeat unit. The first approach is based on the experimental fact of closeness in parts of the empty volume in melting of a crystalline polymer and in transition of an amorphous polymer of the same structure from the glassy-like into the high-elastic state. The second approach is based on the consideration of the repeat unit of a polymer as a selection of anharmonic oscillators. Discussed in the seventh chapter is the most important characteristic of thermal resistance of polymers — initial temperature of their intensive thermal degradation. The formula to calculate this temperature based on the chemical structure of the polymer was deduced, and necessity to take into account the resulting products of thermal degradation which starts with the decay of end groups in polymer macromolecules, are indicated. In the eighth chapter, Lorenz–Lorentz equations are used for deriving equations for calculation of the refractive index of polymers and copolymers from their chemical structure. To obtain the stress-optical coefficient, empirical and semiempirical approaches are established, in which the contribution of each atom and the type of intermolecular interaction are estimated by an appropriate increment. Using the dependencies obtained for the stress-optical coefficient on the chemical structure of the repeat unit of the polymer, the contribution of various atoms and polar groups to the value of this coefficient is estimated, and a polymer with the properties unique for the method of dynamic photo-elasticity is proposed. The ninth chapter displays a scheme for calculating the dielectric constant of polymers and organic liquids with respect to their chemical structure which is important for both synthesis of polymers with the required dielectric constant and prognosis of polymer solubility in organic liquids. Taking into account not only the contribution of various polar groups to the dielectric constant of polymers and liquids, but also different contributions of a polar group in the present class of liquids resulted in the previously unobtainable agreement in the experimental and calculated values of the dielectric constant for a broad spectrum of organic polymers and liquids. Based on the notion of network polymers as an elastic and rotational–isomeric subsystem and taking into account its structure as linear fragments and cross-linked points, the tenth chapter indicates the deduction of formulae for calculating the equilibrium rubbery modulus and molecular mass of a linear fragment between neighboring cross-linked points. Further analysis of the resultant dependencies allowed the formulation of conditions for obtaining a polymer with unique (unusual) properties – different modulus and gradient polymers characterized by large changes of the equilibrium rubbery modulus within the same article. Existence of these unique properties is confirmed experimentally for synthesized network of polyisocyanurates. The eleventh chapter describes the derivation of analytical expressions for relaxation memory functions, necessary for determining the stress relaxation and creep of the polymers. In this case, the production of entropy of a relaxing system is represented by transition of relaxants (kinetic units of a polymer of different nature) into non-relaxants by means of their interaction or diffusion, the mechanism of interaction of relaxants in stress relaxation being found predominant. The apparatus created for description of relaxation events in polymers is applied in description of sorption and swelling processes. Thus, contrary to stress relaxation, the mechanism of relaxants diffusion is predominant in sorption.

7

The twelfth chapter is devoted to the problem of increasing the accuracy of prediction of polymer solubility in organic liquids. It is shown that the predictive ability of the solubility criterion, calculated with respect to the chemical structure of the polymer and the solvent, sharply increases with consideration for the type of supermolecular structure of the polymer and the degree of its polymerization. Based on the chemical structure of the matter, the thirteenth chapter gives a calculation method for the most important property of organic liquids and polymers, i.e. surface tension. Contrary to the additive scheme for summation of parachors which characterizes the contribution of separate atoms to the surface tension, the approach developed allows estimation of the contribution of polar groups and specific intermolecular interaction to the surface tension value and connection of it with the solubility parameter and density of cohesion energy in substances. Invoking the idea of solubility of a single homopolymer in another one, the fourteenth chapter suggests a criterion for estimating the compatibility of polymers basing on the data of the chemical structure of separate components. The analysis of application of the criterion for compatible, partially compatible or incompatible polymers indicates its high predictive ability. On the example of the calculation of the Van-der-Waals volume, molar refraction, heat capacity and other properties of a number of polymers, chapter fifteen displays the role of the chemical structure of macromolecule end groups and importance of their calculation in the study of regularities of changes in the polymer properties on their molecular mass. The sixteenth chapter indicates a method for calculating the molar heat capacity with respect to the chemical structure of polymers. The method is based on a supposition that the contribution of each atom to heat capacity is proportional to its Van-der-Waals volume. It is noted that the heat capacity, thermal diffusivity and heat conductivity of polymers depend not only on their chemical structure, but also on the physical and phase states of the polymeric body. The seventeenth chapter describes methodological ways of solving the direct problem of computerized determination of the physical characteristics of polymers and low-molecular liquids with respect to their chemical structure and the reverse one — computer synthesis of polymers with the given set of properties. These problems are solved by the methods of fragments and separate atoms. The corresponding software which allows calculation of more than 50 chemical properties of linear and network polymers and copolymers, and a number of the most important properties of low molecular weight liquids, as well, is developed. Discussed is the method of depicting diagrams of polymer properties compatibility, application of which may significantly simplify solution of the direct and, especially, reverse problems of computational materials sciences. Appendices demonstrate abilities of the approach, described in the monograph, to determine the properties of some natural polymers (the example of solving the direct problem of polymers synthesis) with respect to their chemical structure (Appendix 1); to search for chemical structures of polyetherketones (the example of solving the reverse problem of polymer synthesis), the properties of which must lie in a given range (Appendix 2); to solve a mixed problem of polymers synthesis on the example of analyzing the chemical structure of phenoloformaldehyde resin, when the direct problem — estimation of the properties of the ideal structures of such resin with respect to their chemical formulae — and the reverse one — searching for a combination of structures with which the chemical formula of phenoloformaldehyde resin obtained provides experimentally observed values of its

8

properties — are solved consecutively (Appendix 3); to analyze the structure and properties of copolymers, composed of from three to five comonomers (Appendix 4); and the influence of a strong intermolecular interaction appearing between two heterogeneous polymers on their compatibility is analyzed (Appendices 5 and 6).

Chapter I. Brief information on types of polymers and their chemical structure The very large number of existing polymers may be subdivided into three main classes forming the basis of the presently accepted classification. The first class contains a large group of carbochain polymers whose macromolecules have a skeleton composed of carbon atoms. Typical representatively of the polymers of this class are polyethylene, polypropylene, polyisobutylene, poly(methyl methacrylate), poly(vinyl alcohol) and many other. A fragment of a macromolecule of the first of them is of the following structure [–CH2–CH2–]n The second class is represented by a similar large group of heterochain polymers, the main chain of macromolecules of which contains heteroatoms, in addition to carbon atoms (for example, oxygen, nitrogen, sulfur, etc.). Numerous polyethers and polyesters, polyamides, polyurethanes, natural proteins, etc., as well as a large group of elemento-organic polymers relate to this class of polymers. The chemical structure of some representatives of this class of polymers is the following: [–CH2–CH2–O–]n Poly(ethylene oxide) (polyether); (CH2)2

O C O

NH

(C H 2 ) 6

Poly(ethylene terephthalate) (polyester);

C O O

NH

C

(C H 2 ) 4

O

n C O

CH3 Si O CH3

n

Polyamide; n

Polydimethylsiloxane (elemento-organic polymer);

Cl N

Polyphosphonitrile chloride (inorganic polymer).

P

Cl n The third class of polymers is composed of high-molecular compounds with a conjugated system of bonds. It includes various polyacetylenes, polyphenylenes, polyoxadiazoles and many other compounds. The examples of these polymers are: [–CH=CH–]n Polyacetylene

Polyphenylene n

N N C

Polyoxadiazole

C O

n

10

An interesting group of chelate polymers possessing various elements in their composition, able to form coordination bonds (usually, they are depicted by arrows), also relates to this class. The elementary unit of these polymers is often complex, for example: O H3C O

P

CH3 O

Zn O P

H3C

O CH3

O

The most widely used type of material in the large group of polymeric materials are still the materials based on the representatives of the first class of polymers which are carbochain high-molecular compounds. The most valuable materials could be produced from carbochain polymers, for example, synthetic rubbers, plastics, fibers, films, etc. Historically, these polymers have been implemented in practice first (production of phenoloformaldehyde resins, synthetic rubber, organic glass, etc.). Many of carbochain polymers became subsequently the classic objects for investigation and creation of a theory of the mechanical behaviour of polymeric substances (for example, polyisobutylene, poly(methyl methacrylate), poly-propylene, phenoloformaldehyde resin, etc.). Subsequently, materials based on heterochain polymers – polyamide and polyester fibers, films, varnishes, coatings and other materials and articles – became widespread. This has given impetus to investigating the properties and formation of notions, in particular, of anisotropic substances possessing extremely different properties in different directions. A special place in the sequence of these polymers is devoted to high-molecular elemento-organic compounds. Finally, the representatives of the third class – polymers with conjugated system of bonds – were used for the preparation of conducting materials. Considering in general terms the chemical structure of polymers of different classes, we have discussed the structural formula of the repeating unit in the macromolecule. However, the existence of many such units in the macromolecule immediately complicates the situation. Let us begin, for example, with an assumption that each unit in the elementary act of macromolecule growth may be differently attached to the neighbouring one; in this case, we are talking about the ‘head-to-head’, ‘tail-to-tail’ or ‘head-to-tail’ addition. Various variants of the unit addition to the propagating macromolecule are possible for asymmetric monomers of the C H2 C H

R type which possess R substituents on one of carbon atoms. Here, variants of ‘head-tohead’ ... CH2 CH CH CH2 CH2 CH CH CH2 ... R

R

R

R

and “head-to-tail” ...

CH2

CH CH2

CH CH2

CH

R

R

R

...

11

additions are possible. Alternation of the types of addition is possible, i.e. units may be differently attached to each other in a single macromolecule. Existence of a great number of units in the polymeric chain and possibility of only several variants of their attachment gives a huge number of isomers in relation to the whole macromolecule. To put it differently, a polymer may contain (and indeed contains) not only the macromolecules of the same chemical structure, but mixtures of a large number of macromolecules, which, of course, makes the polymer to differ from low-molecular substances, composed of identical molecules only. We will not talk about a rapid increase of the number of possible isomers in the sequence of substituted saturated hydrocarbons with the number of carbon atoms (i.e. with propagation of the molecule); even at a small (compared with polymers) number of them this number reaches a tremendous value. It is easy to imagine that when the number of units becomes tens or hundreds of thousands, the number of possible isomers becomes astronomically high [80]. Let us return to monosubstituted unsaturated hydrocarbons. When a polymeric chain is formed during polymerization, the substituents R may dispose differently in relation to the plane of single bonds. In one of possible cases, these substituents are disposed irregularly in relation to the plane of single bonds; such polymers are called irregular or atactic: H C H

H C R

H H H R H R H H H H R C C C C C C C C C C C C C C H H H H H H H R R R R R R R

H

H

H

In other cases, synthesis may be performed in such a manner that substituents would be disposed either by the same side of the plane of the main bonds H H H H H H H H H H H H H H H H C C C C C C C C C C C C C C C C H H H H H H H H R R R R R R R R or by both sides, but with regular alternation of the substituents direction: R R H H H H H R H H R H H H H H C C C C C C C C C C C C C C C C H R R H H R H R H H H H H H H H The polymers composed of the units with regular alternation of substituents were called stereoregular. If the substituents are disposed on one side of the plane of the main bonds, stereoregular polymers are called isotactic. If they are disposed on both sides of the plane, the polymers are called syndiotactic. The situation is more complicated with polymers synthesized from disubstituted monomers. Already in the monomer, substituents may dispose on the same (cis-isomer) or on both sides (trans-isomer) of the plane of the double bonds: H H H R' C C

C C

R

R H

R'

12

Synthesis of macromolecules from cis-isomers leads to the formation of erythro-diisotactic polymers R R R R' R R' R R' R' R' R' C C C C C C C C C C C C C C C C H H H H H H H H H H H H H H H H and trans-isomers give treo-diisotactic polymers H H H H H H R' H R' R' H R' R' R' R' R' C C C C C C C C C C C C C C C C R R R R R R R R H H H H H H H H Needless to say, other more complex modifications are also possible, which immediately cause a change of properties of polymeric materials. The materials composed from stereoregular polymers are often easily crystallized so that gives their physical structure and properties can be regulated. Here we meet for the first time a modification of the properties of polymeric materials, which is caused by practically any change in the chemical structure of macromolecules and the physical structure of the polymeric substance. Physical modification is often indicated by a change of the chemical structure, and sometimes is completely defined by it. One of the main methods of modification is the synthesis of copolymers, when not a single but several monomers participate in the reaction. That is why the macromolecule becomes composed from different units. These units may alternate continuously: –A–B–A–B–A–B–A–B–A–B– the alternating copolymer; but, most often, they are arranged irregularly: –A–A–B–A–B–B–A–A–A–B– the random copolymer. The units may also be linked in separate blocks which are the linked to each other: –A–A–A–A–A–B–B–B–B–B– the block-copolymer. Obviously, each block may contain a different number of units. This is immediately shown up in the properties of the future polymeric substance. In this case, the copolymerization process becomes regulated. Running ahead, recall that mechanical mixtures of polymers and copolymers of the same molar composition may often possess rather different properties, but sometimes they are practically identical. The considered schemes of addition of units during macromolecule growth indicate the only case of copolymerization of two types of monomers. Even if many combinations are realized in these simplest cases, their number grows immeasurably when three or more monomers (or types of units) are used All the above-discussed chains of polymers represent linear formations. However, branched macromolecular chains could be easily synthesized. For this purpose, it is even unnecessary to introduce multifunctional compounds into the chain composition. Branching also occurs in polymerization of unsaturated hydrocarbons with no functional groups. If no special steps are taken, the products of polymerization of ethylene, propylene, isobutylene and other similar compounds will always contain some amount of chains branched from the main chain. Concerning the products of polycondensation (see the above discussion on polyesters and R

R'

R

R'

R

13

polyamides), introduction of a three-functional compound into the main chain always leads to the formation of branched polymers: ...

A A A A' A A A A A A A

...

A A A A .. . It is self-evident that the polymeric body based on the branched macromolecules will differ in the structure and properties from a substance composed of linear macromolecules. However, we must not hurry in concluding about the type of physical structuring of the branched polymers. At first glance, it seems that the presence of large branches will make obstacles to denser packing of the chains, as well as to the crystallization process or regulation of macromolecules in general. Indeed, this is sometimes the case. In other cases, the opposite situation is observed. It depends upon the chemical structure of the main chain and its branches, which determines the volume of units, interaction forces between them and neighbour chains, etc. Recently, special attention has been paid to the structure and properties of socalled dendric polymers, the macromolecule of which is schematically depicted in Figure 1 [98, 212]. Below, we will discuss in more detail the influence of the types of branchings on the properties of the resulting polymers.

Figure 1. Schematic representation of dendric polymers

Branchings may be composed in different ways. They may contain the same units, which compose the main chain. However, ‘grafted’ polymers have become widely used; they are formed in grafting of previously obtained chains of a definite structure to the main chain with an extremely different structure: ...

A A A A' A A A A A A A B B B B .. .

...

14

Sometimes, such grafting is performed many times. We can now easily pass from the branched to three-dimensional ‘cross-linked’ polymers. This requires just an increase of the concentration of multifunctional compounds in the polymer chain. The chains could also be cross-linked by special curing agents, i.e. by compounds containing active groups, capable of reaction with functional groups of the main chain or the end groups. The classic example is the curing of epoxy resins: CH3 ...

O

C

O CH2

CH CH2 O

CH3 CH3 ...

O

O CH2

C

NH2 +

R NH2

CH CH2 O

CH3 CH3 ...

O

C

O CH2

CH3

CH CH2 OH

CH3 ...

O

C

O CH2

CH CH2

NH R NH

CH3 OH Further on, the second hydrogen atom is substituted, and a network is formed. According to the classification described in ref. [202], there exist several main methods of obtaining network polymers: 1) Realization of a chemical reaction between two (or more) different functional end groups, attached to a chain of low molecular mass. As a result, a dense network with short chains between cross-link points is formed. 2) Chemical linking of high-molecular compounds by the end groups with the help of a low-molecular cross-linking agent. Consequently, a network with long linear fragments between the cross-linked points is formed. 3) Formation of a network by copolymerization of two- and polyfunctional monomers. The example of such a network is the styrene–divinylbenzene system: ...

CH2

CH CH2

CH CH2

...

...

CH2

CH CH2

CH CH2

...

4) Vulcanization of polymeric chains by involving, in the reaction, functional groups disposed along the main chain. The reaction is performed either by the application of a low-molecular cross-linking agent or by means of radiation and other types of influence on the functional groups.

15

Other possible (and already realized in practice) ways of producing the network systems should also be added. 5) Formation of networks with by means of a reaction of two (or more) heterogeneous polymers by functional groups disposed along the chain of each polymers (i.e. in the repeating units, but not at the ends). 6) Synthesis of polymeric networks with the help of the polycyclotrimerization reaction. For this purpose, oligomers with end groups capable of forming cycles during the reaction [56, 79, 101, 152] are formed. The example of such a reaction is the trimerization of two-functional oligomers (or monomers) containing cyanate end groups. Clearly, other ways of obtaining the polymeric networks are also possible. Recently, a new type of polymer, called ‘interpolymers’ was produced [16, 215]. The interpolymer is a system composed of two (or more) macromolecules, heterogeneous in the chemical structure, chemically bonded to each other through the functional groups disposed in the repeating units of the each macromolecule. A schematic representation of the interpolymer is displayed in Figure 2.

Figure 2. Schematic representation of interpolymer.

A specific example of this system is, for example, a product of interaction between polystyrene and polytrichlorobutadiene: ...

CH2

CH

... + ...

CH2

CCl2

...

CH CCl

CH2

...

AlCl3

...

CH CCl

CCl

CH2

CH

...

...

The formation of interpolymers gives new possibilities of modifying the structure and properties of polymers. Another type of ‘two-cord’ system is the ladder polymer, the example of which is polyphenylsylsesquioxane [113]:

...

Si

O

O ...

Si

Si

O

...

O

...

O O

Si

Chapter II. Packing of macromolecules and polymer density II.1. Increments method and basic physical assumptions After discussing briefly the chemical structure of polymers, let us pass to the volumetric representation of macromolecules, which is necessary for understanding the features of structure formation in polymers. These considerations will be based on the assumptions developed by A.I. Kitaigorodsky in organic crystal chemistry [75]. According to these assumptions, every atom is presented as a sphere with intermolecular radius R. Values of these radii are determined from the data of X-ray structural analysis of ideal crystals of organic substances. In this case, it is assumed that valency-unbonded atoms, entering into an intermolecular (but not chemical) interaction, contact each other along the borders of the spheres. This is schematically represented in Figure 3. Then, if two identical atoms are in contact, the intermolecular radius will be determined from the relation: R = l/2,

(II.1)

where l is the distance between mass centers of two identical valency-unbonded atoms, which, however, are capable of intermolecular physical interaction.

Figure 3. Schematic representation of intermolecular (Van-der-Waals) interaction of two atoms

According to the same assumptions, chemical interaction between two atoms always causes their compression, because the length of the chemical bond di is always shorter than the sum of two intermolecular radii: d i < R1 + R2 .

(II.2)

This is clear from Figure 4, which schematically depicts two chemically bonded atoms. If the intermolecular radii Ri for all atoms participating in the repeat unit, and all lengths of chemical bonds between these atoms are known, their own (Van-der-Waals) volume of the repeat unit could be easily calculated, and a model of this unit (or greater fragment of the macromolecule), in which the volume of each atom is bordered by a sphere with intermolecular radius Ri, could be composed.

17

Figure 4. Schematic representation of two chemically bonded atoms.

Figure 5. Model of polyethylene chain fragment.

Table 1 shows intermolecular radii of some widespread atoms, which compose the majority of polymers. Table 1 Atom C H O N F Cl Br I

Van-der-Waals radii R of different atoms R, nm Atom 0.180 Si 0.117 Sn 0.136 As 0.157 S 0.150 P 0.178 Pb 0.195 B 0.221 Ti

R, nm 0.210 0.210 0.200 0.180 0.190 0.220 0.165 0.200

Table 2 displays bond lengths of various combinations of atoms, also characteristic for most of existing polymers. If these values are known, the volume of the repeat unit of any polymer may be calculated. To conduct this, the own volume of each atom participating in the repeat unit should be preliminarily determined. It is calculated from the formula 3 1 ∆Vi = πR 3 − ∑ πhi2 (3R − hi ), 4 i 3

(II.3)

where ∆Vi is the increment of the own (Van-der-Waals) volume of the present atom; R is the intermolecular radius of this atom; hi is the height of the sphere segment, cut off from the present atom by a neighbor one, chemically bonded to it. The value hi is calculated from relation

18

hi = R −

R 2 + d i2 − Ri2 , 2d i

(II.4)

where Ri is the intermolecular radius of a neighbor valency-bonded atom; di is the length of the chemical bond (see Figure 4). Table 2 Chemical bond length di for same pairs of atoms Bond* di, nm Bond* di, nm Bond* di, nm C–C 0.154 C–F 0.134 O–F 0.161 C–C 0.148 C–F 0.131 O=N 0.120 C=C 0.140 C–Cl 0.177 O=S 0.144 C=C 0.134 C–Cl 0.164 O=P 0.145 C=C 0.119 C–Br 0.194 N–P 0.165 C–H 0.108 C–Br 0.185 N–P 0.163 C–O 0.150 C–I 0.221 N–P 0.158 C–O 0.137 C–I 0.205 S–S 0.210 C–N 0.140 C–B 0.173 S–As 0.221 C–N 0.137 C–Sn 0.215 S=As 0.208 C=N 0.131 C–As 0.196 Si–Si 0.232 C=N 0.127 C–Pb 0.220 P–F 0.155 0.134 H–O 0.108 P–Cl 0.201 C N C≡N 0.116 H–S 0.133 P–S 0.181 C–S 0.176 H–N 0.108 B–B 0.177 C–S 0.156 H–B 0.108 Sn–Cl 0.235 C–Si 0.188 O–S 0.176 As–Cl 0.216 C–Si 0.168 O–Si 0.164 As–As 0.242 * If the same pair of atoms is linked by a single bond, the longer bond corresponds to attachment of this atom to an aliphatic carbon atom; the shorter bond corresponds to attachment of the same atom to an aromatic carbon atom.

Increments of the volumes of various atoms and atomic groups are shown in Table 3. Obviously, the volume of the given atom depends on its surrounding, i.e. on the type of atoms chemically bonded to it. The greater the volume of the neighbor, chemically bonded atom and the shorter the length of the chemical bond, the greater is the compression of the given atom. When increments of the volumes, ∆Vi, of all the atoms entering into the repeat unit of polymers are determined, the relative part of the occupied volume in the total volume of the polymeric substance may be calculated. In the case of polymer, calculations would be appropriate to conduct basing on molar volumes of the repeat unit, because polymers are always polydispersional (i.e. they contain macromolecules of various length), and also because at long lengths of the macromolecule the influence of end groups may be neglected. Then, the own molar volume will equal Vown = N A ∑ ∆Vi , and the total molar volume Vtotal = M/ρ, ρ is density of the i

polymeric substance; M is the molecular mass of the repeat unit; NA is the Avogadro number. Numerous experiments and calculations show that in all cases the condition Vown < Vtotal is fulfilled. Hence, in the first approximation, the volume of the polymeric substance could be divided into two parts: the own (Van-der-Waals) volume of atoms, which they occupy in a solid, and the volume of spaces determined as the difference of Vtotal and Vown. Of interest is determination of the part

19

Table 3 Van-der-Waals volumes of atoms

20

21

22

23

24

25

26

27

28

29

of the occupied volume or, according to the terminology used in organic crystal chemistry, the molecular packing coefficient k:

V k = own = Vtotal

N A ∑ ∆Vi i

M /ρ

.

(II.5)

Clearly, the value of k for the same polymer will depend on temperature and the physical state of the polymer, because the value of ρ depends on them. Calculations performed for many amorphous bulky polymers existing in the glassy state have indicated that the first approximation of k gives its value constant and practically independent of the chemical structure of the polymer [41]. Passing on to polymers with a complicated chemical structure from those with a simple one causes no significant change of the part of the occupied volume (e.g. the value of k). Table 4 indicates the chemical structure and numerical values of coefficients of the molecular packing of some glassy polymers. It also shows that first approximations of the values of k for each of them are equal, indeed. To demonstrate this experimental fact more clearly, Figure 6 displays the dependence of density ρ of various polymers on the relation M N A ∑ ∆Vi . In Figure 6 it is clearly seen that all i

30

Table 4 Values of the coefficients of molecular packing for some glassy and semi-crystalline polymers Structural formula of the repeat unit of polymer Van-der-Waals Packing volume of the coefficient k 3 unit, cm /mol

CH3 CH2

C

41.6

0.678

32.6

0.682

58.5

0.684

69.1

0.680

144.3

0.679

234.7

0.679

263.1

0.680

277.5

0.688

56.4

0.685

CH3 H CH2

C C N CH3

CH2

C C O CH3 O CH3

CH2

C C O C2H5 O

CH3 C O

C

O

CH3

C

O

C O

O

O C

O

O C O

C O

C O

C O O

(CH2)8

C

O C

HN

NH C

O

NH C O

CH2

CH CH CH2

31

—CH2—CH=CH—CH2— CH2

CH C

CH2

59.1 74.3

0.654 0.659

100

0.699

97.8

0.708

110.3

0.693

269.0

0.692

43.9 72.4

0.753 0.663

33.8 54.9

0.700 0.666

58.7 36.0 123.1

0.654 0.744 0.641

134.3

0.664

CH3 (CH2)5

NH C O

CH2

CH CH

H2C HC

CH2 CH2

N CH3 CH2

N

O

O

C

C

C

C

O

O

C

N

O

—CF2—CF2— CH2

CH O C

CH3

O —CH2—CHF— CH2

CH O CH3

—CH2—CCl2— —CH2—CF2— CH3 CH2

C

CH3

C O CH O

CH3

CH3 CH2

C C O C4H9 O

32

CH3 CH2

168.3

0.651

120.0

0.607

85.9

0.696

163.0

0.687

88.8

0.705

C C O C6H13 O

CH3 Si

O

CH2 CH2 CF3 CH2 CH2 CH2 CH3 C N O CH2

CH N

CH2 H2C

CH N

C O CH2

H2C CH2

CH

111.6

0.669

CH2

Cl CH

115.5

0.657

65.6

0.638

89.3

0.650

40.0

0.681

CH3 CH2

CH

S

CH3 CH2

CH C O C2H5

O O CH2

C O

33

O CH CH2 CH3

69.9

0.684

172.5

0.740

70.6

0.677

21.3 126.1

0.752 0.616

118.5

0.667

53.0

0.733

150.8

0.679

103.0

0.620

76.2

0.568

46.4 144.4

0.680 0.692

227.7

0.693

O

C

C NH

O

O CH2

C

NH

CH C O CH3

O —CH2—O— CH3 Si

CH2

O

CH C O C4H9 O F C

CF2

Cl CH3 CH2

C

CH2 C O CH CH2 O

CH2 CH2 CH2

C2H5 Si

O

C2H5 CH3 Si

O

CH3 —CH2—CH2—S— (CH2)2

O C

C O

O O

O C O

O

34

O

154.1

0.696

157.0

0.721

30.2 46.3

0.682 0.666

99.6

0.665

262.1

0.726

C O

O

SO 2

—CH2—CH2— CH2

CH CH3

CH2

CH2

CH

NH C O

(CH2)4

O C NH

O

O

Figure 6. Dependence of density ρ on

  ∑ ∆'

L

L

the values of ρ determined experimentally fit well the same linear dependence on the relation of atoms mass on their volume. In accordance with Equation (II.5), the tangent of this straight line represents the molecular packing coefficient which, in the case of amorphous bulky systems, serves as an universal constant. If it is true, the polymer density ρ may be calculated from the equation

ρ=

kM , N A ∑ ∆Vi i

(II.6)

35

that yields directly from Equation (II.5) under the condition kavg = const. In the case of amorphous bulky polymers, kavg = 0.681. For silicon-containing polymers, the average coefficient of molecular packing is 0.603. Hence, a change of the polymer chemical structure is unable to cause a significant effect on the part of the occupied volume in amorphous polymeric substance, and the value of density, ρ, itself depends on the relation of mass and the Van-der-Walls volume of the repeat unit only. Obviously, here we are dealing with true bulky substances of the amorphous structure. In reality, a polymeric substance with any porosity may be formed, and the coefficient k will have extremely different values. However, in this case, the notion of the packing density, quantitatively estimated by the value of k, loses its usual meaning and must be calculated for pore walls material only. We return to this problem below when discuss parameters of the porous structure of polymers, determined by the sorption method. For copolymers, equation (II.6) has the form

ρ=

kavg (α1M 1 + α 2 M 2 + ... + α n M n )         N A α1 ∑ ∆Vi  + α 2  ∑ ∆Vi  + ... + α n  ∑ ∆Vi           i 1  i 2  i n  

,

(II.7)

where α1, α2, …, αn are molar parts of the components 1, 2, …, n; M1, M2, …, Mn are     molecular masses of the repeat units of the same components;  ∑ ∆Vi  ,  ∑ ∆Vi  ,      i 1  i 2   …,  ∑ ∆Vi  are their Van-der-Waals volumes.    i n In the reduced form, expression (II.7) is: k =n

k avg

ρ=

k =n

∑α k M k

k =1

  N A ∑ α k  ∑ ∆Vi    k =1  i k

,

(II.8)

  where αk, Mk,  ∑ ∆Vi  are the molar part, the molecular mass, and the Van-der   i k Waals volume of the k-th component, respectively. If we want to express the density of copolymer via densities ρ1, ρ2, …, ρn of homopolymers based on the components 1, 2, …, n, expression (II.7) changes to the following form:

ρ=

α1M 1 + α 2 M 2 + ... + α n M n , M M M α1 1 + α 2 2 + ... + α n n ρ1 ρ2 ρn

(II.9)

36

(in this case, it should be taken into account that α1 + α2 + … + αn = 1). In the reduced form, the expression (II.9) is the following: k =n

ρ

∑α k M k

= k =1 k =n

,

(II.10)

M ∑α k ρ k k k =1

Expressions (II.7)–(II.10) may also be used for calculating the density of miscible blends of polymers. Let us now examine the temperature dependences of the molecular packing coefficients of glassy polymers. Calculation of values of k at different temperatures are performed by formulae yielding from the expression (II.5):

k (T ) =

k (T ) =

N A ∑ ∆Vi

[

i

[

i

(

)] ,

(T < Tg);

(II.11)

(

)] ,

(T > Tg);

(II.12)

MVg 1 + α G T − Tg N A ∑ ∆Vi

MVg 1 + α L T − Tg

where Vg is the specific volume of the polymer at the glass transition temperature Tg; αG and αL are the volume expansion coefficients of polymers below and above the glass transition temperature, respectively.

Figure 7. Temperature dependences of the coefficients of molecular packing k for a series of polymers: 1 – poly(n-butyl methacrylate), 2 – poly(n-propyl methacrylate), 3 – poly(ethyl methacrylate), 4 – polystyrene, 5 – poly(methyl methacrylate), 6 – polycarbonate based on bisphenol A.

Calculations by equations (II.11) and (II.12) indicate that temperature dependences of the molecular packing coefficients are of the form depicted in Figure 7. A remarkable property of these temperature dependences in the real equality of the molecular packing coefficient in the first approximation for all bulky polymers at any temperature below the glass transition point. In the second, more accurate approximation, the molecular packing coefficient is the same for every polymer at the glass transition temperature. This value is kg ≈ 0.667.

Table 5 Name 1 Polyethylene

Coefficients of molecular packing k for a series of crystalline polymers Type of elementary cell Chemical formula 2 3 Rhombic Pseudo-monoclinic CH2CH2 Triclinic

Polypropylene: - isotactic - syndiotactic

Monoclinic Monoclinic

1,2-poly(butadiene): - isotactic - syndiotactic

Rhombic Rhombohedral

1,4-trans-poly(butadiene)

Pseudo-hexagonal

1,4-cis-poly(butadiene)

Monoclinic

1,4-cis-polyisoprene

Monoclinic

Polychloroprene

Rhombic

Poly(ethylene terephthalate)

Triclinic

CH2

CH3 CH2

CH CH

CH2 CH2CH=CHCH2 CH2CH=CHCH2 CH2 CH C CH2 CH3 CH2

O CH2 Poly(hexamethylene terephthalate)

CH

CH2

CH C Cl

CH2

O C

C

O

O

Triclinic

O

(CH2)6

O C

C

O

O

ρ, g/cm3 4 1.000 1.014 0.965 1.013

k 5 0.736 0.746 0.710 0.745

0.936 0.910

0.693 0.674

0.963 0.960

0.692 0.690

1.020

0.733

1.010

0.726

1.000

0.725

1.657

0.893

1.455

0.776

1.131

0.652

37

38

2

3

Triclinic

O CH2

CH2

4 1.358

5 0.724

1.274

0.782

1.240 1.248

0.764 0.769

1.157

0.740

1.230

0.758

1.192

0.789

0.813

0.598

O C O C O

Poly(ethylene adipate)

Triclinic

O

(CH2)2

O C

(CH2)4

O Polyamide 6,6: α-isomer β-isomer

Triclinic Triclinic

O

Polyamide 6,10

Triclinic

C

Polyamide 6

Monoclinic

C

O

(CH2)4

C

C O

HN

(CH2)6

NH

HN

(CH2)6

NH

O (CH2)8

C

O C HN

(CH2)5

O Polyamide 11

Triclinic

C HN

(CH2)10

O Poly-4-methylpentene-1

Tetragonal

CH2

CH CH2 CH CH3 CH3

38

1 Poly(ethylene isophthalate)

39

1 Polyvinylchloride

2 Rhombic Monoclinic

3

CH2

CH

4 1.440 1.455

5 0.680 0.687

2.400 2.360

0.794 0.781

1.440

0.742

1.350

0.770

1.110

0.677

1.230

0.719

1.120

0.711

1.506 1.205

0.808 0.723

Cl Polytetrafluoroethylene

Pseudo-hexagonal Hexagonal

Polyvinylfluoride

Hexagonal

Poly(vinyl alcohol)

Monoclinic

–CF2–CF2– CH2

CH F

CH2

CH OH

Polyacrylonitrile

Rhombic

Poly(methyl methacrylate) isotactic

Pseudo-rhombic

CH2

CH C N

CH3 CH2

C C

O CH3

O Rhombohedral

Polyoxymethylene Polyethylene oxide

Hexagonal Hexagonal

CH2 CH

–CH2–O– –CH2–CH2–O–

39

Polystyrene

40

2

3

Rhombic

CH2 CH O CH3

4 1.102 1.154

5 0.663 0.694

40

1 Polypropylene oxide

41

Taking into account that the specific volume at the glass transition temperature Tg equals

Vg = 1

ρg

=

N A ∑ ∆Vi i

,

kg M

(II.13)

where ρg is the polymer density at Tg; and substituting (13) into (11) and (12), we get k (T ) = k (T ) =

kg

[1 + α G (T − Tg )] , kg

[1 + α L (T − Tg )] ,

(T < Tg);

(II.14)

(T > Tg);

(II.15)

Equations (II.14) and (II.15) can be used for obtaining relations, which describe temperature dependences of the density of polymers ρ in the glassy and rubbery states. For this purpose, we substitute (II.14) and (II.15) into equation (II.6):

ρ (T ) =

kg M

[1 + α G (T − Tg )]N A ∑ ∆Vi ,

(T < Tg);

(II.16)

(T > Tg);

(II.17)

i

k (T ) =

kg M

[1 + α L (T − Tg )]N A ∑ ∆Vi , i

Because, as it is seen from the further considerations, values of expansion coefficients αG and αL, as well as the glass transition temperature Tg, can be calculated from the chemical structure of the repeating polymer unit, temperature dependences of density ρ (T) can also be calculated from relations (II.16) and (II.17). In conclusion, let us note that the constancy of the coefficient of molecular packing k is true only for amorphous bulky substances composed of polymers. In the case of crystalline polymeric substances, the situation is significantly changed. If the coefficients of molecular packing for ideal polymeric crystals are calculated with the help of the X-ray analysis data, one can assure himself that, in spite of amorphous ones, the coefficients of molecular packing of crystalline polymers are extremely different. The smallest values of k are typical of aliphatic systems with volumetric side groups, for example, for poly-4-methylpentene-1 and poly-n-butyraldehyde. The highest coefficients of packing are typical of 1,4-trans-β-polyisoprene and polychloroprene. As an example, Table 5 shows the crystallographic values of densities and molecular packing coefficients for a series of typical crystalline polymers. It is clear that the values of k for them vary in a wide range. Hence, crystalline polymers display a rather wide distribution curve of the coefficients of molecular packing (Figure 8).

42

Figure 8. Curve of distribution of the coefficients of molecular packing k for crystalline polymers.

II.2. Relationship between free volume of polymers, coefficient of molecular packing and porous structure Before we start discussing the relationship between the above-mentioned physical characteristics, the term of the ‘free volume’ must be discussed in brief. There are three definitions of the free volume: 1) The free volume represents the difference between the true molar volume of the substance, VM, and its Van-der-Waals molar volume N A ∑ ∆Vi : ∆V = VM − N A ∑ ∆Vi = M / ρ − N A ∑ ∆Vi . i

i

(II.18)

i

The value of ∆V obtained in this way is often called ‘the empty volume’. Clearly, the empty volume depends on temperature, because the molar volume also depends on it: VM = M/ρ. Substituting this relation into equations (II.16) and (II.17), we obtain: 1 + α G T − Tg  ∆V (T ) = N A ∑ ∆Vi  − 1 , (T < Tg); (II.19) kg i  

(

)

(

)

1 + α L T − Tg  ∆V (T ) = N A ∑ ∆Vi  − 1 , (T > Tg); (II.20) kg i   Relations (II.19) and (II.20) describe the temperature dependences of the empty volume. 2) The free volume represents the difference between the volumes of the substance at the absolute zero and at the assigned temperature; to put it differently, the free volume represents an excessive volume occurring as a result of thermal expansion of the substance. This definition of the free volume is most valuable. Moreover, the present free volume is subdivided into the free volume of fluctuation and the expansion volume. 3) The free volume represents the difference between the volume of polymeric substance at the assigned temperature and the volume of the ideal crystal

43

composed of a polymer of the same chemical structure. This definition of the free volume is used extremely seldom. Let us now pass to analysis of the relationship between the free volume of polymers, the coefficient of molecular packing and the porous structure. The porous structure mostly defines their properties. That is why the methods of estimation of the porous structure of polymers and its connection with such characteristics as the coefficient of molecular packing and the free volume of polymer must be discussed in detail. The case is that the size of micropores depends on the method of its estimation. Clearly, interpretation of their nature and the relationship of the characteristics of the microporous structure with the properties of polymers significantly depends on the method of their determination. The properties of many bulky and film polymers significantly depend on the density of packing of macromolecules, and for such systems as sorbents, ionites, etc., used in gel-chromatography and production of ion exchangers, the volume of pores is very important, together with their size distribution, specific surface. Let us present the definition, given in ref. [68]: “Pores are emptinesses or cavities in solids usually connected with each other. They possess various and different form and size, determined significantly by nature and the way of obtaining absorbents”. Usually, the characteristics of a microporous structure are judged by experimental data on equilibrium adsorption, capillary condensation of vapor and mercury pressing in (mercury porosimetry) [121]. Recently, the positron annihilation method has been used [3, 48, 110, 123, 134, 140, 155, 164, 187, 211]. This method helps in determining the characteristics of the microporous structure, when the size of pores is commensurable with the molecule size. Such micropores are inaccessible for sorbate molecules and especially for mercury when mercury porosimetry is used. Polymers and materials prepared from them possess the feature (in contrast to mineral sorbents) that they swell during sorption of vapors of organic liquids. Consequently, their structure changes and usual methods of calculation give no possibility of estimating the true porous structure of the initial material. It stands to reason that vapors of organic liquids, in which polymer does not swell, can be used in sorption experiments. Then the parameters of the porous structure of the initial material can be determined, but these cases are quite rare [107]. Before passing to comparison of parameters of the porous structure with the free volume of the polymer, it should be noted that parameters of the porous structure for the same polymer could be significantly different due to conditions of its synthesis and further processing. For example, a film or fibers may be obtained from various solvents [81], as well as from a solvent–precipitant mixture [97], and will display a different microporous structure and properties. The same can be said about materials obtained by pressing and injection molding and with the help of hydrostatic extrusion as well. Therewith, macropores may also be formed and their total volume may be quite high. If special synthesis methods are used, materials based on polymer networks may be obtained, which possess a large specific surface and extremely large pore radii [115]. Clearly, such macropores are not defined by the packing density of macromolecules. They may be formed by loose packing of formations larger than macromolecules or may be caused by conduction of a chemical process of the network formation under special conditions [167]. Several more general comments should be made. Besides macropores, as mentioned above, micropores are present in a polymeric substance, the size of which is commensurable with the size of sorbate molecules. Clearly, in this case, sorbate

44

molecules cannot penetrate into these micropores (it is assumed that for sorbate molecules to penetrate into pores, the volume of the latter must be several times greater than that of penetrating molecules). Since sorbate molecules may be different, i.e. may possess different sizes, parameters of the porous structure determined from the sorption data will depend on types and sizes of molecules of sorbed substances. That is why such terms as ‘porosity to nitrogen’, ‘porosity to benzene’, etc. have been introduced. Of interest is that the sorption method of determination of the porous structure of polymeric substances cannot be used in the case when a substance contains quite large macropores. This is associated with the fact that under conditions of polymolecular adsorption, when many molecular layers are formed on walls of macropores, their fusion becomes difficult, i.e. capillary condensation is absent. Then, the total volume of pores calculated by the amount of sorbate penetrated into the polymeric substance will be smaller than the true volume of macropores. Starting the analysis of relationship between the physical characteristics of the polymeric substance and its microporous structure, let us introduce some definitions and designations: Ssp is the specific surface of micropores, W0 is the total volume of pores, W0max is the maximal volume of pores accessible for sorbate molecules of any size (per gram of the substance), VF is the free volume (in the present case, the volume of expansion), VE is the ‘empty volume’ (see above), VT is the specific volume of the polymeric substance at given temperature, VW is the Van-der-Waals volume (per gram of the substance), Vid.cr. is the specific volume of the ideal crystal or bulky amorphous polymer (a bulky amorphous polymer is the one in which no sorbate molecule can penetrate into its pores). Let us write down some relations connecting these characteristics: VF = VT – V0 ; (II.21) VE = VT – VW. (II.22) Next, let connect these characteristics with the coefficient of molecular packing k (see above): k = VW/VT; 1 – k = VE/VT. (II.23) As mentioned above, there are so-called non-porous sorbents (for example, crystalline substances), into which no molecules of sorbate can penetrate without swelling. Clearly, that for such substances W0max = 0. At the same time, as seen from the data in Table 5, coefficients of molecular packing of crystals fall within the range from 0.64 to 0.89. Taking into account that the coefficient of molecular packing, by definition, represents a part of the occupied (Van-der-Waals) volume, it can be said that the part of empty (but inaccessible) volume is 1 – k = 0.11–0.36. This empty volume is inaccessible for even small sorbate molecules to penetrate in; let mark it as Vinacc.. Then the volume of the ideal crystal (or bulky amorphous polymer, Vblk) can be written down as Vid.cr. = VW + Vinacc.; Vblk = VW + Vinacc.. (II.24) The volume of the real polymeric substance (which contains micropores accessible for a sorbate) will be summed up from three parts: VT = VW + Vinacc. + W0max. (II.25) Then W0max = VT – Vid.cr.; W0max = VT – Vblk. (II.26)

45

The coefficient of molecular packing in the bulky part of the polymer will be determined from the relation VW k= . (II.27) VT − W0max In the case of estimation of the density of macromolecule packing for the real polymeric substance containing micropores accessible for sorbate molecules, the coefficient of molecular packing, k, should be calculated by the relation VW k= , (II.28) VT − W0 where W0 is the total volume of micropores (per gram of the substance), determined on the basis of sorption measurements. The value of W0max that represents the difference between the specific volume of the substance at the given temperature and volume of the true bulky substance is conceptually identical to the porosity factor P = 1/ρs – 1/ρt, where ρs is the apparent density; ρt is the true density. Therewith, ρs represents the density of the substance at the current temperature, affected by the pores existing in it. It is best to measure the apparent density of substances with the proper geometrical shape, because when using no solvents ρs can be found by dividing the substance weight by its volume. If the apparent density of substances with the improper shape is measured, the pycnometric or dilatometric method can be used. The difficulty is in selection of a liquid that does not wet the surface of the substance and does not penetrate deep into it. The true density ρt represents density of the bulky part of the substance containing no pores. It is best to measure the density of the ideal crystal, because it can be calculated on the basis of crystalline lattice parameters. In the case of amorphous and partly crystalline substances, the method of gradient tubes may be used applying liquids penetrating well into pores. However, it should be taken into account that a mixture of two liquids is used for creation of the density gradient in the tube, each of which may possess different wettability and penetrability into pores. The picture is then distorted, and the determined density is not true. The relations shown above can be estimated unambiguously if a polymer swells in the sorbate, used for estimation of the porous structure of the polymer. If the experiment indicates that W0 is greater than W0max, this indicates that the volume of vapors absorbed by the polymer is greater than the volume of pores existing in it, i.e. the polymer swells during sorption. Let us now consider the experimental and calculated data on determination of the parameters of the polymer structure and coefficients of their molecular packing. These data are shown in Table 6. For ideal polyethylene crystallites, VE = Vinacc. and W0max = 0. The coefficient of molecular packing is quite high. For semi-crystalline polyethylene, the empty volume, VE, is greater than in the case of the ideal crystal and, therewith, a part of it is accessible for penetration of small sorbate molecules. However, the total volume of pores determined by methanol sorption equals 0.01 cm3/g. The molecular packing coefficient for the bulky part of such polyethylene is significantly lower than for the ideal crystal. Polymers in the rubbery state (polyisobutylene, for example) also possess comparatively low values of free volumes and are practically non-porous sorbents (VE = Vinacc.). Contrary to this, polymers produced by polycondensation or polymerization in solution display immensely high values of W0max. In this synthesis method, pores are formed due to elimination of the solvent, distributed in the volume of the synthesized

46

polymer. This is observed from the fact that the same polymers produced by polymerization in the melt are practically non-porous, and values of VE for them are very small, and W0max = 0. Table 6 Parameters of porous structure and coefficients of molecular packing of a series of polymers VE, W0max, W0, Vinacc., K Polymer cm3/g cm3/g cm3/g cm3/g Polyethylene (100% crystallinity) 0.26 ~0 ~0 0.26 0.736

–CH2–CH2– Polyethylene (crystallinity < 100%)

0.35

0.08

0.01

0.27

0.675

0.36

~0

~0

0.36

0.678

1.28 0.22

1.06 ~0

 

0.22 0.22

0.687 0.687

0.82 0.24

0.58 ~0

0.31 ~0

0.24 0.24

0.688 0.688

–CH2–CH2– Polyisobutylene

–CH2–C(CH3)2– Polymethylidenphthalide

CH2 C O C O Polymerization in dimethylformamide solution Polymerization in melt Polyarylate F-1 C

C O

O

O

O C O C O

Polycondensation in chlorinated bisphenol solution pressed at 360°C and under 312.5 MPa pressure

Pores formed during synthesis may be closed in polymer pressing under high pressure, and the porous polymer then becomes non-porous. Therewith, in all cases, W0 is smaller than W0max that indicates the absence of swelling. For all polymers, values of Vinacc. are close to these characteristics for the density of crystallized samples. Of special attention is the fact that independently of the production method, the molecular packing coefficient for amorphous and semicrystalline polymers in their bulky part is the same and close to the average value kavg = 0.681, which was discussed above. For a crystalline sample, the value of k is significantly higher. There is one more interesting point to discuss, associated with molecular packing, namely, the change of the system volume during polymerization, i.e. at transition from monomer to polymer. It is well known that transition from a monomeric liquid to a solid glassy polymer is accompanied by a significant contraction, i.e. volume decrease [76]. The specific volume of the polymer Vp is always smaller than that of monomer Vm, and their difference ∆V = Vp – Vm < 0. One of the reasons for contraction is substitution of longer intermolecular bonds existing in liquid monomers by shorter chemical bonds

47

formed between monomer molecules in the polymer. Therewith, the own Van-derWaals volumes of atoms decrease owing to their ‘compressing’ (see above). Nevertheless, this is not the only reason of contraction. It follows from consideration of the experimentally determined specific volumes that there is another reason for contraction, which is more dense packing of polymeric chains compared with the packing of monomeric molecules. This is indicated by the fact that the packing coefficients of polymers are always greater than those of their monomers (kp > km). Let the total contraction, ∆Vtotal, be presented as a sum of two values: ∆V1, which is the contraction stipulated by substitution of intermolecular bonds by chemical ones, and ∆V2, which is the contraction involved by more dense packing of chains, ∆Vtotal = ∆V1 + ∆V2,

(II.29)

and each of the summands estimated. To do this, values of the specific volume of a polymer should be calculated on the assumption that it displays the packing coefficient, the same as the monomer km, i.e.    ∑ ∆Vi     i p N Vp′ = A ⋅ , (II.30) M km   where  ∑ ∆Vi  is the Van-der-Waals volume of atoms in the repeat unit of the    i p polymer; M is the molecular mass of the unit. Values of Vp′ for some polymers, calculated in this way, are shown in Table 7. They are always greater than experimentally measured values of specific volumes of the polymer, Vp. The difference between Vp′ and Vm is ∆V1 = Vp′ – Vm,

(II.31)

and the remaining part of the contraction is calculated by the formula ∆V2 = ∆Vtotal – V1.

(II.32)

Relative parts of contraction are determined from the relations:

α1 = ∆V1/∆Vtotal; α2 = ∆V2/∆Vtotal.

(II.33) (II.34)

The data shown in Table 7 indicate that in all the cases the smaller part of contraction depends upon opening of double bonds, and the greater part — on dense packing of polymer chains. Therewith, the chemical structure of a monomer and an appropriate polymer significantly affects the values of α1 and α2.

49

Polymer (monomer) 1

CH3 CH2

∆V1, cm3/g 6 0.080

∆V2, cm3/g 7 0.133

α 1, % 8 37.6

α2, % 9 62.4

C C O CH3 O CH3

CH2

1.102

0.890

1.031

0.212

0.071

0.141

33.5

66.5

1.109

0.928

1.045

0.181

0.064

0.117

35.4

64.6

1.046

0.815

0.951

0.231

0.095

0.136

41.1

58.9

1.082

0.873

1.000

0.209

0.082

0.127

39.2

60.8

C C O C2H5 O CH3

CH2

C C O C3H7 O

CH2

CH C O CH3 O

CH2

CH C O C2H5 O

48

Table 7 Changes in volume of the system as a result of polymerization Vm, cm3/g Vn, cm3/g Vtotal, cm3/g V′n, cm3/g 2 3 4 5 1.068 0.855 0.968 0.213

50

1

CH2

CH

2 1.098

3 0.952

4 1.036

5 0.146

6 0.062

7 0.084

8 42.5

9 57.5

1.073

0.841

0.976

0.232

0.097

0.135

41.8

58.2

1.104

0.942

1.028

0.162

0.076

0.086

46.9

53.1

C O C4H9 CH2

O CH O

CH2

C CH3 O CH

49

50

In the set of polyacrylates and polymethacrylates α2 grows first with the volume of the side substituent and then decreases. Decrease of the intensity of the effect of the dense packing of chains, apparently, depends upon steric hindrances. Hence, it follows from the above-said that the notions of porosity and packing density are inadequate. Porosity reflects almost always cavities greater than the molecular size, i.e. quite large ones. As for the packing density of macromolecules themselves, it may be judged by considering the non-porous part of the sample only. As noted above, application of positron annihilation methods is preferable for analyzing the microporous structure of polymers [3, 48, 110, 123, 134, 140, 155, 164, 187, 211]. With the help of these methods, qualitative and quantitative information about the characteristics of submicropores (2–15 Å) in polymers may be obtained. Let us discuss the results of studying annihilation of positrons in two polymers, which are good models of the limiting characteristics of the packing density of macromolecular chains. One of them is polyimide characterized by a highly regular, quasi-crystalline structure, and the second is poly(1-trimethylsilyl-1-propyne) (PTMSP) which, on the contrary, is characterized by a low coefficient of molecular packing. Consider structural changes in PTMSP, which appear during its long exposure at room temperature after synthesis. For comparison, we also display the data on annihilation of positrons for a series of other model polymers. The chemical structures of all above-mentioned systems are shown below. Poly(1-trimethylsilyl-1-propyne) CH3 C

C

Si

H3C

CH3

CH3 n

Polyisoprene CH2

C CH CH2 CH3

n

Polydimethylsiloxane CH3 O

Si CH3

n

Polystyrene CH2

CH

n Polytetraflouroethylene [—CF2—CF2—]n

51

Polyimide O

O

C

C

C

C

O

O

N

N

O n

Observation of the annihilation of positrons in PTMSP was performed with the help of a method of detection of the lifetime spectra of positrons (measurements were made by S.A. Tishin; data not published). Measurements were performed by a thermostabilized spectrometer, which realizes the traditional fast–slow scheme of detection, with a temporal photomultiplier selected and optimized due to an original method [111]. Processing of experimental spectra was performed with the help of wellknown software ‘Resolution’ and ‘Positron FIT’. Table 8 shows the results of separation of parameters of a long-living component at three-component decomposition of positron lifetime spectra for PTMSP, polyimide, polystyrene, polydimethylsiloxane and polytetrafluoroethylene. Clearly, PTMSP possesses an anomalous long lifetime for an ortho-positronium atom, to annihilation of which by a pick-off–decay the origin of a long-living component of the lifetime spectrum in polymers is bound [3, 48, 110, 123, 134, 140, 155, 164, 187, 211]. Hitherto, the maximal lifetime of the long-living component, τD, was observed in polydimethylsiloxane and teflon in solid polymers [123, 164]. Comparison with the results of measurements in model polymers (see Table 8) indicates that neither the presence of an unsaturated bond, nor the presence of a side group or silicon atom separately is the explanation of so high τD for PTMSP. Table 8 Parameters of the longest component of positron lifetime spectrum for a series of polymers and rated values of radius R and volume V of micropores R, Å V, Å3 E, eV Sample τD + 0.03, ns ID ± 0.25, % R0, Å PTMSP 5.78 38.4 6.76 5.10 416.5 0.41 Polytetrafluoroethylene 4.27 21.6 6.05 4.39 265.8 0.51 Polydimethylsiloxane 3.23 41.3 5.45 3.79 170.9 0.63 Polyimide 2.77 38.1 5.14 3.48 132.1 0.71 Polystyrene (atactic) 2.05 40.5 4.56 2.90 76.9 0.90

Two suggestions about the reasons of anomalous long average lifetime of positrons in PTMSP can be made. First, molecular structure of the repeat unit allows a supposition that a high concentration of bulky, low-mobile side groups creates a porous structure with the pore size of about Van-der-Waals volume of –Si≡C3H9 side fragment. Secondly, the size of pores may be associated with a long relaxation time of synthesized PTMSP at room temperature. It may be suggested that the formation and evolution of microcavities of a large size must depend on the motion of large segments of macromolecules or even structural fragments with a long period of regrouping. The lifetime of an ortho-positronium atom regarding the pick-off–annihilation allows estimation of the size of the microcavity in which it was localized before annihilation [140]. The calculation results are also shown in Table 8.

52

In line with the model [140], positronium is considered in a spherical pit surrounded by a layer of electrons, ∆R thick. For wave functions in spherical coordinates: (2ŒR0 )−1 / 2 ⋅ 1 ⋅ sin (Œr / R0 ) in the pit; r %( r ) =  (II.35)  0 outside the pit. The probability of positronium existence outside the limits of density will be:  2 ŒR  R 1 , W ( R) = 1 − + sin  (II.36) R0 2Œ  R0 

where R = R0 – ∆R. Suggesting that the rate of ortho-positronium annihilation inside the electron layer equals 0.5 ns–1, the decomposition rate averaged over spins will be:

λD = 1/τD = 2W(R)

(II.37)

with the constant ∆R = 1.66 Å, selected empirically for solids. Let us consider the results of measurements of PTMSP films porous structure because of their aging. Long-term relaxation of PTMSP films was investigated with the help of measuring positron lifetime spectra. As Table 9 and Figure 9 indicate displaying a series of characteristics of time spectrum decomposition into three components and the calculated radius of micropores R, and durability of samples aging, lifetime of the long-living component decreases with growth of PTMSP exposure time at room temperature. In practice, the intensity of the long-living component does not depend on the relaxation time. Table 9 Long-term relaxation of PTMSP from the data of measurement of the longest component parameters of positron lifetime spectrum (τn is lifetime of intermediate component) Aging time, days RD ± 0.25, % τD ± 0.03, ns τn ± 0.080, ns 13 5.78 38.40 0.687 17 5.68 37.53 0.607 24 5.72 38.09 0.678 83 5.40 38.08 0.507 210 5.09 37.91 0.453

Figure 9. Dependence of sizes R of the positron-sensitive microcavity on time of exposure tc at 25°C for PTMSP

53

The result observed is connected with slow structural relaxation but not the ‘aging’ (if by the ‘aging’ occurrence of the main chain fission is meant), because the latter process is usually accompanied by changes in intensity ID (results of observing long-term aging of polyethylene by the method of positron lifetime variation may be displayed as an example, although ‘aging’ in polymers is a very specific process). Taking into account the relation between τD and the radius of micropores in polymers [140], it must be concluded that in long-term relaxation of PTMSP sizes of pores decrease (see Figure 9) and, probably, the mobility of macromolecular chains reduces due to free volume decrease. As follows from the constancy of ID, the concentration of positronium traps is independent of the exposure time in the studied time interval. Let us now discuss the results of investigation of positron annihilation in polyimide. As the measurements have shown [48], annihilation of positrons in polyimide is significantly different from the one usually observed in most polymers. The annihilation spectrum in polymers is usually characterized by the presence of three or four components with average lifetimes from 100 ps to 4 ns [54, 164, 187]. However, the different structure of the spectrum is observed for polyimide. It displays a single, short-term, component with τ0 = 0.388 ns (Figure 10). Time distribution is approximated well by a single decay line, the tangent of which determines the average lifetime.

Figure 10. Positron lifetime spectrum τ of the starting polyimide film (here N is the number of readings in a channel)

The value of lifetime and the spectrum structure allow a supposition that annihilation in polyimide proceeds from the positron state without forming a positronium atom as it is typical of metals and semiconductors with high mobility of electrons and a regular crystalline structure. In this meaning, polyimide forms an electron structure unique for polymers, characterized by high values and high homogeneity degree of the density function for electrons.

54

Figure 11. Lifetimes τ and intensities of components (%) in the spectra of the original sample (I) and deformed samples of polyimide after recovery lasting for 1 (II) and 24 (III) hrs. Table 10 Sample Initial Deformed Deformed

Annihilation characteristics of polyimide film Recovery τ0, ps τ1, ps τ2, ps lasting, hr 385±5    1 294±30 440±17  24 361±10 531±30 

I2, %  59±5 9±2

Count rate, k⋅10–9, s  0.60±0.15 0.12±0.05

In relation to interaction with positrons, the microstructure of the initial (undistorted) polyimide film possesses no defects. However, time spectra change after deformation (Figure 11 and Table 10). Two components instead of a single one are observed in the deformed sample: with shorter and longer lifetimes. After recovery (resting) during 24 hours at room temperature, an increase of lifetimes of both components and reduction of intensity of longer-term ones are observed. The character of changes taking place allows a supposition that the submolecular structure of polyimide is rebuilt during deformation; intermolecular bonds break, and microdefect free volumes enough for positron localization – are formed. In this case, the value of the long-term component τ2 must reflect changes in the average size, and intensity I2 – concentration of these defects. Analogous changes in the spectra were also observed in annealing defects in metals and semiconductors. These changes are usually analyzed with the help of a positron entrapment model. This model is qualitatively good in reflecting changes in the time spectra observed in polyimide deformation. Reduction of the lifetime of the short component, bound to annihilation in the undistorted part of the polymer, depends on the high rate of capture in the deformed sample. After partial contraction during recovery, the concentration of defects decreases and lifetime τ2 approaches the characteristic one of the original polymer. Therewith, the intensity of the long-term component, I2, formed due to positron annihilation on defects, decreases, too. Growth of the lifetime τ2 may be explained by coagulation (consolidation of small defects into larger ones) during recovery or fast relaxation of small pores and, consequently, by growth of the average capture radius. As indicated in estimations, the concentration of microdefects after partial relaxation decreases more than 7-fold. Therewith, the free volume induced by deformation decreases by a factor of 4 [48]. The values obtained indicate that two processes proceed – fusion of microdefects and relaxation of the smallest ones, though, apparently, the intensity of the latter process is higher.

55

Hence the one-component spectrum is typical of the original polyimide film. In deformed samples, at least two components are observed in time spectra, which are bound to the positron annihilation from the free state and the one localized in micropores, formed at stretching. The lifetime increases and the intensity of the defect component decreases during relaxation. The results obtained with the help of the model of positron capture describe clearly the changes of time distributions observed and allow a supposition that the structure of the free volume during relaxation changes not only as a result of fast recombination of the smallest pores, but also because of their consolidation with the formation of long-term large-size microcavities. Basing on the analysis performed in ref. [48], the following model of positron annihilation and relaxation mechanism bound to it are suggested: before deformation all positrons, captured in small traps with the bond energy slightly higher that the heat energy, annihilate; after deformation, rather long (compared with the positron diffusion length) areas occur, in which the concentration of small traps (of the size ~10 nm) decreases significantly, loosened up areas with deep centers of positron capture are formed simultaneously in which the lifetime of positrons is longer; relaxation happens in the way that pores formed during deformation recombine and, moreover, increase when consolidate. Hence, measuring the lifetime of positrons, the data on changes in structure of the free volume occurring after polymeric film deformation may be obtained. However, interpretation of the information obtained requires a detailed study of the nature of components of a complex time spectrum of annihilation typical for a nonequilibrium state of polymer. No solution of this problem with the help of one of the positron methods was obtained [3, 110, 156]. That is why a complex study of positron annihilation was performed [49] in deformed polyimide with the help of measuring the lifetime of positrons and angular correlation of annihilation radiation. Two series of experiments are described in ref. [49]. In the first series, a polyimide film was stretched by 20%. Then, the film was set free and relaxed freely. Lifetime spectra for the freely relaxed film were measured every 1.5 hours. Parameters of angular distribution were determined every hour during the day. Table 11 Change of annihilation characteristics of polyimide film depending on duration of relaxation after deforming by 20% Lifetime Angular correlation Relaxation lasting I2±1.5, after deforming, h % FWMH± τavg±1, τ1±10, Γ1±0.07, Θρ±0.07, Iρ±1.5, ps ps mrad mrad % 0.05, mrad 0 365 201 74.3 10.44 10.49 7.14 28.2 1 360 176 73.6 10.77    5 368 208 77.2 10.60    24 362 205 73.0 10.48 10.64 7.14 34.7 240 364 200 74.1 10.43 10.72 6.95 32.3 Separated 368 220 76.3     Note. τavg, τ1 and I2 are characteristics of positron lifetime spectra; FWMH is the full width on the middle height of the full spectrum; Γ1 is FWMH of the first Gaussian; Θρ and Iρ are characteristics of the parabolic component of the angular correlation spectrum.

In the second series of experiments, stress relaxation at deformation ε 0 = 20% was studied. The characteristics of angular distributions were determined for films with fixed ends. Measurements were performed with the help of a device that performs deformation of samples directly in the measurement chamber. Stress

56

relaxation curves (dependences of stress σ on time τ) and recovery curves (dependences of deformation ε on time τ) were taken simultaneously. The values of the positron lifetime obtained from spectra are shown in Table 11 and Figure 12. Similar to the above-described results of two-component analysis, changes of annihilation characteristics, which then relaxed gradually to those typical of the initial polyimide sample, were observed in the structure of the time spectrum, approximated by three components, after deformation.

Figure 12. Positron lifetime spectrum as a function of relaxation time for freely relaxing polyimide films (for designation see Table 11).

Three components were separated: the lifetime of the first short-term components (170–220 ps) significantly depend on relaxation time; as displayed by investigations [49], the lifetime of the second one (388±10 ps) is independent of or weakly depends on the sample state. However, significant changes in the intensity of this component are observed. The characteristics of the third component have not changed during the experiment. In the work cited, experiments on measuring the angular correlation were performed (alongside the measurement of the positron lifetime). Making no detailed analysis of the results of these measurements, note that in experiments with fixed ends (under stress relaxation conditions) the free volume significantly increases after deformation, and its further slow relaxation is displayed well, happened at the sacrifice of a decrease of micropore concentration. In most cases, changes of macro- and microparameters of the polyimide film during stress relaxation and recovery after deformation were indicated by the method of positron diagnostics. Non-monotonous changes in the characteristics of positron lifetime spectra and angular distributions of annihilation photons during recovery were observed. Two ranges of changes in positron-sensitive properties of polyimide,

57

associated with ‘fast’ and ‘slow’ relaxation processes, were separated, and differences in the type of relaxation of the polymer microporous structure depending upon the condition of deformation and ‘rest’ were observed. The effects observed are stipulated by formation of areas of the local ‘defrosting’ of molecular mobility. All these experimental facts indicate that the microporous structure of the polymer is rearranged during stress relaxation; this is expressed by the redistribution of the sizes of micropores and their merging. Hence the method of positron annihilation allows not only estimation of the microporous structure of polymers, but also following its change under mechanical loading.

Chapter III. Temperature coefficient of volumetric expansion

The thermal expansion of solids is a consequence of anharmonicity of thermal oscillations of the substance particles. The thermal expansion of polymers has a number of peculiarities connected with various physical transitions occurring in the polymer as temperature is increased. To estimate experimentally the temperature coefficient of volumetric expansion, the temperature dependence of the specific volume of the polymer is determined. Schematically, this dependence is depicted in Figure 13.

Figure 13. Schematic representation of the dependence of specific volume V on temperature T (dilatometric curve) (rate of heating q1 > q2 > q3 > q4).

This dependence as a broken line is typical of many polymers near the glass transition temperature, Tg. At temperatures below the glass transition temperature this dependence is flatter than in the range of temperatures above it. Hence if T < Tg, the temperature coefficient of volumetric expansion (which represents a tangent of dilatometric dependence) is smaller than when T > Tg. In the first case, the temperature coefficient of volumetric expansion is designated as αG, and in the second one – αL. In this connection, the specific volume of the polymeric substance may be calculated by equations V = Vg[1 + αG(T – Tg)], V = Vg[1 + αL(T – Tg)],

(T < Tg); (T > Tg),

(III.1) (III.2)

where Vg is the specific volume of the polymer at the glass transition temperature; T is temperature. The dilatometric dependence shown in Figure 13 is rather simplified. In fact, we are dealing not with a broken line, but with a curve called dilatometric. The curvature of dilatometric dependences may be ambiguous. First of all, transition from the glassy state into the rubbery one is characterized not by an abrupt fracture on the dilatometric curve but by a smooth transition of one branch of the dilatometric curve into another. This is clearly seen from Figure 14 which displays an experimental dilatometric curve for polystyrene, determined near the glass transition temperature (105°C) of this polymer. The glass transition temperature itself is determined by intersection of tangents of two branches of the dilatometric curve. Secondly, if the

59

dilatometric curve is determined in a wide temperature range, we may ensure that in the area below the glass transition temperature it is not linear all the way, but indicates a clear curvature.

Figure 14. Dependence of specific volume V on temperature T for polystyrene.

Figure 15. Dependence of the temperature coefficient of volumetric expansion αG on temperature T for poly(methyl methacrylate).

According to this curve, with decreasing temperature the coefficient of volumetric (or linear) expansion is not the constant of the polymeric substance. Figure 15 displays the experimental temperature dependence of the coefficient of linear expansion for poly(methyl methacrylate), determined in a wide range of temperatures [154]. It is easy to verify that the value of αG decreases with temperature, i.e. the dilatometric dependence at T < Tg is not linear. In this case, to calculate the volume of the polymeric substance, it is not enough to use equation (37), but it is necessary to turn to a more general relation 1 ∂V αG = ⋅ , (III.3) V0 ∂T where αG is the thermal coefficient of volumetric expansion depending on temperature; V0 is the specific volume of the polymer near the absolute zero. Knowing this dependence, the specific volume of a polymeric substance at any temperature T may be calculated by equation (III.3). Dilatometric dependences are not only of practical meaning as the ones allowing searching of the glass transition temperature of polymers. They are also theoretically valuable. First of all, slope changes not associated with the polymeric substance transition from the glassy into the rubbery state are observed at some temperatures below the glass transition temperature. These transitions occur at temperatures below the glass transition temperature (e.g. inside the glassy state area)

60

and are of a somewhat different nature as compared with the main transition. Hence, temperatures of these transitions may be determined by the dilatometric curve. Secondly, according to the concept developed by Boyer and Simha, and formulated by Flory, the transition from the glassy state into the rubbery one takes place at the temperature at which part of the free volume in the polymer becomes the same and equal to fc = 0.025. Due to this concept, the following relation holds [205]: (αL – αG)Tg = 0.113.

(III.4)

This relation is a rough approximation, because it takes into account no curvature of the dilatometric dependence. Taking into account this curvature enables Simha [154] to refine the free volume concept and to determine it with higher accuracy. However, even in this case, the concept is just a rough approximation, although it allows a description of the glassy state–rubbery state transition. Table 12 displays experimental values of αG for a series of glassy polymers. The lower the glass transition temperature, the higher is the coefficient of thermal expansion. This correlates with the Simha–Boyer concept and equation (III.4). Hence, heat-resistant polymers displaying high glass transition temperatures possess lower αG, and traditional polymers softening at low temperature display higher coefficients of thermal expansion which, as a consequence, depend on the chemical structure of the polymer. Table 12 Calculated αG,calc and experimental αG,exp values of thermal coefficients of volumetric expansion and the glass transition temperature Tg for a series of glassy polymers Tg, K Polymer αG,exp⋅104, K–1 αG,calc⋅104, K–1 Poly(methyl methacrylate) 378 2.69 2.55 Poly(ethylene methacrylate) 338 2.99 2.84 Poly-n-propyl methacrylate 308 3.19 3.05 Poly-n-butyl methacrylate 293 3.34 3.22 Poly(methyl acrylate) 293 3.03 2.80 Polystyrene 378 2.50; 2.83 2.50 Polycarbonate based on bisphenol A 423 — 2.27

In ref. [35], the problems discussed above had been studied in detail for polymer networks based on epoxy resins. Cured bulky samples were obtained using epoxy resin ED-20, methyltetrahydrophthalic anhydride as a curing agent, and azelaic acid (to elongate linear fragments between network cross-linked points), and oleic acid (to obtain ‘suspended’ chains). It was found that the coefficients of molecular packing for cured networks based on epoxy resins are higher than those for linear polymers. This is typical of systems containing no ‘dangled’ chains (branches), i.e. when azelaic acid is used as a co-curing agent. At room temperature, the coefficient of molecular packing for them is almost independent of the network composition, and its average value is kavg = 0.694, which is somewhat higher than the average value kavg = 0.681 for linear glassy polymers. Therewith, the average coefficient of molecular packing of cured networks at their glass transition temperature is kg = 0.681, which is also greater than kg = 0.667, typical of linear polymers. According to the data of these measurements (αL – αG)Tg = 0.106.

(III.5)

61

Calculations and measurements have also indicated that for cured epoxy resins the fraction of the free volume, formed due to thermal expansion, is 0.078. This value is calculated from the formula f =

Vg − V0 Vg

= α G Tg ,

(III.6)

where Vg and V0 are specific volumes of the polymer at the glass transition temperature Tg and near the absolute zero, respectively. The same value is determined from the relation k f = 0 − 1, kg

(III.7)

where kg and k0 are the coefficients of molecular packing at the glass transition temperature Tg and near the absolute zero, respectively. For linear polymers, the value of f equals 0.096. As mentioned above, the thermal expansion of substances is a consequence of anharmonicity of thermal oscillations of the substance particles. On this basis, it can be suggested that the coefficient of thermal expansion consists of contributions of various oscillations of these particles. Above all, the role of a weak dispersion interaction must be taken into account. It should be noted that every atom is characterized by self-dispersion interaction, which depends on both the type of the atom and its surrounding atoms, i.e. on the atoms chemically bonded with it. In the calculation scheme [28, 43], to calculate the coefficient of thermal expansion, it was suggested that contributions of each atom are proportional to the part of the Van-der-Waals volume ∆Vi of it in the total Van-der-Waals volume ∑ ∆Vi of the repeat unit of the polymer. i

Moreover, it is essential to take into account the influence of strong intermolecular interactions, which appear in the presence of various polar groups in C O, the repeat unit of polymer. To them are corresponded, first of all, ester O

nitrile –C≡N groups, and various halogens which substitute hydrogen atoms (–CHCl–, –CHF–, –CF3), etc. These groups cause dipole–dipole interactions of various types. The most significant influence is also caused by polar groups, which lead to occurrence of hydrogen bonds. They are, for example, amide NH C , urethane

NH C O

, hydroxylic –OH, acidic

O C OH groups.

O O Clearly, the energy of hydrogen bonds, similar to the dipole–dipole interaction, will depend on the chemical structure of polar groups. Seemingly, their contribution to the coefficient of thermal expansion must be different. However, if different parameters to characterize the energy of strong intermolecular interaction are introduced for each type of the dipole–dipole interaction and hydrogen bonds, this will not only make the calculation scheme more complicated, but will also make impossible calculations of the coefficient of thermal expansion for polymers

62

containing new polar groups. That is why discussion in works [28, 43] was limited by the first approximation, according to which contribution of any dipole–dipole interaction is defined by the same parameter βd, independent of the chemical structure of the polar group. However, since the Van-der-Waals volume of each polar group is different, it will be seen in discussion below that the contribution of each polar group to the coefficient of thermal expansion is also different. Concerning hydrogen bonds, we may also confine to a single parameter βh, which characterizes the energy of hydrogen bonds. The exception is only the class of polyamides which have a specific behavior and require several parameters βh characterizing the energy of hydrogen bonds. Consequently, a relation to calculate the thermal coefficient of volumetric expansion was obtained for polymers existing in the glassy state as follows:

∑α i ∆Vi + ∑ β j αG =

i

∑ ∆Vi

j

,

(III.8)

i

where αi are partial coefficients of thermal volumetric expansion, stipulated by weak dispersion interaction of the i-th atom with the neighbor atoms; ∆Vi is the Van-derWaals volume of the i-th atom; βj are parameters characterizing contribution of each type of specific intermolecular interaction (dipole–dipole, hydrogen bonds) to the coefficient of thermal expansion. Let us consider the physical meaning of parameters αi which characterize the weak dispersion interaction. It is well known that the coefficient of volumetric expansion is described by the relation

αi =

3 Rδ i

γ i2 r0, i

,

(III.9)

where R is the universal gas constant; δi is the anharmonicity coefficient,

δi = 1

2

∂ 3ϕ ∂r 3 r 0,i

; ϕ is the potential of the i-th atom interaction with the adjacent ones; γi

is the harmonic force constant, γ i =

∂ 2ϕ ∂r 2 r 0,i

; r0,i is the distance between the

considered i-th atom and adjacent atoms. To estimate the coefficient δi and the harmonic force constant γi the Lennard– Jones potential can be used

ϕ(r) = D[(r0/r)12 – 2(r0/r)6].

(III.10)

In equation (III.10), the value D characterizes bond energy, and r0 is the equilibrium distance between atoms, unbonded chemically, but participating in the intermolecular interaction. Then, it may be written that

63

γi =

72 Di r02,i

; δi =

756 Di r03,i

; αi =

7 R 7 R . ; Di = 16 Di 16 α i

(III.11)

Table 13 Values of constants αi, βj, ai and bj for various atoms and types of intermolecular interaction Atom or type of intermolecular ai⋅103, bj⋅103, Symbol Symbol αi interaction K–1 Å3K–1 Carbon 0.00 aC 0.02 — αC Hydrogen 19.98 — 1.92 aH αH Oxygen in the backbone 22.95 — 2.21 aO,m αO,m Oxygen in the side group aO,s — –O– 16.00 1.54 αO,s — =O 0.77 8.00 aO,s′ αO,s′ Nitrogen in the backbone 8.62 — 0.83 aN,m αN,m Nitrogen in the side group 6.35 — 0.61 aN,s αN,s Chlorine 4.01 — 0.39 aCl αCl Fluorine 6.90 — 0.66 aF αF Sulfur in the backbone 7.50 — 0.72 aS,m αS,m Sulfur in the side group 2.04 — 0.20 aS,s αS,s Silicon in the backbone 8.30 — 0.80 aSi,m αSi,m Silicon in the side group 0.20 — 0.00 aSi,s αSi,s Boron in carboranes –10.00 — –0.96 aB αB Dipole–dipole interaction* — –55.4 –5.31 bd βd Hydrogen bond** — –139.6 –13.44 bh βh Type of substitution of benzene rings*** bp –25.6 –2.41 — paraβp 16.0 1.54 — methabm βm 16.0 1.54 — orthobo βo Coefficient for polydienes 12.96 — 135.0 b≠ β≠ Aliphatic cycle — –120.0 –11.52 bcycle βcycle * Parameters βd and bd are introduced for each branching in the main or side chain; they are also introduced in the presence of a polar group of any type; if aliphatic polymers possess two CH3-groups or two atoms of F or Cl at carbon atom, then constant bd is neglected. For fragments - CH – (bd = 51) - CH – (bd = 32) - CH – (bd = 51) - CH - (bd = 32) | | | | C–OO–CC–SS–C|| || || || O O O O the additional constant are introduced shown in brackets. ** Constant bh is introduced in the presence of a hydrogen bond of any type for all polymers, except polyamides; for the latter, constants βh and bh are shown in Table 18. *** Constants βp, βm, βo and bp, bm, bo are introduced at substitution of aromatic rings in para-, methaand ortho-positions, respectively; the number of these constants equals to the number of substituted rings. In the case of

structure, 2βp and 2bp are introduced.

The expressions (III.11) allow estimation of the energy of the dispersion interaction for each atom. These values are shown in Table 13. They indicate that values Di really correspond to the energies of the intermolecular interaction, but not to energies of the chemical bond. However, if these values are estimated by other methods [66] (designate them as Di0), it is found that values Di differ several times from Di0. This happens because every atom in any low-molecular substance or

64

polymer is in intermolecular interaction not with a single atom, but with several atoms, with which it coordinates. Then, it should be written: Di = zDi0,

(III.12)

where z is the coordination number. In this case, the total average energy of the weak dispersion interaction is determined from the relation z, where

< D0 > =

∑ ∆Vi i

(

∑1 D0,i ∆Vi

).

(III.13)

i

For copolymers, equation (III.8) gives:     α1 ∑ α i ∆Vi + ∑ β j  + α 2  ∑ α i ∆Vi + ∑ β j  + ... +     j j  i 1  i 2 → αG =     α1 ∑ ∆Vi  + α 2  ∑ ∆Vi  + ... +      i 1  i 2   + α n  ∑ α i ∆Vi + ∑ β j    j  i n → ,   + α n  ∑ ∆Vi     i n

(III.14)

where α1, α2, …, αn are molar parts of the components 1, 2, …, n (do not mix these values up with the values αi present in brackets in the expressions);        α ∆V + β  ,  α ∆V + β  , …,  α ∆V + β  represent the ∑ ∑ ∑ ∑ ∑ ∑ i i j i i j i i j       j j j  i 1  i 2  i n   selection of constants αi, βj for the components 1, 2, …, n of copolymer;  ∑ ∆Vi  ,    i 1      ∑ ∆Vi  , …,  ∑ ∆Vi  are Van-der-Waals volumes of the repeat units of these      i n  i 2 components. In reduced form, the relation (III.14) can be written as follows:

65

k =n



k =1

 i



∑ α k  ∑α i ∆Vi + ∑ β j 

αG =

k

j

k =n

  ∑ α k  ∑ ∆Vi  k =1  i k

.

(III.15)

If it is advisable to express the thermal coefficient of volumetric expansion αG of the copolymer via analogous coefficients αG,1, αG,2, …, αG,n for appropriate homopolymers, the substitution of (III.8) into (III.14) gives:       α1α G,1 ∑ ∆Vi  + α 2α G,2  ∑ ∆Vi  + ... + α nα G, n  ∑ ∆Vi         i 1  i 2  i n , αG =             α1 ∑ ∆Vi + α 2 ∑ ∆Vi + ... + α n ∑ ∆Vi        i 1  i 2  i n

(III.16)

where α1, α2, …, αn are the molar parts of the components 1, 2, …, n of the copolymer. In reduced form, the relation (III.16) becomes

αG =

k =n





k =1 k =n

 i

k

∑ α kα G, k  ∑ ∆Vi    ∑ α k  ∑ ∆Vi  k =1  i k

.

(III.17)

It should be noted that the dependence of αG on the copolymer composition α is not linear but has a curvature dependent on the energy of intermolecular interaction of components and their Van-der-Waals volume (Figure 16).

Figure 16. Schematic representation of the dependence of the thermal coefficient of volumetric expansion αG on the composition of copolymer α .

The calculated values of the coefficients of thermal expansion of a series of polymers in the glassy state are shown in Table 12. Generally, it should be taken into

66

account that, despite the seeming simplicity of this physical characteristic, its experimental determination is rather difficult. That is the reason why greatly different values of αG for the same polymer can be found in the literature. All calculated and experimental values of αG shown in Table 12 characterize a part of the dilatometric straight line which directly adjoins the glass transition temperature. With regard to the thermal coefficient of volumetric expansion αL in the rubbery state, as mentioned above, it can be determined with the help of relation (III.4), although significant errors are possible in this case. The monograph [214] by Van-Krevelen indicates another relation for estimating αL:

αL = εl/VM = εlρ/M,

(III.18)

where εl = 10–3VM, VM is the molar volume (per repeat unit of a polymer); VM = N A ∑ ∆Vi , where NA is the Avogadro number, ∑ ∆Vi is the Van-der-Waals i

i

volume of the repeat unit; M is the molecular mass of the repeat unit; ρ is the polymer density. Taking into account that according to the data by Van-Krevelen VM = 1.60VW in the rubbery state, it follows from the relation (III.18) that the coefficient of thermal volumetric expansion for polymers in the rubbery state is the same and equals

αL ≈ 6.3⋅10–4 K–1.

Chapter IV. Glass transition temperature of polymers

IV.1. Thermomechanical and other methods of evaluation of the glass transition temperature of polymers The thermomechanical method of studying polymers is one of the most widespread methods of experimental determination of glass transition temperature Tg. This method has been developed by V.A. Kargin and T.I. Sogolova. The essence of the method is the following. A polymeric substance is subjected to a permanent or variable load. Therewith, its deformation at each temperature and selected time of the load effect is recorded. It is known that if a polymeric sample is subjected to a constant stress, creep develops in it. Graphically, this looks as depicted in Figure 17. To perform these experiments under comparable conditions, deformation must be measured during a strictly constant time of observation, which may be any but advisable so that reading of deformation would performed on the second, flattened part of the creep curve. Having performed such an experiment at different temperature, a temperature dependence of deformation may be plotted which, in the general case, will be the same as depicted in Figure 18. Before we proceed to consideration of features of the graphic in Figure 18, note that an analogous curve may also be obtained in the case, when the sample is subjected to effect of a low constant force, and temperature rises permanently with time. Such a view of thermomechanical tests is most widespread at present, with temperature usually increasing in accordance with a linear law T = T0 + αt,

(IV.1)

where T0 is the temperature of the onset of the experiment; t is time; α is the rate of temperature growth with time.

Figure 17. Schematic representation of creep (dependence of deformation ε on time t at constant stress).

Usually, the standard rate of temperature growth is from 1.5 to 4 deg/min. This method of thermomechanical investigation is more suitable for the apparatus, although it gives less information than the first one. This concerns especially the cases when fine structural transformations occurring in the sample at heating are studied by the thermomechanical method. We will return to this question below, and let us now consider the thermomechanical curve of the ideal polymer displaying no structural

68

transformations at heating. Such a curve is shown in Figure 18, and it is obtained in the case when an experiment starts from rather low temperatures.

Figure 18. Schematic representation of the thermomechanical curve (dependence of deformation ε on temperature T) on which I is the glassy state of polymer, II is the rubbery state of polymer and III is the viscous flow state of polymer.

In this temperature range, deformation of the sample is small and increases insignificantly with temperature. When the temperature definite for each polymer is reached, deformation begins growing rapidly. If the load is low, increase of deformation proceeds not infinitely but ends quite fast. A plateau occurs on the curve, which is called ‘the rubber-like plateau’. The extent of this plateau on the temperatre axis may be quite long and, as indicated below, it depends on the molecular mass of the polymer. Further heating induces again a sharp increase of deformation, and the polymer sample spreads. The thermomechanical curve depicted in Figure 18 clearly divides the temperature area of the test into three intervals. In the first of them, the polymer is in the solid, glassy state (if it is amorphous). In this state, deformation is rather low and grows only slowly with temperature: the polymer behaves itself almost like lowmolecular substances. The first sharp increase on the thermomechanical curve is connected with the polymer transition from the solid glassy state into the rubbery state. This state is characterized by acquiring rubbery properties by the polymer, i.e. it possesses the ability to develop high reversible deformations under low stress. This state is typical only for polymers, and it is not displayed in the case of low-molecular weight solids. At further heating, a sharp increase of deformation is connected with occurrence of the viscous flow state, for which viscous flowing of the polymeric substance is typical. Appropriate temperatures of transitions from the glassy state to the rubbery state and from the rubbery state into the viscous flow state have received the names ‘the glass transition temperature’ and ‘the flow temperature’. Before we discuss the nature of each of the physical states of polymers, note that depending on the chemical structure of the polymer, i.e. on flexibility or rigidity of its macromolecules, the glass transition temperature may obtain different values. At the present time, there are polymers which display the glass transition temperature from –123 to 600°C. An example of the first of them is polydimethylsiloxane with the following formula: CH3 Si CH3

O n

69

An example of the second one is polynaphthoylenebenzimidazole of the following chemical structure: N

...

C

C N

N C

C

... N O Synthesis of polymers with the lowest possible glass transition temperatures is of great importance for obtaining polymers resistant to cold. Synthesis of polymers with the highest possible glass transition temperature is of the same importance for obtaining solid heat-resistant polymers, capable of service at increased temperatures and stresses. Many polymers, applied at present, possess glass transition temperatures lying inside this broad interval. Shown in Table 14 are some of them and, considering these data, the influence of the chemical structure of polymers on their glass transition temperature could be easily imagined. It should be noted that transition from the glassy state into the rubbery state appears not at a definitely stated temperature but in some temperature range which may be several tens of degrees wide. This is quite clear because the transition considered is not the phase transition (such as melting, for example) but represents a physical transition from one phase to another, keeping one of the phases. In the case of amorphous glassy substances, this phase is liquid with no regard to the aggregate state of the polymeric substance – glassy (solid), rubbery or viscous flow state. Fundamentally, every polymer, if its molecular mass is quite high, may exist in one of the three physical states. Rubbers differ from plastics by the only thing that the glass transition temperature of polymers, on which they are based, is below room temperature, and for plastics – above room temperature. However, if a rubber is cooled down to temperatures below the glass transition point (for example, to –80°C), then a rubber-like substance becomes solid and behaves itself similar to usual glassy polymers. Vice versa, if a solid glassy polymer (for example, poly(methyl-methacrylate)) is heated up to a temperature above its glass transition point (above 100°C), it becomes a rubber-like material and behaves itself as usual rubber at room temperature. Hence, the subdivision of polymeric substances into rubber-like and solid glassy ones is rather conditional and has been formed historically. Table 14 Glass transition temperature Tg of representatives of various series of polymers Name Structural formula Tg, K 1 2 3 1,4-polybutadiene 170 –CH2–CH=CH–CH2– 150 Polydimethylsiloxane

CH3 Si

O

CH3 202

1,4-polyisoprene

CH2

CH C

CH2

CH3

70

1 Polyisobutylene

2

CH3 CH2

3 199

C CH3

Polyvinylmethyl ether

CH2

258

CH O CH3

Polyvinylethyl ether

CH2

248

CH O C2H5

298

Polyvinylacetate

CH2

CH O C

CH3

O Polyvinylchloride

CH2

CH

355

Cl Poly(methyl methacrylate)

CH3 CH2

378

C C O CH3 O

Poly(ethyl methacrylate)

CH3 CH2

338

C C O C2H5 O

Poly(hexyl methacrylate)

CH3 CH2

268

C C O C6H13 O

Poly(methyl acrylate)

CH2

CH

293

C O CH3 Poly(butyl acrylate)

CH2

O CH

233

C O C4H9 Polystyrene

CH2

O CH

378

71

1 Poly(vinyl alcohol)

2

CH2

3 358

CH OH

353

Poly(ethylene terephthalate)

Polyacrylonitrile

C

C O

O

O

CH2

(CH2)2

O 418

CH C N

Polyacrylamide

CH2

426

CH C NH2 O

Polycarbonate based on bisphenol A

422

CH3 O

C

O C

CH3 Polyester based on sebacic acid and phenolphthalein

O 368

C

(CH2)8

O

O

C O C

O

O C Polyester based on isophthalic acid and phenolphthalein

O 543

C

O

C O

O

C

O

O C Polyamide based on sebacic acid and aniline-phthalein

O 451

C

(CH2)8

O

C NH

NH C

O

O C Polyimide based on pyromellitic dianhydride and aniline-phthalein

CO

783

CO N

N CO

O

C

CO O C

O

72

A polymer cannot exist in the gaseous state, because it is much easier to disrupt a chains of macromolecules than to overcome total forces of intermolecular interaction: polymer chains are extremely long and possess numerous intermolecular bonds between neighboring chains; that is why it is impossible to transfer the polymer to the gaseous state without decomposing it. It was mentioned above that in each of three physical states the polymer may exist only if its molecular mass is quite large. Then, at heating up a solid plastic, it transforms consequently from the solid glassy state to the rubbery state, and then — to the viscous flow state (Figure 18). If the molecular mass of the polymer is low, it is transferred from the glassy state directly to the viscous flow state, and the thermomechanical curve has the form schematically represented in Figure 19. Such a curve is also typical for low-molecular weight substances. Hence, the rubbery state is typical for polymers only and is not displayed by low-molecular weight substances.

Figure 19. Schematic representation of thermomechanical curve for a polymer with small molecular mass on which I is the glassy state of polymer and II is the viscous flow state of polymer.

Figure 20. Schematic representation of a series of thermomechanical curves for polymers having different molecular mass M1 < M2 < M3 < M4 < M5 < M6 .

Now it is necessary to determine the molecular mass at which the polymer begins displaying the rubbery state. To accomplish this, let us consider a series of thermomechanical curves of polymer-homologues with various molecular masses. Figure 20 represents schematically such a series; it is clearly seen that with growth of the molecular mass the glass transition temperature increases at first and then practically stops changing. The molecular mass, at which this change stops, is the segment molecular mass. From this molecular mass, the polymer begins indicating the

73

rubbery state. This is quite clear, because the segment is that part of a macromolecule the ends of which are able to slide independently. Consequently, if a macromolecule is longer than the segment length, thermal motion may be performed in its separate places only, not touching the macromolecule as a whole. This causes typical rubbery properties, whereas high reversible deformations without significant mechanical stresses are typical for the polymer. This is the rubbery state. Clearly, if the molecular mass of the polymer exceeds the segment value, its further increase cannot cause growth of the glass transition temperature, because motion of segments as separate parts of macromolecules is not displayed yet. On the contrary, the temperature of polymer transition to the viscous flow state grows permanently with molecular mass, because flow is nothing but slide of separate molecules relative to each other on the whole. It is clear that the longer macromolecule is, the greater is the heat energy required for moving macromolecules relative to each other, i.e. to induce flow. That is why the temperature of transition into the viscous flow state increases permanently with molecular mass. Therefore, it is absolutely clear that the value of the mechanical segment can be determined with the help of the thermomechanical method. This value will be correspond to the molecular mass at which the rubbery state occurs, and exceeding of which may not increase of the glass transition temperature. Figure 21 represents the dependence of the glass transition temperature on molecular mass Mp for polystyrene. This dependence confirms the validity of the above discussion and is described well by some relations, the most widespread among which is the Flory equation Tg = Tg,∞ – α/M,

(IV.2)

where Tg,∞ is the glass transition temperature at molecular mass tending to infinity; α is a parameter; and the equation

β 1 1 = − , Tg Tg, ∞ M

(IV.3)

where β is a parameter.

Figure 21. Dependence of the glass transition temperature Tg on molecular mass Mp for polystyrene.

Let us now discuss experimental and calculation methods of determination of the mechanical segment value, i.e. molecular mass Ms, starting from which the

74

rubbery state occurs. As mentioned above, one of suitable methods of experimental determination of the mechanical segment value is the thermomechanical method. Considering again Figure 20, it may be said that the molecular mass of the segment determined by the thermomechanical method equals M3. The value of the segment depends on the chemical structure of the macromolecule, and the more rigid macromolecule is, the higher the value of its segment is. The lowest value of the segment is displayed by flexible macromolecules, which display quite free rotation of separate units relative to each other. Table 15 shows molecular masses of segments for macromolecules of various polymers. It is clearly seen from this Table that in dependence on the chemical structure of polymers, their macromolecules display absolutely different sizes of segments. The shortest segment is typical for polyisobutylene macromolecules, and the longest for polyarylate macromolecules1. The most rigid-chain polymers possess extremely large mechanical segments and, in many cases, the value of this segment equals the length of a macromolecule. In other words, no separate parts could be moved in such macromolecules, not touching the whole macromolecule. Since when heating such a polymer macromolecules of the polymer move relative to each other as a whole, the temperature of transition to the viscous flow state and the glass transition temperature coincide for it, because the fluidity of polymers by definition is sliding of separate molecules relative to each other. One more interesting feature is noteworthy, clearly seen in Table 15. Different polymers possessing, however, absolutely the same backbone and differing by side substituents only, display different segment lengths. At first glance, this contradicts the fact that the flexibility of macromolecules is not a consequence of their deflection, but the result of rotation of separate units relative to ordinary bonds, i.e. the bonds which link the backbone atoms (in the present case, they are carbon atoms in polyisobutylene, polyethylene, polystyrene, etc.). However, this contradiction is just apparent. Freedom (or restriction) of rotation of separate groups relative to each other depends not only on the macromolecule backbone, but also on type of its side substituents. The more bulky and polar the substituent is, all other factors being the same, rotation of separate units is restricted. Hence, we must consider not only backbone rigidity, but also kinetic rigidity associated with the restriction of rotation, occurring due to the presence of bulky side substituents. In this respect, polystyrene is typical; it has a phenyl ring as a side substituent in the repeat unit. Consequently, this polymer possesses a larger mechanical segment compared with the other polymers shown in Table 15. Now, it is necessary to relate the molecular mass of the segment with the parameters of the chemical structure of the polymer and with its typical temperatures – the glass transition temperature and the temperature of transition into the viscous flow state. However, first of all, we must agree on the method of determining these temperatures. If such a determination is performed thermomechanically, it is very important to choose a method of obtaining these temperatures from the thermomechanical curve. The theory of the thermomechanical method, developed by V.A. Kargin and G.L. Slonymskii, states that the glass transition temperature and the temperature of transition to the viscous flow state must be determined in the manner depicted in Figure 22. A value of deformation ε0 is chosen, plotted on the x-coordinate and in 1

Mechanical segment of macromolecules, the point of our discussion, must not be identified with the Kuhn segment, which characterizes flexibility of isolated chain and is determined from behavior of macromolecules in solution.

75

relation to the height of the rubbery plateau. A line parallel to the abscissa axis is then drawn and points of intersection of these lines with the thermomechanical curve give the required glass transition temperature to the viscous flow states. Hence, according to this definition, the glass transition temperature is the temperature at which deformation under the effect of a specific load develops by the value ε0. The temperature of transition to the viscous flow state is the temperature at which irreversible deformation (flow) changes by the same value ε0. The value ε0 may be chosen arbitrarily, but it must not be too high in order not to exceed the rubbery plateau height. In practice, a specific fraction of the rubbery plateau height is taken for the value ε0. Table 15 Values of molecular mass of a segment Ms for different polymers determined by the thermomechanical method Polymer Ms 1000–1200 Polyisobutylene

CH3 CH2

C CH3 12000

Polyvinylchloride

CH2

C Cl 30000–40000

Polystyrene

CH2

C

200 000

Poly(ether ketone) CH3 C

O

C

O

O

CH3

300 000

Polyarylate F-1

C O O

O C

C

O

O C

O

The Kargin–Slonymskii theory based on the consideration of deformation of a polymeric body model with the calculation of temperature change leads to the following relation:

76

lg M = lg M s +

(

)

B Tf − Tg , C + Tf − Tg

(

)

(IV.4)

where M is the molecular mass of the polymer; Ms is the molecular mass of the segment; Tf is the temperature of transition to the viscous flow state; Tg is the glass transition temperature; B and C are parameters of the polymer.

Figure 22. Evaluation of temperatures Tg and Tf according to the value ε0 chosen on the thermomechanical curve in accordance with Kargin–Slonymskii’s theory .

Equation (IV.4) links the molecular mass of the polymer with the molecular mass of the segment and the difference of the temperature of transition into the viscous flow state and the glass transition temperature (Tf – Tg). Not dwelling on the practical meaning of this equation yet, note that its parameters B and C have a clear physical meaning. The parameter B is determined from the relation: B = lg

σt 0 , η 0ε 0

(IV.5)

where σ is the constant stress applied to the sample during the thermomechanical test; t0 is loading time; ε0 is the deformation at which Tg and Tf values are determined (its meaning is clearly seen from Figure 22); η0 is the pre-exponential multiplicand in the Fulcher–Tammann equation which links the viscosity of the system with temperature. This equation has the form: A

η = η 0 e T −T0 ,

(IV.6)

where η is the viscosity of the system at temperature T expressed in Kelvin degrees; η0 is the pre-exponential multiplicand; A and T0 are parameters of the material. Hence, all the values composing the parameter B are determined. The constant C in equation (IV.4) is found from the relation C = 0.434

A . B

(IV.7)

77

It should be noted that the Fulcher–Tammann equation describes well the temperature region of the glassy state near the glass transition temperature. We are now interested in this very region. Let us now consider briefly the practical meaning of the Kargin–Slonymskii equation. If parameters Ms, B and C are known, this equation allows determination of the molecular mass of the polymer without its dissolving. This requires determination of the thermomechanical curve for this polymer, determination of the temperature of transition to the viscous flow state Tf and the glass transition temperature Tg and their substitution into the relation (IV.4). Therewith, parameters B and C need not be determined from equations (IV.5) and (IV.7). This only requires determination of three thermomechanical curves of the polymer with the known molecular masses M and solution of the system of three equations composed on the basis of the equation (IV.4) in which the unknown quantities are Ms, B and C. The molecular mass of any amount of polymer-homologues of the given series may then be determined. Table 16 Determination of polymerization degree Ns Ms [174]

M0

Ns [174]

Tg, K

∑ ∆Vi , cm /mol

Ns

Ns*

3460 15625 38073 5625 10000 24287 30246

28 56 104 54 68 86 100

124 279 366 104 147 282 302

195 199 378 171 200 298 378

20.60 41.30 66.00 36.48 48.90 47.73 58.05

128 165 366 136 175 259 351

112 144 320 119 153 227 307

3

Polymer Polyethylene Polyisobutylene Polystyrene Polybutadiene Polyisoprene Poly(vinyl acetate) Poly(methyl methacrylate)

i

However, it should be noted that basing only on the chemical structure of the polymer, the value Ms of it could not be calculated by equation (IV.4). The value of mechanical segment Ms of a macromolecule may be calculated on the basis of the chemical structure of the polymer. The following expression for calculation of Ms (or corresponding polymerization degree Ns = Ms/M0, where M0 is the molecular mass of the repeat unit) has been obtained in the ref. [96]: 1/ 3

  N s = const ⋅ Tg  N A ∑ ∆Vi    i  

.

(IV.8)

The value of Ns may be calculated on the basis of the chemical structure of the repeat unit with the help of atomic approaches, because the glass transition temperature Tg and the Van-der-Waals volume of the unit ∑ ∆Vi (NA is the i

Avogadro number) are estimated with their help. The constant in the formula (IV.8) may be expressed via parameters of the polymeric system and also from the experimental data for standard systems. The estimation gives const = 0.21, if calibration is performed by polystyrene according to data obtained in ref. [177], and const = 0.24 for polystyrene calibration according to refs. [174, 214]. Table 16 shows values of Ns obtained from the data of the ref. [174] and the formula (IV.8), with various constants (Ns with const = 0.24, and Ns* with const =

78

0.21). If const = 0.21 the difference in the values obtained from the ref. [174] does not exceed 10%. So far, we have discussed such physical characteristics of polymers as the glass transition temperature, the temperature of transition to the viscous flow state, the value of the macromolecule segment, which were determined experimentally with the help of the thermomechanical method of polymer investigation. Definite difficulties are met when determining temperature ranges of the solid (glassy), rubbery and viscous flow states of polymers by this method. This especially concerns new polymers. Let us consider generally the possible deformation behavior of polymers in thermomechanical tests. Recall that under these conditions the sample is loaded at increasing temperature. In most cases, the stress acts permanently during the experiment and temperature grows linearly. Fundamentally, the thermomechanical method of investigation allows immediate determination of temperature ranges of all three physical states of the polymer. However, the existence of one or another physical state and appropriate temperature range may be determined reliably only if it is known that the polymer studied behaves itself as a ‘classic’ one, i.e. gives the classic thermomechanical curve depicted in Figure 18. As it is observed in the considerations below, even if the form of the thermomechanical curve coincides with the classic one, in estimation of the properties of a new polymer it is not yet possible to determine unambiguously the temperature ranges of physical states and even of the states themselves. Before we consider this point, let us discuss some procedural questions. A question which appears most often is about the method of determination of transition points from the thermomechanical curve. As mentioned above, the following method is suitable: a definite strain ε0 is chosen, plotted from the temperature axis and from the rubbery plateau. The glass transition temperature and the temperature of transition to the viscous flow state will correspond to temperatures, at which one and the same value ε0 of rubbery and plastic strain occur, respectively. This method is most correct but suitable only when the thermodynamic curve is of the classic form with abrupt bends of the curves in transition temperature ranges. Then, the change of ε0 will not cause large shifts in determination of Tg and Tf. If deformation develops more smoothly, then the adjusted transition points Tg and Tf will be quite undefined. They will be sufficiently dependent on the value of ε0 (Figure 22). That is why another method is used in practice: values of Tg and Tf are determined by cross-points of tangents to two correspondent branches of the thermomechanical curve (Figure 23). In this case, values of Tg and Tf are less dependent on the shape of the thermodynamic curve, and this method is warranted for comparative estimation of polymers. Comparing thermomechanical curves of a series of polymers, the glass transition point may be defined as the temperature at which deformation is developed by the value of a specific percentage of the rubbery plateau height. Then, for each polymer this typical deformation will display different values, because heights of the rubbery plateau are also different. Selection of the determination method of Tg and Tf depends on the shape of the thermomechanical curve of polymers, and any of these methods may be chosen under comparative estimation of their properties. Of importance is just the comparison of several polymers to be performed always by the same method.

79

Figure 23. Evaluation of temperatures Tg and Tf by the points of intersection of tangents to two branches of thermomechanical curve.

Let us now describe deformation of polymers during thermomechanical tests. Very often, especially in the initial estimation, a polymer is tested as a powder. The powder may only be compressed, and as it is placed in a special cell, compression is close to the hydrostatic one. First of all, it should be taken into account that a powderlike polymer is not yet a polymeric material, but its basis only. As a result of the thermomechanical test, the substance disposed beyond the punch is characterized, which transmits the load to the sample. That is why we obtain the thermodynamic curve of not a polymeric material, but of a polymer powder. Since the powder may be not densely packed in the cell (not due to the fault of a scientist, but because of its properties), and in connection with probable existence of small amounts of solvent and by-products of the reaction, the shape of the thermomechanical curve may be significantly distorted. That is why estimation of physical states of the polymer on powder samples is of the most ‘rough’ type, especially in the case of new, unknown polymers. Even if the thermomechanical curve is of the classic shape (see Figure 18) and consists of three parts, the statement that the polymer displays all three physical states transiting from one into another at heating should be neglected. It should be taken into account that growth of deformation in a powder sample may be caused by secondary reasons. When the thermomechanical curve is determined, it is best to take a look on the last branch of it. If it exists in the temperature range in which thermal and thermooxidative degradation does not penetrate deep enough, flowing of polymers may be discussed. To be certain that development of a large deformation (up to 100% at compression) is caused by flow and not by deep degradation of the polymer, thermogravimetric analysis (TGA) must be performed (thermogravimetric curve must be obtained) simultaneously. This is most important in the case of heat-resistant polymers for which high strains start to develop in the temperature range from 600 to 800°C. So, this deformation, caused by deep thermal degradation of the polymer, may be erroneously assumed to be the flow. It should also be taken into account that besides degradation, network formation may also occur during thermomechanical tests. These two processes always coexist at polymer heating, but one of them proceeds with much higher rate and defines direction of the whole process. Structuring may be displayed in formation of cross-links between chains of the

80

polymer, cycle formation, etc. Consequently, the started flowing of polymer will be stopped, and a plateau appears on the thermomechanical curve, analogous by its shape to the plateau of the rubbery state for linear polymers. That is why the existence of the plateau (more correct, retarded deformation) is not the point to state that the polymer in the present temperature range is in the rubbery state. Ensuring that large deformation in the last region of the thermomechanical curve is cause by polymer flow, it should be attempted to transfer it into a bulky sample by any of existing methods (for example, by hot pressing). After that the sample is again thermomechanically tested. If the shape of the repeated thermomechanical curve is close to the initial one (obtained for the powder sample), chemical changes, possibly occurring during processing, are insufficient. Now we should only ensure that the plateau on the thermomechanical curve reflects the rubbery state, and is not caused by secondary reasons. One of the typical features of the rubbery deformation is its complete reversibility, as well as the ability to be expressed at very low loads (remind that the rubbery modulus is usually three-four decimal degrees lower than the modulus of elasticity for a glassy polymer). When a plateau is found on the thermomechanical curve, it must be checked if deformation is reversible in this temperature range. This is performed by regular loading of the sample, with this load exceeding the initial one, sometimes several times. If at application of additional load deformation increases sharply and recovers fast after its removal, a reversibility may be considered. This is reflected in Figure 24. If values of additional load and additional reversible deformation caused by it are known, the rubbery modulus may be easily calculated dividing the additional load by the deformation increment (Eel = ∆σ/∆ε). Ensuring that the elasticity modulus is of the smallest value (below ~1 MPa), it may be stated that the polymer in the plateau area is really in the rubbery state. For rigid-chain polymers, the elasticity modulus will be significantly higher (~10 MPa), and it is most important here to check reversibility of deformation in the plateau area. Therewith, it is often observed that a part of additional deformation is reversible (rubbery), and the rest of it is irreversible (plastic). In this case, the elasticity modulus is determined by division of ∆σ by the increment of the reversible part of deformation, and it is hardly possible to speak about the true rubbery state.

Figure 24. Checking of reversibility of deformation in the zone of the supposed rubbery-like plateau (see text)

81

Figure 25. A lever mechanism with a variable arm for ensuring constant tension in the course of creep process (scheme).

All the above-said is true when thermomechanical tests are also performed under the effect of elongating tension. Secondary effects at elongation may not distort the picture so significantly, as in the case of compression. As thermomechanical investigations are performed at low elongation and the classic thermomechanical curve is obtained, it must only be assured that the plateau reflects the true rubbery. Checking is performed in an analogous way: an additional load is applied, and reversibility of deformation is checked after its removal. If deformation is reversible, it is rubbery. In thermomechanical tests on elongation, the tension should be constant. Contrary to tests on compression, some difficulties are faced here. The cross-section of the sample decreases at deformation and, consequently, stress in it grows under the effect of constant force. To compensate the stress increment caused by developed deformation, the load is transmitted to the sample via a lever mechanism with a variable arm (Figure 25). The arm decreases as deformation is developed, and the load decreases consequently so that the stress in the sample remains constant. After making sure that the plateau on the thermomechanical curve reflects the rubbery state, it can be said with confidence transition to the rubbery state has taken place. The transition ‘point’ is determined by the above-described methods. Until now, we have discussed the thermomechanical curve of semi-crystalline polymers, which is of the classic form and displays three physical states and two transitional temperature areas between them. It should be taken into account that the thermomechanical curve of crystalline polymers may be of the analogous shape (see Figure 18). Besides thermomechanical investigations, X-ray analysis must be performed in order to confirm semi-crystallinity of the sample. Neglecting so far transitions in crystalline polymers, let us discuss separate cases of behavior of semicrystalline polymers under thermomechanical conditions of tests. It may be immediately noticed that classic thermomechanical curves are not always observed. Deviations of the thermomechanical curve shape from the classic one are caused by different reasons. For example, the thermomechanical curve of a semi-crystalline polymer is often of the shape shown in Figure 19. It is absolutely obvious that this polymer displays no viscous flow state. It is also obvious that

82

deformation of the sample (under compression) does not reach 100% and, consequently, it is burnt off at high temperatures, and the remaining part is distributed below the punch and prevents it from reaching the bottom. We should also carefully treat the temperature range, in which deformation grows sharply. If deformation near the onset of the horizontal plateau is completely reversible, it is of the rubbery type. However, it may not be stated without additional experiments that the polymer transits to the rubbery state, and the curve uplift points out the glass transition temperature. It is entirely probable that at this temperature chains of the polymer are intensively cross-linked, which therewith deforms, but subsequently loses meltability and solubility. That is why besides thermomechanical tests, thermogravimetric analysis is obligatory. Sometimes a polymer gives the classic thermomechanical curve, the last branch of which is in the area of very high temperatures (700–800°C). Clearly, development of large deformations in this area is caused not by viscous flow, but by intensive thermal degradation. In this case, it must not be said about the temperature of transition into the viscous flow state and the transition into the viscous flow state. It is specially obvious in the cases, when the thermomechanical curve is of the shape depicted in Figure 26. Distortion of the rubbery plateau (if it exists for the polymer tested) is caused by thermal degradation proceeding, excretion of gas products, etc.

Figure 26. Thermomechanical curve of polymer undergoing thermal degradation during the course of measurement (scheme).

Figure 27. Appearance of ‘negative’ deformation on the thermomechanical curve (see text).

Under compression, the thermomechanical curve may also be of the shape depicted in Figure 27. In this case, decrease and even appearance of ‘negative’ deformation is caused by increase of the sample height, as a result of which the punch transmitting the load to the sample is slightly lifted. This event may be caused by

83

elimination of residual solvent at heating up powder-like or bulky samples, excretion of gas products of degradation, etc. In such a case, determination of the true glass transition temperature and the temperature of transition into the viscous flow state is quite difficult. One of the reasons for the appearance of negative deformation may be the following. Preparing for thermomechanical tests, a polymer powder is pressed at room temperature, which is usually well below the glass transition area. Consequently, the polymer is subjected to the induced elastic deformation. Temperature grows during thermomechanical tests and when it reaches the glass transition area, the induced elastic deformation rapidly becomes reversible. The sample expands and, if the test is performed under compression at low loading, ‘negative’ deformation appears on the thermomechanical curve. The higher the pressure applied to the polymer powder at tableting, the greater the negative deformation is and the greater is the distortion of the shape of thermomechanical curve. In this case, the glass transition temperature corresponds to the lowering and not uplifting branch of the thermomechanical curve. In thermomechanical tests of polymers with elongation, deformation also decreases sometimes as temperature grows (Figure 28). The sample contraction may occur as a result of cross-linking, ring formation, etc., proceeding during the test.

Figure 28. Decreasing of deformation on the thermomechanical curve determining under conditions of tension (see text).

In most cases, the thermomechanical curve consists of two (see Figure 19) and not three parts. Usually, this is associated with the insufficient molecular mass of the polymer and with the fact that the polymer transits from the glassy state to the viscous flow one without reaching the rubbery state. Rising of the appropriate branch of the thermomechanical curve defines the temperature of transition into the viscous flow state, and it may be said that the glass transition (softening) and temperatures of transition into the viscous flow state coincide. When the second branch of the thermomechanical curve lies in the area of high temperatures, it should be confirmed that no degradation of the polymer happens in this area, and sharp increase of deformation is really associated with the polymer flowing and not with its degradation. In the latter case, softening and flowing are not yet reached, and the polymer exists in the glassy state in the whole possible temperature range. When transitions from the glassy state to the rubbery state and from the rubbery state to the viscous flow state are expressed clearly on the thermomechanical curve (in temperature ranges of transitions the deformation sharply increases), transition temperatures Tg and Tf can be easily measured. However, the thermomechanical curve is often of the shape depicted in Figure 29. This thermomechanical curve cannot help in determination of the glass transition

84

temperature: the transition is seriously ‘blurred’. That is why other methods should be used. Transitions from the glassy state to the rubbery state and from the rubbery state to the viscous flow state, and the melting point of polymers as well can be determined by dilatometric, calorimetric, and optical methods; it is appropriate to use also dynamic mechanical methods of investigation, etc. (see below).

Figure 29. Thermomechanical curve with ‘blurred’ transition (scheme).

Let us now turn to crystalline polymers. In some cases, the shape of thermomechanical curves of crystalline polymers differs from that of the same curves for semi-crystalline polymers and, in other cases, they nearly coincide. It is impossible to answer the question as to whether a polymer is semicrystalline or crystalline with the help of only the thermomechanical method of investigation. An X-ray pattern should be obtained first, and then data of the X-ray structural analysis must be compared with the results of the thermomechanical study. Crystalline polymers may be obtained directly during synthesis and further processing. For crystalline polymers, the thermomechanical curve may be of the shape depicted in Figure 30. If a polymer is quite extensively crystallized, the rubbery state is nearly completely suppressed, and the polymer displays no significant deformations in a wide temperature range. When transited to the melting point, deformation grows sharply and reaches the maximal value.

Figure 30. Thermomechanical curve of well-crystallized polymer (scheme).

The thermomechanical curve in Figure 30 corresponds to the case in which the rubbery deformation is completely suppressed by crystallization. Under real conditions, semi-crystalline areas exist in the crystalline polymer, which behave themselves at heating as a semi-crystalline polymer. During thermomechanical investigation of semi-crystalline polymers in the glass transition range, deformation will increase with further formation of a plateau (Figure 31). However, the rubbery plateau will not be of the same height as for pure semi-crystalline polymers of the

85

same structure. It will be significantly lower depending on the crystallinity degree. In any case, the glass transition temperature and the temperature of transition to the viscous flow state can be determined for the semi-crystalline polymer.

Figure 31. Thermomechanical curve of semi-crystalline polymer (scheme).

Particular emphasis should be placed on polymers, which easily crystallize during the thermomechanical test. It is then best to perform the experiment with a regular load2.

Figure 32. Schematic representation of the thermomechanical curve for a semi-crystalline polymer determined at periodic variation of load (see text).

Rapid crystallization of a semi-crystalline polymer occurs at temperatures above Tg. That is why the semi-crystalline polymer capable of rapid crystallization in the glassy state behaves itself similar to the normal semi-crystalline polymer only slightly crystallized. In the thermomechanical test, it gives a low deformation up to the glass transition temperature. Passing through this temperature, the polymer develops a large rubber deformation (Figure 32, curve 2). However, crystallization at T > Tg makes the polymer rigid, and if the load is applied regularly, the deformation decreases abruptly (see Figure 32, curve 2). Once the polymer has been deeply crystallized, its deformation is not yet different from the deformation of the preliminarily crystallized polymer (see Figure 32, curve 1). The temperature of transition to the viscous flow states will also coincide (see Figure 32). Let us now discuss briefly other methods of experimental estimation of the glass transition temperature of polymers. One of them is the dilatometric method in which the dependence of the specific volume of the polymer on temperature is 2

In all the cases, when more fine investigations are performed by the thermomechanical method, the load is best to be applied regularly, giving rest to the sample, i.e. a possibility to recover deformation after load removal. Then all effects of the glass transition, crystallization, etc. will be displayed more clearly.

86

measured. Schematically, this dependence is depicted in Figure 13. This dependence as a broken line is typical of many polymers near the glass transition temperature. At temperatures below the glass transition temperature, this dependence is more flattened, than at temperatures above it. This is the main reason observed at the glass transition temperature (see Figure 13). Obviously, dilatometric dependences may be obtained at different rates of heating (or cooling) of the sample. Consequently, if the heating rate is changed in a quite wide range, the dilatometric dependences change in the manner depicted in Figure 13. The higher the rate of the sample heating, the higher is temperature at which the bending is observed and, vice versa, the lower the heating rate, the lower is temperature of the bending and the specific volume of the sample in the bending point decreases. Hence, the glass transition temperature depends on the rate of heating or cooling of the sample, which is associated with the relaxation mechanism of the glass transition (see below). It should be noted that changing the heating or cooling rate causes has a smaller effect on the type of dilatometric curve and on the glass transition temperature than the effect of mechanical tension on the type of the thermomechanical curve and the glass transition temperature. To cause a significant change of the glass transition temperature in the first case, the heating or cooling rate must be changed by many decimal degrees, which is impossible to do in an experiment. At the same time, ten- or hundred-fold change of the heating rate changes the glass transition temperature by several degrees only. Meanwhile, the change of the mechanical tension by several percents only may cause a sharp increase or abrupt decrease of the glass transition temperature. A special role in this case is played by the rate of mechanical influence. Analysis of these experimental facts enabled G.M. Bartenev [53] to apply the viewpoint that mechanical and structural glass transitions must differ. By the structural glass transition one means transition from the glassy state to the rubbery state (and the reverse process) in the absence of mechanical tension. This transition and its temperature are associated only with the heating and cooling rate. Mechanical glass transition is associated with the rapid mechanical influence on the polymer and its behavior as a solid under the rapid action of the mechanical force. As temperature changes, the mechanical glass transition may occur at rather lower temperatures than the structural glass transition.

Figure 33. Temperature dependence of heat capacity Cp (scheme).

In addition to the dilatometric method of determination of the glass transition temperature, other methods are also widely used, for example, calorimetric one. In this case, heat capacity Cp of the polymeric substance is measured, the dependence of Cp on T is of the typical shape (Figure 33). In the area of the glassy state, heat

87

capacity grows slowly with temperature, but when Tg is reached, a sharp increase of the heat capacity is observed. When the transitional zone is passed, the heat capacity again increases only slowly with temperature. Apparently, dynamic mechanical analysis is used most widely. In this method, the temperature dependences of the storage modulus E′ and the loss modulus E′′ of the complex elasticity modulus E* = E′ + iE′′ change, as well as the loss-factor tgδE = E′′/E′ (Figure 34). The temperature dependence of tgδE displays several maxima, with the most intensive (and high-temperature) one associated with transition from the glassy state to the rubbery state.

Figure 34. Temperature dependence of the mechanical loss-factor tgδE (scheme).

The temperature dependence of the dielectric loss-factor tgδε = ε′′⁄ε′, where ε′′ and ε′ are the true and the imaginary parts of the complex dielectric constant ε* = ε′ + iε′′, looks the same (Figure 35).

Figure 35. Temperature dependence of the dielectric loss factor tgδε (scheme).

Finally, the glass transition temperature may be determined from a sharp increase of the diffusion coefficient. Neglecting discussion of these methods of experimental determination of Tg, let us guide the reader to special literature [5, 51, 124].

88

IV.2. Mechanism of glass transition The mechanism of glass transition has been studied for many years, but there is no general viewpoint on the glass transition mechanism. That is why we shall consider main common viewpoints on this mechanism. Note that these viewpoints do not contradict to each other. First of all, let us consider the concept of the relaxation mechanism of glass transition, put forward by A.P. Alexandrov, Yu.S. Lazurkin, P.P. Kobeko, and G.I. Gurevich. Let us preliminarily note once again that transition to the glassy state and the opposite transition to the rubbery state are not phase transitions of the first and the second kind (remember that according to the Erenfest definition, the phase transition of the first kind is the phase transition at which thermodynamic functions display a sharp jump at the transition temperature, and the derivative of the temperature dependence of the thermodynamic function is ruptured). The phase transition of the second kind is the transition at which temperature dependences of thermodynamic functions at the transition temperature change smoothly, and a sharp jump at the transition temperature is displayed only by first derivatives of these functions. Externally, in the case of polymers, some temperature dependences of thermodynamic functions look as if they were typical of transition of the second kind. For example, the temperature dependence of the specific volume (dilatometric curve) possesses a bend at the glass transition temperature by which this temperature is identified (see Figure 13). However, this resemblance is only superficial, because the transition considered is not associated with appearance of a new phase, as in the case of melting or crystallization from the melt, but is the transition from one physical state to another keeping the unique liquid phase. Hence, by the phase state solid glass represents a liquid, like elastomers and flowing polymers. They differ only by the aggregate state, representing the unique liquid phase.

Figure 36. Location of kinetic unit in the minimum of potential energy (scheme).

Let us now turn to consideration of the relaxation mechanism of glass transition. Let us begin description of this mechanism from low-molecular substances. Each molecule of such substance occupies a definite location in space and oscillates due to thermal fluctuations, i.e. as a result of exceeding the average temperature by the temperature of the present point. To transit to another location in space, a definite amount of energy should be consumed. Let the kinetic unit (atom or molecule) exist in the location, when the potential energy of it is minimal. This case, displayed in Figure 36, corresponds to the stable equilibrium. To transit the kinetic unit to a new state of equilibrium, it is necessary to overcome some energetic barrier, which is the real transition energy and is called the potential barrier. Hence, the potential barrier is the energy, which must be spent by the kinetic unit in order to transit to a new location. Let us consider the composition of this barrier.

89

Every thermodynamic system is characterized by the value of the free energy or isobaric–isothermal potential F: F = U – TS,

(IV.9)

where U is the internal energy of the system; T is absolute temperature; S is entropy. The value of the free energy U is composed of the energy of translation of particles, the energy of their rotation, and the oscillation energy of particles in relation to their equilibrium. Concerning entropy, according to the Boltzman definition, it equals S = kBlnW,

(IV.10)

where kB is the Boltzman constant; W is the thermodynamic probability of existence of the system. The notion of entropy as a statistic characteristic is best demonstrated on the example of various conformations of macromolecules. Let us consider one of the border cases, a completely stretched chain (Figure 37,a). Clearly, such chain may possess only a single conformation, and the distance between its ends h will be equal to the full length of the macromolecule. Probability of existence of this conformation is extremely low, because it just the single one. But if we take a globular chain structure (see Figure 37,b), it will obtain a multiplicity of conformation at the same distance between its ends, i.e. its elements may locate differently in space keeping this distance constant. The shorter this distance h (down to some limit), the more conformations of the macromolecule may be composed and greater is the probability of existence of the macromolecule in this (globular) form. Since according to the Boltzman definition entropy is proportional to the logarithm of thermodynamic probability, it will increase with decrease of the distance between macromolecule ends. According to the second law of thermodynamics, a spontaneous process always proceeds with entropy increase. That is why thermal motion in the case of flexible macromolecules causes their coiling.

Figure 37. Schematic representation of straightened (a) and coiled (b) polymer chain (h is the distance between the chain ends).

Turning back to the system composed of small molecules, note that transiting of kinetic unit from one state into another both the internal energy and entropy will change. Change of the free energy will be determined from the relation ∆F = ∆U – T∆S,

(IV.11)

90

where ∆U is the change of the free energy; ∆S is the change of entropy. The probability of the given kinetic unit being in a specific position in space depends on its energy and absolute temperature. This probability is determined by the relation W = ν0e–E/RT,

(IV.12)

where ν0 is the self frequency of oscillation of atoms or molecules; E is the energy of the particle; R is the universal gas constant; T is the absolute temperature. Equation (IV.12) is used in cases when calculation is performed per mole of the substance. If the calculation is performed per molecule, kB (the Boltzman constant) should be introduced instead of R. These values are connected by the relation kB = R/NA, where NA = 6.023⋅1023 mol–1 (the Avogadro number). It is common knowledge that the fundamental frequency of oscillation of atoms in solids is ~1013 Hz, and the oscillation period is determined from the relation τ0 = 1/ν0. It is of interest that the time of settled life of an atom in this location is 10–10–10–11 s. Considering transition of a polymer from the glassy state to the rubbery state, let us introduce such characteristic as the time of this transition. This time τtr is determined from the relation

τ tr = τ tr,0eU tr RT ,

(IV.13)

where τtr,0 is a pre-exponential multiplicand which represents the value reversible to the fundamental frequency of oscillations of atoms; Utr is the energy, which must be spent to perform the transition. The smaller τtr is, the faster the transition is, i.e. the higher is temperature and the lower is transition energy Utr, the easier the transition conduction is. Let us consider a rubbery polymeric body, cooled down at a definite rate of temperature change. If the time of transition of structural elements (kinetic units) from one state to another is short at a definite temperature, such transition is fast and change of the structure will proceed immediately after the temperature change. It may be said that if the transition time τtr is much shorter than the observation time τobs, then the transition will proceed very fast and the equilibrium state of structure of the polymeric body is reached very rapidly immediately after the temperature change. The heat energy, characterized by the RT product, decreases with temperature, and the relaxation time (see equation (IV.13)) grows significantly. However, if it remains shorter than the time of system observation, the transition proceeds quite rapidly. Further decrease of temperature will lead to a sharp increase of τtr and to fulfillment of the condition τobs ≈ τtr, and then τobs < τtr. This corresponds to the case when the observation time becomes much shorter than the transition time. Clearly, this transition cannot be observed, although it proceeds. The transition proceeds so slowly that observation of it becomes difficult. That is why the polymeric substance becomes solid, i.e. transits to the glassy state. It should be noted once again that the structure of the polymeric substance at this transition is in fact not equilibrium. It is somehow frozen in the state preliminary to the transition. If we could manage to observe the transition for a very long time, it would be noted that this transition proceeds, although very slowly. Hence, according to these notions, the transition from the rubbery state into the glassy state is the relaxation process and is associated with the fact that at temperatures definite for every polymer the relaxation

91

time (time of transition) becomes extremely long, and the polymeric substance begins to behave as a glassy solid. This transition theory was subsequently mathematically justified by M.V. Volkenstein and O.B. Ptitsyn, who had performed mathematical analysis of the relaxation transition from the rubbery state to the glassy state and back, and had adjusted conditions under which such transitions may be performed. According to this theory ln

τ tr,0U tr RTg2

+

U tr 1 = lg , RTg q

(IV.14)

where q is the rate of system cooling. Equation (IV.14) shows that the glass transition temperature depends on the rate of polymer cooling. In its initial form, the Volkenstein–Ptitsyn theory does not consider the cooperative character of thermal motion of kinetic units. As shown subsequently, such calculation is absolutely necessary, because due to large length and flexibility of macromolecules the local motion of any kinetic unit touches upon its neighbors. For example, motion in the frames of a single repeat unit of a macromolecule causes motion of the neighbor units and this is the reason for segmental mobility. Calculation of the cooperative ability of motion of kinetic units of various sizes, performed by Ptitsyn and Sharonov, caused refinement of the Volkenstein–Ptitsyn theory and allowed reasonable values of the activation energy of the relaxation process to be determined.

Figure 38. Schematic representation of thermomechanical (a) and dilatometric (b) curves in the zone of transition from the glassy state to the rubbery state (see text) .

Analysis of a polymeric substance with the help of a non-linear model [87, 89] shows [90] that transition from the glassy state to the rubbery state must proceed not in a point but in some interval of temperatures which depends on the rate of heating or cooling q. Schematically, this is shown in Figure 38, which depicts thermomechanical and dilatometric curves in the transition area. Here Tg,1 is the temperature, at which transition from the rubbery state to the glassy state begins at system cooling; Tg,2 is the temperature at which this transition ends. The results obtained in work [90] indicate that at low rates of cooling the glass transition temperature range degenerates and the glass transition temperature only remains. In the general case of analysis of polymer behavior in the area of T < Tg,1, a significant role is played by the cooling rate. If the cooling rate is high, temperatures

92

Tg,1 and Tg,2 differ significantly, i.e. transition to the glassy state proceeds in a wide temperature range. In practice, the glass transition temperature range is really broadened as the rate of cooling (or heating) increases, not in a jump-like manner, but quite smoothly. Therewith, the temperature dependence of deformation in the transition zone becomes more abrupt as the rate of cooling (or heating) decreases. This is clear from Figure 39, which indicates thermomechanical curves for a series of cured compounds based on epoxy oligomers. In accordance with the theoretical results obtained, the glass transition temperature range windes as the heating rate increases (Figure 40).

Figure 39. Thermomechanical curves of cured epoxy compound measured under conditions of compression. Rate of heating 0.62 (1), 1.07 (2), 2.39 (3), 4.61 (4), 6.39 (5), 9.44 (6), and 15.47 (7) deg/min. Composition of specimen: ED-20 – 1 mole, MTHPA – 0.6 mole, azelaic acid – 0.7 mole.

Figure 40. Dependence of temperature differences ∆T = Tg,1 – Tg,2 on heating rate q: (a) correlates with the same composition as in Figure 39; (b) corresponds to the composition of specimen: ED20 – 1 mole, MTHPA – 1.3 mole, oleic acid – 0.7 mole.

The nonlinear model of polymeric substances [87,89] was also used for estimating the activation energy of γ-transition in polymers. Estimation of many properties of polymers requires the values of the activation energies associated with various transitions in polymeric systems. If a polymer is considered as a linear system, then it will be a selection of activation energies, usually associated with the motion of a definite group of atoms in a chain. But if it is considered as a non-linear system, described by a model suggested in ref. [87] (Figure A-6-8), we must know the activation energy of elementary acts only, associated, for example, with a jump of atoms from one equilibrium state to another in a rotary isomer, and which is usually associated with the activation energy of the γtransition. All other relaxation times stipulated by other transitions are expressed via the desired activation energy and temperature coefficients determined by non-linear

93

model parameters [269]. Hence, a temperature dependence of activation energy in the area of α-transition may be obtained, and the Williams–Landel–Ferry formula may be deduced, etc. To use actively this model for calculations of particular polymeric systems, the relation of the parameters of the model with the chemical structure of the repeat unit must be known. Let us demonstrate how expressions for determining activation energy which participate in the temperature dependences of relaxation times (viscosity) may be deduced from correlations of the ref. [269]. It is shown below that the activation energy is linked by simple dependences with the glass transition temperature and, therefore, it may be calculated on the basis of the chemical structure of the repeat unit. Let us consider expressions for relaxation times τ3 and τ5 of a non-linear model, shown in ref. [269], in the range of temperature of the onset Tg,2 and termination Tg,1 of glass transition. With this aim in view, let us perform series expansion of τ2/τ5 and τ2/τ3 in relation to Tg,1 and Tg,2, respectively, and confine to terms of the smallness order one by T – Tg,1 and T – Tg,2. Then,

τ2  d τ2  ≈ ⋅  ⋅ (T − Tg,1 ) , τ 5  dT τ 5  T =T g ,1 because

τ2 τ5

= 0 and T =Tg ,1

τ2 τ3

= 0, T =Tg , 2

where τ2 is the relaxation time of one of elements of the model, which may be expressed by the Arrhenius–Eiring formula. The expressions τ2/τ5 and τ2/τ3 may be expressed via variable δ0, respectively, as follows:

τ2  d τ2   dδ 0  ≈ ⋅  ⋅ (T − Tg ,1 ),   τ 5  dδ 0 τ 5  T =T  dT  T =T g , 1 g ,1 τ2  d τ2   dδ 0  ≈  ⋅  ⋅ (T − Tg, 2 ) .   τ 3  dT τ 3  T =T  dT  T =T g,2 g,2  d τ2   d τ2  ⋅  ⋅  and  are of As according to ref. [269], values   dδ 0 τ 5  T =Tg ,1  dδ 0 τ 3  T =Tg , 2 the same order of magnitude, future consideration will take into account only the d (δ 0 ) at Tg,1. As expressions τ2/τ5, and Tg will be taken for Tg,1. Let determine dT according to ref. [269],

94

−1

 16 K  δ 0 = 1 − ⋅ 1  , K1 = f1e −Y1 , K 3 = f 3e −Y3 ,  21 K 3  Y1,3 = 1 − 2 1 − T Tg1,3 ,

(

)

then dδ 0 16 2 K1  1 1 1 1  = δ0 ⋅ − ⋅ . dT 21 K 3  Tg3 1 − Y3 Tg1 1 − Y1  The relation

K1 K3

= 57/32, δ0 = –2.8 [269]. K1 value corresponds to the T =Tg ,1

elasticity of a chemical bond, and K3 – to the elasticity modulus of an intermolecular bond, that is why Tg,1 = Td (to the temperature of onset of intense thermal degradation), Tg,3 = Tm (to the melting point). Then,

dδ 0 dT

T =Tg ,1

  T 7.6  1 = − m  Tm  Tg,1 Td  1− T m 

   1 . Tg,1  1− Td 

 d τ2  ⋅  ≈ −0.3 may be found. Taking into account the From ref. [269]   dδ 0 τ 5  T =Tg ,1 expression

dδ 0 and the value dT

 d τ2   ⋅  , the dependence τ2/τ5 on temperature  dδ 0 τ 5  T =Tg ,1

in the area of Tg (suggesting Tg = Tg,1) may be presented as follows:     T τ2 2.3  1 1  ≈− − m⋅  T − Tg .  Tm  Td τ5 Tg Tg  1−  1− T Td  m 

(

)

(IV.15)

The expression obtained, according to ref. [269], describes the transition to the glassy state. It may be displayed that the Bachinski formula is also reduced to an analogous form. Actually, to describe the viscosity of liquids η, Bachinski [768] has suggested an empirical formula:

η=

C . v −ω

(IV.16)

95

Here v is the specific volume of the liquid; ω is the molecular ‘limited’ volume of the liquid (according to Bachinski, Mω = ∑ ε i , where εi are constants of atoms forming i

the molecule; M is the molecular mass), C is the constant. The expression (IV.16) describes well the liquid viscosity in a wide range of temperatures and pressures, the constant C may be found from the Camerling–Ownnes theory of similarity of molecular systems. Bachinski has shown [768] that for many liquids the following correlation is fulfilled: CM 1/ 6 = 0.531⋅10–4, 1 / 2 1/ 3 Tg ω

(IV.17)

Thus, the accuracy of determination of C depending on the chemical structure is ±6.2%. Let us transform the expression (IV.16). For this purpose, let us consider the temperature dependence of the specific volume, which may be presented in the following form: v = ω[1 + αv(T – Tg)],

(IV.18)

where αv is the coefficient of volumetric expansion which, according to ref. [269] in the case of the potential ‘6 – 12’, is equal to 1/42Tg. With regard to equation (IV.16), correlation (IV.18) has the following form:

η0 T − Tg = , η 42Tg

(IV.19)

where η0 = C/ω. Expression (IV.19) will be analogous to equation (IV.15) obtained from the non-linear model, therewith, η0 = η2 = K1τ2, and η = K1τ5. But contrary to the Bachinski formula deduced for transition from liquid to glass, the desired expression describes the transition from the side of low temperatures (transition from the glassy state to the rubbery state). That is why     Tg  Tm 1 1  − ⋅ η 2 = 2.3  42η0 . Tm  Tg Td Tg  1−  1− T Td  m 

(IV.20)

From equation (IV.20) the expression for the activation energy may be deduced. Let us estimate the following value for the real polymeric systems:   Tg  T 1 1 − m⋅ A = 2.3  Tm  T Tg Tg d 1−  1− T Td m 

   42 .   

(IV.21)

96

Shown in the Table are initial data (glass transition temperatures Tg, melting points Tm, temperatures of the onset of intense thermal degradation Td), and results of calculation of values A for a series of polymers. Values of Tg, Tm and Td are usually taken from experimental data but, in some cases, when, for example, a polymer is not crystallized or when its melting point lies above the temperature of onset of intense thermal degradation and thus may not be measured experimentally, they are calculated by the expressions shown below. Calculation results indicate (Table 17′) that the value A falls within the range from 24 to 82. In some cases, it becomes negative. It is typical of polymers, for which temperature of the onset of intense thermal degradation lies near the glass transition temperature, or the melting point and the glass transition temperature are close, i.e. for heat-resistant polymers. As obvious, coefficients A calculated for the most of polymers are positive that, according to equation (IV.20), correspond to positive values of viscosity. Similar to a non-linear model of polymeric body, in which viscosity is associated with relaxation mechanisms, according to the Mandelshtamm– Leontovich theory, the viscosity in our expressions will be the second one, because the non-linear model suggested [269] describes behavior of a polymeric substance by a selection of kinetic equations. However, as the Table indicates, for some polymers A < 0. The latter means that the second viscosity of these polymers is negative. The result obtained has a physical meaning and, as follows from ref. [768], is associated with nonequilibrium of the medium in the range of the glass transition temperature. This result must be analyzed in more detail.  ∆E *  h  expression (IV.20) may With regard to η0 = C/ω and η 2 = 2 ⋅ exp  kTg  Nl q   be presented in the form:  Nl 2 q AC  ∆E * , = ln ⋅ kTg ω   h

(IV.22)

where N is the number units in the macromolecule; l is the unit size; q = exp(∆E/kT); ∆E* is the difference in the energies of rotary isomers.

97

Table 17′ Polymer 1

CH2

Initial data and calculated results of value A for a series of polymers Tm, K Td, K Tg, K (exper./calc.) 2 3 4 263 449/451 673

Tg/Tm

Tg/Tm

Tm/Td

5 0.583

6 0.391

7 0.667

8 39.1

378

513/509

618

0.743

0.612

0.824

46.6

249

405/413

664

0.603

0.375

0.622

46.5

302

508/500

678

0.605

0.445

0.737

35.2

453

633/625

588

0.724

0.770

1.06

-21.5

205

332/314

663

0.654

0.309

0.474

71.4

A

CH CH3

CH2

CH

CH2

CH C2H5

CH2

CH CH2

CH CH3 CH3

CH2

O

(CH2)4

CH

O C

C O

97

O

(CH2)4

98

O

(CH2)3

O C

(CH2)4

O CH2

C

2 214

3 311/315

4 659

5 0.679

6 0.325

7 0.478

8 77.6

254

359/387

704

0.655

0.361

0.550

64.1

260

417/398

704

0.653

0.369

0.565

62.2

150

234/234

771

0.640

0.194

0.303

82.2

O

CH O CH2 CH2

CH3

CH O CH3

CH3 Si O CH3 CH2CH2 CH2

CH

CH3

O CH2

CH

213

410/410

713

0.519

0.575

0.299

37.8

246

438/397

651

0.620

0.379

0.609

50.9

CH3 CH2CH2O CH2

206

339/348

794

0.592

0.259

0.438

60.4

198

348/356

742

0.556

0.267

0.480

50.5

194

309/311

721

0.622

0.269

0.431

67.4

CH O CH3

(CH2)4O

98

1

99

1

2 318

3 433/465

4 629

5 0.682

6 0.506

7 0.739

8 47.6

223

323/334

655

0.667

0.340

0.510

71.2

351

530/539

621

0.651

0.565

0.868

23.7

323

499/494

622

0.654

0.519

0.794

35.1

323; 348

499/496

621

0.651

0.520

0.799

34.0

319

467/481

653

0.662

0.488

0.737

42.5

298

/458

640

0.651

0.716

0.466

44.8

CH3 C

CH2

C O CH3 O (CH2)2

O C

(CH2)4 C O

O C

(C H 2 ) 4

C

O

O NH

(C H 2 ) 6

NH

O

C

(CH2)8

O

C NH

(CH2)6

NH

O NH

(CH2)5

C O

NH

(CH2)10

C O

CH2

CH O C

99

O

CH3

100

2 199

3 /300

4 713

5 0.663

6 0.420

7 0.279

8 78.6

620

/801

667

0.774

0.930

1.200

–180.9

CH3 CH2

C CH3

C O

C O O

O C O C O

100

1

101

Considering a polymer in the glassy state as a frozen liquid and using data of the Camerling–Ownnes theory of molecular similarity, as Bachinski has done, the expression for C may be presented in the following form in analog to formula (IV.17): CM 1/ 6 = 10 −b . Tg1/ 2ω 1/ 3 Here b is the exponent value which, in the case of polymeric systems, is somewhat dependent on chemical structure and will be found during comparison with particular     characteristics of polymers. Because ω ~ N  ∑ ∆Vi  , where  ∑ ∆Vi  is the  i  r.u.  i  r.u. 1/ 3

Van-der-Walls

volume

of

the

repeating

unit,

  l ~  ∑ ∆Vi   i 

and

C = 10 − b Tg1/ 2ω 1/ 3 M 1/ 6 ,  ATg1/ 2 M 1/ 6  ∆E * . = 2.3 27 − b + ln 1/ 3   kTg M r.u.  

(IV.23)

If for real polymer systems logarithm is taken from Tg, M, and Mr.u., average by polymeric systems, it is observed that fluctuations stipulated by the difference of parameters Tg, M, and Mr.u. for particular polymeric system from average ones, give a low error (< 10%) for determination of the activation energy ∆E* of this system. In turn, the logarithm from average values of parameters by polymeric systems is taken into account via constant b. That is why, expression (IV.23) may be reduced to the form: ∆E* = 2.3(27 – b)kTg. In accordance with the experimental data from refs. [214], the value of b may be estimated, which is equal to 15.7. Respectively, ∆E* ≅ 26kTg.

(

(IV.24)

)

(

)

* * Shown below are some calculated ∆Ecalc values and experimental ∆Eexper of the activation energy for a series of polymers according to the data from refs. [214].

Polymer

PEO

PCTFE

PE

PVA

Tg, K * ∆Ecalc , kJ/mol * ∆Eexper , kJ/mol

206 44.8

323 70.3

213 46.0

303 65.8

Butyl rubber 200 45.6

37.7

72.7

50.3

60.8

49.9

102

* * Deviations between ∆Ecalc and ∆Eexper observed do not exceed ~15%. Considering jumps of atoms or groups of atoms along the chain in rotary isomers as diffusion of these atoms in polymer, the ratio ∆E*/d2 may be determined by data from ref. [214] (p. 298, Figure XVIII.7), where d is the size of the groups of atoms diffusing. But ∆E* is deduced from expression (IV.23), from which the size d of the jumping group of atoms may be determined immediately. For example, in the case of PS, ∆E*/d2 = 600, Tg = 378 K, ∆E* = 82.2 kJ/mol, and d = 5.7 Å that corresponds to the group C6H5. However, jumps of a group of hydrogen atoms are possible in PS. If sizes of these atoms are known, the activation energy may be deduced from the expression ∆E*/d2. It is equal ∆EH* = 19.7 kJ/mol. From expression (IV.24) the temperature of transition of this group of atoms Tg,1 may be estimated. If calculated, Cg,1 = 91 K, which by the order of magnitude corresponds to the temperature of δ-transition in PS (accurate coincidence is out of the question, because the constant in expression (IV.24) is found for the γ-transition). Estimations performed allows a supposition that if the repeating unit of polymer possesses side (asymmetric) groups of atoms different by size, a δ-transition appears in such a polymer. Discussed above is one of the concepts of the polymeric substance transition from the glassy state to the rubbery state and back. This concept is based on assumption of the relaxation mechanism of transition, the time of this transition (the relaxation time) depending on temperature and being determined by the energetic barrier height to be overcome in order to provide with the transition. Since different macromolecules possess different flexibility or rigidity, they are characterize by different heights of the energetic barrier and, consequently, by different glass transition temperatures. The more flexible the macromolecule is, the lower the height of the energetic barrier is which characterizes the system composed of such macromolecules. The concept of the polymeric substance transition from the glassy state to the rubbery state and back, based on the relaxation mechanism of transitions, is not unique. Another concept that explains these transitions is the concept by S.N. Zhurkov, based on acceptance of a significant role of intermolecular bonds in polymers. Let us discuss this concept. Every polymeric macromolecule possesses polar groups, which display various energies of interaction with each other. They form bonds which are not chemical, but are of the physical nature and are called intermolecular bonds. Such bonds may be rather weak as, for example, in polyisobutylene, polypropylene, polyethylene, and in other analogous polymers, but they may also be very strong as for example, in polyamides, polyesters, etc. In the former case, it is spoken about weak Van-der-Waals bonds, the energy of which is very low. In the latter case, strong NH C hydrogen bonds which appear due to existence of amide groups (polyO amides), and strong dipole–dipole interaction which appear due to existence of ester O groups are considered. Intermolecular bonds may be stipulated by an C O existence of not only these polar groups, but also of other groups capable of strong
 
 
     

 ≡N groups (for example,
  

  -groups (for example, in poly(vinyl alcohol), and many others. Polar groups in neighboring macromolecules under definite conditions may interact with each other forming cross-linked bridges between them, which are

Š

Š

103

quite strong. Recall that we are dealing not with chemical bonds, but with physical ones. Schematically, it is represented in Figure 41.

Figure 41. Schematic representation of a network of physical (intermolecular) bonds.

It is necessary to pay attention to one more very important circumstance. Contrary to chemical bonds, intermolecular bonds are rather weak. Energy necessary for dissociation them is by a decimal degree lower than that for chemical bonds. Recall that the energy of chemical bonds dissociation is of several tens of kcal/mol, and that of intermolecular bonds is several kcal/mol. The strongest bonds are displayed by amide, ester, hydroxyl and some other groups. However, the energy of dissociation of intermolecular bonds formed by these groups does not exceed ten kcal/mol (in fact, this energy is lower). Hence, intermolecular bonds are not stable, but decompose permanently under the effect of thermal fluctuations and are formed in new places. They somewhat migrate along the polymeric chain and in doing so link not strictly specified chains of macromolecules, but the chains, in which they appear at the current moment. However, at each definite temperature the amount of intermolecular bonds existing simultaneously is much the same for polymers of a definite chemical structure. It may be said that under equivalent consideration, intermolecular bonds act in definite places of macromolecules forming a peculiar network and making impossible their motion in relation to each other. Taking into account that, in fact, macromolecular bonds are formed and dissociate permanently under the effect of thermal fluctuations, an equilibrium may be shifted to one or another side, i.e. to the side of formation or dissociation of intermolecular bonds. As with usual chemical reaction, the equilibrium shifts to the side of decomposition of intermolecular bonds as temperature increases, and to the side of their formation as temperature decreases. When polymeric substance existing in the rubbery state is cooled, the amount of forming intermolecular bonds grows permanently. When a definite temperature is reached, the amount of bridge bonds formed reaches the value enough for fixing separate macromolecules relative to each other and allowing not translation mobility of them. Therewith, vibration mobility remains. Formation of a quite frequent and strong network of intermolecular bonds with polymer cooling down to a definite temperature promotes a definite loss of mobility of macromolecules at this temperature, and the polymeric substance as a whole becomes solid, i.e. transits to the glassy state. Temperature, at which this phenomenon is observed, is the glass transition temperature. When polymeric substance in the glassy state is heated, the equilibrium shifts to the side of intermolecular bond decomposition. When the process of their dissociation is carried far enough, macromolecules obtain translation mobility, and the polymeric substance softens, i.e. transits to the rubbery state. According to the concept considered, this is the nature of transition of polymeric substance from the rubbery state to the glassy state and back.

104

To perform this transition, a definite number of intermolecular bonds must be formed in each polymeric substance with no dependence on their chemical structure. Designate this number as x. Concentration of active groups in the polymer, capable of formation of intermolecular bonds, are designated as N. In this case, taking into account that intermolecular bonds dissociate and are formed permanently in other places, and that an equilibrium between the number of formed and dissociated bonds exists, to describe this process, a common equation of chemical kinetics describing equilibrium process may be used: x ↔ 2(N – 2x).

(IV.25)

Left part of the equation includes the number of intermolecular bonds formed at a definite temperature; right part of it in brackets represents the number of active groups remained, capable of forming these bonds. Digit two appears in brackets, because formation of each bond consumes two active groups. This is also the reason of appearance of two before brackets. Since the reaction considered is equilibrium, the law of mass action may be applied to it, according to which the relation of concentration of the substance formed to concentration of the initial substance is a constant value, equal to the equilibrium constant. Therewith, stoichiometric coefficients of the reaction equation are included in indices of degrees of corresponding concentrations. Hence, in the present case

(N − 2 x )2 x

= k eq ,

(IV.26)

where keq is the equilibrium constant. According to Arrhenius, temperature dependence of the equilibrium constant is described by the following relation k eq = A * e

E − RT

,

(IV.27)

where A* is a steric factor; E is the bond energy (in this case, the intermolecular bonds energy); R is the universal gas constant; T is absolute temperature. Substituting (IV.27) into (IV.26), we get E

x = (N − 2 x )2 A * e RT .

(IV.28)

Equation (IV.28) associates the number of intermolecular bonds formed with the number of active groups capable of formation of these bonds and with temperature. To clear up the mechanism of glass transition, it is necessary to interlock a part of polar groups one way or another in order to exclude them from the interaction. Interlocking may be performed by different methods, for example, by an insignificant change of the chemical structure of the macromolecule or by introducing small molecules of low-molecular substances acting as plasticizers. They may be introduced by sorption of gaseous small molecules of a sorbate by polymer. Assume that n of such small molecules were introduced into a polymeric substance, so that the same number of polar groups were interlocked. In this case, (IV.28) will be written as:

105

E

x = (N − 2 x − n )2 A * e RT1 ,

(IV.29)

where n is the number of solvent molecules. To fulfill the equilibrium condition and the number of intermolecular bonds formed to become x again, temperature must be changes, i.e. it must be decreased to decrease the value in brackets in the right part of equation (IV.29). That is why, T is substituted by T1 in this equation. Solving jointly the system of equations (IV.28) and (IV.29), we obtain the following relation n  E T1 − T  . 2 ln1 − = ⋅  N − 2 x  R T1T

(IV.30)

Š

In equation (IV.30) T correlates with the glass transition temperature of the ZLWK WKH JODVV WUDQVLWLRQ WHPSHUDWXUH RI original non-plasticized polymer, and T1 plasticized polymer, because by the condition x is the number of intermolecular bonds necessary for formation of a firm spatial network. When this network is formed, the polymer transits to the glassy state. Equation (IV.30) may be used for description of transition of a polymer from the solid state to the rubbery state, when a definite amount of plasticizer is introduced into it. However, this equation may be simplified significantly. First, assume that the number of intermolecular bonds is significantly smaller than the total number of polar groups capable of intermolecular interaction (as experiments have indicated, such happens indeed in practice: to obtain a firm network of intermolecular bonds and to ‘cure’ the polymer, it is necessary to fix no more than 10% of polar groups). In other words, the condition is fulfilled: N >> 2x.

(IV.31)

Let us introduce the second assumption, namely, operation with a small number of plasticizer molecules (clearly, such assumption might be not introduced). Then it will be written that n/N 5, additional constants bCH =

Š

Š Š

Š

Š

Š

Š

Š

2

–23.0 are introduced in amount m(n – 5), where m LV WKH DPRXQW RI 1+&2 JURXSV SDUWLFLSDWLQJ LQ the repeating unit. ** When the number (n RI &+2 JURXSV LQ WKe repeating unit n > 6, additional constants bCH = –

Š Š

2

23.0 are introduced in amount (n – 6).

Figure 42. Nature of intermolecular interaction in case of molecules ‘head-to-tail’ (a) and ‘head-tohead’ (b) joined .

Since strong intermolecular interactions are taken into calculation in the relation (IV.41) by parameters bj, clearly, it should be presented that ∑ ∆Vi Tg =

i

∑ ai ∆Vi + (1 − γ )∑ b j i

,

(IV.44)

j

where γ is the part of anomalously joined chains. According to the relation (IV.44), the glass transition temperature of polymer with anomalous attachment of chains will be decreased. It will be displayed on a particular example below.

111

Van-der-Waals volumes of the repeating units

∑ ∆Vi , values i

Polymer

∑ ai ∆Vi , and i

Table 19

∑ b j and the glass transition temperatures Tg for a series of polymers j

∑ ∆Vi , Å

3

i

∑ ai ∆Vi ⋅10 , 3

i

3

1

CH2

CH C

−1

∑ b j ⋅10 ,

Tg

3

j

3

Calc.

Exp.

−1

2 81.3

ÅK 3 319

ÅK 4 81.5

5 203

6 200

79.0 71.8

279 478

81.5 0

219 150

225 150

51.2

239

–55.4

279

258; 293

68.3

319

0

214

199

68.3

319

–45.7

250

248

CH2

CH3

Š&+ Š&+ &&OŠ&+ Š 2

2

CH3 Si

O

CH3 CH2

CH CH3 CH3

CH2

C CH3

CH2

CH

111

C2H5

112

CH

2 60.7

3 295

4 –55.4

5 253

6 258

77.8

375

–55.4

244

248

O CH3

CH2

CH O C2H5

CH2

CH

111.9

534

–36.0

225

221

CH2

O C4H9 CH

48.9

199

–55.4

341

355

63.7 96.4

238 422

0 –166.2

268 377

256 378

113.5

502.0

–166.2

338

338

147.6

661.0

–146.7

287

293

Š&+ Š&&O Š Cl

2

2

CH3 CH2

C C O CH3 O

CH3 CH2

C C O C 2H5 O

CH3 CH2

C C O C4H9 O

112

1

CH2

113

1

CH3 CH2

2 181.8

3 820.0

4 –127

5 262

6 268

41.5

309.0

–195.0

365

358

166

578.4

–136.4

375

353

54.0

183

–55.4

422

418

231.8

1121

–428

335

325

116

560

–214

335

335

64.3

363

–210

421

426

C C O C6H13 O

CH2 CH OH C

C O

O

O

(CH2)2

O

CH2 CH

KN C

(CH2)4

O C

C NH

(CH2)6

NH

O (CH2)5

NH

O CH2

CH C NH2 113

O

114

CH2

CH

CH3 CH2

C

CH2

CH

2 109.8

3 320

4 –27.7

5 376

6 378

127

399

–83.1

401

435

60.2

356

–195.0

374

379; 439

238.8

771

–162.0

431

422

451.1

1480

–300.5

382

363

C OH O CH3 O

C

O C

CH3 C O

(CH2)8

O

C O O

O C O C

O

114

1

115

1

C

C O

O

2 465.4

3 1163

4 –351.3

5 573

6 593

437.3

1060

–242

535

543

395.5

1066

–453.3

646

653

519.9

1331

–298.4

503

500

O C

O

O C

C

C O

O

O

O

O C

NH

C HN C

O C

O

O C O C N O

O

CH3 O

C CH3

O

C N C O

115

C

O

116

O

S

O

2 368.1

3 1133

4 –468

5 553

6 560

262.3

692

–76.8

416

420

389.7

1003

–326.1

576

583

S

O

O

O

C

O

O C O O

O C

C

O

O C

O

116

1

O

Table 19′ Experimental and calculated values of the glass transition temperature, Tg, for the broaden list of polymers, presented in the alphabetic order ( ∑ a i ∆Vi + i ∆ V , ∑ i Tg, K Tg, K No. Polymer References + ∑ b j )⋅103 i (exp.) (calc) 3 j Å , Å3K–1 1. Cyanoethyl cellulose 132(0 gr) 483 (1 gr); 453 389 (1 326 CH2 OH 188(1 gr) 244 (0 gr) gr); 541 CH O (0 gr)

O CH CH CH CH OH O CH2 2.

Ethyl cellulose

CH2 O CH2

CH2

C N

CH3

CH O O CH CH CH CH CH3 3.

CH2

Methyl cellulose

O

O CH2

204(2 gr) 654 (2 gr); 168(1 gr) 449 (1 gr)

316

312 (2 gr); 374 (1 gr)

275, 327

151(1 gr) 370 (1 gr); 170(2 gr) 496 (2 gr)

423

343 (2 gr); 408 (1 gr)

326

318

328

472

CH3

CH2 O CH3

CH O O CH CH CH CH CH3 4.

O

O CH3

Nylon 8,6 [Poly(iminoadipoyliminooctamethylene)]

O

(CH2)4

C NH O

(CH2)8

811

117

NH C

266

2 Nylon 10 [Poly(imino-1-oxodecamethylene)]

NH C

3 184

4 580

5 315

6 317

7 480

368

1161

333, 319

317

472, 473

402

1280

322

314

477

300

929

313

323

472

201

640

315, 316, 365, 333 343

314

480, 668, 681, 716

218

699

313 - 316, 314

312

284, 475, 480, 679

539

1750

323

308

477

235

756

314

311

480

(CH2)9

O 6.

Nylon 10,10 [Poly(iminosebacoyliminodecamethylene)]

NH C

(CH2)8

C NH

O 7.

(CH2)10

O

Nylon 10,12 [Poly(iminodecamethyleneiminododecanedioyl)]

NH

(CH2)10

NH C

(CH2)10

O 8.

O

Nylon 10,6 [Poly(iminoadipoyliminodecamethylene)]

NH C

(CH2)4

O 9.

C

C NH

(CH2)10

O

Nylon 11 [Poly(imino-1-oxoundecamethylene)]

NH C

(CH2)10

O 10.

Nylon 12 [Poly(imino-1-oxododecamethylene)]

NH C

(CH2)11

O 11.

Nylon 12,18 [Poly(iminododecamethyleneiminooctadecanedioyl)]

NH

(CH2)12

NH C

(CH2)16

O 12.

Nylon 13 [Poly(imino-1-oxotridecamethylene)]

NH C O

(CH2)12

C O

118

1 5.

1 13.

2 Nylon 14,18 [Poly(iminotetradecamethyleneiminooctadecanedioyl)]

NH

(CH2)14

NH C

(CH2)16

(CH2)18

NH C

(CH2)16

7 477

641

2102

323

305

477, 478

64.7

170

384

380

469

198

577

316

343

470

215

634

318

339

471, 472

300

929

323

323

284, 317, 320, 325

334

1044

319

320

473, 477, 478

249

752

331

331

464, 473

O

Nylon 3 [Poly(imino-1-oxotrimethylene)]

NH C

6 307

C

O 15.

5 321

O

Nylon 18,18 [Poly(iminooctadecanedioyliminooctadecamethylene)]

NH

4 1866

C

O 14.

3 573

(CH2)2

O 16.

Nylon 4,6 [Poly(iminotetramethyleneiminoadipoyl)]

NH

(CH2)4

NH C

(CH2)4

O 17.

O

Nylon 5,6 [Poly(iminopentamethyleneiminoadipoyl)]

NH

(CH2)5

NH C

(CH2)4

O 18.

C O

Nylon 6,10 [Poly(iminohexamethyleneiminocebacoyl)]

NH

(CH2)6

NH C

(CH2)8

O 19.

C

C O

Nylon 6,12 [Poly(iminohexamethyleneiminododecanedioyl)]

NH

(CH2)6

NH C

(CH2)10

C

O 20.

O

Nylon 6,7 [Poly(iminohexamethyleneiminopimeloyl)]

(CH2)6

NH C O

(CH2)5

C O

119

NH

2 Nylon 6,8 [Poly(iminohexamethyleneiminosuberoyl)]

NH

(CH2)6

NH C

(CH2)6

O 22.

(CH2)6

NH C

(CH2)7

6 328

7 473

283

868

331

326

476

133

405

325

328

325, 473, 479, 480

249

752

318, 333

331

365, 464, 472, 473

266

811

328

328

473

150

464

323

323

480, 680

334

1044

333

320

472

368

1161

323

317

477

C O

Nylon 7 [Poly(imino-1-oxoheptamethylene)]

NH C

5 330

O

O 23.

4 811

C

Nylon 6,9 [Poly(iminohexamethyleneiminoazelaoyl)]

NH

3 266

(CH2)6

O 24.

Nylon 7,6 [Poly(iminoadipoyliminoheptamethylene)]

NH C

(CH2)4

Nylon 7,7 [Poly(iminopimeloyliminoheptamethylene)]

NH C

(CH2)5

C NH

(CH2)7

O

O 26.

(CH2)7

O

O 25.

C NH

Nylon 8 [Poly(imino-1-oxooctamethylene)]

NH C

(CH2)7

O 27.

Nylon 8,10 [Poly(iminooctamethyleneiminodecanedioyl)]

NH

(CH2)8

NH C

(CH2)8

O 28.

C O

Nylon 8,12 [Poly(iminooctamethyleneiminododecanedioyl)]

NH

(CH2)8

NH C O

(CH2)10

C O

120

1 21.

1 29.

2 Nylon 8,22 [Poly(iminooctamethyleneiminodocosanedioyl)]

NH

(CH2)8

NH C

(CH2)20

O 30.

4 1750

5 321

6 308

7 477

167

522

319

320

473, 479, 480

283

868

318

326

471

146

394

354 Vicat softening temperature

371

589

209

641

353

326

733

264

892

330

296

733

C O

Nylon 9 [Poly(imino-1-oxononamethylene)]

NH C

3 539

(CH2)8

O 31.

Nylon 9,6 [Poly(iminoadipoyliminononamethylene)]

NH C

(CH2)4

O 32.

C NH

(CH2)9

O

Poly(1,1,1-trifluoro-isopropyl methacrylate)

CH3 CH2

C C O CH CF3 O

33.

CH3

Poly(1,1,5-trihydrooctafluoroallyl-2-cyanoacrylate)

C N CH2

C CO O CH2 (CF2)3

34.

CF2H

Poly(1,1,7-trihydrododecafluoroheptyl-2-cyanoacrylate)

C N CH2

C CF2H

121

CO O CH2 (CF2)5

2 Poly(1,1-dichloro-2-fluoroethylene)

CCl2

3 68.9

4 205

5 ~320 Low molecular weight

6 336

7 646

86.6

318

263–273

272

445

132

314

373

420

733

76.1

409

191

186

491, 492

102

366

253

279

539

85.3

288

263

296

539-542

CH F

36.

Poly(1,1-difluoro-2-trifluoromethoxyethylene)

CF2

CH O CF3

37.

Poly(1,1-dihydrotrifluoroethyl-2-cyanoacrylate)

C N CH2

C CO O CH2 CF3

38.

Poly(1,1-dimethylsilazane)

CH3 Si

NH

CH3 39.

Poly(1,1-dimethyltetramethylene)

CH3 C

(CH2)3

CH3 40.

Poly(1,1-dimethyltrimethylene)

CH3 C

(CH2)2

CH3

122

1 35.

1 41.

2 Poly(1,2-butadiene)

CH2

3 64.2

4 240

5 266, 269

6 268

7 734

98.3

426

262

231

498

306

494

653

620

296

418

931

453

449

297

165

579

258 Brittle point

285

582

CH CH CH2

42.

Poly(1,2-dimethyl-1-butenylene)

CH3 C

C CH2

CH2

CH3 43.

Poly(1,3,4-oxadiazolediyl-1,4-phenylene-3,3-phthalidylidene-1,4-phenylene)

N N C

C O

C O CO

45.

Poly(1,3,4-oxadiazolediyl-1,4-phenyleneoxy-1,4-phenyleneisopropylidene-1,4-phenyleneoxy-1,4phenylene)

N N C

CH3

C

O

C

O 46.

CH3

Poly(1,3-dimethylbutyl acrylate)

CH2

O

CH3

C O CH CH2

CH CH3

O

CH3

123

CH

2 Poly(1,3-dioxa-2-propyl-4,6-cyclohexylenemethylene)

CH2

CH2

HC O

48.

CH

CF2

CH2

CH2

CF2

O CF2

CH2

O C

C

O

O (CH2)4

O CF2

CH2

O C

(CF2)3

O 50.

51.

CF2

7 273, 324

324

1232

287

263

328

387

1363

303

284

328

230

816

301

282

328

64.2

375

166, 171

171

735, 736

98.3

489

197

201

507, 507

CH3

O CF2

Poly(1,4-butadiene)

CH2

C O

Poly(1,4,7-trioxy-3,3,5,5-tetrafluoroheptamethyleneisophthaloyl)

O CH2

6 289

CH3

Poly(1,4,7-trioxy-3,3,5,5-tetrafluoroheptamethylenecarbonyl-1,3-phenylene-hexafluorotrimethylene1,3-phenylenecarbonyl)

O CH2

5 322

O

O 49.

4 498

CH

Poly(1,4,7-trioxy-3,3,5,5-tetrafluoroheptamethylene-5-pentyloxyisophthaloyl)

O CH2

3 144

O C

C

O

O

–CH2–CH=CH–CH2– 52.

Poly(1-ethyl-1-butenylene)

C

CH CH2

CH2

CH3

CH2

124

1 47.

1 53.

2 Poly(17-fluoroalkyl methacrylate)

3 321

4 1239

5 310

6 259

7 686

86.0

368

241

234

662

132

667

192

198

504

235

1205

220

195

273

119

454

~250

262

525

162

623

251

260

589

CH3 CH2

C C O CH2

(CF2)7

CF3

O 54.

Poly(1-bromo-1-butenylene)

CH2

C CH CH2 Br

55.

Poly(1-butyl-1-butenylene)

CH2

C CH CH2 (CH2)3

56.

CH2

C

CH CH2

(CH2)9 57.

CH3

Poly(1-decyl-1-butenylene)

CH3

Poly(1-ethyl-1-methyltetramethylene)

CH3 C

(CH2)3

CH2 58.

CH3

Poly(1H,1H,3H-hexafluorobutyl acrylate)

CH2

CH C O CH2

CHF

CF3 125

O

CF2

2 Poly(1H,1H,5H-octafluoropentyl acrylate)

CH2

3 189

4 724

5 238

6 261

7 589

206

696

309

296

603

261

946

286

276

603

316

1197

258

264

603

277

1145

256 Crystalline

242

589

CH C O

CH2

(CF2)3

CF2H

O 60.

Poly(1H,1H,5H-octafluoropentyl methacrylate)

CH3 CH2

C C O CH2

(CF2)3

CF2H

O 61.

Poly(1H,1H,7H-dodecafluoroheptyl methacrylate)

CH3 CH2

C C O CH2

(CF2)5

CF2H

O 62.

Poly(1H,1H,9H-hexadecafluorononyl methacrylate)

CH3 CH2

C C O CH2

(CF2)7

CF2H

O 63.

Poly(1H,1H,-pentadecafluorooctyl acrylate)

CH2

CH C O CH2 O

(CF2)6

CF3

126

1 59.

1 64.

2 Poly(1H,1H-heptafluorobutyl acrylate)

CH2

3 167

4 645

5 243

6 259

7 315, 589, 590

184

523

~330

352 (syndio)

602

139

519

247

268

589

119

538

226

221

509

184

939

190

196

286, 505

115

502

221

229

504, 505, 507

CH C O CH2

(CF2)2

CF3

O 65.

Poly(1H,1H-heptafluorobutyl methacrylate) syndiotactic

CH3 CH2

C C O CH2

(CF2)2

CF3

O 66.

Poly(1H,1H-pentafluoropropyl acrylate)

CH2

CH C O CH2

CF2

CF3

O 67.

Poly(1-heptene)

CH2

CH (CH2)4 CH3

68.

Poly(1-heptyl-1-butenylene)

C

CH CH2

(CH2)6 69.

CH2

CH3

Poly(1-isopropyl-1-butenylene)

C CH CH2 CH CH3

127

H3C

CH2

2 Poly(1-methyloctamethylene)

CH

3 154

4 664

5 215

6 232

7 538

81.3

457

159, 183

178

502, 508

140

509

283 low molecular wieght

275

499

115

578

196

199

504

132

528

293

250

286, 396, 505, 506

146

537

282

272

624

(CH2)7

CH3 71.

Poly(1-pentenylene)

–CH=CH–(CH2)3– 72.

Poly(1-phenyl-1-butenylene)

C

73.

CH CH2

CH2

Poly(1-propyl-1-butenylene)

C

CH CH2

CH2

CH2 CH2 74.

CH3

Poly(1-tert-butyl-1-butenylene)

H3C

C

CH CH2

C

CH3

CH2

CH3 75.

Poly(2,2-dimethylbutoxyethylene)

CH2

CH O

CH3

CH2 C CH2 CH3

CH3

128

1 70.

1 76.

2 Poly(2,3,3,3-tetrafluoropropylene)

CH2

3 71.9

4 240

5 315

6 300

7 291

135

371

378

364

291

160

366

435 softening point

437

287

137

338

406

405

548, 557

CF CF3

77.

Poly(2,3,4,5,6-pentafluorostyrene)

CH2

CH

F

F

F

F F

78.

Poly(2,4,6-trimethylstyrene)

CH2

CH

H3C

CH3

CH3 79.

Poly(2,4-dichlorostyrene)

CH2

CH Cl

129

Cl

2 Poly(2,4-diisopropylstyrene)

CH2

3 211

4 548

5 ~435

6 385

7 287

143

340

385

420

300, 548, 555, 563, 574

137

338

379

405

280, 548, 558

120

307

374

391

287

CH CH3 CH CH3

H3C 81.

CH CH3

Poly(2,4-dimethylstyrene)

CH2

CH CH3

CH3 82.

Poly(2,5-dichlorostyrene)

CH2

CH Cl

Cl 83.

Poly(2,5-fluorostyrene)

CH2

CH F

F

130

1 80.

1 84.

2 Poly(2,5-diisopropylstyrene)

CH2

3 211

4 548

5 441

6 385

7 287

143

340

416

420

548

137

338

440

405

287, 494, 559

188

431

440

437

701

CH CH3 CH CH3

H3C CH H3C 85.

Poly(2,5-dimethylstyrene)

CH2

CH CH3

H3C 86.

Poly(2,6-dichlorostyrene)

CH2

CH

Cl

87.

Cl

Poly(2,6-xylenyl methacrylate)

CH3 CH2

CH3

C C O O 131

CH3

2 Poly(2-bromoethyl methacrylate)

3 135

4 380

5 325

6 355

7 560

206

624.6

339

330

551

204

711

340

287

545

135

349

450

388

556

94.5

372

256

254

500

CH3 CH2

C C O (CH2)2

Br

O 89.

Poly(2-butoxycarbonylstyrene)

CH2

CH C O (CH2)3

CH3

O 90.

Poly(2-butoxymethylstyrene)

CH2

CH CH2 O (CH2)3 CH3

91.

Poly(2-carboxystyrene)

CH2

CH C OH O

92.

Poly(2-chloro-1,4,4-trifluoro-1-butenylene)

F C

C CH2 Cl

CF2

132

1 88.

1 93.

2 Poly(2-chlorobenzoyloxyethylene)

CH2

CH

3 152

4 425

5 335

6 355

7 278, 628, 653

128

374

>365

342

361

124

302

392

410

548

159

562

313

283

514

226

518

418

436

706

Cl

O O C 94.

Poly(2-chloroethyl methacrylate)

CH3 C

CH2

C O (CH2)2

Cl

O 95.

Poly(2-chlorostyrene)

CH2

CH Cl

96.

Poly(2-cyclohexylethylethylene)

CH2

CH CH2

97.

CH2

CH2 CH CH2

Poly(2-decanehydronaphthyl methacrylate) CH3 CH2

CH2 CH2 CH2

C

CH2 CH2 C O CH CH CH2 O

133

CH2 CH CH2 CH2 CH2

2 Poly(2-ethoxycarbonylphenyl acrylate)

CH2

3 200

4 617

5 303

6 325

7 560

172

444.6

391

387

551

170

531

347 low viscosity

320

545

126

406

345

310

273

234

659

340, 328338

355

723

CH C

O

O O 99.

C

O

C 2H 5

Poly(2-ethoxycarbonylstyrene) CH2 CH

C O CH2

CH3

O 100.

Poly(2-ethoxymethylstyrene)

CH2

CH CH2

101.

O CH2

CH3

Poly(2-ethyl-1,3-dioxa-4,6-cyclohexylenemethylene)

CH2 CH2

CH CH O

O CH CH2

102.

CH3

Poly(2-ethyl-2-methylpropylene terephthalate)

CH3 CH2

C CH2

H3C CH2

O C O

C O O

134

1 98.

1 103.

2 Poly(2-ethylhexyl methacrylate)

3 216

4 797

5 263 Brittle point

6 271

7 581

143

404

376

354

555

131

337

384

389

562

240

801.6

318

299

551

121

346

358

350

690

CH3 CH2

104.

C C O CH2

CH

(CH2)3

O

CH2

CH3

Poly(2-ethylstyrene)

CH2

CH CH2

105.

CH3

CH3

Poly(2-fluoro-5-methylstyrene) CH2 CH F H3C

106.

Poly(2-hexyloxycarbonylstyrene)

CH2

CH C O

(CH2)5

CH3

O 107.

Poly(2-hydroxyethyl methacrylate)

CH3 CH2

C O CH2

CH2 OH

135

O

C

2 Poly(2-hydroxymethylstyrene)

CH2

4 327

5 433

6 410

7 273

138

433 (80% isotactic), 369 (atactic), 357 (58% syndio)

328, 359, 311 (80%

560, 604606, 663

isotactic),

319(80% isotactic), 374

393 (58%

(atactic),

CH CH2

109.

3 134

OH

Poly(2-hydroxypropyl methacrylate)

CH3 CH2

110.

C O CH2

CH

O

OH

syndiotactic)

CH3 206

548.6

400

376

551

223

637.6

341

350

551

CH C O CH2

CH CH3

O

CH3

Poly(2-isopentyloxycarbonylstyrene)

CH2

387 (58% syndiotact.)

Poly(2-isobutoxycarbonylstyrene)

CH2

111.

C

CH

O C O CH2

CH2 CH CH3

CH3

136

1 108.

1 112.

2 Poly(2-isopentyloxymethylstyrene)

CH2

3 221

4 725

5 351 (low viscosity)

6 305

7 545

204

636

~330

321

553

189

469.6

419

402

551

187

555

361 (low viscosity)

337

545

CH CH2 O

(CH2)2

CH CH3 CH3

113.

Poly(4-isopentyloxystyrene)

CH2

CH

CH3 O 114.

(CH2)2

CH CH3

Poly(2-isopropoxycarbonylstyrene)

CH2

CH CH3 C O CH CH3 O

115.

Poly(2-isopropoxymethylstyrene)

CH2

CH CH2

137

CH3 O CH CH3

2 Poly(2-isopropyl-1,3-dioxa-4,6-cyclohexylenemethylene)

CH2

4 424

5 329

6 340

7 273

182

534

319

341

560

155

421

403 (low viscosity)

368

556

123

496

223

248

587

153

451

362 (low viscosity)

339

545

CH2 CH CH O

CH3 117.

3 144

O CH CH

CH3

Poly(2-methoxycarbonylphenyl acrylate)

O CH3 C O CH2

CH

O C O 118.

Poly(2-methoxycarbonylstyrene)

CH2

CH C O CH3 O

119.

Poly(2-methoxyethyl acrylate)

CH2

CH C O CH2

CH2

O CH3

O 120.

Poly(2-methoxymethylstyrene)

CH2

CH CH2

O CH3

138

1 116.

1 121.

2 Poly(2-methoxystyrene)

CH2

3 136

4 363

5 ~348

6 375

7 568

109

318

355

343

273

148

556

241 Brittle point

266

582, 706

165

645

235 Brittle point

256

582

126

314

293, 371375, 453, 443, 455

401

670, 671, 689, 697, 709, 726

CH O CH3

122.

Poly(2-methyl-1,3-dioxa-4,6-cyclohexylenemethylene) CH2 CH2 CH CH O

O CH CH3

123.

Poly(2-methylbutyl acrylate)

CH2

124.

C O CH2

CH CH2

O

CH3

CH3

Poly(2-methylpentyl acrylate)

CH2

125.

CH

CH C O CH2

CH CH2

O

CH3

Poly(α-methylstyrene)

CH3 CH2

C

CH2

CH3

139

2 Poly(2-methylstyrene)

CH2

3 126

4 315

5 409

6 400

7 282, 548, 555, 563, 568

183

487

358

376

585

199

833

228 Brittle point

239

582

255

977

286

261

575

223

712

365

313

551

CH CH3

127.

Poly(2-naphthyl acrylate)

CH2

CH C O O

128.

Poly(2-octyl acrylate)

CH2

CH

CH3

C O

CH

(CH2)5

CH3

O 129.

Poly(2-octyloxystyrene)

CH2

CH O

130.

(CH2)7

CH3

Poly(2-pentyloxycarbonylstyrene)

CH2

CH C O O

(CH2)4

CH3

140

1 126.

1 131.

2 Poly(2-pentyloxymethylstyrene)

CH2

(CH2)4

6 277

7 545

246

730

336 low viscosity

337

545

213

462

397 (low viscosity)

461

556

189

533.6

381

354

551

187

621

370 low viscosity

301

545

CH CH2 O

133.

5 320

CH3

Poly(2-phenethyloxymethylstyrene)

CH2

4 798

CH CH2 O

132.

3 221

CH2

CH2

Poly(2-phenoxycarbonylstyrene) CH2 CH C O O

134.

Poly(2-propoxycarbonylstyrene)

CH2

CH C O CH2

CH2 CH3

O 135.

Poly(2-propoxymethylstyrene)

CH2

CH CH2 O CH2

CH2 CH3 141

2 Poly(2-tert-butylaminoethyl methacrylate) CH3 CH2

C

4 647

5 306

6 300

7 560, 597

206

563

345

367

585

66.7

217

300

307

291, 620, 647, 648

206

609

293

338

650

182

553

318

329

599, 706

CH3

C O (CH2)2 137.

3 194

NH C CH3

O Poly(2-tert-butylphenyl acrylate) CH2 CH

CH3

C O O H3C C CH3

138.

139.

CH3 Poly(3,3,3-trifluoropropylene) CH2 CH

CF3 Poly(3,3-dimethyl-3-phenylpropionyloxyethylene)

CH2

CH O C O CH3 CH2

C CH3

140.

Poly(3,3-dimethylbutyl methacrylate)

CH3 CH2

C C O CH2 O

CH3 CH2

C

CH3

CH3

142

1 136.

1 141.

2 Poly(3,3-phthalidylidene-1,4-phenyleneoxy-5-tert-butylisophthaloyloxy-1,4-phenylene)

O C

C

H3C

CO

4 870

5 552

6 525

7 313

296

550

513, 538

538

313, 323

390

720

591, 543

542

6, 313

137

338

401

405

548, 558

C O O

O

O

3 457

C

CH3

CH3 142.

Poly(3,3-phthalidylidene-1,4-phenyleneoxycarbonyloxy-1,4-phenylene)

O C O

C

O

O CO 143.

Poly(3,3-phthalidylidene-1,4-phenyleneoxyisophthaloyloxy-1,4-phenylene)

C

O C O

O

C O O

CO 144.

Poly(3,4-dichlorostyrene)

CH2

CH

Cl 143

Cl

2 Poly(3,4-dimethylbenzoylethylene)

CH2

3 162

4 411

5 315

6 346

7 267

143

340

384

420

548

233

747

274

312

601

143

340

377

420

563

CH C O

CH3 CH3 146.

Poly(3,4-dimethylstyrene)

CH2

CH

CH3 CH3 147.

Poly(3,5,5-trimethylhexyl methacrylate)

CH3 CH2

C

CH3

C O CH2 O 148.

Poly(3,5-dimethylstyrene)

CH2

H3C

CH

CH3

CH2

CH CH2

C CH3

CH3

CH3

144

1 145.

1 149.

2 Poly(3-bromobenzoyloxyethylene)

CH2

CH

3 159

4 436

5 331

6 365

7 278, 628

151

428

338

352

278, 628, 653

124

302

363

410

548

176

652

248

270

511

184

505

320

364

560

Br

O O C 150.

Poly(3-chlorobenzoyloxyethylene)

CH2

CH

Cl

O O 151.

C

Poly(3-chlorostyrene)

CH2

CH

Cl 152.

Poly(3-cyclohexylpropylethylene)

CH2

CH CH2

153.

CH2

CH2

CH2 CH CH2

Poly(3-dimethylaminophenyl acrylate)

CH2

CH2 CH2 CH2

CH C O O 145

H3C N CH3

2 Poly(3-ethoxycarbonylphenyl acrylate)

CH2

3 200

4 617

5 297

6 324

7 560

143

404

~303

354

555

117

311

398

376

686

129

369

355

349

686

121

451

277, 278, 223

268

685, 718, 724

CH C O O O C O C2H5

155.

Poly(3-ethylstyrene)

CH2

CH

CH2 CH3 156.

Poly(3-fluoroalkyl α-fluoroacrylate)

F CH2

C

O C O CH2 157.

CF3

Poly(3-fluoroalkyl methacrylate)

CH3 CH2

C

O C O CH2 158.

CF3

Poly(3-hydroxybutyrate)

CH2

CH O

O C

(CH2)3

OH

146

1 154.

1 159.

2 Poly(3-hydroxymethylstyrene)

CH2

(CH2)2

7 273

157

611

217

257

594

182

534

311

341

560

140

586

198

239

587

148

556

228 Brittle point

266

582

CH CH3 O CH3

O Poly(3-methoxycarbonylphenyl acrylate)

CH2

6 410

CH C O

161.

5 398

OH

Poly(3-methoxybutyl acrylate)

CH2

4 327

CH

CH2 160.

3 134

CH C O O C O O CH3

162.

Poly(3-methoxypropyl acrylate)

CH2

CH C O (CH2)3 O CH3 O

163.

Poly(3-methylbutyl acrylate)

CH2

CH C O CH2

CH3

147

O

CH2 CH CH3

2 Poly(3-methylstyrene)

CH2

3 126

4 315

5 370

6 400

7 548, 555, 563, 572

157

561

289

280

596, 597

148

565

267, 257

262

560, 582

145

363.4

389

399

544

208

632

318

329

651

CH

CH3 165.

Poly(3-oxabutyl methacrylate)

CH3 CH2 O 166.

167.

C C O (CH2)3

Poly(3-pentyl acrylate) CH2 CH

CH3

CH3

CH2 O C O CH CH2 Poly(4-acetylstyrene)

CH2

O

CH3

CH

O C CH3 168.

Poly(4-benzoylbutyryloxyethylene)

CH2

CH O

O C

(CH2)3 C O

148

1 164.

1 169.

2 Poly(4-benzoylstyrene)

CH2

3 204

4 528

5 371

6 386

7 544

213

539

383

395

578

175

476

317

329

627

159

436

365

365

278, 628, 652, 653

CH

O C 170.

Poly(4-biphenyl acrylate)

C H2 O 171.

CH C

O

Poly(4-bromo-3-methoxybenzoylethylene)

CH2

CH C O

O CH3 Br 172.

Poly(4-bromobenzoyloxyethylene)

CH2

CH O

O

C

Br 149

Poly(4-bromostyrene)

CH

2

3 131

4 310

5 391, 414430

6 423

7 548-550, 668

174.

Br Poly(4-butoxycarbonylphenyl acrylate)

234

909

286

257

560

254

669

401 softening point

380

611

206

625

349

330

544

204

711

< 283

287

552

CH2

175.

177.

CH C O

C O

O

O

(CH2)3

CH3

Poly(4-butoxycarbonylphenylmethacrylamide) CH3

CH2

176.

CH2

C C NH

C O

O

O

Poly(4-butoxycarbonylstyrene) CH2 CH

O C O (CH2)3 Poly(4-butoxymethylstyrene) CH2

(CH2)3

CH3

CH3

CH

CH2 O (CH2)3 CH3

150

1 173.

1 178.

2 Poly(4-butoxystyrene)

CH2

(CH2)3

7 552, 553

178

586

279

304

552, 553, 555

217

715

334

303

278, 628

183

284

CH3

Poly(4-butylyloxybenzoyloxyethylene)

CH2

6 301

CH

(CH2)3 180.

5 ~320

CH3

Poly(4-butylstyrene)

CH2

4 621

CH

O 179.

3 187

CH O C

O

(CH2)2

CH3

O 181.

Poly(4-carboxyphenylmethacrylamide)

CH3 CH2

527 >473 (Softening (decompoint) position)

611

C C OH

O

O

151

C NH

2 Poly(4-carboxystyrene)

CH2

3 135

4 293

5 386

6 388

7 544

140

354

418

396

548

129

324

395

398

548

140

354

387

396

548

CH

COOH 183.

Poly(4-chloro-2-methylstyrene)

CH2

CH CH3

Cl 184.

Poly(4-chloro-3-fluorostyrene)

CH2

CH

F Cl 186.

Poly(4-chloro-3-methylstyrene)

CH2

CH

CH3 Cl

152

1 182.

1 187.

2 Poly(4-chlorobenzoylethylene)

CH2 O 188.

3 142

4 372

5 310, 362

6 333

7 627, 628

151

428

357

352

278, 628, 652, 653

124

302

383, 388401

410

287, 548550, 667

150

624

233-238

240

754

204

731

~263

279

650

CH Cl

C

Poly(4-chlorobenzoyloxyethylene) CH2 CH

O O

C

Cl

189.

Poly(4-chlorostyrene) CH2 CH

190.

Poly(4-cyanobutyl acrylate)

Cl

CH2

CH C O

C N

(CH2)4

O 191.

Poly(4-cyclohexylbutyryloxyethylene)

CH2

CH O C O CH2

(CH2)2

CH2 CH2 CH2

153

CH2 CH CH2

193.

2 Poly(4-decylstyrene) CH2 CH

(CH2)9 CH3 Poly(4-dimethylaminocarbonylstyrene) CH2 CH

3 280

4 1120

5 208

6 250

7 554

174

437

398

398

544

314

1138

221

276

554

181

568

343

319

278, 628

CH3 O C N CH3 194.

Poly(4-dodecylstyrene)

CH2

CH

(CH2)11 195.

CH3

Poly(4-ethoxybenzoyloxyethylene)

CH2

CH O

O

C

O CH2

CH3

154

1 192.

1 196.

2 Poly(4-ethoxycarbonylphenyl acrylate)

CH2

197.

3 200

4 617

5 310

6 324

7 766

220

491

441 (Softening point)

448

611

172

445

367

387

544

153

442

~359

346

553

162

476

325

305

627, 628

CH C O

C O C2H5

O

O

Poly(4-ethoxycarbonylphenylmethacrylamide)

CH3 CH2

C C NH

C O CH2

O

O

198.

Poly(4-ethoxycarbonylstyrene) CH2 CH

199.

Poly(4-ethoxystyrene)

O C O CH2

CH2

CH3

CH

O CH2 200.

CH3

Poly(4-ethylbenzoylethylene)

CH2 O

CH3

CH C

CH2

CH3 155

2 Poly(4-ethylstyrene)

CH2

4 404

5 300, 351

6 354

7 552, 554, 555

139

390

368

356

686

151

448

353

337

686

115

286

368

402

548-550, 563-565

CH

CH2 202.

3 143

CH3

Poly(4-fluoroalkyl α-fluoroacrylate)

F

CH2

C C O CH2

CF2

CF2H

O 203.

Poly(4-fluoroalkyl methacrylate)

CH3 CH2

C C O CH2

CF2

CF2H

O 204.

Poly(4-fluorostyrene)

CH2

CH

F

156

1 201.

1 205.

2 Poly(4-hexadecylstyrene)

CH2

O 208.

(C H 2 ) 4

213

721.4

339

295

544

240

801.6

339

299

554

238

888

253

268

552

CH

C

O

(C H 2 ) 5 C H 3

Poly(4-hexyloxymethylstyrene)

C H2

7 554

CH3

Poly(4-hexyloxycarbonylstyrene)

CH2

6 325

CH

O C 207.

5 278

CH3

Poly(4-hexanoylstyrene)

C H2

4 1175

CH

(CH2)15 206.

3 382

CH

O

(C H 2 ) 5

C H3

157

C H2

2 Poly(4-hexylstyrene)

CH2

5 246

6 277

7 554

206

549

363

376

544

189

470

368

402

544

189

520

342

363

278, 628

CH3

Poly(4-isobutoxycarbonylstyrene)

CH2

4 765

CH

(CH2)5 210.

3 212

CH

CH3 O C O CH2 211.

CH CH3

Poly(4-isopropoxycarbonylstyrene)

CH2

CH

CH3 O C O CH CH3 212.

Poly(4-isopropylbenzoyloxyethylene)

CH2

CH O C O

CH3 CH CH3

158

1 209.

1 213.

2 Poly(4-methoxy-2-methylstyrene)

CH2

3 152

4 386

5 ~358, 363

6 394

7 568

200

482

379

415

560

202

410

453 (Softening point)

493

611

155

421

386

368

544

CH CH3

O CH3 214.

Poly(4-methoxycarbonylphenyl methacrylate)

CH3 CH2

215.

C C O

C O CH3

O

O

Poly(4-methoxycarbonylphenylmethacrylamide)

CH3 CH2

216.

C C NH

C O CH3

O

O

Poly(4-methoxycarbonylstyrene)

CH2

CH

159

O C O CH3

2 Poly(4-methoxymethylstyrene) CH2 CH

CH2

3 153

4 451

5 350

6 339

7 552

136

363

386

375

553, 568570, 672

126

315

366, 374, 382

400

548, 555, 569, 572, 573, 708

206

509

400

405

544

O CH3

218.

Poly(4-methoxystyrene) CH2 CH

219.

Poly(4-methylstyrene) CH2 CH

220.

Poly(4-morpholinocabonylstyrene) CH2 CH

O CH3

CH3

CH2 O

C N CH2

CH2 O CH2

160

1 217.

1 221.

2 Poly(4-nonadecyl styrene) CH2 CH

(CH2)18 222.

263

1031

220

255

554

417

1198

305

348

554

247

843

323

293

544

CH3

Poly(4-octanoylstyrene)

CH2

7 273

CH

(CH2)17 224.

6 360

CH3

Poly(4-octadecylstyrene)

CH2

5 305

CH

(CH2)8 223.

4 1206

CH3

Poly(4-nonylstyrene)

CH2

3 434

CH

(CH2)6

CH3

161

O C

226.

2 Poly(4-octylstyrene) CH2 CH

(CH2)7 CH3 Poly(4-p-anisoylstyrene) CH2 CH

3 246

4 943

5 228

6 261

7 554

211

521

376

405

544

194

515

~373 (softening point)

377

287

185

423

434

437

571, 576

O CH3 227.

Poly(4-phenoxystyrene) CH2 CH

O 228.

Poly(4-phenyl styrene)

CH2

CH

162

1 225.

1 229.

2 Poly(4-phenylacetylstyrene)

CH2

Poly(4-piperidinocarbonylstyrene) CH2 CH

CH2 CH2

232.

6 393

7 544

214

534

387

401

544

170

453

375

375

544

189

534

365

354

544

CH2 CH2 CH2

Poly(4-propionylstyrene) C H2 C H

O C C H2 C H3 Poly(4-propoxycarbonylstyrene) C H2 C H

C

O

CH2

CH2

C H3

163

O

5 351

CH2

CO N 231.

4 561

CH

O C 230.

3 221

234.

2 Poly(4-propoxymethylstyrene) C H2 C H

C H2 O Poly(4-propoxystyrene)

C H2

C H2

C H2

Poly(4-p-toluoylstyrene)

CH2

5 295

6 301

7 552

170

531

343

320

553

220

524

372

420

544

178

511

359

348

555

CH3

C

O

Poly(4-sec-butylstyrene)

C H2

CH

C H3

CH

CH3

CH

H3C 236.

C H2

4 621

CH

O 235.

C H2

3 187

C H2

C H3

164

1 233.

1 237.

2 Poly(4-tert-butylbenzoylethylene) C H2 C H

H 3C 238.

C

O

C

C H3

C H3 Poly(4-tert-butylbenzoyloxyethylene) CH2 CH

3 196

4 515

5 377

6 344

7 628

206

572

374

360

278, 628, 655

238

607

356, 403451

392

758, 760

206

563

344

366

585

C O

O

H3C

C CH3 CH3

239.

Poly(4-tert-butylcyclohexyl methacrylate) C H3

C H2

C C

240.

C H2 CH C H2

O

O Poly(4-tert-butylphenyl acrylate)

C H2

CH C

C H3 C

C H3

C H3

C H3 O

C C H3

CH3 165

O

C H2 CH C H2

2 Poly(4-tert-butylstyrene) CH2 CH

CH3

C

3 178

4 446

5 399–404

6 399

7 666

348

1156

237

301

554

196

631

343

311

544

127

236

429

494

714

C H3

C H3

242.

Poly(4-tetradecylstyrene)

CH2

CH

(CH2)13 243.

Poly(4-valerylstyrene)

CH2

O 244.

CH3

CH

C (CH2)3

Poly(4-vinyl phenol) CH2 CH

OH

CH3

166

1 241.

1 245.

2 Poly(5,7-dihydro-1,3,5,7-tetraoxobenzo[1,2-c:4,5-c']dipyrrole-2,6[1H,3H]-diyl-1,4-phenyleneoxy1,4phenylene)

N 246.

N

CO

CO

CO

CO

CO

CO

CO

CO

N

N

CO

CO

CO

CO

CO

CO

CO

CO

Poly(5-bromo-2-butoxystyrene) CH2

5 523, 773, 653

6 649

7 298, 300-309

319

519

618

615

303

286

709

408

403

299

303

734

408

413

299

303

844

383

359

299

208

667

320

312

547

S

(CH2)2 CH (CH2)4 CH3

CH3

N

(CH2)3

C

(CH2)3

CH3

N

(CH2)9

CH O

(CH2)3

CH3

167

Br

4 476

O

Poly(5,7-dihydro-1,3,5,7-tetraoxobenzo[1,2-c:4,5-c']dipyrrole-2,6[1H,3H]-diylnonamethylene)

N 250.

CO

Poly(5,7-dihydro-1,3,5,7-tetraoxobenzo[1,2-c:4,5-c']dipyrrole-2,6[1H,3H]-diyl-4,4dimethylheptamethylene)

N 249.

CO

Poly(5,7-dihydro-1,3,5,7-tetraoxobenzo[1,2-c:4,5-c']dipyrrole-2,6[1H,3H]-diyl-3methylheptamethylene)

N 248.

CO

Poly(5,7-dihydro-1,3,5,7-tetraoxobenzo[1,2-c:4,5-c']dipyrrole-2,6[1H,3H]-diyl-1,4-phenylenethio-1,4phenylene)

N 247.

CO

3 309

2 Poly(5-bromo-2-ethoxystyrene)

CH2

3 174

4 487

5 353

6 357

7 547

225

680

310 (low viscosity)

331

547

191

511

308

374

547

157

408

359

385

547

225

755

322 (low viscosity)

298

547

CH O CH2

CH3

Br 252.

Poly(5-bromo-2-isopentyloxystyrene)

CH2

CH

O (CH2)2

CH3

Br 253.

CH CH3

Poly(5-bromo-2-isopropoxystyrene)

CH2

CH CH3 O CH CH3

Br 254.

Poly(5-bromo-2-methoxystyrene)

CH2

CH O CH3

Br 255.

Poly(5-bromo-2-pentyloxystyrene)

CH2

CH O

Br

(CH2)4

CH3

168

1 251.

1 256.

2 Poly(5-bromo-2-propoxystyrene) CH2 CH

O

257.

5 327 (low viscosity)

6 331

7 547

177

644

250

275

580

186

677

223

274

755

156

492

350

317

686

194

469

360

414

548

CH

CH2 CH2 C N C O CH O CH2 CH3 O

Poly(5-cyano-3-thiapentyl acrylate)

CH2

4 577

CH3

Br Poly(5-cyano-3-oxapentyl acrylate)

CH2

258.

(CH2)2

3 191

CH C O

(CH2)3

S

(CH2)2

C N

O 259.

Poly(5-fluoroalkyl methacrylate)

CH3 CH2

C C O CH2

CF2

CF3

O 260.

Poly(5-tert-butyl-2-methylstyrene) CH2 CH

H3C

CH3

H3C C 169

CH3

2 Poly(6-cyano-3-thiahexyl acrylate)

CH2

3 203

4 769

5 215

6 264

7 755

203

769

215

264

755

204

823

233

248

587

237

944

214

251

755

206

696

320

296

686

CH C O

(CH2)3

S

(CH2)3

C N

O 262.

Poly(6-cyano-4-thiahexyl acrylate)

CH2

CH C O

S

(CH2)4

(CH2)2

C N

O 263.

Poly(7,7,8,8-tetrafluoro-3,6-dioxaoctyl acrylate)

CH2

CH C O (CH2)2

(CH2)2

O

O CF2

CF2H

O 264.

Poly(8-cyano-7-thiaoctyl acrylate)

CH2

CH C O

(CH2)7

S

CH2

C N

O 265.

Poly(8-fluoroalkyl methacrylate)

CH3 CH2

C C O CH2 O

(CF2)3

CF2H

170

1 261.

1 266.

2 Poly(9-iodononylethylene)

CH2

5 267

6 260

7 649

125

303

513

413

287, 291, 295, 566

143

210

487-618; 628-649

682

287, 494, 751-753, 759

129

335

395

385

728

173

551

330

314

729

190

576

304

330

732

CH2I

Poly(α,β,β-trifluorostyrene)

CF2

4 858

CH (CH2)8

267.

3 223

CF

268.

Poly(acenaphthylene)

269.

Poly(allyl-2-cyanoacrylate)

CH

CH

C N CH2

C CH CH2

CO O CH2 270.

Poly(allyloxyethyl-2-cyanoacrylate)

C N CH2

C CO O (CH2)2

271.

O CH2

CH CH2

Poly(allyloxyisopropyl-2-cyanoacrylate)

C N CH2

C CO O CH2 CH O CH2

171

CH3

CH CH2

2 Poly(aniline)

3 87.7

4 247

5 373

6 355

7 761

128

390

314, 347

329

627, 628

138

391

344

353

278, 398, 568, 580, 628, 652, 653

127

381

333

333

511, 514, 661

112

498

218, 217

225

588, 600, 620-624, 709

145

472

330 Vicat softening point

307

599

NH 273.

Poly(benzoylethylene)

CH2

CH

O C 274.

Poly(benzoyloxyethylene)

CH2

CH O

O C 275.

Poly(benzylethylene)

CH2

CH CH2

276.

Poly(butoxyethylene)

CH2

CH O

277.

(CH2)3

CH3

Poly(butyl chloroacrylate)

Cl CH2

C C O O

(CH2)3

CH3

172

1 272.

1 278.

2 Poly(butyl cyanoacrylate)

3 150

4 457

5 358

6 328

7 613

245

706

321

347

725

193

785

223

246

699

200

643

291

311

699

200

602

304

332

699

102

449

223

227

509-513

C N CH2

C C O

(CH2)3

CH3

O 279.

Poly(butylene 2,6-naphthalate)

C O C

(CH2)4

O

O

O 280.

Poly(butylene adipate)

C

(CH2)4

C O

O 281.

282.

283.

(CH2)4

O

O

Poly(butylene isophthalate)

C

C O

O

O

(CH2)4

Poly(butylene terephthalate)

C

C O

O

O

Poly(butylethylene)

CH2

(CH2)4

O

O

CH (CH2)3 173

CH3

2 Poly(butylimino-2,2,3,3,4,4-hexafluoropentamethylenebutyliminoadipoyl)

N

285.

CH2

(CF2)3

CH2 N

(CH2)3

(CH2)3 O

CH3

CH3 C

(CF2)3

(CH2)3 O

C N

6 254

7 481

383

1508

~293 Brittle point

252

481

121

476

253

254

600

116

358

~303

324

750

206

500

405

412

6

282

594

480

475

6

O

(CH2)6

CH3 CH S

(CH2)3

CH3

Poly(butyryliminoethylene)

CH2

5 283–288

C

Poly(butylthioethylene)

CH2

4 1508

O (CH2)3

CH3

287.

(CH2)4

Poly(butyliminohexafluoroglutarylbutyliminohexamethylene)

N

286.

C

3 383

CH NH C

(CH2)2

CH3

O 288.

289.

Poly(carbonyl-1,3-phenylenecarbonyloxy-1,3-phenyleneoxy)

C

C O

O

O

O

Poly(carbonyl-1,3-phenylenecarbonyloxy-1,4-phenylene-1,4-phenyleneoxy)

C

C O

O

O

O

174

1 284.

1 290.

2 Poly(carbonyl-1,4-phenylenecarbonyloxy-1,4-phenylene-(methyl)phenylmethylene-1,4-phenyleneoxy)

3 391

4 788

5 483-493

6 496

7 6

282

552

540

511

6

494

834

598

592

6

554

1053

563

526

6

CH3

291.

292.

C

C

O

O

O

C

O

Poly(carbonyl-1,4-phenylenecarbonyloxy-1,4-phenylene-1,4-phenyleneoxy)

C

C O

O

O

O

Poly(carbonyl-1,4-phenylenesulfonyl-1,4-phenylenecarbonyloxy-1,4-phenylene-3,3-phthalidylidene1,4-phenylene)

C

SO2

O

C O O

O C O CO

293.

Poly(carbonyl-1,4-phenylenesulfonyl-1,4-phenylenecarbonyloxy-1,4-phenylenediphenylmethylene1,4-phenyleneoxy)

C O

SO 2

C O

C

O

O 175

2 Poly(carbonyl-1,4-phenylenesulfonyl-1,4-phenylenecarbonyloxy-1,4-phenyleneisopropylidene-1,4phenyleneoxy)

3 437

4 837

5 518

6 522

7 6

64.5

210

~325, 373

307

238

773

331

308

283, 286, 325, 360, 397, 399, 413, 415, 476, 523, 608, 629-645 706

272

932

329

292

706

153

464

349

330

650

CH3

C

SO2

O 295.

C O

C

O

CH3

Poly(chlorotrifluoroethylene)

CF

O

CF2

Cl 296.

Poly(cyclodecyl methacrylate)

CH3 CH2

297.

C

CH2 C O CH CH2 O

CH2

CH2

CH2

CH2

CH2 CH2 CH2

Poly(cyclododecyl methacrylate)

CH3 CH2

298.

C

CH2 C O CH CH2 O

CH2

CH2

CH2

CH2

CH2

CH2

Poly(cyclohexanoyloxyethylene)

CH2

CH O

CH2 C CH CH2 O

CH2 CH2 CH2

CH2 CH2 CH2

176

1 294.

1 299.

2 Poly(cyclohexyl acrylate)

CH2

300.

CH

CH2 C O CH CH2 O

3 153

4 532

5 292

6 288

7 583

167

413

387 Vicat softening point

404

599

170

456

384

373

742

170

552

298

308

650

124

326

393, 406

380

514-520

CH2 CH2 CH2

Poly(cyclohexyl chloroacrylate)

Cl CH2

C

CH2 C O CH

CH2

CH2

CH2

O 301.

CH2

Poly(cyclohexyl methacrylate)

CH3 CH2

302.

C

CH2 C O CH CH2 O

CH2 CH2 CH2

Poly(cyclohexylacetoxyethylene)

CH2

CH O C O CH2

303.

Poly(cyclohexylethylene) CH2 CH H2C

CH2 CH CH2

CH2 CH2 CH2

CH CH2 177

H2C CH2 H2C

2 Poly(cyclohexyloxyethylene)

CH2

CH CH2

306.

5 354

6 306

7 624

204

614

346

332

706

221

695

326

318

706

107

301

348

355

514

250

1050

203

238

277, 581, 596, 756

CH2 CH2 CH2

Poly(cyclooctyl methacrylate)

CH3

CH2

4 438

CH O CH2

305.

3 134

C

CH2 C O CH CH2 O

CH2

CH2 CH2 CH2

CH2

Poly(cyclooctylmethyl methacrylate)

CH3 CH2

C C O CH2 O

307.

CH2 CH2

Poly(cyclopentylethylene)

CH2

308.

CH2 CH CH2

CH CH2 CH CH2

CH2 CH2

Poly(decyl methacrylate)

CH3 CH2

C

O

C

O

CH2 CH2 CH2

(C H 2 ) 9

C H3

178

1 304.

1 309.

2 Poly(decyl-2-cyanoacrylate) C N

CH2 310.

4 996

5 192

6 254

7 731

214

1034

~183, 211

207

600, 620, 622, 623

194

649

289-297

299

597

106

757

134; 138140

140

740, 741

160

489

292

327

560

80.7

504

173, 186

160

493, 711

C

CO O Poly(decyloxyethylene)

CH2

(CH2)9 CH3

CH O

311.

3 253

(CH2)9

CH3

Poly(diethylaminoethyl methacrylate)

CH3 CH2

C C O (CH2)2

CH3

CH2

CH3

N

O 312.

CH2

Poly(diethylsiloxane)

C2H5 Si

O

C2H5 313.

Poly(dimethylaminoethyl methacrylate)

CH3 CH2

C C O CH2 O

314.

Poly(dimethylsilylenemethylene)

CH3 CH2

N CH3

CH3 Si

179

CH3

CH2

2 Poly(dimethylsilylenetrimethylene)

3 115

4 665

5 203

6 173

7 490

263

809

311

325

489

208

967

208

215

461

71.3

330

246

216

351, 352

140

649

199

216

351

147

465

296

316

352, 461

123

572

201

215

351

CH3 Si

(CH2)3

CH3 316.

Poly(di-p-tolylsilylenetrimethylene)

CH3

Si

(CH2)3

CH3 317.

Poly(dithiodecamethylene)

–S–S–(CH2)10– 318.

Poly(dithioethylene)

–S–S–CH2–CH2– 319.

Poly(dithiohexamethylene)

–S–S–(CH2)6– 320.

Poly(dithiomethylene-1,4-phenylenemethylene)

S 321.

S

CH2

Poly(dithiopentamethylene)

–S–S–(CH2)5–

CH2

180

1 315.

1 322.

2 Poly(dodecafluorobutoxyethylene)

CF2

CF

3 174

4 713

5 263–273

6 244

7 445

267

1094

270 Brittle point

244

581, 586

284

1229

208 conflicting data

231

273, 581, 598, 600, 601

262

630

420, 425, 418, 430, 405, 431

416

684, 700, 702, 709, 715

604

1250

483

483

738, 739

478

988

515

484

738, 739

O CF2 CF2 323.

CF2

CF3

Poly(dodecyl acrylate)

CH2

CH C O

(CH2)11

CH3

O 324.

Poly(dodecyl methacrylate)

CH3

CH2

C C O (CH2)11

CH3

O 325.

Poly(ehter ether ketone)

O

O

C O

326.

Poly(ether imide) 1 O N

C

CH3 O

O

C

C

O

C C

CH3

O

327.

C

O

O

Poly(ether imide) 10 O

N

N

O O

O

C C

O

O

N

O 181

C

2 Poly(ether imide) 11 O N

329.

O

O

N

O

O

C

O

O

C

C

C

O

O

N

O

C

C

C

O

O

O

S

O

500

465

738, 739

646

1462

487

442

738, 739

572

1246

485

459

738, 739

488

1030

499

474

738, 739

O

C

C

O

O

O N

Poly(ether imide) 15

N

1028

O

O

C

O

478

N

C

O

7 738, 739

O

O

C

Poly(ether imide) 14 O

6 467

N

Poly(ether imide) 13 O

5 488

O

Poly(ether imide) 12

N

332.

C C

O

331.

O

C

N

330.

O

O

4 1203

O

O

C

3 562

S

O

O

C

C

C

C

O

O

N

182

1 328.

1 333.

2 Poly(ether imide) 16

O N

334.

335.

C

C

O

O S

C

C

C

O

O

C

C

C

O

O

O

SO2

O

C

C

484

738, 739

656

1505

451

436

738, 739

582

1143

533

509

738, 739

520

1074

488

484

738, 739

O

O N

O

O

CH3 O

C CH3

O O

C C O

N 183

O

530

O

O

C

C

1165

N

C

C

564

N

O Poly(ether imide) 2

N

7 738, 739

O

O

C

Poly(ether imide) 19 O

N

S

6 455

O

O

C

O

5 482

N

Poly(ether imide) 18 N

337.

O

4 1073

O

O

C

O

336.

S

C

Poly(ether imide) 17 O

N

O

3 488

2 Poly(ether imide) 20

O N

339.

O

SO2

C

C

C

C

O

O

O

340.

341.

N

342.

O

O

C

C

C

O

O SO 2

7 738, 739

394

812

528

485

738, 739

666

1402

402

475

738, 739

572

1184

483

483

738, 739

487

1008

512

483

738, 739

N

O

O

C

C

C

O

O

O

O

C

O

O

C

C

O

O

O

O

C

O

N

C

C

O Poly(ether imide) 24 O N

O

C

Poly(ether imide) 23 O

6 514

N

Poly(ether imide) 22 N

5 538

O

C

O

4 969

O

O

Poly(ether imide) 21

N

3 498

O N

O C

C

C

C

O

O

O

N

184

1 338.

1 343.

2 Poly(ether imide) 25 O

N

344.

O

C

C

C

C

O

O

CO

CO

347.

N

S

CO

CO

CO

N

401

379

738, 739

572

1246

507

459

738, 739

488

1073

504

455

738, 739

656

1505

475

436

738, 739

O N

S

O

CO

CO

CO

CO

N

S O

1330

O

CO

Poly(ether imide) 29

504

(CH2)6

Poly(ether imide) 28

N

7 738, 739

O CO

O

6 455

O

Poly(ether imide) 27

N 346.

O

CO

O

5 467

N

Poly(ether imide) 26

N 345.

C

O

4 1442

O

O

O

O

3 656

O CO

CO

CO

O

O

N

185

CO

2 Poly(ether imide) 3 O N

349.

O

C

O

C

O

O

CO

CO

CO

CO

CO

CO

N

1143

540

509

738, 739

498

969

539

514

738, 739

666

1402

503

475

738, 739

487

1008

521

483

738, 739

O

N

O

CO

CO

CO

CO

O

O

CO

O

N

Poly(ether imide) 33

N

582

N

SO2 O

7 738, 739

O

SO 2

CO

Poly(ether imide) 32

6 451

O

Poly(ether imide) 31

N

5 472

O

SO2

CO

O

352.

O

4 1246

N

Poly(ether imide) 30

N

351.

C

C

O

350.

O

3 562

O

CO

CO

CO

CO

N

186

1 348.

1 353.

2 Poly(ether imide) 34

N 354.

O

CO

CO

CO

CO

Poly(ether imide) 35

N 355.

O

O

CO

CO

CO

N 356.

562

1286

466

437

738, 739

553

1122

550

493

738, 739

CO

CO

469

862

548

544

738, 739

638

1381

497

462

738, 739

O N

O

CO

CO

CO

CO

N

Poly(ether imide) 38

N

7 738, 739

O CO

O

6 461

O

Poly(ether imide) 37

N

357.

O

CO

O

5 514

N

Poly(ether imide) 36

O

4 855

N

O

CO

3 394

O

CO

CO

CO

CO

O

O

N

187

2 Poly(ether imide) 39

O N 359.

O

CO

CO

CO

CO

C

O

O

C

O

O

N

478

1028

482

465

738, 739

478

1028

505

465

738, 739

646

1462

471

442

738, 739

597

1164

549

513

737

O

O

O CO

CO

CO

N

Poly(ether imide) 41

N

7 738, 739

O

CO

O

362.

C

C

O

361.

6 467

N

Poly(ether imide) 40

N

5 512

O

O

360.

4 1203

O

Poly(ether imide) 4

N

3 562

O

O

CO

CO

CO

CO

O

O

N

Poly(ether imide) 42

CF3 C CF3

N

CO

O CO

CO O

CO

N

188

1 358.

1 363.

2 Poly(ether imide) 43

CF3 C

N

CF3

364.

CO

O

O

CO

CO

CO

C

N

CF3

CO

CO

O

366.

Poly(ether imide) 46

N

CF3

367.

CO

CO

CO

CO

CO

CO

Poly(ether imide) 47

N

1164

491

513

737

597

1164

529

513

737

478

988

536

484

738, 739

394

812

532

485

738, 739

O

CO

CO

O

597

N

O

O N

7 737

N

Poly(ether imide) 45

C

6 513

CO

O

CF3

5 529

O

CO 365.

4 1164

N

Poly(ether imide) 44

CF3

3 597

O N

O

CO

CO

CO

CO

N 189

2 Poly(ether imide) 48

O N 369.

N 370.

371.

CO

CO

CO O

O

5 487

6 451

7 738, 739

478

1047

499

465

738, 739

394

855

497

461

738, 739

683

1444

503

473

737

598

1189

554

503

737

O

N

O

CO

CO

CO

CO

O N

Poly(ether imide) 5 O N

4 1246

O

CO

Poly(ether imide) 49

3 562

O

C

O

O

C C

C

N

O

O Poly(ether imide) 50 O

O

O N

CO CO CO CO

N

O

372.

Poly(ether imide) 51 H3C

CH3 CH2

H3C

N CH3

O CO CO

O CO CO

N

190

1 368.

1 373.

2 Poly(ether imide) 52

CH3

H3C CH2

N

H3C 374.

Poly(ether imide) 53 H3C

5 538

6 503

7 737

598

1189

545

503

737

581

1107

581

525

737

471

975

523

483

737

O

CO

CO

CO

CO

CH3 N

H3C

N

O

O CO

CO

CO

CO

N

CH3

Poly(ether imide) 54

H3C

CH3 N

H3C 376.

4 1189

CH3

CH2

375.

O

3 598

O

O

CO

CO

CO

CO

N

CH3

Poly(ether imide) 55

O N

CO CO

CO

CO O

191

CF3

N

2 Poly(ether imide) 56

O N

O

CO

CO

CO

CO

3 471

4 975

5 523

6 483

7 737

471

975

508

483

737

692

1401

526

494

737

692

1401

519

494

737

562

1286

403

437

738, 739

N

CF3

378.

Poly(ether imide) 57

O

O

N

CO

CO

CO

CO

N

CF3

379.

Poly(ether imide) 58 CH3

CH3

C

C

CH3

CH3

O CO

N

CO

CO

CO

N

O

380.

Poly(ether imide) 59 CH3

CH3

C

C

CH3

CH3

O N

CO CO CO CO

N

O

381.

Poly(ether imide) 6 O

N

C

O O

O

C

C

C

O

O

O N

O

192

1 377.

1 382.

383.

2 Poly(ether imide) 60 CH3

CH3

C

C

CH3

CH3

O

CO

N

CO

CO

CO

O

N

CO

CO

CO

O O

N

O CO

CO

CO

Poly(ether imide) 64

O O

Poly(ether imide) 65 N

O

CO

N

6 494

7 737

608

1310

502

464

737

608

1310

501

464

737

608

1351

481

450

737

683

1444

500

473

737

439

916

533

479

737

N

N

O

CO

CO

CO

CO

O

5 519

N

CO

Poly(ether imide) 63

4 1401

N

O

CO

O

O

387.

CO

CO

Poly(ether imide) 62

O

386.

O

O

O

385.

N

Poly(ether imide) 61 O

384.

O CO

3 692

N

CO CO

CO O

N

193

CO

2 Poly(ether imide) 66

O N

389.

O

CO

CO

CO

CO

Poly(ether imide) 67

4 916

5 528

6 479

7 737

439

916

503

479

737

439

916

527

479

737

523

1092

513

479

737

553

1122

502

493

738, 739

N

O N

3 439

CO CO CO CO

N

O 390.

Poly(ether imide) 68

O N

391.

O

CO

CO

CO

CO

N

O

Poly(ether imide) 69 O

N

CO CO

CO

N

CO O 392.

Poly(ether imide) 7 O N

C

O O

O

C

C

C

O

O

N

O

194

1 388.

1 393.

2 Poly(ether imide) 70

O

O N

394.

Poly(ether imide) 71 O

O

CO

CO

CO

CO

3 523

4 1092

5 508

6 479

7 737

523

1092

522

479

737

523

1092

518

479

737

523

1134

499

461

737

523

1134

498

461

737

N

O CO

N

CO CO CO

N

O 395.

Poly(ether imide) 72

O

O N

396.

Poly(ether imide) 73 O

O

CO

CO

CO

CO O

N

N

CO CO

CO

CO

N

O 397.

Poly(ether imide) 74 O

N

CO

O

CO CO CO

N

195

O

2 Poly(ether imide) 75

O

O N

400.

Poly(ether imide) 76

O

CO

CO

CO

CO

C

N

CH3

4 1134

5 494

6 461

7 737

565

1137

538

497

737

565

1137

509

497

737

565

1137

520

497

737

656

1442

489

455

738, 739

N

O

CH3

3 523

CO CO

CO

CO

N

O 401.

Poly(ether imide) 77

O

CH3 C

N

CH3

CO CO CO CO

N

O 402.

Poly(ether imide) 78

O

CH3 C

N

CH3 403.

Poly(ether imide) 79

CO

CO

CO

CO

CO O

N

O

O

CO

CO

CO

CO

O N

O

N

196

1 399.

1 404.

2 Poly(ether imide) 8

O N

C

O

O

C C

C

C

CO

CO

CO

CO

C

483

738, 739

520

1075

509

484

738, 739

612

1246

503

491

738, 739

577

1378

408

397

738, 739

N

O

CH3

CO CO

CO

CH2 N

CH3 O

C CH3

O CO CO

N

(CH2)6

197

CO

508

N

CH3

CO

CO

1251

O

CH3

Poly(ether imide) 83

N

604

O

CH3

O

408.

CO CO

Poly(ether imide) 82

N

7 738, 739

O

CO O

407.

C CH3

CO

Poly(ether imide) 81

N

6 496

O O

406.

5 520

N

CH3

Poly(ether imide) 80

N

4 946

O

O 405.

3 469

2 Poly(ether imide) 84 O

O

O N

410.

CO

CO

CO

CO

CO

N

C

C C

C

O

O

Poly(ethyl chloroacrylate)

5 500

6 473

7 738, 739

683

1444

504

473

766

638

1381

478

462

738, 739

111

294

366 Vicat softening point

377

588, 599, 614, 615

131

427

300

307

560

176

553

325

318

613

N

O

O

N

Cl CH2

4 1444

O

O

O

3 683 N

O

Poly(ether imide) 9 O

412.

CO

CO

O

O N

411.

CO

Poly(ether imide) 85 O

O

C C O CH2

CH3

O

413.

Poly(ethyl ethacrylate)

CH2 CH2

CH3

C C O CH2

CH3

O

414.

Poly(ethyl ethoxycarbonyl methacrylate) CH2

CH2

C O CH2

C

O

C O CH2 O

CH3

CH3

198

1 409.

1 415.

2 Poly(ethyl-2-cyanoacrylate)

3 116

4 279

5 422

6 416

7 730

85.3

297

268

287

526

211

548

398

385

725

211

548

398

385

699, 727

315

1150

293

274

481

315

1150

~278

274

481

C N CH2

C CO O CH2 CH3

416.

Poly(ethyl-2-propylene) CH2 CH3

CH2 417.

C

CH3 Poly(ethylene 2,6-naphthalate)

O

(CH2)2

O C O

C O

418.

Poly(ethylene 2,6-naphthalenedicarboxylate)

(CH2)2

O C C O

O

O 419.

Poly(ethylimino-2,2,3,3,4,4-hexafluoropentamethyleneethyliminoadipoyl)

N

420.

CH2

(CF2)3

CH2 N

CH2

CH2

CH3

CH3

C

(CH2)4

O

Poly(ethyliminohexafluoroglutarylethyliminohexamethylene)

N

C

CH2 O

C N

O

(CH2)6

O CH2 CH3

199

CH3

(CF2)3

C

2 Poly(ethylthioethylene)

CH2

3 86.5

4 297

5 266

6 291

7 601

62.3

207

310 (~60% syndio)

301

501

128

391

347, 336

327

687, 705

91.8

340

268

270

445

312

1268

269

246

612

137

634

208 - 228

216

496, 509, 512

CH S CH3

CH2 422.

Poly(formyloxyethylene)

CH2

CH O

O C 423.

H

Poly(glycidyl methacrylate)

CH3 CH2

C C O CH2

CH O

O 424.

Poly(hexafluoromethoxyethylene)

CF2

CF O

425.

CF3

Poly(hexyl hexyloxycarbonyl methacrylate)

CH2

CH2

C O

C

O

O C O (CH2)5 426.

CH2

Poly(hexylethylene)

CH2

CH (CH2)5 CH3

(CH2)5

CH3

CH3

200

1 421.

1 427.

2 Poly(hexyloxyethylene)

CH2

CH

3 146

4 676

5 199

6 216

7 600, 620624, 709

212

436

553, 513

486

378, 474, 486

273

713

383

383

485

212

394

< 500

538

378

212

394

< 500

538

378

212

353

618, 580 600

601

378, 379

258

459

578

562

379

O (CH2)5

428.

NH

429.

CH3

Poly(imino-1,3-phenyleneiminoisophthaloyl)

NH C

C

O

O

Poly(imino-1,3-phenyleneiminosebacoyl)

NH

NH C

(CH2)8

O 430.

C

O

O

NH C

C

O

O

Poly(imino-1,4-phenyleneiminoterephthaloyl)

NH 433.

NH C

Poly(imino-1,4-phenyleneiminoisophthaloyl)

NH 432.

O

Poly(imino-1,3-phenyleneiminoterephthaloyl)

NH 431.

C

NH C

C

O

O

Poly(imino-1,5-naphthyleneiminoterephthaloyl) NH C

O

O

201

NH C

1 434.

435.

2 Poly(imino-1-methyl-3-oxotrimethylene)

NH CH CH2

C

CH3

O

Poly(imino-1-oxoethylene-1,4-phenylene-2-oxoethyleneiminooctadecamethylene) NH C CH2

436.

C NH

CH2

CH2

CH2

CH2

C NH

CH2

CH2

CH2

CH2

O 438.

7 469

478

1354

351

353

478

392

1107

358

354

478

512

1467

338

349

478

543

1278

438

425

285

266

826

338

322

406

300

992

336

302

483

(CH2)18

O

Poly(imino-2,2,4-trimethylpentamethyleneiminoadipoyl)

CH3

CH3

C CH2

CH CH2

NH C

CH3 440.

C NH

Poly(imino-1-oxotrimethylenefluoren-9-ylidene-3-oxotrimethyleneiminotrimethylenefluoren-9ylidenetrimethylene) NH C (CH2)2 C (CH2)2 C NH (CH2)3 C (CH2)3

NH CH2

6 407

O

O

439.

5 369

(CH2)11

O O Poly(imino-1-oxotrimethylene-1,4-phenylene-3-oxotrimethyleneiminooctadecamethylene)

NH C

4 201

(CH2)18

O O Poly(imino-1-oxotrimethylene-1,4-phenylene-3-oxotrimethyleneiminododecamethylene) NH C

437.

CH2

3 81.8

O

Poly(imino-2,2-dimethylpentamethyleneiminoazelaoyl)

(CH2)4

C O

CH3 C CH3

(CH2)3

NH C O

(CH2)7

C O

202

NH CH2

1 441.

2 Poly(imino-2,2-dimethylpentamethyleneiminodipoyl)

3 249

4 801

5 350

6 311

7 483

266

878

344

303

483

256

531

430

481

375

255

627

393

407

334

313

749

465

418

444

CH3 NH CH2

C

(CH2)3

NH C

CH3 442.

(CH2)4

O

C O

Poly(imino-2,2-dimethylpentamethyleneiminopimeloyl)

CH3 NH CH2

C

(CH2)3

NH C

CH3 443.

(CH2)5

O

C O

Poly(imino-2,2-dimethylpentamethyleneiminoterephthaloyl)

CH3 NH CH2

C

(CH2)3

NH C

C

O

O

CH3 444.

Poly(imino-5-methylisophthaloyliminohexamethylene)

NH C

C NH

O

(CH2)6

O CH3

445.

Poly(imino-5-tert-butylisophthaloyliminomethylene-1,3-phenylenemethylene)

NH C

C NH

O

CH2

CH2

O

H3C C CH3 203

CH3

2 Poly(imino-5-tert-butylisophthaloyliminomethylene-1,4-phenylenemethylene)

NH C

C NH

O H3C

3 313

4 708

5 477

6 442

7 444

272

696

343

391

373

388

1057

393

367

285, 317

261

906

278

288

464

256

656

377

390

482

CH2

CH2

O C CH3 CH3

447.

Poly(iminoadipoyliminomethylene-2,5-dimethyl-1,4-phenylenemethylene)

H3C NH

C

(CH2)4

O

C

NH CH2

CH2

O H3C

448.

Poly(iminoadipoyliminotrimethylenefluoren-9-ylidenetrimethylene)

NH

C

(CH2)4

O

449.

(CH2)3

C

(CH2)3

O

Poly(iminoadipoyliminotrimethylenemethyliminotrimethylene)

NH C O 450.

C NH

(CH2)4

C NH

(CH2)3

O

N

(CH2)3

CH3

Poly(iminocarbonyl-1,4-phenylene-2-oxoethyleneiminohexamethylene)

NH C O

CH2

C NH O

(CH2)6

204

1 446.

1 451.

2 Poly(iminoethylene-1,4-phenyleneethyleneimino-1,11-dioxoundecamethylene)

NH (CH2)2

(CH2)2

NH C

(CH2)9

O 452.

(CH2)2

NH C

(CH2)12

(CH2)2

NH C

(CH2)14

(CH2)2

NH C

(CH2)16

(CH2)2

NH C

363

478

443

1241

358

357

478

478

1354

348

353

478

341

900

378

379

478

232

721

355

322

483

O

(CH2)8

O 456.

366

C

Poly(iminoethylene-1,4-phenyleneethyleneiminosebacoyl)

NH (CH2)2

1127

O

O 455.

409

C

Poly(iminoethylene-1,4-phenyleneethyleneimino-1,18-dioxooctadecamethylene)

NH (CH2)2

7 478

O

O 454.

6 360

C

Poly(iminoethylene-1,4-phenyleneethyleneimino-1,16-dioxohexadecamethylene)

NH (CH2)2

5 369

O

O 453.

4 994

C

Poly(iminoethylene-1,4-phenyleneethyleneimino-1,14-dioxotetradecamethylene)

NH (CH2)2

3 358

Poly(iminoglutarylimino-2,2-dimethylpentamethylene)

C O

CH3 NH C

C O

NH

CH2

C CH3

(CH2)3 205

O

(CH2)3

2 Poly(iminohexamethyleneimino-1-oxotrimethylenefluoren-9-ylidene-3-oxotrimethylene)

NH

(CH2)6

NH C

(CH2)2

C

(CH2)2

O

458.

5 395

6 367

7 285, 317

249

752

323

331

476

382

1000

427-437

382

318

304

608

Tg),

(VIII.6)

i

2

n −1 2

n +2

=

Rkg

[1 + α L (T − Tg )]N A ∑ ∆Vi , i

where kg = 0.667. Consequently, using equation (VIII.4) for copolymers, we obtain: k =n

n2 −1 n2 + 2

kg =

∑α k Rk

k =1

k =n

  1 + α G T − Tg N A ∑ α k  ∑ ∆Vi    k =1  i k

[

(

)]

, (T < Tg);

(VIII.7)

, (T > Tg).

(VIII.8)

k =n

n2 −1 n2 + 2

kg =

∑α k Rk

k =1

k =n

  1 + α L T − Tg N A ∑ α k  ∑ ∆Vi    k =1  i k

[

(

)]

Table 28 displays refractive indices for a series of amorphous polymers. Clearly, the value of n depends on the chemical structure of the polymer and increases at transition from aliphatic polymers to aromatic ones. It is also clear that for 20 polymers existing in the rubbery state at room temperature (T > Tg), values of nD calculated with regard to the temperature dependence of the coefficient of molecular packing, i.e. with application of expression (VIII.5), correlate much better with

421

20 experimental values of nD . Therewith, values of the glass transition temperature Tg determined by equation (IV.41) and values of the coefficients of volumetric expansion αG and αL determined by correlations (III.8) and (III.5) were used for calculation. Table 28 20 20 Molar refractions R, experimental n D, exp and calculated n D, calc values of the refractive indices for a series of amorphous polymers 20 20 Ri , n D nD , exp Polymer , calc * Tg,calc, K i cm3/mol 1 2 3 4 5 282 20.126 1.479 1.49 / 1.47 CH2 CH

∑

C O CH3 O CH

CH2

24.744

1.469

1.49 / 1.47

267

33.980

1.466

1.50 / 1.48

242

24.744

1.490

1.490

377

29.362

1.485

1.50 / 1.49

338

38.598

1.483

1.50 / 1.49

287

44.233

1.568

1.56

378

33.343

1.591

1.60

376

37.961

1.587

1.59

401

C O C2H5 O CH2

CH C O C4H9 O CH3

CH2

C C O CH3 O CH3

CH2

C C O C2H5 O

CH3 CH2

C C O C4H9 O CH3

CH2

C C O O

CH2

CH

CH3 CH2

C

422

1

CH2

CH

2 38.210

3 1.610

4 1.62

5 356

15.497

1.467

1.49 / 1.47

253

20.126

1.467

1.49

301

34.986

1.578

1.58

353

69.983

1.585

1.58

431

117.662

1.610

1.60

582

Cl

CH2

CH O CH3

CH2

CH O C

CH3

O

CH2

CH O

CH3 O

C

O C

CH3 C

C O

O

O

O O C O C O

* Column 4 indicates two values of ncalc: the first of them is determined by equation (VIII.2), and the second – by equation (VIII.6), i.e. with regard to the temperature dependence of the coefficient of molecular packing k.

More comprehensive data on polymers, for which refractive indices were measured, are shown in Table 28′, the experimental data in which are borrowed from Polymer Handbook [453]. Table 28′ Average refractive indices of polymers Polymer 1 Cellulose Cellulose nitrate Cellulose triacetate Cellulose tripropionate Ethyl cellulose Methyl cellulose (low viscosity) Natural rubber Poly(acrolein) Poly(acrylic acid)

n (exp) 2 1.54 1.5 – 1.514 1.47 – 1.48 1.48 – 1.49 1.479 1.497 1.519 – 1.52 1.529 1.527

n1 (calc) 3 1.49 (am); 1.54 (cryst) 1.52 1.48 1.49 1.47 1.48 1.51 1.51 1.49

423

1 Poly(acrylonitrile) Poly(allyl mathacrylate) Poly(N-allyl methacrylamide) Poly(N-benzyl methacrylamide) Poly(n-butyl methacrylate) Poly(benzyl methacrylate) Poly(bornyl methacrylate) Poly(2-bromoethyl methacrylate) Poly(p-bromophenyl methacrylate) Poly(2-bromo-4-trifluoromethylstyrene) Poly(1,2-butadiene) Poly(1,3-butadiene) Poly(butene) (isotactic) Poly(butyl acrylate) Poly(sec-butyl α-bromoacrylate) Poly(sec-butyl α-chloroacrylate) Poly(2-tert-butyl-1,3-butadiene) Poly(tert-butyl methacrylate) Poly(butylmercaptyl methacrylate) Poly(N-butyl methacrylamide) Poly(o-chlorobenzyl mathacrylate) Poly(2-chloro-1-(chloromethyl)ethyl methacrylate) Poly(2-chlorocyclohexyl methacrylate) Poly(o-chlorodiphenylmethyl methacrylate) Poly(2-chloroethyl α-chloroacrylate) Poly(2-chloroethyl methacrylate) Poly(1-(o-chlorophenyl)ethyl methacrylate) Poly(chloroprene) Poly(o-chlorostyrene) Poly(m-cresyl methacrylate) Poly(o-cresyl methacrylate) Poly(cyclohexyl α-bromoacrylate) Poly(cyclohexyl α-chloroacrylate) Poly(cyclohexyl α-ethoxyacrylate) Poly(cyclohexyl methacrylate) Poly(p-cyclohexylphenyl methacrylate) Poly(1-decene) Poly(2-decyl-1,3-butadiene) Poly(2,3-dibromopropyl methacrylate) Poly(1,3-dibromopropyl methacrylate) Poly(2,6-dichlorostyrene) Poly(2-diethylaminoethyl methacrylate) Poly(1,1-diethylpropyl methacrylate) Poly(2,3-dimethylbutadiene) (methyl rubber) Poly(1,2-diphenylethyl methacrylate) Poly(diphenylmethyl methacrylate) Poly(p-divinylbenzene) Poly(dodecyl methacrylate) Poly(2-ethoxyethyl acrylate) Poly(2-ethoxyethyl methacrylate) Poly(3-ethoxypropyl acrylate) Poly(ethyl acrylate) Poly(ethyl α-chloroacrylate)

2 1.52 (1.5187) 1.5196 1.5476 1.5965 1.483 1.5680 1.5059 1.5426 1.5964 1.5 1.5000 1.5154 1.5125 1.4631 – 1.466 1.542 1.500 1.5060 1.4638 1.5390 1.5135 1.5823 1.5270 1.5179 1.6040 1.533 1.517 1.5624 1.5541.558 1.6098 1.5683 1.5707 1.542 1.532 1.4969 1.5066 1.5575 1.4730 1.4899 1.5739 1.5270 1.6248 1.5174 1.4889 1.525 1.5816 1.5933 1.6150 1.4740 1.471 1.4833 1.465 1.4685 1.502

3 1.49 1.51 1.53 1.57 1.49 1.56 1.53 1.53 1.58 1.55 1.53 1.51 1.50 1.48 1.53 1.52 1.51 1.50 1.56 1.52 1.57 1.53 1.53 1.59 1.53 1.52 1.56 1.54 1.62 1.55 1.55 1.55 1.53 1.51 1.52 1.56 1.49 1.50 1.56 1.53 1.63 1.52 1.51 1.51 1.58 1.58 1.61 1.49 1.46 1.48 1.47 1.47 1.51

424

1 Poly(ethyl methacrylate) Poly(ethylene) (density 0.914 g/cm3) (density 0.94 – 0.945 g/cm3) (density 0.965 g/cm3) Poly(ethylmercaptyl methacrylate) Poly(2-fluoroethyl methacrylate) Poly(4-fluoro-2-trifluoromethylstyrene) Poly(2-(heptafluorobutoxy)ethyl acrylate) Poly(heptafluorobutyl acrylate) Poly(2-heptyl-1,3-butadiene) Poly(hexadecyl methacrylate) Poly(2,2,3,3,4,4-hexafluorobutyl acrylate) Poly(n-hexyl methacrylate) Poly(2-hydroxyethyl methacrylate) Poly(iminoadipoyliminohexamethylene) (Nylon 6,6) Poly(iminoadipoyliminotetramethylene) Poly(imino(1-oxohexamethylene)) (Nylon 6) Polyisobutene Poly(isobutyl methacrylate) Polyisoprene Poly(2-isopropyl-1,3-butadiene) Poly(isopropyl methacrylate) Poly(p-isopropylstyrene) Poly(methacrylonitrile) Poly(p-methoxybenzyl methacrylate) Poly(2-methoxyethyl acrylate) Poly((N-2-methoxyethyl)methacrylamide) Poly(4-methoxy-2-methylstyrene) Poly(o-methoxyphenyl methacrylate) Poly(methoxypropyl acrylate) Poly(o-methoxystyrene) Poly(p-methoxystyrene) Poly(methyl acrylate) Poly(methyl α-bromoacrylate) Poly(methyl α-chloroacrylate) Poly(methyl methacrylate) Poly(N-methyl-methacrylamide) Poly(4-methyl-1-pentene) Poly(1-methylcyclohexyl methacrylate) Poly(2-methylcyclohexyl methacrylate) Poly(3-methylcyclohexyl methacrylate) Poly(4-methylcyclohexyl methacrylate) Poly(o-methylstyrene) Poly(α-naphthyl methacrylate) Poly(β-naphthyl methacrylate) Poly(m-nitrobenzyl methacrylate) Poly(2-nitro-2-methylpropyl methacrylate) Poly(nonafluoropentyl acrylate) Poly(octafluoropentyl acrylate) Poly(oxycarbonyloxybis(1,4-(3,5-dichlorophenylene))) Poly(oxycarbonyloxy1,4-(2,6-dichloro)phenylene-isopropylidene-1,4(2,6-dichloro)phenylene) Poly(oxycarbonyloxy1,4-phenylene-1,3-dimethylbutylidene-1,4phenylene) Poly(oxycarbonyloxy1,4-phenylene-1-methyl-butylidene-1,4-phenylene)

2 1.485 1.51 1.52–1.53 1.545 1.547 1.4768 1.46 1.390 1.367 1.5000 1.4750 1.392 1.4813 1.5119 1.53 1.53 1.53 1.505–1.51 1.477 1.521 1.5028 1.4728 1.554 1.52 1.552 1.463 1.5246 1.5868 1.5705 1.471 1.5932 1.5967 1.472 – 1.480 1.5672 1.517 1.4893 1.5398 1.459 – 1.465 1.5111 1.5028 1.4947 1.4975 1.5874 1.6410 1.6298 1.5845 1.4868 1.360 1.380 1.6056 1.6056

3 1.50 1.49 1.52 1.54 1.54 1.47 1.51 1.40 1.39 1.50 1.50 1.41 1.49 1.49 1.52 1.52 1.52 1.49 1.50 1.51 1.51 1.50 1.58 1.49 1.54 1.46 1.51 1.57 1.54 1.46 1.57 1.57 1.46

1.5671

1.57

1.5745

1.57

1.54 1.51 1.49 1.52 1.51 1.52 1.52 1.52 1.52 1.60 1.59 1.59 1.57 1.53 1.37 1.38 1.61 1.60

425

1 Poly(oxycarbonyloxy1,4-phenylene-1-propylbutylidene-1,4-phenylene) Poly(oxycarbonyloxy1,4-phenylene-sec-butylidene-1,4-phenylene) Poly(oxycarbonyloxy1,4-phenylenebutylidene-1,4-phenylene) Poly(oxycarbonyloxy1,4-phenylenecyclohexylidene-1,4-phenylene) Poly(oxycarbonyloxy1,4-phenylenediphenyl-methylene-1,4-phenylene) Poly(oxycarbonyloxy1,4-phenyleneethylidene-1,4-phenylene) Poly(oxycarbonyloxy1,4-phenyleneisobutylidene-1,4-phenylene) Poly(oxycarbonyloxy1,4-phenyleneisopropylidene-1,4-phenylene) Poly(oxy-2,6-dimethylphenylene) Poly(oxydimethylsilylene) (poly(dimethyl siloxane)) Poly(oxyethylene) (high molecular weight) Poly(oxyethyleneoxymaleoyl) (poly(ethylene maleate) Poly(oxyethyleneoxysuccinoyl) (poly(ethylene succinate)) Poly(oxyethyleneoxyterephthaloyl) (amorphous) (poly(ethylene terephthalate)) Poly(oxymethylene) Poly(oxy-1-oxopentamethylene) Poly(oxypropylene) Poly(pentachlorophenyl methacrylate) Poly(pentadecafuorooctyl acrylate) Poly(pentafluoropropyl acrylate) Poly(pentafluorovinyl propionate) Poly(1-phenyl-n-amyl methacrylate) Poly(phenyl α-bromoacrylate) Poly(phenyl methacrylate) Poly(1-phenylallyl methacrylate) Poly(1-phenylcyclohexyl methacrylate) Poly(1-phenylethyl methacrylate) Poly(2-phenylethyl methacrylate) Poly(N-(2-phenylethyl)methacrylate) Poly(2-(phenylsulfonyl)ethyl methacrylate) Poly(n-propyl methacrylate) Poly(propylene) (density 0.9075 g/cm3) Poly(styrene) Poly(tetradecyl methacrylate) Poly(tetrafluoro-3-(heptafluoropropoxy)propyl acrylate) Poly(tetrafluoro-3-(pentafluoroethoxy)propyl acrylate) Poly(tetrafluoro-3-(trifluoromethoxy)propyl acrylate) Poly(2-(1,1,2,2-tetrafluoroethoxy)ethyl acrylate) Poly(tetrafluoroethylene) Poly(2,2,2-trifluoro-1-methylethyl methacrylate) Poly(trifluorochloroethylene) Poly(2-trifluoroethoxy)ethyl acrylate) Poly(trifluoroethyl acrylate) Poly(trifluoroethyl methacrylate) Poly(trifluoroisopropyl methacrylate) Poly(trifluorovinyl acetate) Poly(3,3,5-trimethylcyclohexyl methacrylate) Poly(undecafluorohexyl acrylate) Poly(vinyl acetate) Poly(vinyl alcohol) Poly(vinyl benzoate) Poly(vinyl butyl ether) Poly(viny sec-butyl ether) (isotactic) Poly(vinyl butyral) Poly(vinyl chloride)

2 1.5602 1.5827 1.5792 1.5900 1.6539 1.5937 1.5702 1.5850 1.575 1.43 1.4563 1.4840 1.4744 1.5750

3 1.57 1.57 1.57 1.58 1.61 1.58 1.57 1.58 1.59 1.41 1.45 1.46 1.46 1.54

1.48 1.465 1.4495 1.608 1.339 1.385 1.364 1.5396 1.612 1.5706 1.5573 1.5645 1.5487 1.5592 1.5857 1.5682 1.484 1.5030 1.59 – 1.592 1.4746 1.346 1.348 1.360 1.412 1.35 – 1.38 1.4185 1.42 – 1.43 1.419 1.407 1.437 1.4177 1.375 1.485 1.356 1.4665 1.49 – 1.53 1.5775 1.4563 1.4740 1.48 – 1.49 1.54 – 1.55

1.42 1.47 1.46 1.61 1.35 1.39 1.37 1.55 1.59 1.56 1.56 1.56 1.55 1.55 1.57 1.56 1.50 1.51 1.60 1.49 1.36 1.36 1.37 1.41 1.31 1.45 1.42 1.42 1.41 1.44 1.45 1.40 1.52 1.36 1.49 1.50 1.58 1.48 1.48 1.50 1.57

426

1 Poly(vinyl chloroacetate) Poly(vinyl decyl ether) Poly(vinyl dodecyl ether) Poly(vinyl ethyl ether) Poly(vinyl-2-ethylhexyl ether) Poly(vinyl formal) Poly(vinyl hexyl ether) Poly(vinyl isobutyl ether) Poly(vinyl methyl ether) Poly(vinyl methyl ether) (isotactic) Poly(vinyl octyl ether) Poly(vinyl pentyl ether) Poly(vinyl phenyl sulfide) Poly(vinyl propionate) Poly(vinylcarbazole) Poly(vinylfuran) Poly(vinylidene chloride) Poly(vinylidene fluoride) Poly(vinylnaphthalene) Poly(1-vinyl-2-pyrrolidone) Poly(N-vinylphthalimide) Poly(2-vinyltetrahydrofuran) Poly(2-vinylthiophene)

2 1.512 1.4628 1.4640 1.4540 1.4626 1.50 1.4591 1.4507 1.467 1.4700 1.4613 1.4581 1.6568 1.4665 1.683 1.55 1.60 – 1.63 1.42 1.6818 1.53 1.6200 1.55 1.6376

3 1.54 1.48 1.48 1.47 1.49 1.50 1.48 1.48 1.47 1.47 1.48 1.48 1.67 1.48 1.64 1.56 1.57 1.38 1.63 1.55 1.60 1.53 1.65

VIII.2 Stress-optical coefficient Polymeric materials have been used widely in the photoelasticity method of investigation of stresses. This method is based on the phenomenon of birefringence, found by D. Brüster, which appears in transparent optically isotropic materials under deformation and is stipulated by anisotropy of the refraction index in the mutually perpendicular directions. In the case of glassy polymers, the first consequence of applied load is the variation of interatomic distances and valence angles in a polymeric chain. These changes determine the instaneous elastic deformation. Elastic deformation is associated with the mobility of atoms composing chains of macromolecules within a statistical segment of a macrochain. Occurrence of the birefringence and its value at deformation of polymers existing in the glassy state are generally stipulated by the dislocation of electronic shells of atoms and electronic clouds forming chemical bonds, as well as by distortion of the valence angles that leads to anisotropy of polarizability of elementary units of macromolecules. In the glassy state, birefringence may also be associated sometimes with the elastic orientation of optically anisotropic macromolecules or their parts (for example, mobile side methyl groups in polyacrylates and fluoride groups in poly(methacrylate) esters near their equilibrium state. Therewith, the so-called elastic component of birefringence occurs, which reaches its maximum almost immediately after the load application. In the case of the ideal elastic body, total birefringence would be controlled by elastic deformation, because under these conditions elastically deformed polymer would exist in the equilibrium state. However, it should be noted that the behavior of real polymeric substances differs from the elastic one. The change of deformation and values of birefringence with time is typical of them even in the glassy state.

427

For optically sensitive polymeric materials that are in the glassy state, the experimental Wertheim law is applicable up to certain stress levels. This law connects the optical retardation δ at any point of the polymeric model existing in the planestress state with the difference of the main principal stresses σ1 and σ2 acting in the plane model in the same point, and thickness of the model d:

or

δ = Cσ(σ1 – σ2)d

(VIII.9)

∆n = n1 – n2 = Cσ(σ1 – σ2)d,

(VIII.10)

where Cσ is the stress-optical coefficient; ∆n is the birefringence; n1 and n2 are refractive indices along and perpendicular to the optical axis. Introducing the light wavelength λ into equation (VIII.10), a correlation is obtained which connects birefringence with the fringe order: C d m = σ (σ 1 − σ 2 ) , λ

(VIII.11)

where m is the fringe order for a given wavelength λ. Coefficient Cσ is usually considered to be independent of the wavelength, but as more accurate investigation has indicated, it is not true. In practice of the photoelasticity method, to characterize he optical sensitivity of polymeric materials, another value – the stress-related value of material strip σ 10.0 – is used. This value equals

σ 10.0 =

λ . Cσ d

(VIII.12)

In the case of a linear dependence between stress and strain, birefringence may be expressed via strain. Then, the dependence is reduced to the following form:

δ = Cε(ε1 – ε2)d,

(VIII.13)

where Cε is the strain-optical coefficient of the material; ε1 and ε2 are the principal strains. Both optical coefficients are connected with each other by the correlation: C E λ Cε = σ = , 1 1 + µ ε 0.0

(VIII.14)

where µ is the Poisson ratio; E is the elasticity modulus; ε 10.0 is the strain-related value of material strip. Since the value of birefringence of a polymer in the glassy state, in a definite range, is proportional to the anisotropy of polarizability of the elementary unit bonds, the increase of polarizability anisotropy of macromolecules and, consequently, the optical sensitivity of the polymer may be achieved by introduction into the starting monomer or oligomer of groups with high polarizability anisotropy (such as aromatic

428

cycles of types of benzene, naphthalene, anthracene, carbonyl groups and any molecular groupings containing double or triple bonds, i.e. groupings containing mobile π-electrons) to the molecule. At the present time, there exist two approaches to numerical estimation of the stress-optical coefficient Cσ for polymers based on the chemical structure of the repeating unit of them. The first approach suggested in ref. [36] is empirical. On the basis of numerous experimental data, treated in the cited reference, a correlation has been suggested that connects Cσ with the parameters of the chemical structure of the repeat unit of the polymer:

Cσ =

∑ Ci i

N A ∑ ∆Vi

+∏,

(VIII.15)

i

where Ci are constants which characterize contributions of every atom and type of intermolecular interaction into the stress-optical coefficient (Table 29); ∑ ∆Vi is the i

Van-der-Waals volume of the repeat unit composed of volumes of atoms participating in this unit; NA is the Avogadro number; ∏ = 0.3544⋅10−4 cm2/kG is the universal parameter. Table 29 Values Ci characterizing contributions of each atom and type of intermolecular interaction to the stress-optical coefficient Atom or type of intermolecular interaction Ci⋅103, Symbol MPa–1 cm3/mol CC Carbon –2.0492 CH Hydrogen –0.5227 CO,b Oxygen in the backbone 3.1980 CO,s Oxygen in the side group –0.7568 Nitrogen in the backbone 7.1750 CΝ,b Nitrogen in the side group 1.3030 CΝ,s CCl Chlorine –3.4760 CS Sulfur –0.7900 Cd Dipole–dipole interaction * –1.6000 Ch Hydrogen bond –6.2100 p-Substitution of aromatic cycles ** Cp 1.7000 * Coefficient Cd is applied to every group of any chemical nature; if two identical groups locate at the same atom, a single coefficient Cd must be introduced. For phenyl group, Cd = –2.15⋅10–3. ** Coefficient Cp is introduced in the case of p-substitution of aromatic cycles; the number of coefficients Cp introduced equals to the number of aromatic cycles substituted in the p-position.

Table 30 shows values of stress-optical coefficient Cσ for a series of polymers in the glassy state. The value of Cσ changes is extremely wide range in relation to chemical structure of polymer – from low negative values for poly(methyl methacrylate) and poly-α-methylstyrene to extremely high positive values typical of aromatic polymers. High optical sensitivity of these polymers is indicated by their structure: the presence of a large number of condensed cycles characterized by a significant anisotropy of polarizability. As follows from Table 30, compounds saturated by nitrogen and sulfur atoms and aromatic cycles possess the highest values

429

of Cσ. A significant influence on the optical sensitivity is also caused by the type of substitution of aromatic cycles. Para-substitution promotes increase of Cσ. The presence of a large number of polar C=O-groups leads to a decrease of optical sensitivity. Possessing high negative anisotropy of polarizability, this group decreases the total positive effect. The fact that the C=O-group is the carrier of the negative effect has been observed in ref. [206] and confirmed in ref. [100] in the study of the opto-mechanical properties of polymers displayed in Table 30. Table 30 Experimental and calculated values of stress-optical coefficients Cσ for a series of glassy polymers Polymer Cσ⋅106, Cσ⋅106, Mpa-1 exper. MPa-1 calc. 1 2 3 10.7 10.65

CH2

CH

CH3 CH2

–3.3

–2.80

–2.0

–4.57

15.7

22.30

7.3

14.80

22.9

16.70

C C

CH3

O

CH3 CH2

CH2

C

CH

CH3

CH2

CH Cl

Cl CH2

CH

Cl

430

1

CH3 CH2

2 24.5

3 10.10

57.5

43.9

111.0

105.0

161.0

160.0

90

77.3

150.0

143.0

93

83.0

C C O CH2 O

CH2

CH N

CH3 O

C

O C

CH3

C C

N

O

N

O

N

C

N

C C

C HN

O

NH C

O

O C O

C C

C O

O

N

N

S O

N

N

C C

C O O

O C O C O

431

1

C

C NH

O

O

2 77.4

3 66.4

62.0

60.1

NH C

C

C NH

O

O

NH C

Using equation (VIII.15), the contribution of each group to the stress-optical coefficient may be estimated quantitatively. This contribution is characterized by the value of ∑ Ci N A ∑ ∆Vi , with the higher value of Cσ corresponding to the lower i

i

absolute value of ∑ Ci i

N A ∑ ∆Vi , because this relation is negative. A sequence of i

separate groups is formed due to the contribution

∑ Ci i

N A ∑ ∆Vi ⋅107 to the stressi

optical coefficient:

;

C O O

O

O

O

O

C

C

C

C

N

N

;

;

;

O;

C

.

O

O

C

C

C

C

O

O

O

O

–145.2

–157.5

–166.8

C ;

–223.4 C

;

;

–323.3

–336.0

C ;

C

–315.9

N

N

O –345.7

C

–348.3

–486.4

The calculation scheme considered for determination the stress-optical coefficient enables the expected optical sensitivity of the polymer to be estimated and is of a definite meaning for synthesis of polymers applicable in the photoelasticity method of investigation of stresses. For copolymers, equation (VIII.15) obtains the following form:

432

      α1  ∑ Ci  + α 2  ∑ Ci  + ... + α n  ∑ Ci         i 1  i 2  i n + ∏, Cσ =         N A α1 ∑ ∆Vi  + α 2  ∑ ∆Vi  + ... + α n  ∑ ∆Vi          i 1  i 2  i  n  

(VIII.16)

  where α1, α2, …, αn are the molar parts of the components 1, 2, …, n;  ∑ Ci  ,    i 1      ∑ Ci  , …,  ∑ Ci  are series of constants for the components 1, 2, …, n;      i 2  i n        ∑ ∆Vi  ,  ∑ ∆Vi  , …,  ∑ ∆Vi  are Van-der-Waals volumes of the        i n  i 1  i 2 components 1, 2, …, n; NA is the Avogadro number. In the reduced form, equation (VIII.16) obtains the form: k =n

Cσ =





∑ α k  ∑ Ci 

k =1  i k + ∏, k = n    N A  ∑ α k  ∑ ∆Vi      k =1  i k  

(VIII.17)

    where αk,  ∑ Ci  and  ∑ ∆Vi  are the molar part, the series of constants and the      i k  i k Van-der-Waals volume of the k-th element, respectively. If it is desired to express the stress-optical coefficient for copolymers via stress-optical coefficients of the components, equation (VIII.16) changes to:     α1 (Cσ ,1 − ∏ ) ∑ ∆Vi  + α 2 (Cσ ,2 − ∏ ) ∑ ∆Vi  + ... +      i 1  i 2 → Cσ =     α1 ∑ ∆Vi  + α 2  ∑ ∆Vi  + ... +      i 1  i 2   + α n Cσ , n − ∏  ∑ ∆Vi     i n → ,   + α n  ∑ ∆Vi     i n

(

)

(VIII.18)

where Cσ,1, Cσ,2, …, Cσ,n are stress-optical coefficient of the components 1, 2, …, n. In the reduced form, equation (VIII.18) obtains the following form:

433

k =n

Cσ =





 i

k

∑ α k (Cσ , k − ∏ ) ∑ ∆Vi 

k =1

k =n

  ∑ α k  ∑ ∆Vi  k =1  i k

,

(VIII.19)

where Cσ,k is the stress-optical coefficient of the k-th component. Let us now consider a semi-empirical method of estimation of the stressoptical coefficient Cσ suggested in ref. [91]. The matter is that the calculation scheme for determination of Cσ, described above, which enables Cσ of polymer to be determined with high accuracy based on chemical structure of the repeating unit, does not link Cσ with other opto-mechanical thermal parameters (elasticity modulus, glass transition temperature, etc.). Let us first perform general analysis. Let us consider a thin plate lying in the XOY plane. Because the light wavelength is much less than transverse sizes of the sample, it may be considered as an infinite plate. The light beam falls along the Z axis. Since the plate is thin, then according to [86] U ZZ =

µ (U XX + U YY ) , 1− µ

(VIII.20)

where UZZ, UXX and UYY are displacements along the corresponding axes; µ is the Poisson ratio. When the plate is undistorted, its material represents an isotropic dielectric with the dielectric constant ε0. When the plate is deformed, the optical symmetry of the medium changes and, consequently, the substance becomes optically anisotropic and may be described by introducing dielectric constant tensor εik. According to [85]

εik = ε0δik + a1Uik + a2Ullδik,

(VIII.21)

where Uik is the strain tensor; a1 and a2 are opto-elastic constants. We shall be interested in the value of εZZ which, in accordance with (VIII.21), may be presented in the following form:

ε ZZ = ε 0 − a1

  µ (U XX + U YY ) + a2 1 − 2µ U XX + 1 − 2 µ U YY  = 1− µ 1− µ  1− µ 

 1 − 2µ µ  (U XX + U YY ). = ε 0 +  a2 − a1 − − 1 1 µ µ  

(VIII.22)

Let σYY = 0 (uniaxial deformation). Then µUXX = –UYY and

εZZ = ε0 + [a2(1 – 2µ) – a1µ]UXX; E U XX − µ 2U XX = EU XX , σ XX = 1− µ 2

(

)

(VIII.23) (VIII.24)

434

where E is the elasticity modulus. From the system of equations (VIII.23) and (VIII.24), the dependence of εZZ on σYY may be obtained:

ε ZZ = ε 0 +

1 [(1 − 2µ )a2 − µa1 ]σ XX . E

(VIII.25)

2 , and ε0 by n02 (where nZZ and n0 are refractive indices Substituting εZZ by nZZ in the Z direction and of isotropic substance, respectively), the stress-optical coefficient Cσ may be found from expression (VIII.25) which, according to the definition, will be equal:

Cσ =

∂nZZ 1 = [(1 − 2 µ )a2 − µa1 ]. ∂σ XX σ = 0 2n0 E XX

(VIII.26)

Using for a1 and a2 the expressions deduced in ref. [50], according to which  ∂ε  1 a1 = 6 ρ   − (ε 0 − 1)(ε 0 + 2 ) ; ∂ ρ  T 3  ∂ε  2 a2 = −3ρ   + (ε 0 − 1)(ε 0 + 2 ), ∂ ρ  T 3 where ρ is the polymer density, we obtain the final expression: Cσ =

(

)(

)

 ∂ε   1 2 2 2  (µ + 1) n0 + 2 n0 − 1 − 3ρ    . 2n0 E  3  ∂ρ T 

(VIII.27) (VIII.28)

(VIII.29)

 ∂ε  Let us estimate the term   by equation (VIII.29). Let us rewrite  ∂ρ T

 ∂ε     ∂ρ  T

as  ∂ε   ∂ε ∂T    =   . ⋅ ∂ ρ  T  ∂T ∂ρ T

(VIII.30)

When T ∆EH, if ∆Ei > ∆EH, and ∆Eeff < ∆EH, if ∆Ei < ∆EH. Let us now consider the influence of the cross-linking degree on the elasticity modulus of a polymer network existing in the rubbery state. Representing the polymer network as a mixture of linear fragments and cross-linked points, let us write down that 1/Enet = γ/El.f. + (1 – γ)/Ecrl.p., or E net =

E l.f.

γ + (1 − γ )

El.f. Ecrl.p.

,

(X.15)

where El.f. and Ecrl.p. are the moduli for linear fragments and cross-linked points, respectively; γ is the concentration of linear fragments. Because equation (X.15) was deduced by summing up compressibilities of linear fragments of the polymeric chain and cross-linked points, consequently,     γ =  ∑ ∆Vi  ∑ ∆Vi , where  ∑ ∆Vi  is the Van-der-Waals volume of the    i  l.f. i  i  l.f. linear fragment;

∑ ∆Vi

is the Van-der-Waals volume of the repeating fragment of

i

the polymer network. As regards the notion of the cross-linked point from the present viewpoint, it was formulated above: the cross-linked point of a network is a group of atoms consisted of the atom, from which branching starts, plus neighboring atoms, chemically bonded to the former one, and their nearest substituents.   The value  ∑ ∆Vi  ∑ ∆Vi may be reduced to the following form:   i  l.f. i 0

     ∑ ∆Vi  n ∑ ∆Vi       i  l.f.  i  l.f. = , 0 ∑ ∆Vi     i n ∑ ∆Vi  +  ∑ ∆Vi       i  l.f.  i  crl.p.

(X.16)

0

  where  ∑ ∆Vi  is the Van-der-Waals volume of the repeat unit of the linear    i  l.f. fragment; n is the number of repeat units per single cross-linked point. Introducing designations ξ = El.f./Ecrl.p.

  and β =  ∑ ∆Vi     i  crl.p.

0

   ∑ ∆Vi  ,    i  l.f.

where El.f. is the elasticity modulus of the linear polymer; Ecrl.p. is the elasticity

461

  modulus of a polymer network consisted of cross-linked points only;  ∑ ∆Vi  is    i  crl.p. the Van-der-Waals volume of the network cross-linked point, we reduce to the following correlation: γ = n/(n + β), and expression (X.15) is transformed to the form: El.f. n βξ = γ + (1 − γ )ξ = + . E net n+β n+β

(X.17)

Since the polymer composed of cross-linked points only has the modulus many orders of magnitude higher than the modulus of the linear elastomer, then ξ 1. Therewith, to keep glass transition temperature Tg low, linear fragments connecting cross-linked points must be extremely flexible. Polyisocyanurates networks, the chemical structure of which is displayed in Chapter VIII, were synthesized [45, 46] as the structures containing rigid bulky cross-linked points bonded by linear flexible chains (R). The role of a cross-linked point (marked by dotted lines) is played by isocyanurate cycle possessing the functionality equal to three. Short organosilicon chains, the structure of which is indicated in Chapter VIII, were used as linear fragments. In another method, polyisocyanurate copolymer networks were produced [127]. The general principle of synthesis of these materials is that application of olygomeric diols as one of the original components interacting with a diisocyanate, 2,4-toluene diisocyanate, in particular, by the urethane-forming reaction, gives first macrodiisocyanates:

468

H3C

CH3

O C N

N C O O NH C O

O R O C

HN

Industrial oligomeric rubbers with hydroxyl end groups may be used as diols. One of them is PF-OP-15 polyether representing the oligomeric copolymer of tetrahydrofurane and propylene oxide: R:{

[O

(CH2)4]m

(O CH2

CH)n }p CH3

m/n = 19.7/1.7; p = 1.2.

Figure 78. Dependence of calculated glass transition temperature Tg of polyisocyanurate polymers based on diisocyanates with different structure R as dictated by the mole fraction α of rubber PF-OP-15:

1) R:

3) R:

; 2) R:

CH2

H

CH2

H

; 4) R:

;

(CH2)6

.

Macrodiisocyanates obtained from oligomeric rubbers form polymer networks by the reaction of polycyclotrimerization in situ and copolymerize with diisocyanates of any chemical structure (aromatic, alicyclic or aliphatic), capable of forming polyisocyanurate networks at an acceptable rate. In reality, mixed copolymeric structure is formed in this case. The polymer may contain a network composed of products of homopolycyclotrimerization of oligomer and diisocyanate simultaneously

469

with a network formed by interaction of the oligomer with diisocyanate producing structures with the arbitrary disposition of linking chains. As the excess of diisocyanate in the initial reactionary mixture increases compared with oligomeric macrodiisocyanate, the concentration of rigid cyclic structures in the network formed increases. Hence, the ratio of flexible (polyether) and rigid (isocyanurate cycles with joint aromatic cycles) fragments may be changed as desired that regulates mechanical properties in a wide range. To check the real possibility of this regulation of polymer networks properties, calculation of Tg value was performed preliminarily with application of equation (IV.85). Figure 78 indicates a smooth decrease of Tg value as the part of flexible rubber fragment increases. Calculations of the equilibrium elasticity modulus performed by equation (X.27) indicated [127] that at low Tg (below room temperature) the equilibrium modulus E∞ may obtain high values, intermediate between values of the moduli for rubber and plastics. Such preliminary calculations were performed for networks with organosilicon linear fragments [45]. Consequently, an expression was deduced for the structure considered, which connects Tg of the network with the amount of dimethylsiloxane units n in the linear fragment: Tg =

751 + 108.15n . 2,450 + 721.5n

(X.38)

Calculations performed according to expression (X.38) are shown in Table 37, which indicates that the glass transition temperature lies below room temperature and decreases as the value of n increases approaching the glass transition temperature of polydimethylsiloxane at n = 44. Table 37 also indicates the values of equilibrium moduli, which obtain different values in the range from 3 to 870 MPa in dependence on the value of n. Synthesis of polymer networks with the above-discussed structure performed confirmed correctness of the suppositions and calculations made [45, 46]. For example, E∞ of obtained networks with organosilicon linear fragments changes in the range from 3 to 3⋅103 MPa (Figure 79) in dependence on the length of the linear fragment. Table 37 Values of calculated glass transition temperatures Tg and equilibrium modulus of elasticity E∞ of cured macrodiisocyanate depending on the number of dimethylsiloxane repeat units n Eexper, MPa Ecalc, MPa Tg, °C 0 33   1 –2 884 886 2 –5 249 283 3 – 41 123 149 6 – 67 40 43 9 – 80 22 24 19 – 99 8 7 44 – 112 3 3

Of special importance for these materials is the process of microphase separation associated with the substantially different surface energy of organosilicon chains (21 dyn/cm) and isocyanurate cross-linked points (35 dyn/cm). Microphase separation has been confirmed by X-ray photoelectron spectroscopy, electron microscopy and dynamic mechanical analysis.

470

Figure 79. Logarithmic dependence of the elasticity modulus E on a number of dimethylsiloxane units n in linear fragment.

Generally speaking, the microphase separation may proceed both in linear block-copolymers or mixtures of polymers and in networks. In these cases, two clearly expressed maxima are observed on the temperature dependence of mechanical loss factor tgδ. Figure 80 represents the temperature dependence of mechanical loss factor tgδ for bulky samples of considered polyisocyanurates possessing different lengths of linear organosilicon fragments. The low-temperature peak is shifted to the side of low temperatures with increasing length of the linear fragment, approaching Tg of polydimethylsiloxane. The high-temperature maximum associated with devitrification of the whole system does not practically depend on the value n starting from n = 2.

Figure 80. Temperature dependence of the mechanical loss-factor tgδ for bulky specimens of polyisocyanurate networks with different length of linear organosilicon fragments n: 1 – 1.2; 2 – 2.1; 3 – 3.2; 4 – 5.4; 5 – 9.2; 6 – 22 .

Hence, two transition temperatures, one of which may be related to the devitrification temperature of the polydimethylsiloxane microphase in the polymeric network and the second – to the devitrification temperature of a microphase

471

containing isocyanurate cross-linked points with attached branchings, are clearly observed. Thereby, the existence of microphase separation in the system associated with thermodynamic incompatibility of polydimethylsiloxane fragments with isocyanurate cross-linked points and branchings attached to them should be admitted. Taking into account that the transition temperatures of both microphases are shifted towards each other, the composition of microphases may be calculated basing on the condition that the transition temperature must coincide with the glass transition temperature of microphases of the present composition. Because the transition temperature in the microphase generally composed of organosilicon fragments is higher than the glass transition temperature of polydimethylsiloxane, it is obvious that neighboring fragments are contained in the polydimethylsiloxane microphase. To answer the question about the structure of these fragments, the glass transition temperatures of the structures shown below have been calculated in ref. [45]: CH3 NH C O CH2 O

CH2

O CH2

Si CH3

CH3 O

Si n CH3

CH2

O CH2

CH2

O C NH O

The glass transition temperature was calculated from formula (IV.41), the step-by-step calculation of Tg for polydimethylsiloxane fragment with different n and attached parts of chains marked by dotted lines being performed. These parts were ‘lengthened’ until the calculated glass transition temperature coincided with the experimental temperature of the first transition. Consequently, the coincidence of calculated and experimental values of the transition temperature was observed in the case when polydimethylsiloxane domains contained parts of chains marked by double dotted lines. Therewith, the structure of these parts is independent of the value n, i.e. of the length of the organosilicon chain. This method of estimating the composition of microdomains may be extended to any object characterized by microphase separation. If a microphase separation proceeds in the system, then in calculation of the equilibrium rubbery modulus the notion of the ‘network cross-linked point’ from the viewpoint of its chemical structure must be broadened. Actually, the presence of a rigid microphase (the above-considered one, for example, which includes isocyanurate cross-linked points with attached branchings) enables the microphase to play the role of a cross-linked point. Therewith, all one needs to do is to be convinced that the glass transition temperature of this microphase is above room temperature. The presence of this ‘macrocross-linked point’ causes a significant increase of β value in equation (X.27) that promotes an increase of the equilibrium rubbery modulus. Ref. [45] displays this analysis performed for the system discussed above. Consequently, it was obtained that the glass transition temperature of rigid domains was 33°C, and their Van-der-Waals volume equaled 751 Å3. Taking into account that the Van-der-Waals volume of the repeat unit of polydimethylsiloxane equals 180.15 Å3, the value β = 751/180.15 ≈ 4.2. Experimentally, the equilibrium rubbery moduli were determined [46] with the help of measurements of stress relaxation curves approximated with the help of a physically proved relaxation memory function (see below). The mechanical behavior of polyisocyanurate networks containing organosilicon linear fragments was demonstrated above (see Figure 71). Figure 79 indicates the dependence of the elasticity modulus of polyisocyanurate networks on the number of repeat units of polydimethylsiloxane chains linking cross-linked points.

472

The elasticity modulus of such networks overlaps the range of moduli typical of the transition zone from the glassy state to the rubbery state. However, in spite of this, the mechanical behavior of present materials is not viscoelastic as for all polymers in the transition zone, but elastic typical of polymeric glasses. This is proved by the form of stress relaxation curves displayed in Figure 71. Let us call attention once again to the mechanical behavior of polyisocyanurate network with linear organosilicon fragments with n = 6.2. At these sizes of linear chains, the initial stress σ0 is approximately coincident with σ0 for a viscoelastic material (7.5 MPa), but mechanical behavior is significantly different from the former one: stress relaxes fast by a low value at the initial moment of time, and then stress decrease stops, i.e. the material behaves itself as an elastic glassy polymer1. Let us now turn to analysis of the properties of gradient-modulus materials produced on the basis of oligomeric rubber PF-OP-15 and 2,4-toluylene diisocyanate. For producing gradient-modulus materials, initial components are dosed smoothly to ensure directed control of the chemical composition of the network in the same sample.

Figure 81. Dependence of the elasticity modulus lgE or E on concentration of 2,4-toluylene diisocyanate G in its mixture with oligomeric macrodiisocyanate; the concentration of G varies along the specimen length l.

In this manner, the samples were produced in refs. [19, 129] in which the elasticity modulus changed from 4.5 MPa (typical of rubbers) to 2000 MPa (typical of 1 It should be taken into account that there are no absolute elastic polymeric materials (excluding ideal crystals). That is why the terms ‘elastic behavior’ and ‘elastic material’ in relation to polymers are conditional: by elastic behavior we mean extremely slow stress relaxation.

473

plastics). Therewith, this change proceeded smoothly in the same material with no interfaces and intermediate layers. Figure 81 displays an example of the dependence of the elasticity modulus on the concentration of 2,4-toluylene diisocyanate in the initial mixture. It is clearly observed that the elasticity modulus changes linearly along the sample and, hence, as mentioned above, a smooth transition from rubber to plastic is performed with no interfaces. To analyze the mechanical behavior of materials obtained, stress relaxation curves were measured for microspecimens cut off from the initial macrospecimen in different points of the gradient (Figure 82). This Figure indicates for comparison the stress relaxation curve for a viscoelastic material – epoxy resin ED-20 cured by polysebacic acid anhydride in the presence of azelaic acid, for which Tg is located near room temperature, i.e. for the same material, the relaxation behavior of which is shown in Figure 71. Stress relaxation curves were plotted in ‘relative stress’ – time coordinates. Relative stress was calculated as σ/σ0, where σ is the current relaxing stress, σ0 is the initial stress developed at the moment of the end of ‘immediate’ setting of deformation.

Figure 82. Curves of relative stress relaxation σ/σ0 for polyisocyanurate networks prepared from oligomeric macrodiisocyanate and 2,4-toluylene diisocyanate when the concentration of the latter in percent by weight is: 1 – 6, 2 – 46, 3 – 27, respectively; 4 – epoxy oligomer ED-20 cured with methyltetrahydrophthalic anhydride; 5 – epoxy viscoelastic polymer (the composition is indicated in the text).

From this Figure, it is obvious that as for usual viscoelastic material the relative stress relaxes fast down to zero, for polymer networks obtained in refs. [19, 129] a slower decrease of stress is observed, typical of polymeric glasses or rubbers with further transition to extremely low stress relaxation. Hence, in spite of the fact that a definite part of the material in the same specimen possesses values of the modulus typical of the transition zone, mechanical behavior is elastic as for glasses of rubbers but not viscoelastic typical of all polymers in the transition zone. Dynamic mechanical analysis indicates that tgδ for the networks obtained is extremely low which is typical of elastic materials, despite the values of the storage modulus E′ typical of the transition zone. Basing on polyisocyanurate networks, films with a gradient of the elasticity modulus perpendicular to the film surface (in direction of thin) were obtained. These

474

films formed from high-crosslinked polymer networks, possess good mechanical properties (strength of 50 MPa and ultimate elongation of 90%). Hence, obtaining of gradient-modulus materials allows us to avoid the main drawback of high-crosslinked polymer networks – their brittleness.

Chapter XI. Description of relaxation processes in polymers

XI.1 Stress relaxation Various variants of the memory function in the appropriate Boltzmann– Volterra equations have been suggested to date to describe processes of stress relaxation and creep. Combined description of these memory functions and their resolvent is present in monograph [112]. The memory function contains three or four parameters, moreover they usually possess a fractional exponent of time, because only in this case experimental data may be described with a good approximation by stress relaxation and creep. Analysis of proposed memory functions has indicated that at proper selection of parameters they give the course of relaxation processes with acceptable accuracy. However, the physical meaning of these parameters is not always clear, although attempts to disclose the physical meaning of some memory functions have been made [74, 104]. Reference [7] suggested an approach to production of relaxation memory functions based on consideration of thermodynamic functions and their changes during relaxation. Suppose that the stress relaxation proceeds as a result of interaction and diffusion of kinetic units – relaxants. Relaxants may be various groups of atoms, repeat units, larger fragments and the whole fragments of macromolecules. Among relaxants are also separate elements of the free (empty) volume, i.e. microcavities, stress concentrators, etc. Interacting with each other, these microcavities may unite, be rearranged and diffuse in a polymeric material during relaxation, forming a structure which promotes a decrease of relaxing stress. The polymeric material may then be considered as the one consisting of relaxants and non-relaxants, the most part of the sample material after ‘instantaneous’ setting of deformation consisting of relaxants interacting with each other forming a non-relaxing material. Appearance of particles of two types (relaxants and non-relaxants) and their diffusion cause production of entropy in the system, which increases in the course of stress relaxation. The production of entropy (or the rate of appearance of entropy) is determined dS 1 by the expression , where S is entropy, t is time, V is the volume of the system. dt V Relaxation memory functions were obtained in ref. [7], assuming that the driving force of the process is production of the system (sample) entropy, which increases up to the maximum value during stress relaxation. It is common knowledge that if the system consists of two types of particles, the entropy of mixing S in this system determined with the help of the Boltzmann equation is calculated from the expression m*! , S = k B ln m1*! m2*!

(XI.1)

where m* is the total number of particles (in this case, the number of relaxants and non-relaxants per specific volume); m1* and m*2 are numbers of relaxants and non-

476

relaxants in the specific volume, respectively; kB is the Boltzmann constant. Taking into account that two types of particles are present, it may be written down that S = kB ln

m* !

(α m ) !(1 − α ) m  ! *

*

,

(XI.2)

where α is the part of relaxants in the total number of particles. Using an approximate formula for calculating the factorial at large m*, basing on equation (XI.2), we obtain:

S = kB ln

( )

2π m* m*

(

2πα m* α m*

)

α m*

m*

*

e− m

2π (1 − α )m* (1 − α ) m* 

(1−α ) m* − (1−α ) m*

.,

(XI.3)

e

After some transformations and neglecting low components of the expression, we obtain the following form: S = –kBm*[αlnα + (1 – α)ln(1 – α)].

(XI.4)

The value α of changes with time t from 1 to 0.5, because at α = 0.5 the entropy of mixing reaches its maximum. Assume that the memory function in the Boltzmann–Volterra equation is associated with the reverse dependence of the type 1 1 T (τ ) = S 0  −  S S max

∞

 *  ∫ T (τ ) dτ , 0

(XI.5)

where T*(τ) is the variable part of the memory function. Then, substituting expression (XI.4) into equation (XI.5), we obtain T (τ ) =

S0  1 1   , − k B m  α lnα + (1 − α ) ln(1 − α ) ln 0.5 

(XI.6)

∞

where m = m* ∫ T * (τ )dτ . 0

Now it is necessary to indicate the dependence of α on τ (remember that α is the part of relaxants in the total number of particles in the system). As mentioned above, the change of α with time τ may be stipulated by two reasons: interaction of relaxants and their transition into non-relaxants, and diffusion of kinetic units (note that the mechanism associated with diffusion of microdefects is described in refs. [104, 119]). Let us discuss these reasons. Since the interaction of relaxants is complicated, it is reasonable to describe it by the reaction equation of the n-th order. If in a usual chemical reaction, for example, the third order is rarely observed (because this requires active collision of three particles simultaneously), in this case, relaxants are ‘condensed’ in the sample, and the elementary act of their interaction may include several relaxants together (for

477

example, fusion of several microcavities into a single one). Therewith, the reaction order may be fractional. For this case, the following kinetic equation is true: dc = kc n , dτ

(XI.7)

where k is the reaction constant; c is the concentration. Integrating (XI.7) from τ = 0 to t, we obtain that c=

c0

(

)

1

1 + c0n −1 (n − 1) kτ n−1

,

where c0 is the initial concentration of relaxants of any type (assume for ease that these concentrations are equal for different types of relaxants). Then

α=

c = c0

1

(1 + k *τ / β )β

,

(XI.8)

1 where k * = kc0n −1 ; β = ; n is the reaction order. n −1 To obtain the relaxation memory function, it is necessary to substitute expression (XI.8) into equation (XI.6). Therewith, it should be taken into account that at the end of deformation the fraction of relaxants is not 1, but somewhat smaller, equal to 1 – α0. Taking into account all the above-mentioned, we obtain    S0  1 → T1 (τ ) = −  k B m1      1 1     − α 0  ln −α0  +  β β * *      1+ k τ / β   1+ k τ / β  

(

)

(

)

   1 1  → − .     ln 0.5  1 1     + α 0  ln1 − +α0   1 − β β * *      1+ k τ / β   1+ k τ / β  

(

)

(

(XI.9)

)

The function T1(τ) is of the physical sense only under the condition that 1 ≥ 0.5 . Hence, the memory function T1(τ) contains four parameters: β * 1+ k τ / β S 1 and α0. A = 0 ; k * = kc0n −1 ; β = k B m1 n −1

(

)

478

According to requirements on the relaxation memory function, the value α0 must be extremely low; in ref. [7] α0 was assumed to be equal to 10–10 basing on approximation of stress relaxation curves for a series of polymers. At low values of k*τ/β, i.e. in initial stages of relaxation, the function T1(τ) is

(

substantially simplified. Actually, at low k*τ/β, the value 1 + k *τ / β Then

)β

  S0  1 → T1 (τ ) = −  k B m1   1   1   − α 0  ln − α0  +  *   1 + k *τ  + k τ 1    

(

)

(

)

(XI.10)

  1 1  − → .     ln 0.5  1 1 1 − + α 0  ln1 − +α0    1 + k *τ    1 + k *τ     

(

)

(

= 1 + k*τ.

)

After further transformations, we obtain T1 (τ ) = −

  S0  1 1  −  * . kB m1  k τ + α 0 ln k *τ + α 0 − 1 ln 0.5     

(

) (

(XI.11)

)

Neglecting the second summand in the braces due to its smallness, it is obtained that T1 (τ ) = −

S0 1 . * kB m1 k τ + α 0 ln k *τ + α 0 − 1  

(

) (

(XI.12)

)

Let us integrate expression (XI.12) after some preliminary transformations: t

∫ T1 (τ )dτ = −

0

 k *τ + α  0 .  d *∫ * *   e k B m1k 0 k τ + α 0 k τ + α 0   ln e e S0

t

1

(XI.13)

Then, we obtain t

∫ T1 (τ )dτ = −

0

S0 k B m1k

*

ln

(

ln k *τ + α 0 e

)t = − 0

S0 k B m1k

*

ln

(

)

ln k *t + α 0 − 1 . ln α 0 − 1

(XI.14)

479

t

Let us substitute the value of ∫ T1 (τ )dτ into the Boltzmann equation: 0

 t  σ = σ 0 1 − ∫ T1 (τ )dτ  ,  0 

(XI.15)

where σ0 is the initial stress appeared as a result of ‘instantaneous’ deformation. Consequently, we obtain the relation for description of stress relaxation in the initial part (at low values of t):

σ =σ0 +

σ 0 S0 k B m1k

*

ln

(

)

ln k *t + α 0 − 1 . ln α 0 − 1

If expression (XI.16) is true, the dependence of σ on ln

σ 0 S0

(XI.16)

(

)

ln k *t + α 0 − 1 must lnα 0 − 1

, and the section cut-off on k B m1k * the axis of ordinates – σ0. Figure 83 displays such dependence for poly(methyl methacrylate). It is clear that experimental points fit the straight line with high accuracy. represent a straight line, tangent of which equals

(

)

ln k *t + α 0 − 1 (for explanation see text). Stress relaxation for ln α 0 − 1 PMMA-material under conditions of uniaxial compression when the temperature is 295 K and the deformation is 2.2%.

Figure 83. Dependence of σ on ln

Let us now consider the diffusion mechanism of relaxation. When the continuous-time random walks of kinetic units take place, the amount of sites occupied by them at time τ and, consequently, the part of non-relaxants 1 – α is determined from the correlation [146]: (1 – α) = aτb/2,

(XI.17)

480

where 0 < b < 1; a is a constant. In the case, if b = 1, correlation (XI.17) corresponds to the Fick diffusion: 1/ 2

4  Dτ  1−α =   l π 

, 1/ 2

4 D   l π  Substituting correlation (XI.17) into equation (XI.6), we obtain

where l is the sample size; D is the diffusion coefficient; i.e. a =

T2 (τ ) = −

S0 k B m2

 1 1  −  γ , γ γ γ  aτ ln aτ + (1 − aτ ) ln(1 − aτ ) ln 0.5 

.

(XI.18)

where γ = b/2. The function T2(τ) is of the physical meaning only under the condition, if aτγ ≤ 0.5. S The memory function (XI.18) contains three parameters: A = − 0 , a and k B m2 γ. It represents a function with a non-essential singularity at τ = 0. At low values of aτγ the function T2(τ) may be simplified. In this case, correlation (XI.18) will be reduced to the form: T2 (τ ) = −

S0  1 1  −  γ . k B m2  aτ (ln aτ γ − 1) ln 0.5 

(XI.19)

Neglecting the second summand in the square brackets, we obtain     S0  1 . T2 (τ ) = − (XI.20) k B m2  γ ln aτ γ   aτ  e   After a series of preliminary transformations, let us integrate correlation (XI.20): t

∫ T2 (τ )dτ = −

0

S0 k B m2 aγ

 aτ γ d ∫ aτ γ ln aτ γ  e  0 e e t

τ 1−γ

Let us make variable substitution: 1/ γ

aτ γ ex  ex  = x ; τγ = ; τ =   e a a Then

.

    .

481

t

1 / γ −1

 xe    a x ln x

x2 

S0

∫ T2 (τ )dτ = − k Bm2 aγ ∫

0

x1

dx.

(XI.21)

dx.

(XI.22)

In what follows we obtain that t

∫ T2 (τ )dτ = −

0

S 0 e1 / γ −1 k B m2 a

Taking into account the x1 = 0 and x2 = t

∫ T2 (τ )dτ = −

0

1/ γ

x2 1 / γ − 2

∫

γ x 1

x

ln x

at γ , we get e

 a 1 / γ −1 li  t1−γ 1/ γ e   k B m2 a γ  S 0 e1 / γ −1

 , 

(XI.23)

where li is the integral logarithm. t

Substituting the value of

∫ T2 (τ )dτ

into the Boltzmann equation (XI.15), we

0

deduce the correlation describing stress relaxation in the initial section of the relaxation curve under the condition that atγ δs or δp 0 . 



(XII.12)

For globules, 8r/3R γs-p.

(XII.13)

The second condition is formed in the following manner: the work performed by the surface tension forces of the solvent A must exceed the energy of rupture of intermolecular bonds in the bond belt, i.e. specific cohesive energy of the polymer δ p2 would be lower or equal to the work of the solvent on rupture of the linking tore, 2

related to the specific volume of the linking tore δ p* . The value A may be presented in the form: A = (ft – fgl)εmaxr, and 2

δ p* =

(

)

A 8r  ε  γ s + γ p − γ s - p  3 −  max . Vt R  4πr 

(XII.14)

Because 8r/3R > δp and δs 0, has the same form as in the case of the globular structure (see above)

γ s + γ p > γ s-p . This condition is always fulfilled. The second condition of detachment is associated with the work of detachment: p A = ( f c − f f )ε max r,

(XII.43)

p performed by forces of the surface tension of the solvent; ε max is the deformation at break of the connecting cylinder. This work must exceed the energy of disruption of intermolecular bonds. The work of the solvent consumed for disruption of connective cylinders and related to the volume of two connecting cylinders should be presented in the following form:

(δ s* )2 = A (2Vc ) .

(XII.44)

Here Vc is the volume of the connecting cylinder, equal to Vc = πr2Lf. Using expressions (XII.41) and (XII.42), we obtain

(δ s* )2 = δ s2 ρf γ s + γγp − γ s-p ,

(XII.45)

s

where

s (δ s* )2 = 3γ sε max

4πrs ;

r 2(π − 1) εp ρ f = max ⋅ s ⋅ . s r 3 ε max f Consequently, the second condition may be presented in the following form:

( )2

δ s2 ≤ δ s* or

µ ≤ ρ fβ ,

(XII.46)

526

where µ and β are of the same meaning as in the case of the globular supermolecular structure. This condition differs from condition (XII.24) by the value of coefficient ρ only. The relation ρf/ρgl, where ρgl corresponds to the polymer with the globular supermolecular structure, may be presented in the form:

ρ f 2(π − 1) rgl = ⋅ , rf ρ gl 3 where rgl is the radius of the connecting globule; rf is the radius of the connecting cylinder. Because according to estimations made in ref. [94] rgl/rf ~ (1/3)0.5, consequently,

ρf ≈ 0.82. ρ gl As a consequence, the condition of polymer solubility with the fibril structure is stricter than for the globular structure. The same criterion is valuable, but with lower coefficient 2ρf = 1.125:

µ ≤ 1.125β = 1.125Φ Φ − Φ 2 − 1 + a  .  

(XII.47)

Hence, the polymer with the fibrillar supermolecular structure may not dissolve even under the condition of polymer solubility with the globular structure.

Chapter XIII. Surface properties of organic liquids and polymers

It is important to know the surface tension value and be able to predict it on the basis of the chemical structure of the substance is important, because many individual properties of liquids and solids, as well as miscibility and solubility of them in each other, depend on the surface tension of liquids and surface energy of solids. Among existing methods of calculation of surface tension, the most wide-spread is the additive scheme based on summing up of parachors which characterize the contribution of separate atoms to surface tension. The calculation is performed by the formula  ∑ Pi  P γ =  = i V   V  4

4

   ,  

(XIII.1)

where P is the total parachor of the molecule (or the repeat unit of the polymer); Pi are parachors typical of every atom. Values of atomic parachors Pi, as well as constants which characterize contribution of various types of bonds (double, triple) and cycles (three-component, four-component, etc.) to the general parachor of the substance, are indicated in Table 45. Table 45 Values of atomic parachors Pi and parachors for a series of constants Pj Constants Pj Atom Pi C 4.8 Double bond 23.2 H

17.1

O

20.0

O2*

60.0

N S F

12.5 48.2 27.5

Cl Br

54.3 68.0

I 91.0 * For two oxygen atoms participating in the ester

Triple bond

46.4

Three-component cycle

16.7

Four-component cycle

11.6

Five-component cycle

8.5

Six-component cycle

6.1

C O

group.

O

Formula (XIII.1) enables the value γ to be calculated with high accuracy for organic liquids and polymers. However, the physical meaning of values Pi participating in correlation (XIII.1) is not clear yet. This makes it difficult to analyze the influence of the weak Van-der-Waals interaction and strong polar groups on formation of some surface properties of organic liquids and polymers. This problem is quite important, because analysis of such an influence on the quantitative level allows

528

regulation of the chemical structure of substances to ensure that they have the necessary surface properties.

XIII.1. Surface tension of organic liquids Let us consider the approach to analysis of influence of the chemical structure on surface tension, suggested in ref. [34]. This analysis was based on the following ideas. It is common knowledge that molecules of a liquid located on the surface participate in an intermolecular interaction, different from that in the volume. If the volumetric problem is considered (Figure 97), then at hexagonal packing of spherical molecules present in the volume the coordination number equals 12, and on the surface – 9, i.e. their ratio is 4/3. As the free energy decreases with the coordination number increase, molecules strive to transit from the surface layer into the volume. That is why the formation of a unit of new surface require consumption of energy.

Figure 97. Schematic representation of arrangement and interaction of molecules in the vertical (a) and horizontal (b) planes.

Let us calculate first the number of molecules n located on the surface unit. It may be easily displayed [34] that at hexagonal packing (see Figure 97) the value n per 1 cm2 of surface will be n=

1016 ⋅ 0.2887 r2

,

(XIII.2)

where r is the molecule radius, expressed in Å. Therewith,  ∑ ∆Vi    r = i ⋅ 3  4   

1/ 3 1/ 3

  = 0.6204 ∑ ∆Vi     i 

,

(XIII.3)

where ∆Vi are Van-der-Waals volumes of atoms participating in the molecule composition. With regard to correlations (XIII.2) and (XIII.3), we obtain that

529

n=

1016    ∑ ∆Vi     i 

2/3

⋅ 0.75 .

(XIII.3)

Let us calculate the cohesive energy e* accounted for one molecule. According to the approach for estimating the solubility parameter (see above), the

∑ ∆Ei*

cohesive energy accounted for one mole of the substance equals

k , where

i

∆Ei* are molar constants displaying the meaning of the energy of intermolecular interaction for each type of atoms and separate polar groups participating in the molecule or the repeat unit of the polymer (values of ∆Ei* are shown in Table 43); k is the coefficient of molecular packing in the volume of the substance considered. Then

∑ ∆Ei* ∑ ∆Ei*

e* = i kN A

= i ⋅ 0.166 . k ⋅ 1016

In formula (XIII.5), the value e* is expressed in ergs, and

(XIII.5)

∑ ∆Ei*

– in Joules.

i

The cohesive energy γ*, which would be possessed by all molecules in the volume located in the surface layer of 1 cm2 square equals ne* and, according to correlations (XIII.4) and (XIII.5), equals

γ * = 0.125

∑ ∆Ei* i

  k  ∑ ∆Vi*     i 

2/3

.

(XIII.6)

The value of γ* significantly exceeds the value of surface tension, because the formation of a specific new surface requires overcoming of not the whole cohesive energy, but just a part of it, because in the surface layer the molecule possesses the coordination number different from zero. Figure 97b indicates that approximately 1/4 part of the cohesive energy is consumed for the molecule yield from the volume to the surface, because in this case the coordination number changes from 12 to 9. Moreover, it should be taken into account that packing of molecules in the surface layer is not perfect, as it is observed from Figure 97b. Let us designate the true coefficient of molecules packing in the surface layer as ksrf. For future calculations, let us determine the coefficient of packing ksrf,p in the surface layer at the ideal hexagonal packing of spheres. To determine the maximum possible occupied volume Vocc, let us multiply the number of molecules n in the specific surface layer by the volume of a single molecule:

530

Vocc =

1016 r

2

4 ⋅ 0.2887 πr 3 = 1.2086⋅1016 Å3 3

(r is expressed in ångströms). The total volume of the surface layer Vtot = 2⋅1016 Å3, and then ksrp,p = Vocc/Vtot = 0.604. Hence, the coefficient of packing ksrf,p at the ideal packing of spheres in the surface layer equals 0.604, whereas the appropriate coefficient kvol,p in the volume equals 0.740. Consequently, the part of molecules present on the surface equal ksrf/0.604, where ksrf is the true coefficient of molecular packing in the surface layer. Then for the value γ*, we obtain

γ * = 0.125

ksrf ∑ ∆Ei* i

  0.604 ∑ ∆Vi     i 

2/3

.

(XIII.7)

Let us now take into account the part of the cohesive energy which must be overcome for the molecule to transit to the surface from the volume. This part α stipulated in this transition by the coordination number change, will be determined from the correlation:

α=

12

k k − 9 srf 0.740 0.604 = 1 − 3 ksrf ⋅1.225 . k 4 k 12 0.740

(XIII.8)

Then, for the surface tension of liquids, we obtain:

γ s = αγ * =

0.207ksrf ∑ ∆Ei* i

  k 0.74  ∑ ∆Vi*     i 

 0.919ksrf  1 − . k 

2/3 

(XIII.9)

Basing on correlation (XIII.9), ref. [34] indicates the calculation of values ksrf/k for a great number of organic liquids of various nature. Initial data and results of this calculation for representatives of various classes of liquids are indicated in Table 46. Clearly, for all organic liquids the value ksrf/k < 1. Therewith, it was found that for many organic liquids, especially for unitypical ones, for example, for hydrocarbons, alcohols, etc., the value ksrf/k is approximately constant. The calculations performed indicate [34] that for hydrocarbons, perfluorocompounds, halogen-containing compounds, aldehydes, ketones and nitrocompounds the average value (ksrf/k)avg = 0.851. For alcohols, amides, and acids, (ksrf/k)avg = 0.954, and for nitriles (ksrf/k)avg = 0.910. The values of the coefficient of molecular packing in the surface layer are also displayed in Table 46.

531

Because for some series of organic liquids the value ksrf/k plays the role of a constant, then correlation (XIII.9) may be reduced to the form:

γs = A

∑ ∆Ei* i

   ∑ ∆Vi*     i 

2/3

,

(XIII.10)

where A = 0.207⋅(ksrf/k)⋅(1 – 0.919⋅ksrf/k). Taking into account the above-displayed values of ksrf/k, the following expression for calculation of the surface tension of organic liquids may be presented:

γ s = Aj

∑ ∆Ei* i

   ∑ ∆Vi*     i 

2/3

.

(XIII.11)

For hydrocarbons, perfluorocompounds, halogen-containing compounds, esters, aldehydes, ketones and nitrocompounds (group I), A1 = 0.0287; for alcohols, amides, and acids (group II), A2 = 0.0181; for nitriles (group III), A3 = 0.0229. Recall that ∆Ei* is expressed in Joules, ∆Vi – Å3, and then, with indicated coefficients Aj, the value γs is expressed in dyn/cm. Table 46 Initial data and results of calculation of the surface tension of a series of organic liquids 2/3 γ, dyn/cm ∑ ∆Ei*,  ∑ ∆Vi*  , k ksrf Compound i   Exper. Calc.  i  J/mol 3 Å 1 2 3 4 5 6 7 Hydrocarbons n-Pentane 21.30 0.510 0.453 16.03 17.960 13,903 Isopentane 12,180 21.40 0.510 0.447 15.00 17.330 n-Hexane 23.70 0.527 0.462 18.41 19.895 16,603 Cyclohexane 16,206 21.90 0.567 0.443 25.12 23.760 n-Heptane 19,303 25.90 0.541 0.469 20.21 21.604 n-Octane 22,003 28.20 0.549 0.472 21.75 22.700 Isooctane 20,281 28.20 0.545 0.479 18.85 21.710 n-Nonane 30.30 0.558 0.479 22.91 23.940 24,704 n-Decane 27,404 32.30 0.571 0.489 23.92 25.900 n-Tetradecane 38,209 39.90 0.589 0.506 26.96 28.770 Benzene 19,186 19.80 0.597 0.501 28.78 29.760 Toluene 20,687 22.30 0.592 0.489 28.53 28.680 n-Xylene 23,391 24.70 0.610 0.960 30.03 30.650 m-Xylene 23,391 24.70 0.600 0.515 26.63 29.740 o-Xylene 23,391 24.70 0.595 0.499 28.31 29.250 Ethylbenzene 23,391 24.60 0.598 0.514 29.04 29.599 Isopropylbenzene 24,369 26.80 0.596 0.490 28.20 28.790

532

1 n-Perfluoropentane n-Perfluoroheptane n-Perfluorooctane Dichloromethane Chloroform Tetrachlorocarbon Ethyl chloride 1,1-Dichloroethane 1,2-Dichloroethane 1,1,1-Trichloroethane Tetrachloroethane Isobutyl chloride cis-Dichloroethylene trans-Dichloroethylene Trichloroethylene Tetrachloroethylene Chlorobenzene Bromobenzene Iodobenzene Bromoform Ethyl bromide 1,2-Dibromoethane Ethyliodide Glycol Glycerol Cyclohexanol Methanol Ethanol n-Propanol n-Butanol Isobutyl alcohol n-Amyl alcohol n-Hexanol n-Octanol Acetic Butyric Isovaleric n-Valeric Methyl formiate Ethyl formiate Methyl acetate Ethyl acetate n-Propyl acetate Isopropyl acetate Ethyl propyonate n-Butyl acetate Amyl acetate Ethyl isovaleate Diethyl carbonate Benzaldehyde Acetaldehyde

2

3 4 Perfluorocompounds 12,724 29.50 0.574 15,228 32.80 0.551 17,732 35.90 0.571 Halogen-containing compounds 14,408 15.14 0.554 13,275 17.60 0.555 12,147 19.87 0.553 11,453 15.52 0.527 17,109 17.94 0.544 17,109 17.94 0.579 15,976 20.24 0.555 28,416 22.40 0.607 15,132 20.96 0.550 15,357 17.20 0.571 15,357 17.20 0.563 18,313 19.57 0.582 21,268 21.70 0.605 23,642 21.80 0.605 27,011 23.00 0.634 31,688 24.60 0.661 23,379 20.73 0.650 14,822 16.70 0.542 23,843 20.05 0.628 19,491 18.41 0.590 Alcohols 39,840 15.50 0.659 59,557 19.41 0.705 33,443 22.96 0.658 20,118 11.02 0.544 22,819 14.10 0.565 25,511 17.20 0.563 28,219 19.77 0.578 26,497 19.77 0.573 30,919 22.30 0.587 33,624 24.70 0.590 39,024 21.90 0.597 Acids 23,015 14.60 0.589 28,420 20.00 0.587 29,398 22.80 0.597 31,120 22.50 0.519 Esters 13,376 14.90 0.567 16,076 17.80 0.565 16,076 17.80 0.565 18,781 20.40 0.565 21,481 22.87 0.573 19,758 22.90 0.567 21,481 22.87 0.573 24,181 25.20 0.577 26,882 27.40 0.584 25,159 27.00 0.570 22,075 24.20 0.593 Aldehydes and ketones 27,672 22.50 0.636 12,782 13.20 0.509

5

6

7

0.523 0.478 0.493

9.87 12.60 13.60

16.904 17.330 18.680

0.458 0.424 0.350 0.423 0.475 0.455 0.440 0.518 0.458 0.468 0.484 0.472 0.481 0.479 0.522 0.558 0.609 0.470 0.497 0.535

28.12 27.16 26.75 22.18 24.75 32.23 25.77 36.04 21.99 28.00 25.00 29.50 32.26 33.19 36.34 37.65 31.68 24.15 38.91 28.10

24.800 23.600 20.900 20.500 23.800 28.010 23.700 34.230 22.160 26.090 25.195 28.600 30.720 32.600 36.790 41.753 38.000 22.520 36.800 30.400

0.625 0.660 0.576 0.539 0.558 0.547 0.562 0.564 0.559 0.564 0.557

46.49 62.29 34.37 22.55 22.32 23.70 24.57 22.98 25.68 24.48 27.53

51.900 71.100 44.600 33.100 23.600 23.930 29.200 28.300 30.820 31.460 32.840

0.566 0.556 0.563 0.555

27.42 26.96 25.31 27.35

30.450 30.700 32.640 31.680

0.490 0.495 0.490 0.499 0.505 0.498 0.505 0.506 0.511 0.504 0.502

24.62 23.84 24.49 23.75 24.28 22.35 24.27 25.20 25.88 23.77 26.44

25.696 25.510 25.510 25.650 26.770 25.350 26.770 27.430 28.470 26.350 28.550

0.513 0.468

39.70 23.32

37.890 24.900

533

1 Acetone Methylethylketone Diethylketone Cyclohexanon

2 15,483 18,183 20,883 23,186

Diethyl ether 1,4-Dioxane

11,796 25,564

Aniline Pyridine Formamide

30,008 17,514 31,739

Acetonitrile Propyonitrile n-Valeonitrile Capronitrile Methacrylonitrile

17,021 19,725 25,126 27,826 20,674

Nitromethane Nitroethane 2-Nitropropane Nitrobenzene

15,913 18,613 19,592 31,199

3 16.30 18.98 21.50 22.10 Ethers 20.20 19.70 Amines, amides 21.50 18.50 12.30 Nitriles 13.50 16.40 21.70 24.00 18.50 Nitrocompounds 12.86 15.88 18.70 22.30

4 0.534 0.556 0.570 0.575

5 0.478 0.491 0.503 0.450

6 24.60 25.18 25.18 35.62

7 21.299 24.690 26.660 27.850

0.521 0.614

0.411 0.540

16.49 33.70

18.270 35.590

0.658 0.595 0.640

0.541 0.403 0.585

43.31 37.25 58.35

43.230 29.700 43.700

0.565 0.565 0.589 0.592 0.574

0.514 0.546 0.532 0.533 0.529

29.10 27.25 27.44 27.87 24.40

26.210 26.390 30.600 31.080 27.990

0.518 0.534 0.547 0.615

0.428 0.433 0.471 0.506

36.98 32.06 29.12 43.35

35.500 33.600 32.900 39.700

Calculations performed by formula (XIII.11) indicate quite good agreement of the calculated and experimental values of γ, deviations being approximately the same as in calculations with the help of parachors. Correlation (XIII.11) enables the contribution of separate groups and specific intermolecular interaction to the surface tension to be estimated. For example, usually, of interest is the contribution of hydrogen bonds made in formation of the surface properties of organic liquids. Let us estimate such contribution on the example of alcohols and acids. For this purpose, let us transform correlation (XIII.11) to the following form:

γs =

where

∑ ∆Eih*

  * *   ∑ ∆Eih + ∑ ∆Eid , 2/3     i i    ∑ ∆Vi*     i  0.0181

is the contribution of hydrogen bonds to cohesive energy;

i

∑ ∆Eid* = ∑ ∆Ei* − ∑ ∆Eih* is the contribution of weak dispersion interaction to i

i

i

cohesive energy. For ethanol,

∑ ∆Ei*

* * * = 2 ∆EC + 6 ∆EH + + ∆EO

i

5,460 cal/mol = 22,820 J/mol, and

∑ ∆Eih*

= 2⋅550.7 + 6⋅47.7 + 142.6 + 3929 =

i

∑ ∆Eih*

= 16,423 J/mol. Then a part of the surface

i

tension stipulated by hydrogen bonding will be determined as

534

γ sh =

0.0181

∑ ∆Eih*

= 20.9 dyn/cm.   i  ∑ ∆Vi*     i  The contribution associated with weak dispersion interaction gives 2/3

γ sq =

0.0181    ∑ ∆Vi*     i 

2/3

∑ ∆Eid*

= 8.1 dyn/cm.

i

Total surface tension γs = γsh + γsd = 29 dyn/cm, and the contribution of each component equal 72.0 and 28.0%, respectively. Analogously, for acetic acid γsh = 20.5, and γsd = 8.2 dyn/cm; the contribution of each component equals 71.0 and 29.0%, respectively. This analysis may be performed not only for hydrogen bonds, but also for specific interactions of other types. It should be noted that according to the Fowkes method [143] significantly different contributions of hydrogen bonding to the total value of surface tension are obtained. For example, for formamide γsh = 19 and γsd = 58.2 dyn/cm [143]. The part of the surface tension stipulated by hydrogen bonding is 33%. According to calculations performed with the help of data from Table 46, for

∑ ∆Eih*

formamide

= 16,423 and

i

∑ ∆Eih* ∑ ∆Ei* ≈ i

∑ ∆Ei*

= 31,739 J/mol. Then this part is

i

0.52 or 52%, which is significantly higher than that obtained by

i

Fowkes. Besides estimation of the surface tension γ of organic liquids, of interest is the relationship of the value γ with the specific cohesive energy of the liquid δ2 or solubility parameter δ. This problem has been discussed many times in the literature; there are empirical correlations, which allow setting of this connection. For example, the correlation is known [122]

δ = 4.1(γ/V1/3)0.43,

(XIII.12)

where V is the molar volume of the liquid. The physical meaning of this correlation is not clear and, moreover, it does not describe the properties of all organic liquids. For example, calculation of δ for alcohols and organic acids by this correlation leads to significantly reduced values. With the help of correlation (XIII.11), the dependence connecting the solubility parameter value with the surface tension may be deduced. For this purpose, let us use correlation (XII.3), according to which solubility parameter δ is calculated. First, correlation (XIII.11) is transformed by multiplying the numerator and 1/ 3

  denominator by  ∑ ∆Vi     i 

. Then, the following expression is obtained

535

∑

γs = A i

1/ 3



 ∑ ∆Vi   i  ∆ V ∑ i

∆Ei*  

.

(XIII.13)

i

Substituting correlation (XII.3) into formula (XIII.13), we obtain 1/ 3

  γs = A⋅0.6023  ∑ ∆Vi     i 

δ2 .

(XIII.14)

In correlation (XIII.14), values of ∆Vi are expressed in ångströms, δ2 – in J/cm . Taking into account that A displays several different values for various different groups of organic liquids, we obtain the correlation: 3

1/ 3

  γs = Bj  ∑ ∆Vi     i 

δ2 ,

(XIII.15)

where Bj = 0.6023⋅Aj. For liquids from the group I, B1 = 0.0172, from the group II – B2 = 0.0109, from the group III – B3 = 0.0138. To determine the value γ by correlation (XIII.15), both the calculated and experimental values of δ may be used. The results of calculation of γ performed with application of experimental values of δ are shown in Table 46. Clearly, the experimental values γexper and calculated values γcalc coincide quite well. The opposite task (which is more important) may also be solved, i.e. values of the solubility parameters δ may be calculated from the experimental value of surface tension. For this purpose, let us transform correlation (XIII.15) to the following form (with regard to the fact that N A ∑ ∆Vi = Vk ): i

1/ 2

δ=

(0.6023)1 / 6  γ s    B1j / 2 ⋅ k 1 / 6  V 1 / 3 

.

(XIII.16)

Clearly, correlation (XIII.16) by its form is similar to empirical formula (XIII.12). However, the multiplicand before the value (γs/V1/3) is not constant but depends upon the chemical structure of organic liquids, because the coefficient of packing k depends on it. In the first approximation, it may be assumed that for groups of organic compounds considered above the values of k vary in a narrow range, and their average value may be applied. The calculations performed indicate that for the group I of organic liquids kavg,1 = 0.580, for the group II – kavg,2 = 0.601, and for the group III – kavg,3 = 0.586. Then basing on formula (XIII.16), we obtain:

δ

1/ 2 * γ s   , = C j  1/ 3 

V



(XIII.17)

536

where C1* = 7.67; C2* = 9.58; C3* = 8.56.

XIII.2. Surface tension of polymers Let us now turn to calculations of the surface tension of solid polymers. At first glance, it seems that the surface tension of polymers may be calculated directly from formula (XIII.11), where

∑ ∆Ei*

and

i

∑ ∆Vi

are determined per repeat unit of

i

the polymer. However, some difficulties appear in this case associated with both chain structure of the polymer and somewhat ambiguity of interpretation of the repeat unit. Because the value ∑ ∆Vi participates in this correlation in the degree 2/3, and the value

∑

i * ∆Ei – in the first degree, then the more the number of chains n is considered

i

as a kinetic unit (the length of the whole chain, the segment length), the higher value of γ will be obtained by formula (XIII.11). The second reason is clear from the example of polyethylene and other polymers. If for polyethylene the repeat unit is assumed in the form (CH2CH2), then from correlation (XIII.11) we obtain γ = 14.7 dyn/cm. But if the repeat unit is assumed in the form (CH2), then γ = 11.65 dyn/cm. The same result is also obtained in the case of polyamides. For example, for polyamide 6 (CH2)5

C NH O

n

and polyamide 6,6 (CH2)4

C NH

(CH2)6

NH C

O O n when formula (XIII.11) is applied, we obtain γ = 45.9 dyn/cm (polyamide 6) and γ = 58.0 dyn/cm (polyamide 6,6). From the point of view of the gross formula, the chemical structure of these polyamides is identical (polyamide 6,6 contains twice the number of the same elements, which are contained in polyamide 6). Experimental values of γ for these polyamides are approximately equal and vary in the range from 40 to 47 dyn/cm. The above-discussed problems are analyzed in detail in ref. [33]. Consequently, the following correlation is obtained:

γp =Cj

∑ ∆Ei* i

   ∑ ∆Vi     i 

,

2/3

(XIII.18)

m1 / 3

where m is the number of atoms in the repeat unit of polymer. For non-polar polymers of the group I (hydrocarbons, perfluoropolymers, polyethers), C1n-p = 0.1277; for

537

polar polymers of the group II (polyesters, polymers containing a nitrogroup, etc.), C1p = 0.0751; for polymers containing alcohol, acidic and amide groups (all of them are polar and indicate hydrogen bonding), C2 = 0.0476; for polymers containing nitrile groups (all of them are polar), C3 = 0.0600. If a polymer contains aromatic cycles (for example, polystyrene, polyphenylene, etc.), the value C4 = 0.1014. Calculations performed due to formula (XIII.18) display (Table 47) that in the most of cases, good coincidence of experimental and calculated values of the surface tension γp is observed. The greatest deviations are observed for polymers which crystallize easily; to them polyethylene oxide and polyformaldehyde, for which the coefficient of molecular packing exceeds significantly the average value. Table 47 Initial data and results of calculation of the surface tension of polymers γp, by eqs. γp, by eq. γp, exper. ∆Ei* ∑ (XIII.28) and ∆ V ∑ i [133, 214] (XIII.18) Polymer i (XIII.29) i dyn/cm Polyethylene 5,401 34.2 31.0-35.7 36.0 35.6 Polypropylene 14,885 51.3 29.0-29.6 38.8 39.6 Polyisobutylene 10,801 68.6 27.0-33.6 28.8 34.8 Rubber SCB 9,054 64.3 32.0 33.5 32.9 Rubber SCI 10,030 81.5 31.0 29.0 28.6 Polyvinyl fluoride 12,087 39.3 28.0-36.7 43.2 44.3 Polyvinyl chloride 11,055 49.0 39.0-41.5 34.2 36.3 Polyvinyliden fluoride 5,205 44.6 23.0-32.7 29.1 29.0 Polytrifluoroethylene 11,891 49.7 22.0-23.9 36.3 38.9 Polychlorotrifluoroethylene 10,761 65.7 31.0 27.4 30.7 Polytetrafluoroethylene 5,008 55.0 18.5-19.0 24.5 18.8 Polystyrene 22,990 109.7 33.0-43.0 40.5 38.0 Polyvinyl alcohol 23,675 41.6 37.0 46.5 61.0 Polyacrylonitrile 19,324 54.0 44.0 42.6 50.0 Polymethylacrylate 18,379 79.5 41.0 32.6 33.8 Polyamide II 51,562 201.2 31.0-33.0 34.9 31.4 Polyamide 6 38,059 116.0 40.0-47.0 45.0 39.5 Polyamide 6,6 76.118 231.5 39.3-46.0 45.2 35.1 Polyamide 10,10 97,723 368.3 28.5-32.0 36.1 29.1 Polyethyleneterephthalate 43,547 169.9 41.0-47.0 38.1 35.2 Polyethylacrylate 21,080 96.7 35.0 30.4 31.6 Poly(methyl methacrylate) 21,080 96.7 39.0-40.2 30.4 31.6 Poly(ethyl methacrylate) 23,780 113.8 33.0 29.1 30.0 Poly(vinyl acetate) 18,379 79.6 36.0 32.6 33.8 Polyformaldehyde 3,297 27.2 36.0 29.1 36.0 Poly(ethylene oxide) 5,997 43.8 43.0 32.1 43.0 Poly(propylene oxide) 8,698 60.9 32.0 33.2 31.9

For polymers, it is desirable to calculate the surface energy γp with the help of solubility parameter δ. Clearly, from equation (XII.3) we obtain:

∑ ∆Ei* = δ 2 N A ∑ ∆Vi . i

i

Substituting formula (XIII.19) into equation (XIII.18), we obtain

(XIII.19)

538

1/ 2

   ∑ ∆Vi  δ 2 N A   i  γp =Cj  m1 / 2

(XIII.20)

or

γ p = D jδ

∑ ∆Vi

2

i

m

,

(XIII.21)

where Dj = CjNA (Dj is the parameter which, similar to Cj, depends on affiliation of the polymer to the given group). With regard to values of Cj shown above, it may be stated that for non-polar polymers (hydrocarbons, polyethers, etc.), D1n-p = 0.0769. For polar polymers containing ester and other polar groups, D1p = 0.0452. For polymers containing hydroxyl, acidic and amide groups (strong hydrogen bonding), D2 = 0.0287; for polymers containing nitrile groups, D3 = 0.0361. For polymers containing aromatic cycles only (for example, polystyrene, polyphenylene, etc.), D4 = 0.061. Therewith, if the Van-der-Waals volume is expressed in Å3, and the specific cohesive energy δ2 in J/cm3, then the surface tension calculated by formula (XIII.21) is determined in dyn/cm. The drawback of the calculation scheme described above concludes in the fact that transition from one sequence of liquids or from one group of polymers to another requires application of the own coefficient Aj or Cj in equations (XIII.11) and (XIII.18). Difficulties in this case are associated with the fact that molecules of the liquid or repeat units of polymers will possess larger volumes, and the relative fraction of specific groups, by which they are separated according to the current feature, will be small. For example, nitrile groups may be contained not only in polyacrylonitrile, where their relative contribution to the Van-der-Waals volume and the cohesive energy will be high, but also in other polymeric systems, where their contribution may be rather low. Moreover, difficulties appear in the calculation of the surface energy of copolymers, units of which belong to different classes of homopolymers. In this connection, ref. [37] indicates development of the calculation scheme for estimating the surface tension of organic liquids and polymers, parameters of which depend on the chemical structure of the organic liquid or polymer only, but not on their belonging to any class. In the work cited, the value of kp is expressed via the correlation:

δ* =

∑ ∆Ei* i

   ∑ ∆Vi     i 

2/3

.

(XIII.22)

Here δ* is the specific surface cohesive energy, i.e. the cohesive energy per specific surface. Note that this value differs from the usual density of the cohesive energy determined by correlation (XII.3). The following dependence connects the coefficient of molecular packing of the liquid on its surface kp and the specific surface cohesive energy δ* [37]:

539

Ksrf = –0.4112 + 0.3012 lgδ*.

(XIII.23)

After substituting expression (XIII.9) into formula (XIII.23), we obtain

γs =δ*

0.0461⋅ lg δ * − 0.063  0.2768 ⋅ lg δ * − 0.378  ⋅ 1 − . k k  

(XIII.24)

Substituting expression (II.5) into formula (XIII.24), finally we get:  (0.2768 ⋅ lg δ * − 0.378) M  ⋅ 1 − . ∆ N V ρ ∑ i A   i   

γs =δ

* * (0.0461⋅ lg δ − 0.063) M 

ρN A ∑ ∆Vi i

(XIII.25)

Correlation (XIII.25) enables the surface tension of organic liquids to be estimated with accuracy valuable for practical calculations independently of the class, to which the current liquid belongs. Results of calculation indicate [37] that the calculated and experimental data are in satisfactory agreement in most cases (see Table 46). Let us now turn to estimation of the surface energy of polymers. The initial correlation for deducing equation (XIII.18) has the form [37]: k  k δ*  γ p = α ⋅ 0.1532 srf ⋅ 1 − 0.919 srf  , k  k m1 / 3 

(XIII.26)

where α is the constant dependent on the polymer belonging to the class of polar or non-polar polymers only. Let us assume that the dependence of the coefficient of molar packing in the surface layer ksrf on δ* is the same as for liquids. As often mentioned above, the coefficient of molecular packing of the polymer in the volume is almost independent of the chemical structure of polymers, and its average value kavg = 0.681 for solid polymeric substances. Using the dependence ksrf on δ* in the form of correlation (XIII.23) and kavg = 0.681, basing on correlation (XIII.23) we obtain:

γp =α

δ* 1/ 3

m

(0.067761⋅ lg δ * − 0.0925)(1.5549 − 0.40671⋅ lg δ * ).

(XIII.27)

The analysis performed indicates [37] that values of α are indeed approximately equal; for polar polymers, αavg = 2.097, and for non-polar polymers – αavg = 3.055. Then, the formula for calculation of the surface energy of polar polymers changes to:

γ pp =

δ* 1/ 3

m

(0.1421⋅ lg δ * − 0.194)(1.5549 − 0.4067 ⋅ lg δ * ),

(XIII.28)

540

and for non-polar polymers,

γ pn =

δ* 1/ 3

m

(0.2070 ⋅ lg δ * − 0.2826)(1.5549 − 0.4067 ⋅ lg δ * ).

(XIII.29)

The surface energy values calculated from formulae (XIII.28) and (XIII.29) are displayed in Table 47. Clearly, in most cases, good correspondence between the calculated and experimental surface energy values is observed. It should be noted that experimental determination of the surface energy for solids, including polymers, is rather difficult, although there are various modifications of the method for estimating γp. That is why greatly different data on the surface energy for the same polymer may be observed in the literature. Correlations (XIII.28) and (XIII.29) deduced in ref. [37] enable the surface energy of polymers of any chemical structure to be estimated regardless of their belonging to any class of chemical compounds. This removes the difficulties typical of calculation of the surface tension of organic liquids, mentioned above. In conclusion, let us discuss one more connection between the surface energy of organic liquids and polymers and the solubility parameter δ, the value of which is determined from relation (XII.3). Taking into account that δ * =

∑ ∆Ei* i

   ∑ ∆Vi     i 

2/3

and substituting this expression

into equation (XII.3), we obtain that 1/ 3

  δ = δ N A  ∑ ∆Vi     i  *

2

.

(XIII.30)

Furthermore, substituting expression (XIII.30) into formula (XIII.29) and performing necessary transformations, we get: 

   ∆  − V 0 . 073 ∑ i   i  ×    

 1 / 3  0.09221lg δ − 0.01537 lg

  γ s = N Aδ 2  ∑ ∆Vi     i 

    

k

. (XIII.31)      0.554 lg δ − 0.0923 lg ∑ ∆Vi  − 0.439       i  × 1 −  k       Correlation (XIII.31) links value of the surface tension of liquids γs with the solubility parameter δ. According to the correlation mentioned, the value δ may be obtained if experimental values of the surface tension of liquids are known

541

(estimation is performed by the method of inspection). This is of importance because the surface tension of liquids can be measured quite easily, and the solubility parameter associated with the latent heat of evaporation of the liquid is more difficult to calculate. It is especially difficult for polymers, because their solubility parameter may be determined by indirect methods only – by measurements of swelling in different solvents, viscosity of solutions, etc. It should be noted that the possibility of estimating the surface energy of polymers experimentally is also important, because their surface energy is related by simple correlations with cohesive energy and sublimation energy. Various situations may appear when calculating the surface energy of copolymers or homogeneous mixtures. If components of a copolymer relate to the same group of substances (according to the above-mentioned classification), then, as the value Cj is identical for them, correlation (XIII.18) applied to copolymers obtains the form:

γp =Cj

    α1 ∑ ∆Ei*  + α 2  ∑ ∆Ei*  + ... +      i 1  i 2         α1 ∑ ∆Vi  + α 2  ∑ ∆Vi  + ... + α n  ∑ ∆Vi           i 1  i 2  i n     + α n  ∑ ∆Ei*     i n → , × (α1m1 + α 2 m2 + ... + α n mn )1 / 3

→

2/3

×

,

(XIII.32)

  where α1, α2, …, αn are molar parts of the components 1, 2, …, n;  ∑ ∆Ei*  ,    i 1      ∑ ∆Ei*  , …,  ∑ ∆Ei*  are values of the cohesive energy for the components 1,      i n  i 2       2, …, n;  ∑ ∆Vi  ,  ∑ ∆Vi  , …,  ∑ ∆Vi  are their Van-der-Waals volumes;        i n  i 1  i 2 m1, m2, …, mn are numbers of atoms in repeat units of the components 1, 2, …, n. In the reduced form, correlation (XIII.32) gives

γp = Cj

k =n



k =1

 i



∑ α k  ∑ ∆Ei* 

k

. (XIII.33) 1/ 3 k = n     k =n   ∑ α k  ∑ ∆Vi    ∑ α k mk      k =1  i  k   k =1   If it is desirable to express the surface energy of a copolymer via the surface energies of homopolymers γp,1, γp,2, …, γp,n obtained from components 1, 2, …, n, then equation (XIII.32) is reduced to the following form: 2/3

542

2/3

γp = Cj

  α1γ p,1 ∑ ∆Vi     i 1

2/3



 ∑ ∆Vi  m12/ 3 + ... +  i 2

m11 / 3 + α 2γ p,2  

        α1 ∑ ∆Vi  + α 2  ∑ ∆Vi  + ... + α n  ∑ ∆Vi           i 1  i 2  i n  

2/3

×

→ , (XIII.34)

2/3

→

  + α nγ p, n  ∑ ∆Vi  m1n/ 3    i n

× (α1m1 + α 2 m2 + ... + α n mn )1 / 3

.

In the reduced form, correlation (XIII.34) looks as follows: 2/3

k =n

γp = Cj

  ∑ α k γ p, k  ∑ ∆Vi  k =1  i k

k = n     ∑ α k  ∑ ∆Vi      k =1  i k  

2/3

m1k / 3 1/ 3

.

(XIII.35)

 k =n   ∑ α k mk     k =1 

If all components of the copolymer relate to different groups of substances (they possess different values of Cj), then correlation (XIII.32) for this copolymer (on the example of a double copolymer) is presented in the form:

(

γ p = α1C j , I + α 2C j , II

)

    α1 ∑ ∆Ei*  + α 2  ∑ ∆Ei*       i 1  i 2       α1  ∑ ∆Vi  + α 2  ∑ ∆Vi        i 1  i  2  

(XIII.36)

2/3

(α1m1 + α 2 m2 )1 / 3

or 2/3

(

γ p = α1C j , I + α 2C j , II

)

  α1γ p,1 ∑ ∆Vi     i 1

m11 / 3 C j , I +

      α1 ∑ ∆Vi  + α 2  ∑ ∆Vi         i 1  i 2  

→

2/3

×

(XIII.37)

2/3

→

  + α 2γ p,2  ∑ ∆Vi     i 2

m12/ 3 C j , II

. × (α1m1 + α 2 m2 )1 / 3 In the case of a multicomponent copolymer, various situations may appear: a part of components may belong to the same group of substances, and the rest belongs to another group. In the general case, we obtain:

543

Cj = α1Cj,1 + α2Cj,2 + … + αnCj,n,

(XIII.38)

where Cj,1 is the value of Cj for the group of substances, to which component 1 belongs (it may be Cj,I, Cj,II, Cj,III, or Cj,IV); Cj,2, …, Cj,n is the same for components 2, …, n. Then, with regard to equation (XIII.38), correlation (XIII.33) obtains the form:

γp =

k =1



k =1

 i



∑ α k  ∑ ∆Ei* 

k =n

∑α k C j,k

k =n

k = n     ∑ α k  ∑ ∆Vi     k =1  i  k  

k

2/3

1/ 3

 k =n

,

(XIII.39)

  ∑ α k mk     k =1 

and correlation (XIII.35) is reduced to 2/3

k =n

γp =

k =n

∑α k C j,k

k =1

  ∑ α k γ p, k  ∑ ∆Vi  k =1  i k

k = n     ∑ α k  ∑ ∆Vi      k =1  i k  

2/3

m1k / 3 C j , k 1/ 3

.

(XIII.40)

 k =n   ∑ α k mk     k =1 

The above-described correlations for calculation of the surface energy of copolymers are not quite suitable, because affiliation of the polymer to some group must be taken into account every time. That is why, for computer realization of the method, it is desirable to express values Cj via the surface energies of copolymer components. From equation (XIII.18) we obtain that 2/3

  γ p  ∑ ∆Vi  m1 / 3    Cj =  i . ∑ ∆Ei* i

Then for the copolymer, we obtain: 2/3 2/3       γ  ∆V  m1 / 3   m12/ 3 γ p2 ∑ ∆Vi i p1  ∑ 1     i 1  i 2 + α2 + ... + γ p = α1      * *  ∑ ∆Ei   ∑ ∆Ei         i 1  i 2 

544

2/3          m1n/ 3  α1 ∑ ∆Ei*  + α 2  ∑ ∆Ei*  + γ p, n ∑ ∆Vi         i n 1  i 2 ⋅  i → αn          ∑ ∆Ei*   α1 ∑ ∆Vi  + α 2  ∑ ∆Vi  +         i  i n 1  i 2  

→

  + ... + α n  ∑ ∆Ei*     i n    + ... + α n  ∑ ∆Vi      i  n 

(XIII.41)

,

2/3

(α1m1 + α 2 m2 + ... + α n mn )1 / 3

where all designations are identical to the above-considered formulae. In the reduced form, correlation (XIII.41) will have the form: 2/3

k =n     γ pk  ∑ ∆Vi  m1k / 3 α k  ∑ ∆Ei*  ∑     k =n k =1  i k  i k ⋅ γ p = ∑ αk . 2/3 1/ 3   k = n  k =1    k =n   ∑ ∆Ei*   ∑ α k  ∑ ∆Vi    ∑α k mk         i k  k =1  i  k   k =1  

(XIII.42)

Let us show an example of calculation of the surface energy for polyvinyl alcohol copolymer with poly(vinyl acetate): CH2

CH

CH2

OH

CH O C CH3 O

Polyvinyl alcohol (PVA)

Poly(vinyl acetate) (PVAc)

For PVA we obtain

∑ ∆Ei*

* * * = 2 ∆EC + 4 ∆EH + ∆EO + ∆Eh* = 2⋅550.7 + 4⋅47.7 + 142.6 + 3929 =

i

5,363.8 cal/mol = 22,420.6 J/mol. ∑ ∆Vi = ∆VC,10 + ∆VC,39 + ∆VH,125 + ∆VH,124 + ∆VO,132 = 13.1 + 12.2 + 3⋅2.0 + 4.7 + i

5.6 = 41.6 Å3. The number of atoms m in the repeat unit of PVA equals 7. Substituting values

∑ ∆Ei* , ∑ ∆Vi , and m into equation (XIII.18) and taking into i

i

account that the present polymer belongs to group II of polar polymers (C2 = 0.0476), we obtain that

545

γ p = 0.0476

22,420.6 (41.6) 2 / 3 ⋅ 71 / 3

= 46.5 dyn/cm.

For PVAc we obtain:

∑ ∆Ei*

* * * = 4 ∆EC + 6 ∆EH + 2 ∆EO + ∆Ed* = 4⋅550.7 + 6⋅47.7 + 2⋅142.6 + 1623 =

i

4,397 cal/mol = 18,380 J/mol. ∑ ∆Vi = ∆VC,10 + ∆VC,39 + ∆VC,48 + ∆VC,13 + 6∆VH,124 + ∆VO,129 + ∆VO,139 = 13.1 + i

12.2 + 15.9 + 17.2 + 6⋅2.0 + 3.4 + 5.8 = 79.6 Å3. The number of atoms m in the repeat unit of PVAc equals 12. Using equation (XIII.18) and taking into account that PVAc belongs to polar polymers from group I (Cp1 = 0.0751), we obtain that

γ p = 0.0751

18,380 (79.6) 2 / 3 ⋅121 / 3

= 32.6 dyn/cm.

To calculate γp of the copolymer, let us first use correlation (XIII.36); assume that the molar part of PVA α1 = 0.4, and for PVAc – α2 = 0.6. Substituting all parameters of the copolymer into correlation (XIII.36), we obtain: γ p = (0.4 ⋅ 0.0476 + 0.6 ⋅ 0.0751)

0.4 ⋅ 22,420.6 + 0.6 ⋅ 18,380 (0.4 ⋅ 41.6 + 0.6 ⋅ 79.6) 2 / 3 ⋅ (0.4 ⋅ 7 + 0.6 ⋅ 12)1 / 3

= 37.0 dyn/cm.

Let us now use correlation (XIII.37):

γ p = (0.4 ⋅ 0.0476 + 0.6 ⋅ 0.0751) →

0.4 ⋅ 46.5 ⋅ 41.6 2 / 3 ⋅ 71 / 3 / 0.0476 + (0.4 ⋅ 41.6 + 0.6 ⋅ 79.6) 2 / 3 ×

0.6 ⋅ 32.6 ⋅ 79.6 2 / 3 ⋅121 / 3 / 0.0751 × (0.4 ⋅ 7 + 0.6 ⋅12)1 / 3

→

= 37.0 dyn/cm.

Let us now consider the surface energy of a triple copolymer based on acrylonitrile, butadiene and styrene (ABS–plastic): CH2

CH

–CH2–CH=CH–CH2–

CH2

CH

C N

Polyacrylonitrile (PAN)

Polybutadiene (PB)

Polystyrene (PS)

For PAN,

∑

* * ∆Ei* = 3 ∆EC + 3 ∆EH +

i

4623.2 cal/mol = 19,325 J/mol.

∆E *N + ∆Ed* = 3⋅550.7 + 3⋅47.7 + 1205 + 1623 =

546

∑ ∆Vi

= ∆VC,10 + ∆VC,6 + ∆VC,71 + 3∆VH,124 + ∆VN,154 = 13.1 + 9.0 + 15.9 + 3⋅2.0 +

i

10 = 54 Å3. PAN belongs to polymers of group III, because it contains a nitrile group (C3 = 0.060). The number of atoms, m, in the repeat unit of PAN equals 7. For it, according to formula (XIII.18), we obtain that

γ p = 0.060

19,325 54 2 / 3 ⋅ 71 / 3

= 42.4 dyn/cm.

For PB,

∑

* * ∆Ei* = 4 ∆EC + 6 ∆EH +

∆E≠* = 4⋅550.7 + 6⋅47.7 – 323 = 2,166 cal/mol = 9,054

i

J/mol. ∑ ∆Vi = 2∆VC,10 + 2∆VC,16 + 6∆VH,124 = 2⋅13.1 + 2⋅13.1 + 6⋅2.0 = 64.4 Å3. i

PB belongs to non-polar polymers of the group I (C1n = 0.1277); for it, m = 10. Application of formula (XIII.18) leads to the following result:

γ p = 0.1277

9,054 (64.4) 2 / 3 ⋅101 / 3

= 33.4 dyn/cm.

For PS,

∑

* * ∆Ei* = 8 ∆EC + 8 ∆EH +

∆E * = 8⋅550.7 + 8⋅47.7 + 713 = 5,500 cal/mol = 22,991

i

J/mol. ∑ ∆Vi = ∆VC,10 + ∆VC,7 + ∆VC,19 + 5∆VC,18 + 8∆VH,124 = 13.1 + 8.7 + 8.4 + 5⋅12.7 + i

8⋅2.0 = 109.7 Å3. PS belongs to group IV of polymers (C4 = 0.1014); for it, m = 16. Substitution of all values of PS parameters into formula (XIII.18) gives

γ p = 0.1014

22,991 (109.7) 2 / 3 ⋅ 161 / 3

= 40.4 dyn/cm.

Calculating the surface energy of the copolymer, we assume that the part of PAN units α1 = 0.3, the part of PB α2 = 0.2, and the part of PS α3 = 0.5. Then it is obtained from equation (XIII.37) that γ p = (0.3 ⋅ 0.06 + 0.2 ⋅ 0.1277 + 0.5 ⋅ 0.1014) →

0.3 ⋅ 42.4 ⋅ 54 2 / 3 ⋅ 71 / 3 / 0.06 + (0.3 ⋅ 54 + 0.2 ⋅ 64.4 + 0.5 ⋅109.7) 2 / 3 ×

0.2 ⋅ 33.4 ⋅ 64.4 2 / 3 ⋅101 / 3 / 0.1277 + 0.5 ⋅ 40.4 ⋅109.7 2 / 3 ⋅161 / 3 / 0.1014 × (0.3 ⋅ 7 + 0.2 ⋅10 + 0.5 ⋅16)1 / 3

→

= 40.9 dyn/cm.

Chapter XIV. Miscibility of polymers

The problem of miscibility of polymers is one of the most important problems at present. The point is is that new polymeric materials are now created, as a rule, not by synthesizing new polymers, but by composing mixtures of the known polymers. Therewith, it is essential to consider not only mixed composites, into which components of the mixture are injected in comparable amounts, but also the introduction of microadditions of polymers, their surface modification, etc. There are also problems appearing in this case, such as microphase separation, facilities to control the composition and size of microphases, etc. Having no way of discussing numerous publications which have appeared recently in this field, let us analyze one of possible ways of predicting the miscibility of polymers and estimating the composition of microphases. One of possible ways of looking at the problem of predicting the miscibility of polymers is the application of criterion (XII.21), which is intended for analyzing the solubility of polymers. Therewith, if one polymer is introduced in small amounts into another polymer, the former of them is considered as the ‘polymer’ and the latter – as the ‘solvent’ when criterion (XII.21) is applied. In principle, the following variants are probable. 1. When criterion (XII.21) is used, it turns out that, in all cases, the left part of the criterion is greater than the right part, i.e. total incompatibility takes place. Under all cases we mean those when the first polymer is introduced in small quantities into the second one and, vice versa, the second polymer is introduced in small quantities into the first one. Then the criterion of the miscibility of polymers obtains the form:  at introduction of the first polymer into the second one:

µ1 =

δ p2,1 δ p2,2

> 1.374Φ Φ − Φ 2 − 1 + a1  = 2 ρβ1 ;  

(XIV.1)

 at introduction of the second polymer into the first one:

µ2 =

δ p2,2 δ p2,1

> 1.374Φ Φ − Φ 2 − 1 + a2  = 2 ρβ 2 ;  

(XIV.2)

where δp,1 and δp,2 are the solubility parameters of polymers 1 and 2, respectively; Φ=

(

)

4 Vp,1 ⋅ Vp,2 1 / 3

(Vp,11/ 3 + Vp,21/ 3 )2

,

(XIV.3)

where Vp,1 and Vp,2 are the molar volumes of polymers 1 and 2, respectively; a1 = γp,1;p,2/γp,2; a2 = γp,1;p,2/γp,1, where

(XIV.4)

548

γp,1;p,2 = γp,1 + γp,2 – 2Φ(γp,1⋅γp,2)1/2,

(XIV.5)

where γp,1 and γp,2 are values of the surface energy for polymers 1 and 2, respectively. Criteria (XIV.1) and (XIV.2) mean that the polymers display total incompatibility. 2. When small quantities of the first polymer are introduced into the second one, criterion (XII.21) indicates that they are miscible, i.e.

µ1 =

δ p2,1 δ p2,2

< 1.374Φ Φ − Φ 2 − 1 + a1  = 2 ρβ1 .  

(XIV.6)

However, when the second polymer is introduced into the first one, it may appear that miscibility is not observed, i.e.

δ p2,2

> 1.374Φ Φ − Φ 2 − 1 + a2  = 2 ρβ 2 . (XIV.7)   δ p2,1 This, at first glance, a paradoxic conclusion is indicated, indeed, which will be shown below. Here, it should also be noted that, usually, the miscibility of two polymers is judged by the glass transition temperature of their mixture. A single glass transition temperature is typical of totally miscible polymers and lies between the glass transition temperatures of original components. A mixture of totally incompatible polymers display two glass transition temperatures, each of which is identical to the glass transition temperature of the original component. For partial miscibility, when both components are present in different quantities in the microphase, two glass transition temperatures are also indicated but, compared with the glass transition temperatures of original components, they are shifted towards each other. For the case under consideration, when the first polymer is combined with the second one, the dependence of the glass transition temperature on the composition is of the shape schematically represented in Figure 98, curve 1. This form of the curve will be explained below on the example of a ‘polymer 1–polymer 2’ specific system.

µ2 =

Figure 98. Schematic representation of dependence of the glass transition temperature Tg on the composition of the mixture α: 1 – partially miscible polymers; 2 – totally miscible polymers.

549

3. This case is appropriate to the total miscibility of polymers, i.e. the first polymer is ‘dissolved’ in the second one, and the second polymer is ‘dissolved’ in the first one. The miscibility criterion obtains the form: – at introduction of the first polymer into the second one:

µ1 =

δ p2,1 δ p2,2

< 1.374Φ Φ − Φ 2 − 1 + a1  = 2 ρβ1 ;  

(XIV.8)

– at introduction of the second polymer into the first one:

µ2 =

δ p2,2 δ p2,1

< 1.374Φ Φ − Φ 2 − 1 + a2  = 2 ρβ 2 .  

(XIV.9)

In the case as the one above-mentioned, a single glass transition temperature Tg is displayed, and the dependence of Tg on the composition of the mixture has the shape schematically represented in Figure 98, curve 2. Let us discuss now the behavior of a series of particular well-studied polymeric mixtures. The first of them is the mixture of polystyrene with poly(vinylmethyl ether): CH2

CH

Polymer 1

CH2

CH

Polymer 2.

O CH3 The behavior of this mixture of various compositions is studied in detail in a series of works [131, 153, 168, 198–200]. The dependence of the glass transition temperature Tg of this mixture on the composition is displayed in Figure 99.

Figure 99. Dependence of the glass transition temperature Tg on mole fraction α of polystyrene for the mixture of poly(vinylmethyl ether) with polystyrene (2). Dotted curve (1) represents dependence of Tg on α on the condition, as components are completely miscible.

Clearly, as polystyrene concentration increases from 0 to 40%, the change of Tg is extremely weak and is almost independent of the composition of the mixture.

550

This dependence is not described by equation (IV.55) valid for statistic copolymers and homogenous mixtures of polymers (curve 1). Let us analyze in detail the miscibility of polystyrene (PS) and poly(vinylmethyl ether) (PVME) with the help of criterion (XII.21). Suppose first that PS is the ‘solvent’ for PVME. The initial characteristics necessary for the application of criterion (XII.21) are shown in Table 48. Substituting values of these characteristics into equation (XIV.20), we obtain that

µ2= 0.684 < 1.218 = 2ρβ2. Table 48 Initial data for estimating compatibility of a series of polmers: polystyrene (PS), poly(vinylmethyl ether) (PVME) and poly(2,6-dimethyl-1,4-phenylene oxide) (PPO) Physical characteristics PS PVME PPO 9.12 7.54 8.93 Solubility parameter δ, (cal/cm3)1/2 41.6 33.4 44.4 Surface energy γ, dyn/cm Molar volume V, cm3/mol 97.08 60.7 103.75 22988 8696 23587 ∆Ei* , J/mol Cohesive energy i 109.8 60.7 117.4 ∆Vi , Å3 Van-der-Waals volume i Glass transition temperature Tg , K 373 245 

∑

∑

Hence, because the left part of the miscibility criterion is smaller than the right part, then PVME is ‘dissolved’ well in PS. Suggest now that PVME is the ‘solvent’ for PS. Then, with the help of miscibility criterion (XIV.1) we obtain that

µ1= 1.462 > 1.175 = 2ρβ1. Because the left part of the criterion is greater than the right part, this means that poly(vinylmethyl ether) is not ‘dissolved’ in polystyrene. That is why when PS is injected into PVME, a microphase separation should be expected. However, because PS is the ‘solvent’ for PVME, a part of PVME will be miscible with PS. Consequently, two microphases will be formed, one of which contains PVME, and the second – a mixture of PVME with PS. When the PVME concentration in the second microphase increases, miscibility of this microphase with PVME is improved and at a definite concentration of PVME, the second microphase will be miscible with PVME. Let us determine this critical concentration of PVME. For this purpose, let us write down the correlation for calculating the solubility parameter of the current mixture of polymers. Basing on equation (XII.3), we obtain that     α  ∑ ∆Ei*  + (1 − α ) ∑ ∆Ei*       i 2  i 1 2 = , δ mixture       N A α  ∑ ∆Vi  + (1 − α ) ∑ ∆Vi        i 2  i 1  

(XIV.10)

551

    where α is the molar part of PVME in the mixture;  ∑ ∆Ei*  and  ∑ ∆Ei*  are      i 1  i 2     molar cohesive energies for PS and PVME, respectively;  ∑ ∆Vi  and  ∑ ∆Vi       i 1  i 2 are Van-der-Waals volumes of repeat units of PS and PVME, respectively. Substituting characteristics of polymers shown in Table 48 into correlation (XIV.10), we obtain that 2 = δ mixture

22,988 − 14,292α cal/cm3. 4.18(66.13 − 29.57α )

(XIV.11)

Let us now estimate the surface energy of the mixture according to equation (XIII.39):

γ mixture = [αC1n + (1 − α )C4 ]

  α  ∑ ∆Ei*  +    i 2       N A α  ∑ ∆Vi  + (1 − α ) ∑ ∆Vi         i 2  i 1  

→

  + (1 − α ) ∑ ∆Ei*     i 1

[αm2 + (1 − α )m1 ]1 / 3

2/3

→ (XIV.12)

,

where C1n and C4 are coefficients from equation (XIII.39) for PVME (non-polar polymer) and PS, respectively; m1 and m2 are the numbers of atoms in repeat units of PS and PVME, respectively. Substituting all the values from Table 48 into correlation (XIII.39), we obtain that

γ mixture = (0.0231α − 0.1046)

22,988 − 14,292α (109.8 − 49.1α ) 2 / 3 (16 − 6α )1 / 3

.

(XIV.13)

Future analysis requires estimation of the molar volume of the mixture: Vmixture = α53.68 + (1 – α)97.088.

(XIV.14)

To calculate left and right parts of criterion (XII.21), let us use correlations (XIV.11), (XIV.13) and (XIV.14). Therewith, let us consider a two-component mixture, one of the components of which represents PVME, and the second one is a mixture (microphase) of PVME/PS type with different molar part α of PVME. Calculation results are displayed in Figure 100 in the shape of two dependences of both parts of the criterion (XII.21) on the molar part of PVME. The cross-point of these two dependences corresponds to the PVME concentration in the microphase at

552

which the miscibility of PVME with this microphase appears. This threshold concentration αcr = 0.62. The Van-der-Waals volume of the mixture with the threshold concentration of PVME will equal    ∑ ∆V  = 60.7⋅0.62 + 109.8⋅0.38 = 79.36 Å3. i   i  th

Figure 100. Dependences of µ (2) and 2ρβ (1) on the molar fraction α of poly(vinylmethyl ether) within microphase (for explanation see text).

Now the glass transition temperature of the mixture with the threshold concentration of PVME may be calculated. For this purpose, let us use equation (IV.55):        α th  ∑ ∆Vi  −  ∑ ∆Vi   +  ∑ ∆Vi        i 2  i 1   i 1  = Tg, th . (XIV.15)              ∆V  ∆V  ∑ ∆Vi  ∑ i   ∑ i    i 2  i 1  i 1 − + 2α th (1 − α th ) ⋅ 0.03 α th  + Tg,1  Tg,1  Tg,2     Substituting all parameters of the system from Table 48 into correlation (XIV.15) and taking into account that αth = 0.62, we obtain that Tg,th = 284 K. Now the dependence of glass transition temperature Tg on the composition of the mixture consisting of PVME and ‘critical’ mixture, i.e. a mixture consisting of PS and PVME with the critical concentration αth of PVME equal to 0.62, may be determined. Using equation (IV.55) for this purpose, we obtain that

553

       α  ∑ ∆Vi  −  ∑ ∆Vi   +  ∑ ∆Vi         i 2  i  th   i  th  Tg, th = ,         ∑ ∆Vi    ∑ ∆Vi    ∑ ∆Vi          i  th  i  th 2  i + 2α (1 − α ) ⋅ 0.03 − + α  T T T g,2 g, th g, th      

(XIV.16)

where α is the molar part of PVME. Correlation (XIV.16) is true only in the range of α from 1 down to 0.62. The curve composed in accordance with correlation (XIV.16) is shown in Figure 99 (curve 2). Clearly, experimental points fit well this dependence. To describe the second part of the dependence of Tg on the composition of PVME/PS mixture (inside the range of α from 0.62 down to 0), it is necessary first to determine the Van-der-Waals volume of the mixture, for which Tg = 284 K: 

      + 0.380.62 ∑ ∆Vi  + 0.38 ∑ ∆Vi   ;       2  i 2  i 1   

∑ ∆Vi = 0.62 ∑ ∆Vi   i

i

∑ ∆Vi

= 67.8 Å3.

i

Now, the dependence of Tg on the composition of the mixture, one of the components of which represents PS, and the second – the microphase with Tg = 284 K (see above), may be described. For this system, we obtain that Tg =

α ′(109.8 − 67.8) + 67.8 ,  109.8 67.8  67.8 ′ ′ − + + − ⋅ 2 ( 1 ) 0 . 03 α ′ α α   373 248  248

(XIV.17)

where α′ is the molar part of PS on the scale from 1 down to 0.38. To determine the true molar part of PS in the mixture, it should be presented: (1 – α) = 0.38 + α′⋅0.62, where α is the molar part of PVME, and (1 – α) is the molar part of PS in the total mixture. (1 − α ) − 0.38 into correlation (XIV.17), we find that the Substituting α′ = 0.62 correlation obtained describes well the second part of dependence of Tg in the range of α from 0 to 0.62 on the composition of the mixture at high concentration of PS (see Figure 99). Hence, solubility criterion (XII.21) may be successfully applied to description of the dependence of glass transition temperature Tg of the polymer system, in which one of polymers ‘dissolves’ well the second one, but the first polymer is badly ‘dissolved’ in the second one.

554

Let us analyze now a simpler case, when two polymers are totally miscible with each other. As an example of such mixture, let us consider the polystyrene (PS)–poly(2,6dimethyl-1,4-phenylenoxide) (PPO) system, studied well in a series of works [139, 166, 169, 197, 203, 204, 209]. Suggest that PS is the ‘solvent’ for PPO. Applying solubility criterion (XII.21) with regard to all physical characteristics of the mixture components (see Table 48), it is found that µ2 = δ 22 δ12 = 0.959; Φ = 1.0; γ1,2 = 0.0456; a = 0.001096; 2ρβ2 = 1.328 (δ1 and δ2 are solubility parameters of PS and PPO, respectively). Because µ2 < 2ρβ2, then according to criterion (XII.17) PS is a good ‘solvent’ for PPO, i.e. miscibility must be observed. It should be assumed now that PPO is the “solvent” for PS. Then µ1 = δ12 δ 22 = 1.043; Φ = 1.0; γ1,2 = 0.0456; a = 0.00103; 2ρβ1 = 1.33. Clearly, in this case also, the left part of criterion (XII.21) is smaller than the right part of it, i.e. miscibility is also possible. Experiments indicate that, indeed, polymers in the present pair are totally miscible. This leads to a description of the glass transition temperature of the PS/PVME mixture by the same dependence on the composition as for statistic copolymers, i.e. by correlation (IV.55). This dependence is shown in Figure 101, which indicates that experimental points fit well the calculated curve. It should be noted that the approach considered possesses the advantage before some other approaches that it requires no introduction of ‘fitted’ parameters. To put it differently, this analysis requires understanding of the chemical structure of components, based on which all physical characteristics of polymers are calculated.

Figure 101. Dependence of the glass transition temperature Tg on the molar fraction α of poly(2,6dimethyl-1,4-phenyleneoxide) for the polymer blend with polystyrene.

Chapter XV. Influence of the end groups on the properties of polymers

The problem of influence of the molecular mass of the polymer and the problem of the end groups role and their influence on the properties associated with it has been discussed many times in the literature. For example, there are data on the dependence of glass transition temperature Tg and melting point Tm on the molecular mass in the shape of curves with a plateau, as well as information on other properties dependent on the molecular mass. As an example, Figure 21 displays the dependence of Tg on the mean molecular mass of polystyrene. There is a series of correlations describing these dependences, for example [144], Tg = Tg(∞) – k/M, where Tg(∞) is the glass transition temperature of the polymer at the molecular mass M → ∞; k is the polymer constant. Dependences of this kind do not describe Tg(M) curves along their length. More complicated dependence Tg(M) is of the form [145]: Tg = Tg(∞) – K*/(M + M*), where K* and M* are fitted parameters. Obviously, not only glass transition temperature Tg, but also all other properties depend on the molecular mass. Searching for these dependences is of special interest. This problem is of prime importance for analysis of the molecular mass influence on the properties of propagating chains at a very low number of units n. The circumstance that the chemical structure of end groups may significantly (and even principally sometimes) differ from the structure of the repeat unit of the polymer is not always taken into account in this analysis. This causes that the composition of the dependence of a parameter of any physical property on n indicates every new value of n nonequivalent to the former one, because the chemical structure of the averaged unit changes with transition from n to (n + 1), etc. Only when n ≈ 10 – 20, the influence of end groups becomes low and dependences of the properties on n approach the values of parameters typical of the repeat unit of the polymer. Ref. [8] indicates quantitative description of the dependences of three physical parameters – Van-der-Waals volume, molar refraction and molar cohesive energy – on the number of units in a polymeric chain starting from n = 1. Therewith, the influence of the type of initiator applied to polymerization on the chemical structure of end groups and properties of dimers, trimers, etc. followed from it, is taken into account. Calculations were performed on the example of four polymers – poly(methyl methacrylate) (PMMA), polystyrene (PS), poly(ethylene terephthalate) (PET) and polycarbonate (PC) based on bisphenol A. The following types of systems were considered:

556

CH3 H3C

C

(CH2

C OCH3

CH3

CH3

C)n- 2 CH2 C OCH3

CH C OCH3

O CH3

O CH3 C

C OCH3

C)n- 2 CH C OCH3

O

O

O

O CH3 C

CH

(CH2

CH3 H3C

PMMA-2

C OCH3

CH3

CH3 C

C OCH3

C)n- 2 CH C OCH3

C OCH3

O

O

O

C

(CH2

O C

(CH2

O C

PMMA-1

PMMA-3

CH3

CH3

C)n- 1 CH2 C OCH3

CH C OCH3

O

O

PMMA-4

CH3 O (CH2

PMMA-5

C)n C C OCH3 O

H3C

CH

(CH2

CH)n - 2

CH2

H3C

CH

(CH2

CH)n - 2

CH

CH2

CH

PS-1

PS-2

O H3C

CH

(CH2

CH)n- 1

C

PS-3

557

O

O

C

HO

HO

(CH2

CH)n C

[C

C O

O

O

[C

C O

O

O

(CH2)2

PS-4

(CH2)2

O]n H

PET-1

C OH PET-2

O]n C O

O

CH3 H

C

[O

PC-1

O C] n OH O

CH3 CH3 H

C

[O

O C] n O O

CH3

CH3

CH3 H

[O

C

PC-2

C

O C] n O

CH3

PC-3

CH3

O

For all structures, Van-der-Waals volumes

OH

∑ ∆Vi , molar refractions ∑ Ri i

i

and molar cohesive energies ∑ ∆Ei* have been calculated. As an example, let us i

consider in detail the calculation of these characteristics for PMMA-1 structure.    ∑ ∆Vi  = 3∆VC,13 + ∆VC,1 + 2∆VC,48 + 2∆VC,41 + ∆VC,10 + ∆VC,6 + 18∆VH,124    i  PMMA -1 + 2∆VO,129 + 2∆VO,139 + (∆VC,10 + ∆VC,1 + ∆VC,13 + ∆VC,48 + ∆VC,41 + 8∆VH,124 + ∆VO,129 + ∆VO,139)(n – 2);    ∑ ∆Vi  = 3⋅17.2 + 5.0 + 2⋅15.9 + 2⋅20.3 + 13.1 + 9.0 + 18⋅2.0 + 2⋅3.4 +   i   PMMA -1 2⋅5.8 + (13.1 + 5.0 + 17.2 + 15.9 + 20.3 + 8⋅2.0 + 3.4 + 5.8)(n – 2) = 205.5 + (n – 2)⋅96.7 Å3.

558

  * * * * * *  ∑ ∆Ei*  = 10∆ EC + 18∆ EH + 2∆ Ed* (5∆ EC + 8∆ EH + 4∆ EO + 2∆ EO    i  PMMA -1 + ∆ Ed* )(n – 2);    ∑ ∆Ei*  = 10⋅550.7 + 18⋅47.7 + 4⋅142.6 + 2⋅1623 + (5⋅550.7 + 8⋅47.7 +    i  PMMA -1 2⋅142.6 + 1623)(n – 2) = 10,182 + (n – 2)⋅5,043 cal/mol = 42,561 + (n – 2)⋅21,080 J/mol.    ∑ Ri  = 10RC + 18RH + 2RO< + 2RO= + (5RC + 8RH + RO< + RO=)(n – 2);    i  PMMA -1    ∑ Ri  = 10⋅2.418 + 18⋅1.100 + 2⋅1.643 + 2⋅2.211 + (5⋅2.418 + 8⋅1.100 +    i  PMMA -1 1.643 + 2.211)(n – 2) = 51.688 + (n – 2)⋅24.744 cm3/mol. Besides these characteristics, let us also calculate heat capacity in the liquid state Cpl . For PMMA-1, we obtain:

(Cpl )PMMA-1 =

l Cp, C ⋅(3∆VC,13 + ∆VC,1 + 2∆VC,48 + 2∆VC,41 + ∆VC,10 + ∆VC,6) +

l l l Cp, H ⋅18VH,124 + C p, O ⋅(2∆VO,129 + 2∆VO,139) + [ C p, C (∆VC,10 + ∆VC,1 + ∆VC,13 + l l ∆VC,48 + ∆VC,41) + Cp, H ⋅8∆VH,124 + C p, O ⋅(∆VO,129 + ∆VO,139)](n – 2);

(Cpl )PMMA-1 = 0.34565⋅(3⋅17.2 + 5.0 + 2⋅15.9 + 2⋅20.3 + 13.1 + 9.0) + 0.62289⋅18⋅2.0

+ 0.92998⋅(2⋅3.4 + 2⋅5.8) + [0.34565⋅(13.1 + 5.0 + 17.2 + 15.9 + 20.3) + 0.62289⋅8⋅2.0 + 0.92998⋅(3.4 + 5.8)](n – 2) = 91.8 + 43.2(n – 2) cal/(mol⋅deg).

Values

∑ ∆Vi , ∑ i

i

∆Ei* ,

∑

Table 49 l Ri and Cp for PMMA-5 with different values of the

i

polymerization degree n n 1 2 3 4 5 7 10 15 20

   ∑ ∆Vi  , Å3    i 0

   ∑ ∆Ei*  , cal/mol    i 0

   ∑ Ri  , cm3/mol    i 0

297.0 197.0 163.0 146.5 136.6 115.6 107.0 100.3 97.0

17541 11292 9209 8168 7543 6363 5828 5411 5203

84.42 54.50 44.70 39.80 36.60 31.60 29.07 27.08 26.08

l , Cp,0 cal/(mol⋅deg) 125.0 84.5 70.7 63.8 59.6 50.3 46.8 44.0 42.7

559

Analogous calculations were also performed for all other structures. Then values obtained for

∑ ∆Vi , ∑ ∆Ei* , ∑ Ri i

i

and Cpl were recalculated for a single

i

    unit of polymer by simple division by n, and dependences  ∑ ∆Vi  n =  ∑ ∆Vi  ;      i   i 0         l  ∑ ∆Ei*  n =  ∑ ∆Ei*  ,  ∑ Ri  n =  ∑ Ri  and Cpl n = Cp,0 on the number          i   i 0  i   i 0 of units n have been plotted. These dependences for PMMA with various end groups     are presented in Figure 102. Table 49 showing values of  ∑ ∆Vi  ,  ∑ ∆Ei*  ,      i 0  i 0   l  ∑ Ri  and Cp,0 depended on n for PMMA-5, is also displayed as an example.    i 0



Figure 102. Dependences of 





∑ ∆'  L

L





(a), 





∑ ∆  L

L





(b), 





∑ #  L

L



l (c) and C p,0 (d) as a

function of degree of polymerization n for poly(methyl methacrylate). Numbers of curves correspond to the numbers of PMMA specimens (see text).

Curves in Figure 102 and Table 49 clearly display that dependences of the Van-der-Waals volume, the cohesive energy, the molar refraction and heat capacity   represent by shape the curves asymptotically approaching values  ∑ ∆Vi  ,    i 0     l  ∑ ∆Ei*  ,  ∑ Ri  and Cp,0 typical of the repeat unit of the polymer. Therewith,      i 0  i 0 the shape of curves is different for different end groups of the polymer. In some cases, when end groups make no significant contribution into the characteristics considered,       l even at low n values of  ∑ ∆Vi  ,  ∑ ∆Ei*  ,  ∑ Ri  and Cp,0 differ        i 0  i 0  i 0 insignificantly from asymptotic one, typical of the current chain. In the case, when the

560

end group possesses a significant Van-der-Waals volume, it contributes substantially       to the physical characteristics, and values  ∑ ∆Vi  ,  ∑ ∆Ei*  ,  ∑ Ri  and        i 0  i 0  i 0 l Cp,0 at low n appear sharply different from asymptotic ones. The asymptote is

approached (depending on type of the end group) at n = 10–20, which is assumed sometimes for the value of the chain segment. This situation is typical, for example, of PMMA-4, when benzoyl peroxide is used as an initiator in polymerization of methyl-methacrylate. Analyzing the data obtained in ref. [8], some other regularities of the influence of the chemical structure of end groups on the physical characteristics of the polymer may be observed. For example, the Van-der-Waals volume of the averaged repeat unit of the polymer is generally affected by the volume of end groups. The same may be indicated for molar refraction. Consideration of Figure 102 confirms this conclusion. For systems PMMA-1, PMMA-2 and PMMA-3, the Van-der-Waals volume and the molar refraction weakly depend on n. This is clearly indicated by consideration of curves 1–3 in Figure 102. The same may be also said about the cohesive energy of these systems. This is associated with the fact that in the case of PMMA-1, PMMA-2 and PMMA-3, end groups do not enter any specific intermolecular interaction. That is why they cause no significant change of the cohesive energy. In turn, the presence of bulky end groups significantly different from the repeat unit of the polymer by the chemical structure leads to a sharp change of all the characteristics discussed (see Figure 102, curves 4, 5). All the above-said also relates fully to systems based on polystyrene. Systems containing end groups, although of small volume but possessing a strong specific intermolecular interaction, behave themselves differently. For example, they may be end OH-groups in the case of poly(ethylene terephthalate) and polycarbonate. This specificity of the structure of end groups leads to different regularities: the characteristics associated with volume and molecular refraction change insignificantly with n; in turn, cohesive energy, in which specific intermolecular interaction plays a highly significant role, changes greatly as n increases. All this must be taken into account when the influence of the polymerization degree (especially, on initial stages of the process) on the measured physical characteristics is analyzed. Above, we analyzed the physical characteristics of a series of polymers dependent on the chain length. These characteristics are initial for the estimation of the physical parameters of polymeric substances. For example, due to the Van-der    Waals volume  ∑ ∆Vi  and cohesive energy  ∑ ∆Ei*  important parameters of      i 0  i 0 the substance such as the density of cohesive energy or Hildebrand solubility parameter may be calculated. Of interest is also the dependence of this parameter δ on n at transition from monomer to dimer, trimer, etc. These calculations were performed in ref. [8] for systems PMMA-4, PS-4, PETP-1 and PC-1. Calculation results in the form of dependence of δ on n are displayed in Figure 103. One can recognize that for some systems (PMMA-4, PS-4) regardless of whether they contain bulky end groups or not, the solubility parameter depends significantly on n. This is associated with the fact that the presence of end OH-groups in these polymers causes the appearance of hydrogen bonds that requires

561

introduction of constants ∆Eh* which take into account the contribution of the energy of hydrogen bonds to total cohesive energy. As n increases, the contribution of these bonds becomes weaker and at n = 10 – 20 is almost negligible.

Figure 103. Dependence of solubility parameter δ on the degree of polymerization n for PS-4 (1), PMMA-4 (2), PC-1 (3) and PET-1 (4).

Besides the solubility parameter, of special interest is also consideration of the influence of the chemical structure of end groups on surface tension. Figure 104 indicates the dependence of the surface tension on polymerization degree n for PMMA-5. Obviously, the surface tension decreases as n increases, striving to the border value typical for PMMA.

Figure 104. Dependence of the surface tension γp as a function of the degree of polymerization n for PMMA-5.

Hence, consideration of the influence of the chemical structure of end groups of polymers on their molecular characteristics and macroscopic properties indicates that this influence may be quite different. The presence of the effect of bulky end groups affects mainly the Van-der-Waals volume of the ‘averaged’ unit, cohesive energy and molar refraction. The presence of groups (of the hydroxyl type) with small volume but possessing specific intermolecular interaction has a strong effect on the cohesive energy and solubility parameter, as well as on surface tension, with a small influence on the Van-der-Waals volume and molar refraction. Considering the dependence of any physical properties on the chain length n, these factors must be taken into account.

Chapter XVI. Thermophysical properties of polymers

The thermophysical properties are heat capacity, thermal diffusivity and heat conductivity.

XVI.1 Heat capacity Heat capacity is the amount of heat which must be consumed for heating a body up by 1°C. Molar heat capacity, if a mole of substance is considered, and specific heat capacity in the case of 1 g of substance, differ. Heat capacity at constant pressure Cp equals the rate of enthalpy change with temperature increase, and heat capacity at constant volume Cv – the rate of internal energy change with temperature increase. In a quite wide temperature range, heat capacity increases linearly with temperature, the temperature coefficient of heat capacity increase for solid polymers possessing the average value of 3⋅10–3. At phase or physical transition of the polymer, heat capacity changes in a jump-like manner. For example, transition from the glassy to rubbery state indicates quite a sharp jump-like increase of heat capacity. When the physical transition is passed, heat capacity returns to weak growth with temperature. The heat capacity of polymers depends on their chemical structure (Table 50). Among polymeric hydrocarbons, the lowest heat capacity is displayed by polyethylene and polyoxymethylene. When hydrogen atoms are substituted by polar groups, heat capacity increases. Also, heat capacity rapidly increases in transition from aliphatic to aromatic polymers. Many attempts have been made to calculate the heat capacity of polymers on the basis of the chemical structure of the repeat unit. Let us consider the method of calculation discussed in ref. [22]. In the work cited, it is supposed that the molar heat capacity of a polymeric substance is proportional to the Van-der-Waals volume of atoms of the repeat unit of the polymer. To put it differently, C sp = ∑ C sp, i ∆Vi + As

(XVI.1)

C lp = ∑ C lp,i ∆Vi + Al ,

(XVI.2)

i

and i

where C sp and C lp are the molar heat capacities of the polymer in the glassy state and the rubbery state, respectively; C sp,i and C lp,i are constants for each atom having the meaning of heat capacities reduced to the unit Van-der-Waals volume and applicable for the glassy state and the rubbery state, respectively; As and Al are parameters equal to: As = 0.77 cal/(mol⋅deg), Al = 0.69 cal/(mol⋅deg).

563

Table 50 Calculated and experimental values of molar heat capacities for a series of polymers C sp , cal/(mol⋅deg) C lp , cal/(mol⋅deg) Polymer Calc. Experimental Calc. Experimental Polyethylene 11.02 10.4; 11.1; 11.8; 10.15 14.7 15.1 Polypropylene 16.9 15.7; 16.5 21.7 21.6 Polyisobutylene 22.8 22.4 28.8 26.4 Poly-4-methylpentene-1 34.6 33.6   Polybutadiene 20.0 21.0 26.3 24.3 Polyisoprene 25.8 25.7 33.3 31.3 Polystyrene 32.4 30.5; 29.3 43.0 42.6 Polyoxymethylene 8.8 10.2; 8.9 13.2 15.0 Polyoxytetramethylene 26.4 28.2 34.1 35.7 Polyoxypropylene 19.8 19.7 26.0 26.5 Poly(vinyl chloride) 16.2 14.4; 13.8; 16.2; 18.1 18.1 Poly(chlorotrifluoroethylene) 25.4 25.0; 23.3   Poly(tetrafluoroethylene) 23.4 23.0; 21.1 23.0 23.0 Poly(vinyl alcohol) 16.3 13.6; 15.4   Poly(vinyl acetate) 27.2 30.2; 23.6 37.0 39.5 Poly(methyl methacrylate) 33.1 33.0; 32.0 44.0 43.5 Poly(acrylonitrile) 15.5 15.9   Polyamide-6 40.2 39.1; 39.2 59.4 57.8 Polyamide-6,6 81.1 79.0; 76.6   Polyamide-6,10 104.7 107 146.2 147.0 Poly(ethylene terephthalate) 52.9 52.0; 52.2 73.3 71.0 Polycarbonate based on bisphenol A 72.7 72.4; 71.0 97.6 97.8 Poly(propylene sulfone) 29.4 29.4 38.8 38.8 Poly-2,6-dimethyl-1,4-phenyleneoxide 35.1 36.4; 34.9 47.0 50.5 Table 51

Atom Carbon Hydrogen Oxygen Nitrogen Fluorine Chlorine Sulfur

s l Values C p and C p for different atoms Numerical value, Designation Designation cal/(mol⋅deg) Å3 0.232030 C Cs C Cl s l 0.714129 CH CH l 0.634726 C Os CO s l 0.314997 CN CN 0.543367 C Fs C Fl l s 0.368819 C Cl C Cl 0.273109 CSs CSl

Numerical value, cal/(mol⋅deg) Å3 0.345646 0.622889 0.929977 2.099874 0.444909 0.284693 0.303031

Values of C sp,i and C lp,i were obtained by regression analysis with the help of solving the excessive system of equations deduced on the basis of correlation (XVI.1) or (XVI.2) using the experimental data on heat capacity for well-studied polymers (so-called polymeric standards–polyethylene, polystyrene, poly(methyl methacrylate), etc.).

564

Values of C sp,i and C lp,i obtained for each atom are shown in Table 51. With the help of these values and Van-der-Waals volumes displayed in Table 3, molar heat capacities C sp and C lp may be calculated for many polymers. Satisfactory accuracy of calculation is clear from Table 50. For copolymers, equations (XVI.1) and (XVI.2) are reduced to the following form:       C sp = α1 ∑ C sp,i ∆Vi  + α 2  ∑ C sp,i ∆Vi  + ... + α n  ∑ C sp,i ∆Vi  + As ,        i 1  i 2  i n

(XVI.3)

      C lp = α1 ∑ C lp,i ∆Vi  + α 2  ∑ C lp,i ∆Vi  + ... + α n  ∑ C lp,i ∆Vi  + Al ,        i 1  i 2  i n

(XVI.4)

  where α1, α2, …, αn are the molar parts of the components 1, 2, …, n;  ∑ C sp, i ∆Vi  ,    i 1            ∑ C lp, i ∆Vi  ,  ∑ C sp, i ∆Vi  ,  ∑ C lp, i ∆Vi  , …,  ∑ C sp, i ∆Vi  ,  ∑ C lp, i ∆Vi             i n  i n  i 1  i 2  i 2 are the sets of constants for the components 1, 2, …, n, respectively. If it is required to express the heat capacity of a copolymer via the heat capacity of homopolymers based on the components 1, 2, …, n, it should be written down that C sp = α1C sp,1 + α 2C sp,2 + ... + α n C sp, n ,

(XVI.5)

C lp = α1C lp,1 + α 2C lp,2 + ... + α nC lp, n ,

(XVI.6)

where C sp,1 , C sp,2 , …, C sp, n are the molar heat capacities of polymers based on the components 1, 2, …, n in the glassy state; C lp,1 , C lp,2 , …, C lp, n are the molar heat capacities of polymers based on the components 1, 2, …, n in the rubbery state.

XVI.2 Thermal diffusivity and heat conductivity Thermal diffusivity is a characteristic that describes the rate of temperature propagation under the effect of heat flow under non-stationary temperature conditions. This characteristic is determined from the correlation:

α=

λ Cpρ

,

(XVI.7)

where λ is heat conductivity; Cp is the specific heat capacity under constant pressure; ρ is polymer density.

565

For solid (glassy and crystalline) polymers, thermal diffusivity decreases slowly with temperature increase. However, when a polymer transits from the glassy to the rubbery state, thermal diffusivity decreases abruptly. Thermal diffusivity depends on the chemical structure of the polymer, as well as on the crystallinity degree, molecular mass and pressure. Table 52 shows the values of thermal diffusivity for a series of polymers with different chemical structures. Table 52 Polymer

Thermal diffusivity α for a series of polymers at 293 K Structural formula

High pressure polyethylene Polyisoprene

CH2CH2 CH2

CH C CH2

α⋅107, m2/sec 1.40 0.90

CH3 Poly(ethylene oxide) Poly(dimethyl siloxane)

CH2CH2O

1.08

CH3 Si

0.90

O

CH3 Polystyrene

CH2

Poly(vinyl chloride)

CH2

CH

CH

0.99

1.21

Cl Poly(methyl methacrylate)

CH3 CH2

1.19

C C O CH3 O

Heat conductivity represents the capability of polymeric substances for heat transfer from more heated substances to less heated ones. The coefficient of heat conductivity λ represents the proportionality coefficient between the heat flow and the temperature gradient. Heat conductivity is associated with the propagation and dissipation of elastic waves caused by thermal oscillations of particles in the substance. At temperatures approaching the absolute zero, heat conductivity also strives to zero. The heat conductivity of polymers depends on their chemical structure in the frame of one and the same physical state. For amorphous glassy polymers, heat conductivity is somewhat lower than for crystalline polymers. The temperature dependence of heat conductivity is affected by the chemical structure of the polymer. For one series of polymers, the slope of this dependence is positive, and for another one – negative. In the area of physical transition from the glassy to rubbery state, a low maximum of heat conductivity is observed. Table 53 shows heat conductivity values for a series of polymers with different chemical structures, from which the type of the effect of the chemical structure on heat conductivity is clear. Of special meaning is the anisotropy of the heat conductivity of polymers. This property is typical of oriented polymeric systems, in which heat conductivity is different along

566

and transverse to the orientation axis. The thermal properties of polymers are discussed in more detail in reviews [59, 61, 62]. Polymer Polyethylene of: High pressure Low pressure Polypropylene: Atactic Isotactic Polystyrene

Heat conductivity λ for a series of polymers at 293 K Structural formula

Poly(vinyl chloride)

CH2CH2 CH3

Table 53

λ, W/(m⋅K) 0.380 0.470

CH2

CH

CH2

CH

0.175 0.230 0.130

CH2

CH

0.170

Cl CH3

0.190

Poly(methyl methacrylate)

CH2

C C O CH3

Polytetrafluoroethylene Poly(dimethyl siloxane)

O CF2CF2 CH3

Si CH3

O

0.250 0.167

Chapter XVII. Molecular design and computer synthesis of polymers with predetermined properties

In previous sections of the book, the possibility of calculating the physical properties of polymers on the basis on the chemical structure of the repeat unit of linear polymers or the repeating fragment of polymer networks was demonstrated. At the present time, the above-mentioned calculations are performed in a computer. Therewith, main direct and reverse tasks and secondary tasks may be solved. The direct task concludes in calculating the polymer properties from the data on the chemical structure of the repeat unit of the polymer or a fragment of network. The reverse task (which is more complicated) consists of predicting the structural formula of the repeat unit of the polymer which would have a single or several required characteristics of the physical properties. A solution of both tasks is described in refs. [9, 17, 26, 126]. When setting and solving problems, two border approaches and a series of intermediate approaches are possible. The first border approach concludes in recording in computer memory a large number of polymers with different chemical structure for which the physical characteristics mentioned above were previously calculated. Then, computer’s role will conclude only in the search for necessary structural formulas in the database and layout of the required information, when both direct and reverse tasks are solved. In the case of such approach, the accuracy of layout characteristics is close to 100%, but the predictive power for structures absent in the database equals zero. In fact, such approach enables just to create a database. The second border variant concludes in the following. A table of Van-derWaals volumes of atoms is recorded in the computer memory. A fragment of this Table is shown as an example below. H O H C 1.54 1.54

C

C

1.54

C

1.08 1.54

C

C

1.28

5

2

C

1.54

C

O

C C

1.54

C

C

3

H

C

1.08 1.54

C C

C

O

1.54

C

1.08

4

C

1.54

1.54

H C

C

1.28

1.08

6

C

1.54

1.54

1.54

1.54

1

C

1.50 1.54

1.54

7

C

8

O

In principle, each of the atoms squared by dotted lines may be valently bonded to other atoms; for the above-depicted structures, this possibility is demonstrated by the matrix (1 – joining is possible; 0 – prohibition): Atom, No. 1 2 3 4 5 6 7 8

1 1 1 1 1 1 0 0 0

2 1 1 1 1 1 1 0 0

3 1 1 1 1 1 0 1 0

4 1 1 1 1 1 1 0 0

5 1 1 1 1 1 0 0 1

6 0 1 0 1 0 0 0 0

7 0 0 1 0 0 0 0 0

8 0 0 0 0 1 0 0 0

568

The table representing Van-der-Waals volumes of atoms, shown in the present monograph, contains over 200 values of volumes for atoms valently bonded with other various atoms. The task of building a repeat unit of a polymer from all this multiplicity of atoms, even at their limited amount in the repeat unit, is rather difficult to be computerized, and its solution by a computer requires too much computer time due to the appearance of a tremendous amount of variants. In the present case, we are talking about solving the reverse problem, when polymers with given properties are to be ‘synthesized’ using a computer. The above-discussed situation led to the need to develop an intermediate approach (between the border ones described) to computerized prognosis of the physical characteristics of polymers and their computerized synthesis. This approach concludes in preliminary summation of all constants participating in the initial correlations for calculation of properties for separate fragments (‘basic fragment’), from which then a repeat unit of a polymer is constructed on a computer. The variant of the software described in ref. [17] provides constructing of polymers, repeat units of which contain two fragments only possessing a possibility of chemical bonding with each other. According to the method of mutual joining, all the fragments discussed are subdivided into 8 classes: Class I

Structure C

II

C

III

C

IV

C

1.50

1.37

where R1: CH2;

O O

1.54

1.48

R1 R2

R1,2 R1,2

Class V

1.54

C C

O

O

VI

1.48

O

Structure

1.50

VII

1.37

VIII

C C

O N C

; (CH2)4, etc.; R2:

CH

1.50

1.37

1.37

1.37

1.50

O

R1,2

1.37

R2

O

1.37

N

R1,2 R3

1.37

C

;

OH , etc.;

O O C R3:,

O

O

C

N

C N

;

O O

C N

N

C

C

C

C

O

O

O

O

, etc.

The matrix shown below reflects possibilities of mutual joinings of the fragments related to different classes (1 –joining is possible; 0 – prohibition):

569

Fragment, No. I II III IV V VI VII VIII

I 1 0 0 0 0 0 0 0

II 0 1 0 0 0 0 0 0

III 0 0 0 0 1 0 0 0

IV 0 0 0 0 0 1 0 0

V 0 0 1 0 0 0 0 0

VI 0 0 0 1 0 0 0 0

VII 0 0 0 0 0 0 0 1

VIII 0 0 0 0 0 0 1 0

Generally, ref. [17] presents series of constants calculated for 194 fragments (‘basic fragments’) of various chemical structures. As an example, some of them are shown in Table 54. Dotted squares mark the chemical structure of the fragment itself; also displayed are atoms, joined to the fragment, and lengths of chemical bonds expressed in Å. The possibility of joining of one of 18 fragments to another, taking into account their belonging to different classes, is demonstrated in the following matrix (1 – joining is possible; 0 – prohibition): Fragment, No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

1 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0

2 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0

3 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0

4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0

5 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0

6 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0

7 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0

8 1 1 1 0 1 1 1 1 1 0 0 0 0 0 0 0 0 0

9 10 1 0 1 0 1 1 0 0 1 0 1 0 1 0 1 0 1 0 0 1 0 1 0 1 0 1 0 0 0 0 0 0 0 0 0 0

11 0 0 0 0 0 0 0 0 0 1 1 1 1 0 0 0 0 0

12 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0

13 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0

14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1

17 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 0 0

The program contemplates both the solutions of the direct task concluded in the determination of polymer properties basing on the chemical structure of the repeat unit and the reverse task consisted in searching for the units such that the polymer composed from them would possess the given physico-chemical properties. Solving the reverse task, the computer calculates a parameter of one of the required properties using all probable variants of combinations from ‘basic fragments’ recorded by its memory. For polymers, the property of which appears in the required interval, the parameter of another property is calculated, after which the required polymers are also selected, etc. The drawback of this software is that composition of a repeat unit of a polymer from two large ‘basic fragment’ does not embrace the tremendous amount of probable structures. Obviously, the smaller the size of ‘basic fragments’ used for composing the repeat unit, the more variants of polymers may be obtained due to the great amount and multiplicity of ‘basic fragments’ in the unit and for calculating their properties.

570

That is why A.A. Askadskii, E.G. Galpern, A.L. Chistyakov, and I.V. Stankevich [126] have created a software for computer ‘synthesis’ of polymers from the scarcest ‘basic fragments’, i.e. those which, in principle, cannot be sectioned. These basic fragments are shown in Table 55. To denote the possibility of joining these small fragments, recorded in the computer memory, to each other, definite labels are attributed to every end of ‘basic fragments’. Note that the fragments used for composing the repeat unit possess only 20 different end groups and, consequently, 20 different labels (see Table 55), which may interact with each other in accordance with the matrix recorded by the computer memory: LABELS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0 1

2 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

3 1 1 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 1 0

4 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0

5 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0

6 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 0 1 0 0

7 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0

8 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 10 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

11 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0

12 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

13 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0

14 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

15 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

16 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0

17 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

18 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0

19 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

20 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

In this matrix, no difference is made for the given C–C bond of 1.54 Å (in aliphatic fragments) and 1.48 Å (in aromatic fragments), because transition from one bond to another causes only insignificant changes in the Van-der-Waals volume, which display no substantial influence on the accuracy of calculation of physical properties.

Figure 105. Schematic representation of construction of the combinatorial tree when constructing a repeat unit of polymer (see text).

571

Table 54 Fragment No.

Class

1 1

2 I

2

Chemical structure of fragment

Chemical structure and sets of constants for various fragments 3 ∑Vi , M ∑ (ai ∆Vi + bi ) ⋅10 , ∑ K i ∆Vi ⋅103, ∑ (δ i ∆Vi + γ i ) , i

3

C

I

C

1.54

1.54

C

CH2

1.54

i

1.54

Å3 4 17.1

5 14

Å3K−1 6 80.2

43.9

44

79.6

i

i

∑ Ri ,

∑ Ei* ,

∑ Ci ⋅103,

cal/mol 10 646

(cm3/mol)⋅MPa−1 11 –3.090

i

i

i

Å3K−1 7 24.3

8 1.434

cm3/mol 9 4.618

129.0

62.3

3.122

10.879

3058

–9.458

86

195.2

129.5

6.778

15.290

6020

–17.871

82.1

76

135.8

100.7

7.028

24.107

4208

–12.686

24.5

30

33.9

54.2

2.076

6.143

4718

–10.061

124.9

144

449

194.4

10.440

31.016

7502

–16.618

Å

C

CH O CH3

3

I

CH3 C

1.54

1.54

C

C C O CH3 O

4

VI

O 5

1.37

I

C

1.37

O

1.54

CH

1.54

C

OH 6

I

C

1.54

C O O

(CH2)4

O C

1.54

C

O 571

572

2 I

3

C

1.54

C O

O C

O 8

I

C

1.54

C

6 231.8

7 191.6

8 11.090

9 36.651

10 9126

11 –16.926

128.9

142

216.2

226.9

9.911

34.934

14334

–17.106

136.5

162

208.0

226.4

10.655

40.570

15958

–19.113

75.6

76

135.7

96.2

6.463

24.107

4208

–12.686

159.8

168

319.6

200.0

14.521

49.864

8559

–22.174

130.6

164

273.4

190.6

11.047

36.651

9126

–18.626

1.54

C

C HN (CH2)4 NH C

1.54

C

O

I 1.54

5 164

O

O 9

4 131.0

C HN O NH C

1.54

C

O 10

II

C 11

1.48

C

II

C 12

1.48

1.48

1.48

C

O

II 1.54

C

C O O O

C O

1.54

C

572

1 7

573

1 13

2 II

3

C

1.48

C HN (CH2)6 NH C O

14

16

1.50

O

III

C

1.50

O

1.50

C

O

1.37

O

7 274.4

8 12.736

9 44.170

10 15626

11 –23.295

163.1

184

395.4

199.0

14.786

51.500

8701

–18.976

3.4

16

78

0.20

0.211

1.643

143

+3.198

87.5

108

259.7

103

7.363

27.393

4494

–6.290

86.3

108

273

103

7.288

27.393

4494

–7.990

74.6

56

321

104.9

6.318

18.472

2584

–12.378

C

C

O O

18

6 376.6

1.50

IV

C

5 170

1.50

III 1.50

4 162.7

O

O

C 17

C

III

C 15

1.48

V

1.54

(CH2)4

C

1.54

C

573

C

1.37

574

Fragment No. 1 1 2

C

CH

C

Molar refraction Ri, cm3/mol 8 4.618

Cohesive energy ∆Ε*, cal/mol 9 646

1.48; 1.54

1.48; 1.54

2

2

34.2

9.236

2915

1.54

1.54

2

2

51.3

13.854

1938

1.48; 1.54

1.48; 1.54

2

2

51.3

13.854

3561

1.48; 1.54

1.48; 1.54

2

2

43.9

10.879

3058

1.48; 1.54

1.48; 1.54

2

2

31.9

9.485

1999

1.48; 1.54

1.48; 1.54

2

2

46.8

12.752

2705

1.48; 1.54

1.48; 1.54

2

2

92.6

28.725

4854

CH3 3

CH3 C

C

C

CH3 4

C

CH

C

C2H5 5

C

CH

C

O CH3 6

7 8

C

CH

C

Cl C……CCl2……C C CH C

574

Table 55 Smallest basic fragments for the computer synthesis of polymers Length of bonds with Labels Chemical structure of fragment Van-derneighboring atoms, Å Waals volume, Å3 Left Right Left Right 2 3 4 5 6 7 1.48; 1.54 1.48; 1.54 I I 17.1 C……CH2……C

575

1 9

2

CH3

10

11

C

C

C

C

C

C

C

O C

C

3 1.48; 1.54

4 1.48; 1.54

5 2

6 2

7 109.8

8 33.343

9 7123

1.48; 1.54

1.48; 1.54

2

2

18.6

4.629

693

1.48; 1.54

1.48; 1.54

2

2

108.9

32.797

7218

1.48; 1.54

1.48; 1.54

2

2

155.2

40.234

8966

1.48; 1.54

1.48; 1.54

2

2

81.1

14.694

1797

1.48

1.48

3

3

75.6

24.107

4208

O C 12

C

13

O

C

C

CF3 C

C

C

CF3 14

C

C 575

576

2

C

3 1.48

4 1.48

5 3

6 3

7 75.6

8 24.107

9 4208

1.54

1.54

2

2

54.6

13.399

6084

1.48

1.48

3

3

100.3

33.127

8791

1.54

1.50

1

4

20.2

4.618

646

1.54

1.50

2

4

37.8

9.236

2915

1.54

1.50

2

4

54.9

13.854

3561

1.54

1.50

2

4

96.2

24.725

4854

1.48

1.37

3

5

78.8

24.107

4208

C

16

N C

N

C

C

C

O 17

NH

C

C

C

N 18 19

C……CH2……O C CH O CH3 CH3

20

C

C

O

CH3 21

C

CH

O

22

C

O

576

1 15

577

1 23

2

C

25

4 1.37

5 3

6 5

7 78.8

8 24.107

9 4208

1.50

1.50

4

4

23.3

4.618

646

1.37

1.37

5

5

82.1

24.107

4208

1.37

1.37

5

5

82.1

24.107

4208

1.37

1.37

5

5

115.5

33.343

8746

1.50

1.50

8

8

3.4

1.643

143

1.37

1.50

9

8

2.7

1.643

143

1.37

1.37

9

9

2.1

1.643

143

1.54

1.50

2

8

25.1

6.272

2460

1.54

1.37

2

9

24.4

6.272

2460

1.54

1.37

1

6

18.6

4.618

646

1.54

1.37

2

6

20.1

4.629

2316

O

O……CH2……O

24

3 1.48

O

O

26

O

O

27

CH3 O

O CH3

28

31

C……O……C C……O……C C……O……C C C O C

32

C

29 30

33 34

O C O

C

O C……CH2……N C C N

577

O

578

2

C

4 1.37

5 3

6 6

7 77.4

8 24.107

9 4208

1.48

1.37

3

6

77.4

24.107

4208

1.37

1.48; 1.54

11

14

28.4

8.231

5875

1.37

1.37

5

6

80.6

24.107

4208

1.37

1.37

5

6

80.6

24.107

4208

1.37

1.37

6

6

79.2

24.107

4208

1.37

1.37

6

6

79.2

24.107

4208

1.37

1.37

11

11

8.5

3.602

1253

1.76

1.48

7

3

76.8

24.107

4208

N

36

C 37

3 1.48

N

C

NHC

C

O 38

O

N

39

O 40

N

N N

41

N 42

N

C……NH……C

43

S

C

578

1 35

579

1 44

2

S 45

S

S

S S

N

S S

O

S

52

6 3

7 76.8

8 24.107

9 4208

1.76

1.76

7

7

78.0

24.107

4208

1.76

1.76

7

7

78.0

24.107

4208

1.76

1.37

7

6

78.6

24.107

4208

1.76

1.37

7

6

78.6

24.107

4208

1.76

1.37

7

5

80.0

24.107

4208

1.76

1.37

7

5

80.0

24.107

4208

1.76

1.76

12

12

16.5

8.00

1750

1.76

1.76

12

12

26.1

8.870

3656

N

50

51

5 7

S

48

49

4 1.48

C

46

47

3 1.76

O C……S……C O C

S

579

O

C

580

2

C

O

O

C

C

C

C

O

O

N

54

O

C

C

N

C

N C

6 11

7 144.6

8 46.103

9 12542

1.37

1.37

11

11

190.2

61.441

15553

1.37

1.37

5

11

113.4

35.105

8375

1.48

1.37

3

11

110.1

35.105

8375

1.37

1.48

3

5

103.4

33.126

8791

C

O O

O

5 11

C

O 55

4 1.37

C

N

O

3 1.37

C N

C

C O O

56

C

C N

C

C 57

O

O NH

C N

C

580

1 53

581

1 58

2

O

3 1.76

4 1.37

5 7

6 11

7 111.3

8 35.105

9 8375

1.76

1.48

7

3

101.3

33.127

8791

1.64

1.64

13

13

71.6





1.64

1.64

10

10

0.5

1.50

1.50

4

4

24.8

 4.629

 2316

1.37

1.37

11

11

25.6

8.558

1899

1.37

1.37

6

6

124.8

39.445

7219

1.48

1.48

3

3

121.2

39.445

7219

1.48; 1.54

1.48; 1.54

1

1

27.1

4.898

599

C

S

C

N C O NH

59

S

C

C

N CH3

60

O

Si

O

CH3 Si……O……Si O C O

61 62

C

63

O N

C

CH3 64

N

N

65

C

C……CF2……C

581

66

C

582

As an example illustrating building of the repeat unit, Figure 105 shows a combinatorial tree, which is composed from three fragments (‘basic fragments’) with various end labels. The rule, according to which the formation of a bond between end groups is permitted, or prohibited, is reflected in the matrix of their interactions. Clearly, the quantity of probable variants of the repeat unit of the polymer increases with every step of joining a consequent fragment. It should be taken into account that if all ‘basic fragments’ recorded by the computer memory participate in the composition and therewith each of them may join to the propagating unit by both one or another ends, then 2n of variants of the repeat unit (where n is the number of ‘basic fragments’) appear on every stage of joining of the next fragment. Hence, this procedure represents a geometric progression with denominator 2. Besides direct and reverse tasks, software for prognosis of the physical properties of polymers enables other tasks to be solved. For example, the upper and lower ranges of the physical characteristics may be determined which, in principle, organic polymers are able to display; for example, the lower value of the onset temperature of intense thermal degradation of organic polymers, Td, is 150°C, and the upper limit is 575°C. Hence, an organic polymer possessing the onset temperature of intense thermal degradation above 575°C is difficult to produce. ‘Combination’ of various properties in the same polymer may also be estimated, etc. (see below). Software based on using the finest basic fragments enables calculations and ‘synthesis’ of polymers of the following classes: 1. Polyolefins, vinyl polymers, etc. 2. Polyethers and polyetherketones 3. Polyesters 4. Polyamides 5. Polysulfones, polyethersulfones 6. Polyimides 7. Polyoxadiazoles 8. Polybenzimidazoles 9. Polysulfides 10. Organosilicon polymers 11. Polycarbonates The number of polymer classes may be increased, if necessary. This requires introduction of a group determining affiliation of polymers to the chosen class into the database; for example, introduction of urethane group into the database enables to calculate properties of polyurethanes and to synthesize polyurethanes with the given properties in a computer. The drawback of this software is that the above-mentioned tasks may be solved only for polymers containing the basic fragments present in the database. Although the number of polymers is great in this case, some limits do exist. In this connection, A.A. Askadskii and A.F. Klinskikh [22] created software, according to which the chemical structure of a polymer is ‘gathered’ not from ‘basic fragments’, but from separate atoms. In this case, the chemical structure of a repeat unit is displayed on the screen in the form of a structural formula of an organic compound, as a chemist writes it down on paper. After that, the physical properties of the polymer of the given structure are calculated and laid out immediately to the user. Therewith, the molecular design of a polymer may be performed by changing its chemical structure, introducing various groups, etc., and its physical characteristics are obtained immediately. This program enables us to solve the first (direct) task only, because when polymers are synthesized from separate atoms (but not ‘basic

583

fragments’), the number of variants is so high that they cannot be realized on a computer of any power. This program enables to calculate the properties of polymers and copolymers, and polymer networks, listed below: 1. Molecular mass of the repeat unit; 2. Molar volume at room temperature; 3. Temperature dependence of the molar volume; 4. Dependence of molar volume on crystallinity degree; 5. The Van-der-Waals volume; 6. Density at room temperature; 7. Dependence of density on crystallinity degree; 8. Temperature dependence of density; 9. Thermal expansion value in the given temperature range; 10. The Hildebrand parameter of solubility; 11. Surface energy; 12. Refractive index at room temperature; 13. Temperature dependence of refractive index; 14. Dielectric constant at room temperature; 15. Birefringence; 16. Dipole moment; 17. Stress-optical coefficient in the glassy state; 18. Glass transition temperature; 19. Dependence of glass transition temperature on molecular mass; 20. Temperature of the onset of intense thermal degradation; 21. Dependence of temperature of polymer transition to the viscous-flow state on molecular mass; 22. Coefficient of volumetric expansion in the glassy state; 23. Coefficient of volumetric expansion in the rubbery state; 24. Molar heat capacity under constant pressure in the glassy state at room temperature; 25. Molar heat capacity under constant pressure in the rubbery state at room temperature; 26. Temperature dependence of molar heat capacity in the glassy state and the rubbery state; 27. Specific heat capacity at room temperature under constant pressure in the glassy state; 28. Specific heat capacity at room temperature under constant pressure in the rubbery state; 29. Jump of molar heat capacity at transition from the glassy state to the rubbery state; 30. Jump of specific heat capacity at transition from the glassy state to the rubbery state; 31. Total energy of intermolecular interaction; 32. Energy of dispersion interaction; 33. Energy of strong dipole–dipole interaction and hydrogen bonds; 34. The part of energy of dispersion interaction in total energy of intermolecular interaction; 35. The part of energy of dipole–dipole interaction and hydrogen bonds in total energy of intermolecular interaction; 36. Molar refraction; 37. Molar polarizability;

584

38. Total cohesive energy; 39. The part of cohesive energy stipulated by hydrogen bonds; 40. The part of cohesive energy stipulated by dipole–dipole interaction; 41. The part of cohesive energy stipulated by dispersion interaction; 42. Permeability by oxygen; 43. Permeability by carbon dioxide; 44. Permeability by nitrogen; 45. Interface tension on the polymer–solvent interface; 46. Interface tension on the polymer–polymer interface; 47. Elasticity modulus in the area of rubber-like plateau; 48. Value of mechanical segment (molecular mass or polymerization degree, at which the rubbery state is displayed); 49. Activation energy of low-temperature γ-transition; 50. Newtonian viscosity of polymeric melts; 51. Prediction of solubility of polymers in organic solvents; 52. Influence of molecular mass on solubility; 53. Influence of orientation degree on solubility; 54. Prediction of miscibility of polymers. For low-molecular liquids, calculation of the properties listed below is involved in the program: 1. Molecular mass; 2. Molar volume; 3. The Van-der-Waals volume; 4. Density; 5. The Hildebrand parameter of solubility; 6. Surface tension; 7. Refractive index; 8. Dielectric constant; 9. Molar heat capacity in the solid state; 10. Molar heat capacity in the liquid state; 11. Molar refraction; 12. Molar polarizability; 13. Total cohesive energy; 14. The part of cohesive energy stipulated by hydrogen bonds; 15. The part of cohesive energy stipulated by dipole–dipole interaction; 16. The part of cohesive energy stipulated by dispersion interaction. Let us now turn to the principles of computer realization of the method of atomic constants. Preliminarily, it should be noted that practical validity of this method for solving the problem of searching for structures of the repeat unit providing required physicochemical properties of polymer is obvious. For example, in the frames of the method of constants, the values of typical temperatures (glass transition, degradation and melting) of polymers may be calculated and structures fulfilling the requirements on the total complex of the above-mentioned properties may be found. The structures found may form the base for applying software of computer planning of organic synthesis (CPOS). Let us consider in greater detail the calculation scheme of the method of constants on the example of calculation of the glass transition temperature of polymer Tg by the chemical formula of its repeat unit. Tg is calculated from equation (IV.39). The algorithm involves: 1) analysis of the structure by atoms and bonds; 2) separation of groups of atoms responsible for dipole–dipole interaction and hydrogen

585

bonds (including various cases of hydrogen bonding typical of polyamides); 3) determination of ortho-, metha- and para-substitutions for aromatic cycles in the main chain; 4) determination of double ‘carbon–carbon’ bonds in the main chain. As these rules are not in contradiction with each other, they assume a formalized description providing computer realization of the algorithm. Analogous analysis is performed in calculation of all other properties of polymers, networks and organic liquids. Computerization of the method of atomic constants is based on modularity, developed, compatible Windows-interface and conformity with CPOS programs. First two principles are well known and common. That is why let us dwell on the third principle. Being the original object for CPOS application, the structure of the target compound such be such as to ensure the required physico-chemical properties. Because searching for such structure is one of the tasks in the method of constants, coordinated description of structures in the method of constants and CPOS must be provided. Main blocks for CPOS programs are tables of atoms and the table of connectivity, which sets a selection of atoms and types of bonds in structure of the compound. For realization of the method of constants, it has been assumed desirable to form such tables for each calculated formula of the repeat unit. Of special attention was solution of the problem of user communication with the program. To depict the structure of the repeat unit of polymer, the planar (two-dimensional) image of disposition of atoms linked by definite types of bonds was used. If necessary, correspondence to linear Wiswesser formulae or to the writing form by Morgan is set with the help of tables of atoms and connectivity. The problem of the unambiguous interpretation of the structure of the repeat unit displayed on the screen is also important. For this purpose, control of the existence of data on atoms, groups of atoms and bonds in the database is used in the program. The program represents an assembly of modules providing: 1) the regime of editing the structure analyzed (entering, deleting and transposition of symbols of atoms, groups of atoms, data files recording on disk and reading from disk with the structure, etc.); 2) Analysis of the structure, the calculation of parameters and treatment of structural errors. Separation of modules of the second group enables to make the program easily transmitted between various systems. In practice, the program is used since 1994, first applied to DOS, and at present – to Windows’98.

Figure 106. Schematic representation of the region of possible existence for two properties of polymers (see text).

586

The program was tested on all compounds for which, on the one hand, experimental data were known and, on the other hand, calculations by the method of constants had been performed before. For example, the properties of polyolefins, vinyl, acrylic and dienic polymers, aliphatic and aromatic polymers (including polyamides), polyesters, polyimides, polysulfones, polyetherketones, etc. were calculated. It has been shown that the program successfully interprets the structure of the repeat unit in accordance with the calculation scheme of the method of constants, and provides for required accuracy of the calculation method of 3–5%. Examples of solving the direct, reverse and combined tasks of computerized synthesis of polymers based on the above-described programs are indicated in Appendices 1 – 3. Let us consider one more task, which may be solved by the above-described software. At present, in connection with the application of polymers to various spheres, requirements on their physical properties have become much stricter. Problems appear, solutions of which require polymers with a combination of a series of physical properties, simultaneously falling within the given ranges of the values of their characteristics. A question is raised about the combination of properties of polymers. Described in ref. [23] is the method of its solving with the help of ‘miscibility diagrams’, which consists of the following: assume that for a large group of polymers values of parameters of any two physical properties (from experiment or calculation) are known. Let us compose a diagram on which a specific point (Figure 106) corresponds to every polymer, where the abscissa axis (X) represents the values of the parameters of the first property, and on the ordinate axis (Y) – of the second one. All these points are located inside some region, which may be contoured. This region is called ‘the miscibility region’ of the mentioned physical properties for the given group of polymers. Attention should be paid to the fact that the density of points distribution in the region may be rather irregular. Such diagrams enable to estimate possibility of existence of polymers with given properties without additional consumption of labor. Actually, let the ranges (X2 – X1) and (Y2 – Y1) of values of properties, which must be possessed by polymers, be given. If the area determined by these ranges, falls within the miscibility region in the diagram, and some points exist there, i.e. the polymer may exist (case I). In the opposite case, obtaining the required polymer among polymers of these classes is of low probability (case II). To compose miscibility diagrams of this kind, either experimental data on various physical properties of polymers, or calculated data may be used. Combinations of these data may also be used. To calculate various physical properties of polymers, it is desirable to apply the computer program suggested in ref. [17], because with the help of it the properties of polymers either already synthesized, or the ones which may be, in fact, synthesized are considered. This very program was used in ref. [23] for composing combination regions of various properties of polymers. Among these properties the following were considered: density, ρ; refractive index, n; glass transition temperature, Tg; the relation of glass transition temperature to the melting point, Tg/Tm; the onset temperature of intense thermal degradation, Td; the Hildebrand solubility parameter, δ (density of cohesive energy); stress-optical coefficient Cσ. Ref. [23] indicates 27 diagrams built on a computer, which reflect combination of any two of the above-mentioned physical properties. Formulae, with the help of which the connection between two given parameters of properties may be searched, are shown in monograph [6].

587

Figure 107. Combination diagrams of Td and Tg (a), δ and Tg (b), δ and n (c) (see text).

As an example, Figure 107 shows miscibility diagrams of the following properties of polymers: glass transition temperature, Tg, and the onset temperature of intense thermal degradation, Td; Tg and solubility parameter, δ; refractive index, n, and δ. Let us consider several features of these and other similar diagrams. All regions of miscibility display different density. This means that there are sub-regions of miscibility exist containing the main bulk of polymers, and from these very sub-regions the chemical structure of polymers may be most easily chosen, which would fit the two given properties. All the diagrams display the presence of clearly expressed dependences of one property on another. Each of these dependencies characterizes definite series of polymers, for example, polyesters, polyamides, polyimides, etc.

588

Every diagram contains a point from which these dependences start. This is associated with the program feature [17], in which several homologues (CH2)n up to n = 20 are set as original fragments from the total 194 ones, and the point, from which these dependences start, characterizes polyethylene. Other features inherent to each diagram are clearly seen in corresponding figures. Having these diagrams, the possibility of obtaining polymers, which would possess the necessary combination of one of several properties may be predicted. For example, if polymers with the solubility parameter δ = 10 (cal/cm3)1/2 and Tg ≈ 300°C should be obtained, it may be made easily, because the point corresponded to these coordinates falls within the densest part of the diagram in Figure 107b. It would be quite difficult to produce a polymer with the glass transition temperature Tg ~ 500°C at the same solubility parameter, and at Tg = 600°C this becomes practically impossible, because the point corresponding to these coordinates is out of the range of the ‘miscibility’ region. This analysis may be easily performed for any diagram presented in ref. [23], as well as for a set of these diagrams, which enables us to predict the possibility of obtaining polymers with a a set of the required properties. Clearly, that if such diagrams are composed with the help of a computer program, according to which the polymer is composed from the finest ‘basic fragments’, the regions of miscibility of polymers will be significantly expanded by points reflecting properties of the very large number of polymers.

Appendix 1. Examples of solution of direct problems of polymer synthesis

Let us consider solution of the direct problem of estimation of the properties of polymers based on their chemical structure on an example of natural polymers. The specific features of these polymers are the following: 1) These polymers contain cyclic non-aromatic structures with a large number of OH-groups able to form hydrogen bonds. 2) Hydrogen bonds in these polymers may be formed both between neighboring chains and in the range of a single chain, and even in a single repeat unit. The scheme representing these interactions is shown in Figure 41. The presence of interchain and intrachain (including intra-unit) hydrogen bonds depends on the steric factor – dislocation of OH-groups in relation to the plane of circles. 3) Many high-molecular compounds, including cellulose, degrade thermally at heating before the process of devitrification is onset. Consequently, the glass transition temperature (the most important characteristic for polymers) may not be determined experimentally. 4) Many natural high-molecular compounds possess different units, i.e. contain fragments of different chemical nature in their chains. In this Section, we will discuss application of the approach developed for estimating the physical properties of polymers based on their chemical structure to natural high-molecular compounds, which possess quite complicated but well studied chemical structure. Table A-1-1 indicates chemical structures of 16 fragments of hemicelluloses structures, most often met in the structure of natural polymers. Of special attention is the fact that in some cases, despite the identical gross-formula, these fragments included in polymeric chains involve different physical properties of natural polymers. For example, for structures Fs1 and Fs2, gross-formulae are identical, but in the structure of Fs2 fragment OH-groups disposed at one side of the circle plane may form hydrogen bonds between each other. Hence, they participate in the formation of bonds between neighboring chains. This circumstance influences the glass transition temperature and some other properties of polymers containing these fragments. Let consider in greater detail the influence of the chemical structure of the above-mentioned natural polymers on their glass transition temperature. The glass transition temperature is calculated from equation (IV.39). Calculating the glass transition temperature from this equation, all fine features of the structure of the polymeric unit should be taken into account. If hydrogen bonds are formed between chains of the polymer (as a result, a physical network is formed at the sacrifice of intermolecular bonds), then parameter bh = –140⋅10–3 Å3K–1 should be introduced into equation (IV.39). In the case if OH-groups in the repeat unit are disposed in the manner that hydrogen bonds are formed between them in the range of the same unit, then the network of physical intermolecular bonds between chains is not formed (see Figure A-3-1,b), and for other groups, constants bd instead of bh must be introduced into equation (IV.39), which are introduced for every branching from the main chain of the polymer. The use of this approximation leads to values of the glass transition temperature and all other properties, which are displayed in Table A-1-2. It is clearly

590

observed that at the identical gross-formula the glass transition temperature of the structure Fs1 (541 K) is much higher than for the structure Fs2 (319 K). Therewith, such important characteristic of polymers as Mc (molecular mass of the mechanical segment of macromolecule, at which the rubbery state appears) is also changed. Saturation of the structure of hemicelluloses by OH- and COOH-groups leads to a sharp increase of the glass transition temperature, if these groups are capable of forming hydrogen bonds between chains of polymers. If hydrogen bonds are formed inside the repeat unit, the glass transition temperature is abruptly decreased. Let us consider in brief some other properties. The densities of solid samples are approximately equal, the lowest density being possessed by the structure Fs5, in which only a single OH-group is present. Consequently, this structure possesses the highest onset temperature of intense thermal degradation. It should be noted that, in some cases, the onset temperature of intense thermal degradation lies below the glass transition temperature or is close to it, which is the reason that experimental determination of Tg for natural polymers is rather difficult. The surface energy for 16 calculated structures changes in quite wide ranges, the lowest surface energy being typical of the structure Fs5 containing the smallest number of OH-groups, and the highest value is typical of the structure Fs8 containing the greatest number of these groups. Dielectric constants are approximately equal, the solubility parameter is quite high compared with synthetic polymers, refractive indices are approximately equal, and the temperature coefficient of volumetric expansion in the glassy state significantly depends upon the chemical structure of the fragment and changes antibatically to the glass transition temperature. Further on, let us consider the properties of hemicelluloses composed from the above-mentioned fragments. The chemical composition of 8 hemicelluloses and disposition of fragments in them are shown in Table A-1-3. The main properties of hemicelluloses of the given composition are shown in Table A-1-4. All properties were calculated on the basis of the molar content of fragments. Actually, the glass transition temperature of hemicelluloses of various chemical structures varies from 332 to 517 K, and the onset temperature of intense thermal degradation – from 517 to 580 K. The main characteristics indicated in Table A-1-4 show that the values of these temperatures for hemicelluloses C4 are very similar. Of special attention is the extremely low permeability of films from hemicelluloses to various gases. Experimental testing of the calculation results was performed on the basis of 1,4-β-D-glucomannan, the structure of which (F8) is shown on Table A-1-3. The thermomechanical curve for the initial preparation containing an uncontrolled amount of water is shown in Figure A-1-1. After drying in vacuum at a temperature of 80°C during two hours, the form of the thermomechanical curve changed a little (Figure A1-2). The form of Debye patterns (Figure A-1-3) also changes during such thermal processing in vacuum. They indicate that the glucomannan specimens studied were practically amorphous. The calculated value of the glass transition temperature (356 K) with the accuracy, typical of such calculations, coincides with the experimental value which, according to the thermomechanical curve (see Figure A-1-2), is 333 K. It is not inconcievable that after further drying the glass transition temperature might be somewhat increased. The second peak of deformation on the thermomechanical curve appears at a temperature close to the temperature of intense thermal degradation and is probably associated with it.

591

Needless to say that the results of all the calculations performed may be considered only as preliminary ones, and in future they must be related to not only with the primary, but also with the secondary structure of chemicelluoses. Table A-1-1 Chemical formulae of the fragments of hemicellulose structures Designation of structures Chemical formulae of structures fragments fragments 1 2 CH2OH Fs1 O O

OH OH

Fs2

CH2OH O O

OH

HO

Fs3 O O

OH OH

Fs4

COOCH3 O O OH OH

Fs5 O O

COOCH3 OH

Fs6 O O

OH O OH HO OH

O

592

1 Fs7

2 COOH O O

OH O

O

OH HO OH

Fs8 O O

OH

O

OH

O

OH OH

Fs9 O O

OH O

O

COOCH3 HO COOCH3

Fs10 O O

OH

COOH O

O HO OCH3 OH

593

1 Fs11

2 OH HO OH O

O

CH2OH CH2 O O

OH

HO

CH2OH

Fs12

O O

OH

O

OH OH

OH O

CH2OH

Fs13 O O

OH

OH

O

H3CO OH O COOH

Fs14

CH2OH O

HO OH

OH O CH2 HO

O

O

HO

O OH

CH2OH O

OH

594

1 Fs15

2 O O

O OH O

O

OCH3 OH

OH OH

O OH

Fs16

CH2OH

CH2OH O

HO

COOH

O

HO

OH

OH OH

OH OH

O CH2

HO

O

O

OH

O

OH

HO

O

O CH2

CH2 HO

O

O OH

O

OH

O

OH

Table A-1-2 Properties of hemicellulose structure fragments Values of properties of structures fragments Designation of structures ∑ ∆Vi , Å3 ρ, 3 Tg, K Td, K properties MM Vm, cm3/mol g/cm i Fs1 162 116 132 1.39 541 556 Fs2 162 116 132 1.39 319 556 Fs3 132 95 107 1.40 511 571 Fs4 190 135 152 1.41 459 585 Fs5 174 128 145 1.36 403 607 Fs6 264 189 214 1.40 574 527 Fs7 308 212 240 1.45 641 520 Fs8 250 174 197 1.44 427 520 Fs9 348 256 290 1.36 436 570 Fs10 322 229 259 1.41 518 530 Fs11 324 233 263 1.39 431 511 Fs12 324 233 263 1.39 432 511 Fs13 322 229 259 1.41 518 530 Fs14 486 349 395 1.39 388 525 Fs15 454 324 367 1.40 552 517 Fs16 929 661 748 1.41 437 513 Values of properties of structures fragments Designation of E*, E, γ, αh, αdd, αd, ε, structures properties kcal/mol rel. un. rel. un. rel. un. rel. un. kcal/mol dyn/cm Fs1 45.5 23.9 0.72 0.00 0.28 3.36 49.6 Fs2 45.5 23.9 0.72 0.00 0.28 3.36 49.6 Fs3 54.8 18.2 0.63 0.07 0.30 3.34 37.96

595

Fs4 Fs5 Fs6 Fs7 Fs8 Fs9 Fs10 Fs11 Fs12 Fs13 Fs14 Fs15 Fs16 Designation of structures properties Fs1 Fs2 Fs3 Fs4 Fs5 Fs6 Fs7 Fs8 Fs9 Fs10 Fs11 Fs12 Fs13 Fs14 Fs15 Fs16

46.4 37.9 53.0 58.9 62.1 36.5 49.9 45.5 45.5 49.9 45.5 50.3 46.6 Edd+h, kcal/mol 37.60 22.20 27.70 30.18 21.53 64.07 80.77 39.00 48.40 63.65 84.83 84.83 63.65 70.17 99.57 157.40

Designation of structures properties

αL⋅104, K−1

Fs1 Fs2 Fs3 Fs4 Fs5 Fs6 Fs7 Fs8 Fs9 Fs10 Fs11 Fs12 Fs13 Fs14 Fs15 Fs16

4.46 4.46 4.71 5.25 5.97 4.20 3.76 3.59 5.52 4.65 4.04 4.04 4.65 4.18 4.37 3.90

Designation of structures properties

P, cm3/mol

Fs1 Fs2

51.2 51.2

21.5 0.54 0.11 0.35 3.49 16.8 0.34 0.21 0.44 3.33 35.2 0.66 0.03 0.31 3.34 43.3 0.67 0.05 0.28 3.56 37.8 0.61 0.13 0.26 3.45 32.3 0.36 0.18 0.46 3.33 39.7 0.58 0.09 0.33 3.43 47.8 0.72 0.00 0.28 3.36 47.8 0.72 0.00 0.28 3.36 39.7 0.58 0.09 0.33 3.43 71.7 0.72 0.00 0.28 3.36 56.7 0.61 0.06 0.33 3.40 139.1 0.70 0.03 0.27 3.38 Values of properties of structures fragments Ed, n, ∆U, δ, kcal/mol rel. un. kcal/mol (cal/cm3)1/2 12.0 14.30 1.49 27.9 12.0 14.30 1.49 27.9 10.26 13.85 1.49 26.4 15.97 12.65 1.48 23.7 17.23 11.43 1.48 20.8 21.15 13.63 1.49 29.7 22.83 14.29 1.48 33.1 18.74 14.72 1.48 34.7 35.45 11.23 1.48 22.6 26.87 13.16 1.48 26.8 24.60 14.34 1.49 30.8 24.60 14.34 1.49 30.8 26.87 13.16 1.48 26.8 36.61 14.34 1.49 29.8 37.76 13.23 1.48 28.5 69.68 14.51 1.49 31.9 Values of properties of structures fragments n l, R, C ps , C pl , rel. un. cm3/mol cal/(mol⋅deg) cal/(mol⋅deg) 467 52.7 67.6 33.37 487 52.7 67.6 33.37 431 41.5 54.0 27.23 435 57.6 76.1 38.12 376 52.3 69.5 36.59 609 83.8 107.3 54.45 707 95.7 123.7 60.61 693 77.9 100.3 49.83 512 105.4 138.3 73.18 586 99.9 129.4 65.30 678 106.1 134.5 66.74 678 106.1 134.5 66.74 586 99.9 129.4 65.30 750 159.5 201.3 100.11 700 142.1 182.7 92.57 995 302.7 381.4 189.45 Values of properties of structures fragments Cσ, µ, PO 2 , PCO 2 , B D DU DU 104 104

1.55 1.55

0.03 0.03

0.07 0.07

46.15 38.76 85.22 103.60 90.93 83.85 90.52 109.43 109.43 90.52 158.65 137.33 321.32

αG⋅104, K–4 1.78 3.01 1.88 2.09 2.38 1.67 1.50 1.43 2.20 1.85 2.22 2.22 1.85 1.66 1.74 1.55 Ml 79034 46602 56980 82740 65434 160900 217850 110198 178375 188853 219817 219817 188853 245324 318105 653567 PN 2 , DU 0.00 0.00

596

Fs3 Fs4 Fs5 Fs6 Fs7 Fs8 Fs9 Fs10 Fs11 Fs12 Fs13 Fs14 Fs15 Fs16

41.4 61.1 56.0 82.9 97.8 78.3 112.0 102.5 102.3 102.3 102.5 153.5 144.0 292.6

132 91 104 108 99 113 95 108 95 95 108 98 101 96

1.39 1.70 1.63 1.99 2.16 1.93 2.32 2.21 2.21 2.21 2.21 2.72 2.63 3.76

Note: MM is the molecular mass; Vm is the molar volume;

0.04 0.22 1.38 0.11 0.02 0.00 3.17 0.11 0.03 0.03 0.11 0.03 0.15 0.01

∑ ∆V i

0.09 0.56 4.12 0.27 0.03 0.00 10.23 0.26 0.07 0.07 0.26 0.07 0.37 0.03

0.01 0.03 0.24 0.02 0.00 0.00 0.60 0.02 0.00 0.00 0.02 0.00 0.02 0.00

is the Van-der-Waals volume; ρ is

i

the density; Tg is the glass transition temperature; Td is the onset temperature of intense thermal degradation; γ is the surface energy; E* is the cohesive energy; αh is the relation of hydrogen bonds energy to total cohesive energy; αdd is the relation of dipole–dipole interaction energy to total cohesive energy; αd is the relation of dispersion interaction energy to total cohesive energy; ε is the dielectric constant; E is the total energy of intermolecular interaction; Edd+h is the energy of dipole–dipole interaction and hydrogen bonds; Ed is the energy of dispersion interaction; δ is the solubility parameter; n is the refractive index; ∆U is the activation energy of low-temperature γ-transition; αG is the coefficient of thermal expansion in the glassy state; αL is the coefficient of thermal expansion in the rubbery state; nl is the polymerization degree of the polymer when the rubbery state appears; C ps is the molar heat capacity in the glassy state; C pl is the molar heat capacity in the rubbery state; R is the molar refraction; Ml is the molecular mass of polymer when the rubbery state appears; P is the polarizability; Cσ is the stress-optical coefficient; µ is the dipole moment; PO 2 , PCO 2 , PN 2 are the permeabilities by oxygen, carbon dioxide and nitrogen, respectively (the unit of measurement of permeability 1 DU = 0.45⋅10–10 cm2⋅s–1⋅atm–1).

ε

 





ε

 





Figure A-1-1. Thermomechanical curve of initial 1,4-β-D-glucomannan.

597

Table A-1-3 Designations of hemicelluloses 1 C1

Fragmentary composition and structural formulae of hemicelluloses Fragmentary composition and name Structural formulae of hemicelluloses of natural biopolymer 2 3 (Fs12)3–(Fs2)42–(Fs1)23–(Fs11)5 aspen glucomannan [208]

OH OH OH O

O

CH 2O H CH 2O H

CH2 O H O

O

O

OH

CH2

CH2 O H O OH

OH

O

O O

OH

42

OH

O OH

OH

23

5

O

OH OH

OH O

CH2 O H

C2

(Fs12)2–(Fs2)13–(Fs1)5–(Fs12)3 spruce glucomannan [116]

3

CH2 O H

CH 2O H O

O

O OH

OH

CH 2OH

CH2 O H O

O

OH

O 13

O

OH

OH

O OH

5

O

O

OH OH

OH

OH

OH

O

O 2

CH2 O H

3

597

CH2 O H

OH

598

2 (Fs10)19–(Fs3)125–(Fs6)5 aspen 4-0-methylglucuronoxylan [117]

3

598

1 C3

O

O

O

OH

O

OH

O

O OH

OH

125

COOH O

OH

OH

OH

OCH3 OH C4

O

O

O

OH

19

5

Fs3–Fs10–Fs3–Fs6–Fs8–Fs15 spruce arabinoglucuronoxylan [118] O O

O O

OH

O

O O

OH

OH

OH

OH OH

O O

O

O

O

OH

O

O

OCH3

O OH

OH

OH OH

O

OH

OH

OCH3

O

O

COOH

O

O

O

OH

OH

OH

OH OH

OH

O OH

COOH

599

1 C5

2 Fs7–(Fs4)50–Fs7 Galactouronan from plants [130]

3

COOH

COOCH3

COOH

O

O

O OH

O

OH

O

O OH

O

OH

50

O OH

OH

OH

OH

OH

OH C6

O

O

(Fs9)8–(Fs5)21–(Fs3)52–(Fs13)15–(Fs5)3 birch xylan [118] O

O

O

O

O

O O OH

O

CO OCH 3 OH

O 21

O

OH OH

OH COOCH3 3

52 OH

O

COO CH3

O

OH

O

H3CO OH

OH O COO CH3 8

COOH

15

599

600

2 Fs16–Fs14 larch arabinogalactan [60]

3 CH2OH

CH2OH O

OH

CH2OH O

OH

OH

OH

O

CH2OH

CH2OH

OH

OH

O

O OH

O OH

OH

OH

O

CH2OH O

OH

CH2OH O

OH

OH

CH2OH O

O

O

O OH

OH

OH

CH2OH O

O

OH

O

CH2OH O

CH2OH

O

OH

OH

CH2OH O

O

O CH2

O

O

OH

OH

O CH2

OH

O

[Fs2–Fs1–(Fs2)4–Fs1–Fs2]48 1,4-β-D-glucomannan [2]

OH

O

O

OH

OH

C8

OH

CH2

O

O

OH

OH

CH2 OH

O

OH

OH

OH

600

1 C7

OH

OH

O O

OH

O OH

OH

OH

48

Note: chemical formulae of hemicelluloses and the sample of 1,4-β-D-glucomannan shown in the Table were presented by Doctors of Biology V.D. Shcherbukhin and A.V. Bolobova.

601

Table A-1-4 Properties of hemicelluloses Properties of hemicelluloses δ, Tg, Td, γ, αG⋅10–4, (cal/cm3) K K dyn/cm K-1 1/2

Designations of PO 2 , PCO 2 , ∑ ∆Vi , ρ, hemiceli 3 DU DU g/cm luloses Å3 C1 146 1.39 332 546 2.90 14.3 45.5 0.03 0.07 C2 160 1.39 367 538 2.62 14.3 45.5 0.03 0.07 C3 130 1.40 499 557 1.92 13.7 53.4 0.05 0.12 C4 211 1.41 517 530 1.83 13.6 53.3 0.05 0.11 C5 156 1.42 464 580 2.07 12.8 47.2 0.19 0.47 C6 154 1.38 435 566 2.21 12.8 47.0 0.21 0.54 C7 571 1.40 419 517 1.62 14.5 46.2 0.02 0.04 C8 1,052 1.39 356 556 2.70 14.3 45.5 0.03 0.07 Note: Designations of properties of hemicelluloses correspond to those used in Table A-1-2.

PN 2 , DU 0.00 0.00 0.01 0.01 0.03 0.03 0.00 0.00

Figure A-1-2. Thermomechanical curve of dry 1,4-β-D-glucomannan.

Figure A-1-3. Debye patterns of powder-like initial (a) and dry (b) specimens of 1,4-β-D glucomannan

Appendix 2. Examples of solving the reverse problem of polymer synthesis

The reverse task concludes in synthesis, i.e. in finding a chemical formula or formulae of polymers whose properties must fall within the given range. Let poly(ether ketones) be required to be synthesized possessing the glass transition temperature above 493 K and simultaneously with the melting point below 653 K (the latter is important for successful processing). There are no limits on the values of the rest of properties (solubility parameter, density, dielectric constant, refractive index). The given task will be solved with the help of the program operating with the finest basic fragments. Let us select the number of basic fragments in repeat units, equal to 7. The solution of the given task yields the chemical formulae of poly(ether ketones), shown in Table A-2-1 (450 000 structures were calculated, from which only 24 structures fell within the required range of properties). Let us widen a little the range of properties by introduction of the lower border for the glass transition temperature, equal to 483 K. In this case, from the same number of calculated structures 84 structures of poly(ether ketones) were selected, the chemical formulae of which are shown in Table A-2-2.

603

Table A-2-1 Chemical formulae of poly(ether ketones) with the glass transition temperature Tg above 493 K and the melting point Tm below 653 K Properties of poly(ether ketones) Numbers of poly(ether ketones) Chemical formulae of poly(ether ketones) n, Tg, Tm, δ, ρ, ε, structures rel. un. K K (cal/cm3)1/2 g/cm3 rel. un. 1 2 3 4 5 6 7 8 1 495 632 9.78 1.24 2.95 1.62 −COpC6H4OpC6H4phtC10H6mC6H4− 2 495 632 9.78 1.24 2.95 1.62 −COpC6H4OpC6H4phtmC6H4ClOH6− 3 498 652 9.63 1.20 2.83 1.59 −COpC6H4OpC6H4flClOH6mC6H4− 4 498 652 9.63 1.20 2.83 1.59 −COpC6H4OpC6H4flmC6H4C10H6− 5 495 632 9.78 1.24 2.95 1.62 −COpC6H4OpC6H4C10H6phtmC6H4− 6 498 652 9.63 1.20 2.83 1.59 −COpC6H4OpC6H4C10H6flmC6H4− 7 495 632 9.78 1.24 2.95 1.62 −COpC6H4OpC6H4mC6H4phtC10H6− 8 498 652 9.63 1.20 2.83 1.59 −COpC6H4OpC6H4mC6H4flC10H6− 9 495 632 9.78 1.24 2.95 1.62 −COC10H6phtpC6H4ΟpC6H4mC6H4− 10 495 632 9.78 1.24 2.95 1.62 −COC10H6phtmC6H4pC6H4ΟpC6H4− 11 498 652 9.63 1.20 2.83 1.59 −COC10H6flpC6H4ΟpC6H4mC6H4− 12 498 652 9.63 1.20 2.83 1.59 −COC10H6flmC6H4pC6H4ΟpC6H4− 13 495 632 9.78 1.24 2.95 1.62 −COC10H6pC6H4ΟpC6H4phtmC6H4− 14 498 652 9.63 1.20 2.83 1.59 −COC10H6pC6H4ΟpC6H4flmC6H4− 15 495 632 9.78 1.24 2.95 1.62 −COC10H6mC6H4phtpC6H4ΟpC6H4− 16 498 652 9.63 1.20 2.83 1.59 −COC10H6mC6H4flpC6H4ΟpC6H4− 17 495 632 9.78 1.24 2.95 1.62 −COmC6H4phtpC6H4ΟpC6H4C10H6− 18 495 632 9.78 1.24 2.95 1.62 −COmC6H4phtC10H6pC6H4ΟpC6H4− 19 489 652 9.63 1.20 2.83 1.59 −COmC6H4flpC6H4ΟpC6H4C10H6− 20 498 652 9.63 1.20 2.83 1.59 −COmC6H4flC10H6pC6H4ΟpC6H4− 21 495 632 9.78 1.24 2.95 1.62 −COmC6H4pC6H4ΟpC6H4phtC10H6− 22 498 652 9.63 1.20 2.83 1.59 −COmC6H4pC6H4ΟpC6H4flC10H6− 23 495 632 9.78 1.24 2.95 1.62 −COmC6H4C10H6phtpC6H4ΟpC6H4− 24 498 652 9.63 1.20 2.83 1.59 −COmC6H4C10H6flpC6H4ΟpC6H4− Note: Designations are the same as in the Note to Table A-2-2. 603

604

26

489

550

9.71

1.24

2.96

1.62

−COpC6H4ΟpC6H4mC6H4phtmC6H4−

604

Table A-2-2 Chemical formulae of poly(ether ketones) with the glass transition temperature Tg above 483 K and the melting point Tm below 653 K Properties of poly(ether ketones) Numbers of poly(ether ketones) Chemical formulae of poly(ether ketones) n, Tg, Tm, δ, ρ, ε, structures rel. un. K K (cal/cm 3)1/2 g/cm3 rel. un. 1 2 3 4 5 6 7 8 1 489 626 9.71 1.24 2.96 1.62 −COmC6H4ΟpC6H4phtmC6H4pC6H4− 2 489 626 9.71 1.24 2.96 1.62 −COmC6H4ΟpC6H4phtpC6H4mC6H4− 3 493 648 9.55 1.19 2.83 1.58 −COmC6H4ΟpC6H4flmC6H4pC6H4− 4 493 648 9.55 1.19 2.83 1.58 −COmC6H4ΟpC6H4flmC6H4pC6H4− 5 489 626 9.71 1.24 2.96 1.62 −COmC6H4ΟpC6H4mC6H4phtpC6H4− 6 493 648 9.55 1.19 2.83 1.58 −COmC6H4ΟpC6H4mC6H4flpC6H4− 7 489 626 9.71 1.24 2.96 1.62 −COmC6H4ΟpC6H4pC6H4phtmC6H4− 8 493 648 9.55 1.19 2.83 1.58 −COmC6H4ΟpC6H4pC6H4flmC6H4− 9 489 626 9.71 1.24 2.96 1.62 −COpC6H4ΟmC6H4phtmC6H4pC6H4− 10 489 626 9.71 1.24 2.96 1.62 −COpC6H4ΟmC6H4phtpC6H4mC6H4− 11 493 648 9.55 1.19 2.83 1.58 −COpC6H4ΟmC6H4flmC6H4pC6H4− 12 493 648 9.55 1.19 2.83 1.58 −COpC6H4ΟmC6H4flpC6H4mC6H4− 13 498 626 9.71 1.24 2.96 1.62 −COpC6H4ΟmC6H4mC6H4phtpC6H4− 14 493 648 9.55 1.19 2.83 1.58 −COpC6H4ΟmC6H4mC6H4flpC6H4− 15 489 626 9.71 1.24 2.96 1.62 −COpC6H4ΟmC6H4pC6H4phtmC6H4− 16 493 648 9.55 1.19 2.83 1.58 −COpC6H4ΟmC6H4pC6H4flmC6H4− 17 495 632 9.78 1.24 2.95 1.62 −COpC6H4ΟpC6H4phtC10H6mC6H4− 18 495 632 9.78 1.24 2.95 1.62 −COpC6H4ΟpC6H4phtmC6H4C10H6− 19 498 550 9.71 1.24 2.96 1.62 −COpC6H4ΟpC6H4phtmC6H4mC6H4− 20 498 652 9.63 1.20 2.83 1.59 −COpC6H4ΟpC6H4flC10H6mC6H4− 21 498 652 9.63 1.20 2.83 1.59 −COpC6H4ΟpC6H4flmC6H4C10H6− 22 493 578 9.55 1.19 2.83 1.58 −COpC6H4ΟpC6H4flmC6H4mC6H4− 23 495 632 9.78 1.24 2.95 1.62 −COpC6H4ΟpC6H4C10H6phbmC6H4− 24 498 652 9.63 1.20 2.83 1.59 −COpC6H4ΟpC6H4C10H6flmC6H4− 25 495 632 9.78 1.24 2.95 1.62 −COpC6H4ΟpC6H4mC6H4phtC10H6−

605

2 498 493 495 495 498 498 495 498 495 498 489 489 495 480 495 489 489 489 493 493 498 493 498 493 493 493 489 493 489 493 495

3 652 578 632 632 652 652 632 652 632 652 626 626 632 550 632 550 626 626 648 648 652 578 652 578 648 648 626 648 626 648 632

4 9.63 9.55 9.78 9.78 9.63 9.63 9.78 9.63 9.78 6.63 9.71 9.71 9.78 9.71 9.78 9.71 9.71 9.71 9.55 9.55 9.63 9.55 9.63 9.55 9.55 9.55 9.71 9.55 9.71 9.55 9.78

5 1.20 1.19 1.24 1.24 1.20 1.20 1.24 1.20 1.24 1.20 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.24 1.19 1.19 1.20 1.19 1.20 1.19 1.19 1.19 1.24 1.19 1.24 1.19 1.24

6 2.83 2.83 2.95 2.95 2.83 2.83 2.95 2.83 2.95 2.83 2.96 2.96 2.95 2.96 2.95 2.96 2.96 2.96 2.83 2.83 2.83 2.83 2.83 2.83 2.83 2.83 2.96 2.83 2.96 2.83 2.95

7 1.59 1.58 1.62 1.62 1.59 1.59 1.62 1.59 1.62 1.59 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.62 1.58 1.58 1.59 1.58 1.59 1.58 1.58 1.58 1.62 1.58 1.62 1.58 1.62

8 −COpC6H4ΟpC6H4mC6H4flC10H6− −COpC6H4ΟpC6H4mC6H4flmC6H4− −COC10H6phtpC6H4OpC6H4mC6H4− −COC10H6phtmC6H4pC6H4OpC6H4− −COC10H6flpC6H4ΟpC6H4mC6H4− −COC10H6flmC6H4pC6H4OpC6H4− −COC10H6pC6H4ΟpC6H4phtmC6H4− −COC10H6pC6H4ΟpC6H4flmC6H4− −COC10H6mC6H4phtpC6H4OpC6H4− −COC10H6mC6H4flpC6H4OpC6H4− −COmC6H4phtmC6H4ΟpC6H4pC6H4− −COmC6H4phtpC6H4ΟmC6H4pC6H4− −COmC6H4phtpC6H4ΟpC6H4C10H6− −COmC6H4phtpC6H4ΟpC6H4mC6H4− −COmC6H4phtC10H6pC6H4ΟpC6H4− −COmC6H4phtmC6H4pC6H4ΟpC6H4− −COmC6H4phtpC6H4mC6H4ΟpC6H4− −COmC6H4phtpC6H4pC6H4ΟmC6H4− −COmC6H4flmC6H4ΟpC6H4pC6H4− −COmC6H4flpC6H4ΟmC6H4pC6H4− −COmC6H4flpC6H4ΟpC6H4C10H6− −COmC6H4flpC6H4ΟpC6H4mC6H4− −COmC6H4flC10H6pC6H4ΟpC6H4− −COmC6H4flmC6H4pC6H4ΟpC6H4− −COmC6H4flpC6H4mC6H4ΟpC6H4− −COmC6H4flpC6H4pC6H4ΟmC6H4− −COmC6H4mC6H4ΟpC6H4phtpC6H4− −COmC6H4mC6H4ΟpC6H4flpC6H4− −COmC6H4pC6H4ΟmC6H4phtpC6H4− −COmC6H4pC6H4ΟmC6H4flpC6H4− −COmC6H4pC6H4ΟpC6H4phtC10H6−

605

1 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57

606

C

–pht–

C

O, C

8 −COmC6H4pC6H4ΟpC6H4phtmC6H4− −COmC6H4pC6H4ΟpC6H4flC10H6− −COmC6H4pC6H4ΟpC6H4flmC6H4− −COmC6H4C10H6phtpC6H4OpC6H4− −COmC6H4C10H6flpC6H4OpC6H4− −COmC6H4mC6H4phtpC6H4OpC6H4− −COmC6H4mC6H4flpC6H4OpC6H4− −COmC6H4pC6H4phtmC6H4OpC6H4− −COmC6H4pC6H4phtpC6H4OmC6H4− −COmC6H4mC6H4flmC6H4OpC6H4− −COmC6H4pC6H4flpC6H4OmC6H4− −COpC6H4phtmC6H4ΟpC6H4mC6H4− −COpC6H4phtpC6H4ΟmC6H4mC6H4− −COpC6H4phtmC6H4mC6H4ΟpC6H4− −COpC6H4phtmC6H4pC6H4ΟmC6H4− −COpC6H4flmC6H4ΟpC6H4mC6H4− −COpC6H4flpC6H4ΟmC6H4mC6H4− −COpC6H4flmC6H4mC6H4ΟpC6H4− −COpC6H4flmC6H4pC6H4ΟmC6H4− −COpC6H4mC6H4ΟpC6H4phtmC6H4− −COpC6H4mC6H4ΟpC6H4flmC6H4− −COpC6H4pC6H4ΟmC6H4phtmC6H4− −COpC6H4pC6H4ΟmC6H4flmC6H4− −COpC6H4mC6H4phtmC6H4OpC6H4− −COpC6H4mC6H4phtpC6H4OmC6H4− −COpC6H4mC6H4flmC6H4ΟpC6H4− −COpC6H4mC6H4flpC6H4OmC6H4−

O

–fl–

, –mC6H4–

, –pC6H4–

.

2) Tg is the glass transition temperature; Tm is the melting point; δ is the solubility parameter; ρ is the density; ε is the dielectric constant; n is the refractive index.

606

1 2 3 4 5 6 7 58 489 550 9.71 1.24 2.96 1.62 59 498 652 9.63 1.20 2.83 1.59 60 493 578 9.55 1.19 2.83 1.58 61 495 632 9.78 1.24 2.95 1.62 62 498 652 9.63 1.20 2.83 1.59 63 489 550 9.71 1.24 2.96 1.62 64 493 578 9.55 1.19 2.83 1.58 65 489 626 9.71 1.24 2.96 1.62 66 489 626 9.71 1.24 2.96 1.62 67 493 648 9.55 1.19 2.83 1.58 68 493 648 9.55 1.19 2.83 1.58 69 489 626 9.71 1.24 2.96 1.62 70 489 626 9.71 1.24 2.96 1.62 71 489 626 9.71 1.24 2.96 1.62 72 489 626 9.71 1.24 2.96 1.62 73 493 648 9.55 1.19 2.83 1.58 74 493 648 9.55 1.19 2.83 1.58 75 493 648 9.55 1.19 2.83 1.58 76 493 648 9.55 1.19 2.83 1.58 77 489 626 9.71 1.24 2.96 1.62 78 493 648 9.55 1.19 2.83 1.58 79 489 626 9.71 1.24 2.96 1.62 80 493 648 9.55 1.19 2.83 1.58 81 489 626 9.71 1.24 2.96 1.62 82 489 626 9.71 1.24 2.96 1.62 83 493 648 9.55 1.19 2.83 1.58 84 493 648 9.55 1.19 2.83 1.58 Note: 1) The following designations of the basic fragments are used in chemical formulae of poly(ether ketones):

Appendix 3. The example of solving the complex problem – analysis of the chemical structure of phenol formaldehyde resin

The example of solving the complex problem of polymer synthesis belongs to the analysis of the chemical structure of one of the representatives of polymer networks – phenol-formaldehyde resin widely applied, in particular, to production of pressed woody articles. Before analyzing the structure of a polymer network based on phenol formaldehyde resin, it should be noted that although phenol formaldehyde resins (PFR) are one of the oldest representatives of high cross-linked polymer networks, their structure is still of great interest [201]. There is a broad list of works devoted to the analysis of the structure and properties of PFR. However, there is still no general point of view on the chemical structure of the network formed by these resins. The reason is, apparently, in the fact that due to proceeding of the PFR curing the network structure obtained may be different. Another reason is associated with the fact that OH-groups capable of forming hydrogen bonds are present in the network structure. These hydrogen bonds may be displayed in both intermolecular interaction of these groups disposed in neighboring PFR chains and at the sacrifice of the same interaction OH-groups disposed in the same repeat unit.

Figure A-3-1. Schematic representation of a network of hydrogen bonds (a) appearing between neighboring chains and (b) within the same repeat unit.

The meaning of the notions of ‘intermolecular interaction’ and ‘intramolecular interaction’ in the context of the approach under discussion should be explained with the help of a simplified scheme represented in Figure A-3-1. Figure A-3-1a demonstrates the case corresponding to the intermolecular interaction, which leads to the formation of a network of physical (hydrogen) bonds linking chains. Clearly, the formation of this network promotes an increase of the glass transition temperature. The case displayed in Figure A-3-1b reflects the situation when two OH-groups are in the same unit of the linear fragment of PFR, and hydrogen bonding then occurs in the frames of the same unit, and the network of physical bonds between neighboring ones is not formed. This problem was analyzed above in detail on the example of poly(imidophenyl quinoxalines) and poly(amidophenyl quinoxalines). It stands to reason that various types of intermolecular interaction (hydrogen bonding) causing a significant influence on PFR properties, as it will be shown below, may coexist in reality. In cured PFR, according to the existing data, the following structures (repeating fragments of the network) may exist:

608

Structure 1:

CH2

CH2

CH2 OH

This structure is included only in the network the repeat unit of which is marked by dotted lines. The glass transition temperature of the network will be calculated using equation (IV.85). According to the definition of the chemical structure of the cross-linked point of the network, the structure of the cross-linked point is formed by a selection of atoms, including the one from which the chain is branched, and the neighboring atoms with their substituents, as well. For structure 1 of the network, the structure of the cross-linked point is marked by dotted lines: CH2

OH Clearly, the whole cross-linked point contains three such selections of atoms. Then for the structure 1, we obtain*:    ∑ ∆Vi  = 3(∆VC,19 + ½∆VC,12 + ½⋅2∆VH,124) + 2∆VC,18 + 2∆VH,124 + ∆VC,20 + ∆VO,133  i 1 + ∆VH,125 = 3(8.4 + ½⋅12.6 + ½⋅2⋅2.0) + 2⋅12.7 + 2⋅2.0 + 11.65 + 5.2 + 4.7 = 101.1 Å3;    ∑ ai ∆Vi + ∑ b j  = aC(2∆VC,18 + ∆VC,20) + aH(2∆VH,124 + ∆VC,125) + aO,s∆VO,133 + bh  i  j  1 = [0.021(2⋅12.7 + 11.65) + 19.93(2⋅2.0 + 4.7) 7.03⋅5.2 – 139.6]⋅10–3 = 71.6⋅10–3 Å3 K–1;    ∑ K i ∆Vi  = KC(∆VC,19 + ½∆VC,12) + KH2⋅1/2∆VH,124 = [1.15(8.4 + ½⋅12.6) +  i 1 2.307⋅2⋅1/2⋅2.0]⋅10–3 = 21.5⋅10–3 Å3K–1.       Substituting values of  ∑ ∆Vi  ,  ∑ ai ∆Vi + ∑ b j  , and  ∑ K i ∆Vi  into j  i 1  i  i 1 1 equation (IV.85), we obtain the following value of the glass transition temperature of the network in the case of the ideal structure 1:

*

Here and below, numbers of atoms correspond to their numbers in Table 3.

609

Tg =

101.1 ⋅103 = 743 K. 21.5 ⋅ 3 + 71.6

(A-3-1)

The calculated value of Tg is significantly above the range of experimental values, Tg,exper, shown in Table A-3-1 and, consequently, the real PFR network will differ by structure from the ideal structure 1. Table A-3-1 Experimental values of the characteristics of cured PFR Property name Unit Limits of measurements Glass transition temperature, Tg,exper K 343–433 1.24–1.33 g/cm3 Density, ρ (exper.) Refractive index, n (exper.) rel. un. 1.57–1.63 K–1 Coefficient of volumetric expansion, αG (exper.) (1.80–2.25)⋅10–4 s 29–48 cal/(mol⋅deg) Molar heat capacity, (exper.)

Cp

Structure 2: CH2

CH2 HO CH2 OH

This possible structure of PFR relates to a linear polymer (the repeat unit is marked by dotted lines). For this structure, V ∆ ∑ i = 3∆VC,19 + 2∆VC,18 + 1/2⋅2∆VC,12 + ∆VC,20 + ∆VC,40 + 4⋅1/2∆VH,124 + 2∆VH,124 i

+ 2∆VH,124 + 2∆VH,125 + ∆VO,133 + ∆VO,132 = 3⋅8.4 + 2⋅12.7 + 1/2⋅2⋅12.6 + 11.65 + 16.0 + 4⋅1/2⋅2.0 + 2⋅2.0 + 2⋅2.0 + 2⋅4.7 + 5.2 + 5.6 = 123.05 Å3; ∑ ai ∆Vi = aC(3∆VC,19 + 2∆VC,18 + 1/2⋅2∆VC,12 + ∆VC,20 + ∆VC,40) + aH(4⋅1/2∆VH,124 + i

2∆VH,124 + 2∆VH,124 + 2∆VH,125) + aO,s(∆VO,133 + ∆VO,132) = [0.021(3⋅8.4 + 2⋅12.7 + 1/2⋅2⋅12.6 + 11.65 + 16.0) + 19.98(4⋅1/2⋅2.0 + 2⋅2.0 + 2⋅2.0 + 2⋅4.7) + 7.03(5.2 + 5.6)]⋅10–3 = 505.4⋅10–3 Å3K–1. If both OH-groups participate in the formation of hydrogen bonds between chains (as shown in Figure A-3-1), then

∑bj j

= 2bh + bM;

∑bj

= (–139.6⋅2 + 16.0)⋅10–3 = –263.2⋅10–3 Å3K–1.

j

Substitution of all values of parameters into equation (IV.41) leads to the following value of Tg of the ideal structure 2: Tg =

123.05 ⋅103 = 508 K. 505.4 − 263.2

(A-3-2)

610

Similar to the structure 1, this value is higher than the experimental temperature interval in which the α-transition is observed for PFR. Structure 3:

CH2

CH2 OH

This structure forms only linear chains, the repeat unit of which is marked by dotted lines. For structure 3, we obtain:    ∑ ∆Vi  = 2∆VC,19 + ∆VC,20 + 3∆VC,18 + 1/2⋅2∆VC,12 + 1/2⋅4∆VH,124 + ∆VH,125 +  i 3 3∆VH,124 + ∆VO,133 = 2⋅8.4 + 11.65 + 3⋅12.7 + 1/2⋅2⋅12.6 + 1/2⋅4⋅2.0 + 4.7 + 3⋅2.0 + 5.2 = 99.05 Å3;    ∑ ai ∆Vi  = aC(2∆VC,19 + ∆VC,20 + 3∆VC,18 + 1/2⋅2∆VC,12) + aH(1/2⋅4∆VH,124 +  i 3 ∆VH,125 + 3∆VH,124) + aO,s⋅∆VO,133 = [0.021(2⋅8.4 + 11.65 + 3⋅12.7 + 1/2⋅2⋅12.6) + 19.98(1/2⋅4⋅2.0 + 4.7+ 3⋅2.0) + 7.03 5.2]⋅10–3 = 331.9⋅10–3 Å3K–1. ∑ b j = 2bh + bM; ∑ b j = (–139.6 + 16.0)⋅10–3 = –123.6⋅10–3 Å3K–1. j

j

Substitution of all these values of parameters into equation (IV.41) leads to the following value of Tg of the ideal structure 3: Tg =

99.05 ⋅ 103 = 476 K. 331.9 − 123.6

(A-3-3)

This value of Tg is somewhat above the temperature range of the α-transition for PFR. Structure 4:

CH2

CH2 O

This structure forms a network, the repeating fragment of which is marked by dotted lines. The structure of the cross-linked point of this network is the following (marked by dotted lines):

H2C

CH2 O

611

For structure 4, we obtain:    ∑ ∆Vi  = 2∆VC,19 + ∆VC,20 + 1/2⋅2∆VC,12 + 3∆VC,18 + 3∆VH,124 + 4⋅1/2∆VH,124 +  i 4 ∆VO,131 = 3⋅8.4 + 11.65 + 1/2⋅2⋅12.6 + 3⋅12.7 + 3⋅2.0 + 4⋅1/2⋅2.0 + 2.1 = 91.25 Å3;    ∑ ai ∆Vi  = aC(3∆VC,18) + aH(3∆VH,124) = (0.021⋅3⋅12.7 + 19.98⋅3⋅2.0)⋅10–3 =  i 4 120.7⋅10–3 Å3K–1; ∑ b j = 0; j

   ∑ K i ∆Vi  = KC(2∆VC,19 + ∆VC,20 + 1/2⋅2∆VC,12) + KH⋅4⋅1/2∆VH,124 + KO∆VO,131 =  i 4 [1.15(2⋅8.4 + 11.65 + 1/2⋅2⋅12.6) + 2.307⋅4⋅1/2⋅2.0 + 0.058⋅2.1]⋅10–3 = 56.5⋅10–3 Å3K– 1 . Substituting these values into equation (IV.85), we obtain the following value of Tg for the ideal network, composed from the structure 4: Tg =

91.25 ⋅103 = 515 K. 56.5 + 120.7

(A-3-4)

Hence, the glass transition temperature of this cross-linked polymer network would be quite high compared with Tg,exper. Structure 5: CH2

CH2 HO

CH2 OH From the viewpoint of the gross-formula, this structure is identical to the structure 2, but in the present case, hydrogen bonding appears within the single repeat unit. Such a structure is described in ref. [99]. If hydrogen bonds are formed between neighboring OH-groups disposed within the same repeat unit, then, as mentioned above, the physical network between chains stipulated by hydrogen bonds is not formed. Then calculating the glass transition temperature, the value of ∑ b j is calculated in the following way: because j

this structure is linear, the constant bM must be taken into calculation when considering the m-substitution in an aromatic cycle; moreover, there are two branches from the aromatic cycle, which requires introduction of two constants bd. Then ∑ b j j

= bM + 2bd = [16.0 – 2⋅55.4]⋅10–3 = –94.8⋅10–3 Å3K–1. Substituting values

∑ ai ∆Vi i

and

∑bj

∑ ∆Vi , i

into equation (IV.85), the following value of the glass transition

j

temperature is obtained for the structure 5:

612

Tg =

123.05 ⋅ 103 = 300 K. 505.4 − 94.8

(A-3-5)

This value of Tg falls below the range of the α-transition for cured PFR. As indicated, no calculated values of the glass transition temperature of the ideal structures of PFR discussed falls within the range of experimental values of the glass transition temperature, Tg,exper. It may therefore be assumed that there is a more complicated structure of cured PFR than the considered ideal ones; this has been indicated by many investigators. Most probably, the real structure of PFR consists of the selection of the considered ideal structures. To state the most probablr real PFR structure, let us calculate, besides Tg, the following characteristics of cured PFR: density ρ, refractive index n, coefficient of volumetric expansion αG, and molar heat capacity C ps . Selection of these characteristics is stipulated by both their importance and sensitivity to changes of the structural formula of the substance and the fact that for various ideal PFR structures, as the glass transition temperature increases, values of other characteristics may increase or decrease, which is important for search of the most probable structure of PFR by the method of experiment design (see below). The calculated values of PFR density for structures 1–5, obtained due to equation (II.6), are indicated in Table A-3-2. Table A-3-2 Calculated values of Tg, ρ, n, αG and C sp for the ideal structures of cured PFR Ideal structure of PFR Structure 1 Structure 2 Structure 3 Structure 4 Structure 5

Tg, K

ρ, g/cm3

n, rel. un.

αG⋅104, K–1

743 507 476 515 300

1.253 1.250 1.205 1.301 1.250

1.621 1.583 1.604 1.645 1.583

1.30 3.20 2.02 1.86 3.20

C sp , cal/(mol⋅deg) 31.9 42.4 31.4 26.1 42.4

Let us calculate the refractive index n by equation (VIII.2), which contains the molar refraction summed up from the refraction indices of separate atoms and constants for different types of bonds (double, triple). For structure 1, we obtain (values of Ri are taken from [28]): R1 = 3⋅(RC + 1/2⋅RC + RH) + 2RC + 2RH + RC + RO′ + RH + 3R≠ = 3⋅(2.418 + 1/2⋅2.418 + 1.10) + 2⋅2.418 + 2⋅1.10 + 2.418 + 1.525 + 1.10 + 3⋅1.733 = 31.459 cm3/mol. For structure 2: R2 = 8RC + 8RH + 2RO′ + 3R≠ = 8⋅2.418 + 8⋅1.10 + 2⋅1.525 + 3⋅1.733 = 36.393 cm3/mol. For structure 3: R3 = 7RC + 6RH + RO′ + 3R≠ = 7⋅2.418 + 6⋅1.10 + 1.525 + 3⋅1.733 = 30.25 cm3/mol. For structure 4: R4 = 7RC + 5RH + RO< + 3R≠ = 7⋅2.418 + 5⋅1.10 + 1.643 + 3⋅1.733 = 29.268 cm3/mol. For structure 5, the value R5 coincides with the value R2. Values of n for various structures calculated by equation (VIII.2) are shown in Table A-3-2. Heat capacity C ps in the glassy state of the polymer was calculated by correlation (XVI.1).

613

The value αG is directly connected with the glass transition temperature Tg by the correlation:

αG =

0.096 . Tg ( K )

(A-3-6)

The calculated values of C ps and αG for all five ideal structures are shown in Table A-3-2. Comparison of the calculated values of PFR characteristics for possible ideal structures, shown in Table A-3-2, with their experimental values (see Table A-3-1) enables us to conclude that cured PFR does not represent an ideal network, but contains a set of structures; this set can be determined using the method of experiment design for multi-component systems with composing simplex networks and polynomial ‘composition – property’ models. For independent variables X of these models, let us assume the above-considered ideal structures the combination of which will determine the real structural composition of cured PFR: x1 for structure 1; x2 for structure 2; x3 for structure 3; and x4 for structure 4. For the response function Y, the following properties of cured PFR will be taken: glass transition temperature, Tg (K); density, ρ (g/cm3); refractive index, n (rel. un.); coefficient of volumetric expansion, αG (K–1); and molar heat capacity, C ps (cal/(mol⋅deg)). As indicated, instead of the ideal structure 2, the structure 5 is assumed as the independent variable; this structure differs by the existence of hydrogen bonding of OH-groups within the same repeat unit which, with all other characteristics being the same, provides for lower glass transition temperatures (see Table A-3-2). The dependence of the response functions Y on variables X will be searched for in the form of the second order model [70]: Y = ∑βij + ∑βijxixj; where

β i = y i;

1 ≤ i ≤ 4;

1 ≤ j ≤ 4,

βij = 4yij – 2yi – 2yj.

(A-3-7) (A-3-8)

Design of the experiment and appropriate simplex lattice are shown in Table A-3-3 and Figure A-3-2a, respectively. Table A-3-3 Matrix of the experimental design and calculated values of PFR at the experimental design Coordinates of Calculated values of PFR Point of the experiment design points experiment C sp , Tg, n, ρ, αG⋅104, design x1 x2 x3 x4 3 –1 rel. un. K g/cm K cal/(mol⋅deg) y1 1 0 0 0 743 1.253 1.621 1.30 31.90 y2 0 1 0 0 300 1.250 1.583 3.20 42.40 y3 0 0 1 0 476 1.205 1.604 2.02 31.40 y4 0 0 0 1 515 1.301 1.645 1.86 26.10 y12 ½ 1/2 0 0 410 1.251 1.600 2.34 37.20 y23 0 1/2 1/2 0 359 1.232 1.594 2.67 36.90 y13 ½ 0 1/2 0 582 1.232 1.613 1.65 31.65 y14 ½ 0 0 1/2 615 1.276 1.633 1.56 29.00 y24 0 1/2 0 1/2 364 1.272 1.614 2.64 34.25 y34 0 0 1/2 1/2 494 1.254 1.624 1.94 28.75

614

Figure A-3-2. Designation of responses at the points of simplex lattice: a) experimental design points; b) control design points.

As indicated by the diagram, the experimental design points with the single index, yi, are located in the tetrahedron apexes, with two indices, yij – in the middle of the tetrahedron edges possessing apexes, i and j. Therewith, values of the response functions Tg, ρ, n, αG, and C ps in the points of the experimental design yi, located in the apexes of the tetrahedron, are calculated by equations (IV.85), (II.6), (VIII.2), (XVI.1) and (A-3-6), and in intermediate points of the experiment, i.e. with two or more indices at y, by the equations: – for the glass transition temperature,       α 1  ∑ ∆Vi  + α 3  ∑ ∆Vi  + α 4  ∑ ∆Vi  +  i 1  i 3  i 4 → Tg =        α 1  ∑ α i ∆Vi + ∑ b j  +  ∑ K i ∆Vi   + α 3  ∑ α i ∆Vi + ∑ b j  + j j 1   i 1  i  i 3   + α 5  ∑ ∆Vi   i 5 → ;        + α 4  ∑ α i ∆Vi + ∑ b j  +  ∑ K i ∆Vi   + α 5  ∑ α i ∆Vi + ∑ b j  j j  i  4  4  i  i 5 –

for the density,

ρ=

–

0.681(α1 M 1 + α 3 M 3 + α 4 M 4 + α 5 M 5 )

;

(A-3-10)

          N A α 1  ∑ ∆Vi  + α 3  ∑ ∆Vi  + α 4  ∑ ∆Vi  + α 5  ∑ ∆Vi   1  i 3  i 4  i  5    i

; (A-3-11)

          N A α1  ∑ ∆Vi  + α 3  ∑ ∆Vi  + α 4  ∑ ∆Vi  + α 5  ∑ ∆Vi     i 1  i 3  i 4  i  5 

for the refractive index,

n2 −1 = n2 + 2

–

(A-3-9)

0.681(α 1 R1 + α 3 R3 + α 4 R4 + α 5 R5 )

for the molar heat capacity,

615

      C ps = α1  ∑ C ps ,i ∆Vi  + α 3  ∑ C ps ,i ∆Vi  + α 4  ∑ C ps ,i ∆Vi  +  i 1  i 3  i 4   + α 5  ∑ C ps ,i ∆Vi  + C 0 ;  i 5

(A-3-12)

C ps = α 1C ps ,1 + α 3C ps ,3 + α 4 C ps , 4 + α 5C ps ,5 + C 0 . The coefficient of volumetric expansion is calculated by correlation (A-3-6), the value Tg being determined from equation (A-3-9). In correlations (A-3-9) – (A-312), α1, α3, α4, and α5 are the molar parts of the structures 1, 3, 4, and 5, respectively; therewith, α1 = x1, α3 = x3, α4 = x4, and α5 = x5. Using the response values in the design points shown in Table A-3-3 and equations (A-3-8) for calculation of the coefficient β for the second order model (A-37), polynomial models for cured PFR are found, in which insignificant coefficients are neglected: – for the glass transition temperature, K: Tg = 743x1 + 300x2 + 476x3 + 515x4 – 446x1x2 – 116x1x3 – – 56x1x4 – 116x2x3 – 174x2x4; –

for the density, g/cm3:

ρ = 1.253x1 + 1.250x2 + 1.205x3 + 1.301x4 + 0.012x1x3 + + 0.018x2x3 – 0.014x2x4; –

(A-3-15)

for the coefficient of volumetric expansion, K–1:

αG = (1.3x1 + 3.2x2 + 2.02x3 + 1.86x4 + 0.36x1x2 + + 0.24x2x3 + 0.44x2x4)⋅10–4; –

(A-3-14)

for the refractive index, rel. un.: n = 1.621x1 + 1.583x2 + 1.604x3 + 1.646x4 – 0.009x1x2;

–

(A-3-13)

(A-3-16)

for the molar heat capacity, cal/(mol⋅deg): C ps = 31.9x1 + 42.4x2 + 31.4x3 + 26.1x4 + 0.2x1x2.

(A-3-17)

Using polynomial models (A-3-13) – (A-3-17) obtained and equations (IV.85), (II.6), (VIII.2), (XVI.1), and (A-3-6) in the control design points shown in Figure A-3-2b (the design point with three indices, yijk, locates in the middle of the tetrahedron designe with apexes i, j and k), the properties of cured PFR are calculated. As indicated in Table A-3-2, the relative error of the properties prognosis for cured PFR does not exceed 1.7%, which is quite acceptable for application to polynomial models both in order to determine the real structure of cured PFR and the degree of influence of the ideal structure type on the PFR properties. In particular, indicated as an example in Figure A-3-3 is graphic interpretation of the polynomial model of the glass transition temperature for PFR (A-3-13) in the area of change of

616

Control design points

Coordinates of control design points

Values of PFR properties in control design points

x1

x2

x3

x4

Tg/T ′g

ρ/ρ′

n/n′

(αG/αG′)⋅104

y123

1/3

1/3

1/3

0

y124

1/3

1/3

0

1/3

y134

1/3

0

1/3

1/3

y234

0

1/3

1/3

1/3

428 431 436 442 559 558 394 397

1.238 1.259 1.265 1.266 1.253 1.254 1.252 1.253

1.603 1.602 1.617 1.615 1.623 1.624 1.611 1.611

2.240 2.235 2.200 2.200 1.720 1.714 2.440 2.436

C sp C sp 35.23 35.23 33.47 33.47 29.80 29.80 33.3 33.3

′

Relative error of the predicted properties of PFR, % δn δαG δTg δρ δCs

p

– 0.7

– 1.7

0.1

0.2

0

– 1.4

– 0.1

0.1

0

0

0.2

– 0.1

0.1

0.4

0

– 0.8

– 0.1

0

0.2

0

Notes: 1. Shown in the numerator are properties of PFR calculated by equations (109), (6), (VII.2), (XVI.1), and (A-3-6). The denominator indicates the properties calculated by polynomial models (A-3-13) – (A-3-17). 2. Relative error of the predicted properties of PFR is calculated by the formula: δy ijjk =

′ y ijk − y ijk ⋅ 100% . ′ y ijk

616

Table A-3-4 Errors of the predicted properties of cured PFRs

617

the ideal structures 1, 3 and 5 ratio (in the absence of the ideal structure 4). As indicated, isolines of the glass transition temperature of PFR represent straight lines, suggesting that contributions of separate ideal structures into formation of properties of the real desired PFR structure are additive and, the more so, the glass transition of PFR is preferably determined by the relative concentration of the ideal structures 1 and 5.

Figure A-3-3. Isolines of the glass transition temperature Tg of PFR in the region of ideal structures x1, x2 and x3 (x4 = 0).

Searching for the real structure of cured PFR includes the determination of the ratio between contents of the ideal structures 1, 3, 4, and 5, at which border conditions on the experimental values of the resin properties, indicated in Table A-3-1, are fulfilled. The acceptable selection of these ideal structures Ω x (at ∑ xi = 1, 0 ≤ xi ≤ 1, i

i = 1 − 4 ) is set on in the following sequence. When the concentration of the structure 4 is fixed (x4 = const) for every tested property of the resin (Tg, ρ, n, αG, and C ps ), regions of acceptable selections of the remaining three ideal structures are determined in the plane of change of variables x1, x2 and x3. The desired value x1x4 =const is obtained by the consequent superimposition of these regions. The example of this procedure at x4 = const is indicated in Figure A-3-4. As indicated, such indices of cured PFR as the refractive index (Figure A-3-4c) and the molar heat capacity (Figure A-3-4e) cause no influence on the formation of the region of the acceptable selection of the ideal structures x1x4 =0 (Figure A-3-4d). Apparently, the influence of these characteristics of PFR is evident only for ideal structure 4 and increases with the concentration of the latter (Figure A-3-5).

618

Figure A-3-4. Schematic representation of the search procedure for an acceptable set Ωx of ideal PFR 7 structures for x4 = 0. Showing domains of the acceptable sets of structures: (a) [[ =

º

º

ρ

[[ = for the density; (c) Q G [[ = for the refractive index; (d) x1x4 =0 for the coefficient of volumetric & expansion; (e) [ [ = for the molar heat capacity; (f) x x =0 for the ideal PFR

for the glass transition temperature of cured PFR: (b)

º

º

 

1 4

structures with the coordinates of vertices T1 (0.35; 0.34; 0.31; 0.00); T2 (0.34; 0.35; 0.31; 0.00); T3 (0.55; 0.45; 0.00; 0.00).

The region of acceptable selection of the ideal structures of cured PFR is determined by consecutive sorting out of the regions x1x4 =const at variation of the structure x4 content with step 0.01 from 0 to 1. Consequently, it is obtained that that the desired region Ω x represents an improper figure and the coordinates of apexes of this figure are shown in Figure A-3-6. Disposition of Ω x regions in the factor space of ideal structures of PFR enables us to conclude that the real structure of cured PFR may be represented only by the combination of linear (structures 3 and 5) and network (structures 1 and 4) fragments of the polymeric chain; this has also been confirmed by other investigators [99].

Figure A-3-5. Effect of the ideal structure 4 on the change of the domain Ωx of acceptable set of ideal structures of cured PFR for the refractive index (I) and for the molar heat capacity (II) at x4 = 0 (a); 0.2 (b); 0.4 (c).

619

For the quantitative estimation of the properties of PFR containing various types of structures, let us substitute all calculated parameters into equations (A-3-13) – (A-3-17). Consequently, we obtain the following expressions for calculation of the glass transition temperature Tg, density ρ, refractive index n, coefficient of volumetric expansion αG, and molar heat capacity C ps : Tg =

ρ=

α1 ⋅101.1 + α 5 ⋅123.05 + α 3 ⋅ 99.05 + α 4 ⋅ 91.25 3 ⋅10 ; α1 ⋅136.1 + α 5 ⋅ 410.6 + α 3 ⋅ 208.3 + α 4 ⋅177.2

0.681(α1 ⋅ 112 + α 5 ⋅ 136 + α 3 ⋅ 106 + α 4 ⋅ 105) ⋅ 103 ; 0.6023(α1 ⋅ 101.1 + α 5 ⋅ 123.05 + α 3 ⋅ 99.05 + α 4 ⋅ 91.25)

(A-3-18)

(A-3-19)

n 2 − 1 0.681(α1 ⋅ 31.459 + α 5 ⋅ 36.393 + α 3 ⋅ 30.25 + α 4 ⋅ 29.268) 3 ⋅10 ; (A-3-20) = n 2 + 2 0.6023(α1 ⋅101.1 + α 5 ⋅123.05 + α 3 ⋅ 99.05 + α 4 ⋅ 91.25)

αG = 0.0096/Tg; C ps = α1⋅31.9 + α5⋅42.4 + α3⋅31.4 + α4⋅26.1,

(A-3-21) (A-3-22)

where α1, α3, α4, and α5 are the molar parts of the structures 1, 3, 4 and 5, respectively. One of the possible relations between relative content of ideal structures, responded to the region of admissible selection (Figure A-3-6) has the following form: α1 = 0.345, α5 = 0.345, α3 = 0.2, and α4 = 0.11.

Figure A-3-6. Coordinates of vetrices of the domain of admissible set of ideal structures Ωx for cured PFR: T1 (0.35; 0.34; 0.31; 0.00); T2 (0.34; 0.35; 0.31; 0.00); T3 (0.55; 0.45; 0.00; 0.00); T4 (0.00; 0.22; 0.13; 0.65).

Substituting these values into correlations (A-3-18) – (A-3-22), for the real network we obtain: Tg = 429 K; ρ = 1.248 g/cm3; n = 1.6057; αG = 2.238⋅10–4 K–1; C ps = 34.8 cal/(mol⋅deg); as indicated (see Figure A-3-3), all these values fall within the range of experimental values.

620

Taking into account the presence of a narrow region of the acceptable set of ideal structures for cured PFR (see Figure A-3-6), it may be concluded that the real structure of the network obtained is close to the most probable one. Hence, the approach described in the Section IV.4, combined with the method of experiment design, enables, firstly, to made definite conclusions about the structure of cross-linked systems, basing on the comparison of experimental and calculated characteristics of the network. Secondly, the examined problem of the analysis of phenol formaldehyde resin structure relates to the mixed problem, because the direct problem is solved in the initial stage – the properties of ideal structures of PFR are determined by their chemical structure. In the second stage of investigations, solution of the reverse problem is considered – the chemical structure of PFR is searched, which provides for the desirable set of properties of this resin. In this case, such set of properties is given by their experimental values shown in Table A-3-1. In the present example, note also the application of the approach to solving the reverse problem of polymers synthesis, different from the one described in Appendix 2.

Appendix 4. Application of the approach to multicomponent copolymers

Usually, analysis of the structure and properties of copolymers was performed for the systems containing two components. It has been was performed much less frequently for triple copolymers. In this appendix, applicability of the approach, described in the present monograph, to analysis of the structure and properties of copolymers containing from three to five copolymers will be discussed. Simultaneously, let us compare experimental and calculated values of the physical characteristics for both homopolymers and homopolymer-based multicomponent copolymers. To analyze the properties of multicomponent copolymers, six monomers are chosen in ref. [39], used in reactions of polymerization and copolymerization: methyl methacrylate (MMA), butyl methacrylate (BMA), butyl acrylate (BA), n-nonyl acrylate (NA), 2-ethylhexyl acrylate (EHA), and n-heptyl acrylate (HA). Homopolymers and copolymers based on these compounds are fully amorphous highmolecular substances, which are easily formed in a block and suitable for investigation of thermal and optical characteristics. Indicated in Table A-4-1 is the composition of five copolymers synthesized in ref. [39]. Calculation of the glass transition temperature Tg for multicomponent copolymers is performed by equations (IV.55) and (IV.57). The first of these equations for calculation of the glass transition temperature of copolymers requires no understanding of the experimental glass transition temperatures of homopolymers. Equation (IV.57) contains values of glass transition temperature of homopolymers, for calculation of Tg of copolymers experimental values of Tg for appropriate homopolymers being used. Table A-4-1 Copolymer 1 2 3 4 5

MMA 0.333 0.250 0.250 0.200 0.250

Composition of copolymers Molar parts of units in copolymer BMA BA NA 0.333 0.333  0.250 0.250 0.250 0.250 0.250  0.200 0.200 0.200 0.250 0.250 

EHA   0.250 0.200 

HA     0.250

Density is calculated by equations (II.7), (A-4-1) and (A-4-2). The first of them is approximate, obtained on the base of suggestion that the coefficient of molecular packing is approximately the same for all polymers, and equals kavg = 0.681 for all block polymers at room temperature. However, for polymer and copolymers existing in the rubbery state at room temperature, it is desirable to take into account temperature dependences of the coefficient of molecular packing, k, in the density calculation, because the difference of the real coefficient of packing for them from the average value kavg, increases with a decrease of the glass transition temperature. Equations (A-4-1) and (A-4-2) are obtained with regard to this circumstance and enable, as indicated below, to calculate more accurately the density of polymers and copolymers. For the latter, we obtain:

622

Tg, K Td, K Cσ, B ρ, g/cm3 αG⋅104, K-1 −3.30 1.17 − 1.23 378 2.70 623 − 2.85 1.17; 1.17 377 2.55 629 PBMA − − − − 300 1.48 2.82 17.7 − 18.4 1.06 1.09; 1.06 287 1.50 2.71 18.2 27.2 3.05 627 16.6 PBA − − − 221 1.47 18.2 − 18.4 30.7 2.80 1.04 1.11; 1.05 242 1.50 2.76 18.4 28.0 3.05 627 32.2 PNA − − − − − − − − 215 1.04; 0.97 219 1.51 2.58 17.5 25.3 3.05 626 40.5 PEHA  − − − − − − − −  1.05; 0.99 242 1.51 2.60 17.5 3.05 626 39.4 PHA − − − − − − − − 220 1.06; 0.99 225 1.51 2.63 17.7 26.1 3.05 626 38.1 Notes: 1. * - shown in the numerator are experimental values of physical characteristics; indicated in the denominator are calculated values. In the case calculated ρ values, the first of them was obtained by equation (II.7), and the second – by equations (A-4-1) and (A-4-2); 2. ρ is the density; Tg is the glass transition temperature; n is the refractive index; ε is the dielectric constant; δ is the solubility parameter; γ is the surface energy; αG is the thermal coefficient of volumetric expansion in the glassy state; Cσ is the stress-optical coefficient. Homopolymer PMMA

622

Table A-4-2 Calculated and experimental characteristics of homopolymers* N δ, (J/cm3)1/2 γ, dyn/cm ε 1.49; 1.55 3.10 18.6 39.0 − 40.2 1.49 2.94 19.0 31.0

623

k =n

ρ G20 =

0.667 ∑α k M k k =1

k =n   [1 + α G ( 293 − Tg )]N A ∑α k  ∑ ∆Vi  k =1  i k

, 293 < Tg;

(A-4-1)

, 293 > Tg.

(A-4-2)

k =n

ρ G20 =

0.667 ∑ α k M k k =1

k =n   [1 + α L (293 − Tg )]N A ∑ α k  ∑ ∆Vi  k =1  i k

Besides the glass transition temperature and density, the following characteristics are calculated for copolymers: the refractive index n, the stress-optical coefficient Cσ, temperature of the onset of intense thermal degradation Td, the dielectric constant ε, the solubility parameter δ, the surface energy γ. Calculations were performed using equations (VIII.3), (VII.7), (VIII.16), (IX.4), (XII.4), and (XIII.39), respectively. First of all, let us compare the calculated and experimental values of the properties of homopolymers. These data are indicated in Table A-4-2. In most cases, good coincidence between experimental and calculated data is observed. Separately, we must dwell on the calculation of such characteristic of homo- and copolymers as density ρ, for which two values are shown in the Table. The first of them is determined with the help of equation (II.7), and the second – by correlations (A-4-1) and (A-4-2), which take into account the temperature dependence of the coefficient of molecular packing. In the case of a glassy polymer (poly(methyl methacrylate)), the calculated value of density obtained by equation (II.7) coincides with the experimental value. For homopolymers with low glass transition temperatures, which are in the rubbery state at room temperature, consideration of the temperature dependence to the coefficient of molecular packing leads to lower values of density compared with those determined on the base of the value kavg. Therewith, the data on density values coincide with experimental ones. The glass transition temperature, determined from equation (IV.41) with the accuracy usual for such calculations, coincides with the experimental values. The refractive index for homopolymers is calculated from equation (VIII.1), as well as from equation (VIII.6), which takes into account the temperature dependence of the coefficient of molecular packing. The latter circumstance enables us to calculate the refractive index with high accuracy. With regard to such characteristics as the solubility parameter, surface energy, temperature of the onset of intense thermal degradation, the thermal coefficient of volumetric expansion in the glassy state, and the stress-optical coefficient, they coincide with the experimental ones with the accuracy usual for such calculations. The properties of multi-component copolymers are indicated in Table A-4-3. Here, the coincidence of the calculated and experimental characteristics is approximately the same as for homopolymers. The density calculated from equation (II.7) using the average value of the coefficient of molecular packing is somewhat higher than the values, determined experimentally. This is stipulated by the fact that all copolymers possess the glass transition temperature below room temperature. Values of density ρ calculated by correlation (A-4-2) with regard to the temperature dependence of the coefficient of molecular packing, is somewhat lower than these calculated by equation (II.7), and coincide well with the experimental values of ρ.

624

Table A-4-3 Physical characteristics of homopolymers* Van-der-Waals volume, n Tg, K Td, K Copolymer Cσ, B ρ, g/cm3 Å 1 125 − − 563 298 1.09 1.50 15.5 273;268 627 1.12;1.08 2 148 − − 573 237 1.04 1.50 21.6 247;243 627 1.09;1.03 3 143 − − 570 233 1.04 1.50 21.3 258;255 627 1.09;1.04 4 158 − − 610 240 1.02 1.50 25.2 244;240 627 1.08;1.02 5 139 − − 570 243 1.06 1.50 21.0 252;247 627 1.10;1.04 Notes: 1. * Indicated in the numerator are experimental values, and in the denominator – calculated ones; for density ρ, the first value is obtained from equation (II.7), and the second – from equation (A4-2); for Tg, the first value is calculated by equation (IV.55), and the second – by correlation (IV.57), using experimental values of Tg for homopolymers. 2. ρ is the density; n is the refractive index; Cσ is the stress-optical coefficient; Tg is the glass transition temperature; Td is the onset temperature of intense thermal degradation.

For all copolymers, the refractive index n is approximately the same, and is associated with the close values of the refractive index for all homopolymers, mentioned above. The stress-optical coefficient is also almost identical for all copolymers, excluding the copolymer 1 with increased concentration of MMA units possessing a negative value of Cσ. The glass transition temperature of copolymers indicated in Table A-4-3 is calculated by equations (IV.55) and (IV.57). The former requires no understanding of experimental values of the glass transition temperature of homopolymers, and the latter uses these values. By and large good coincidence of calculated and experimental values of Td is observed. In most cases, when experimental values of Tg for homopolymers are used and substituted to equation (IV.57), correspondence of the calculation to the experiment becomes somewhat better. As for temperature of the onset of rapid thermal degradation Td, good coincidence is observed for the copolymer 4, for which the error is 2.7%. For other copolymers, the calculated values deviated from the experimental ones for this characteristic by 50° to higher values which gives 8%. This phenomenon has not as yet been explained. It should be taken into account only that the characteristic such as the dependence of the temperature of the onset of intense thermal degradation on the presence of admixtures and other reasons is stronger. The calculated values of this characteristic are determined for the ideal polymeric system. Hence, the possibility of predicting various characteristics of multi-component copolymers is obvious. Therewith, the approach used does not require any experimentally determined values. The prognosis is performed on the basis of only the chemical structure of the multi-component copolymer.

Appendix 5. Influence of strong intermolecular interaction occurring between two dissimilar polymers on their miscibility

When two or more polymers are mixed, the situation may appear when an additional strong intermolecular interaction occurs between chains of these polymers, which is not displayed between macromolecules of each of polymers, taken separately. These may be hydrogen bonds or strong dipole–dipole interactions. Analysis of the influence of these interactions on the glass transition temperature will be shown below. In a series of works devoted to the analysis of miscibility of polymers and the properties of mixtures obtained, the main attention is paid to these special interactions occurring between macromolecular chains of the mixed polymers. The scheme of this interaction is demonstrated by the following example:

F3C

CF3 O H O

Let us consider in detail examples of such interactions and experimental methods of their determination. Mixtures of styrene copolymer with vinylphenylhexafluoromethylcarbynol with the polymers as polycarbonate based on bisphenol A, poly(butyl methacrylate), poly-2,6-dimethyl-1,4-phenylene oxide may represent an example of this significant event [209]. Introduction of hydroxyl groups to the mentioned polymer leads to the formation of hydrogen bonds between the copolymer and polycarbonate, which causes a sharp increase of miscibility. The thermograms obtained by the DSC method for polystyrene mixtures with polycarbonate show clearly two glass transition temperatures indicating immiscibility of these polymers. The situation is changed abruptly when polystyrene introduced to the mixture is substituted by a copolymer of the above given structure: thermograms indicate the single glass transition temperature (which indicates miscibility). Therewith, the glass transition temperature regularly increases with the concentration of polycarbonate. Mixtures of copolymers of the above-mentioned structure with poly(ethylene oxide) (PEO), which represents the solid polymer, also display this effect [210]. Crystallinity of PEO in the mixture varies in the manner by which the melting point decreases. The formation of hydrogen bonds between PEO and copolymer has been studied in dependence on temperature. As temperature increases, hydrogen bonds between copolymer and PEO dissociate, but are restored when cooled down. Even in the case of solid polymer such as PEO, the presence of hydrogen bonding between chains of

626

mixed polymers improves their miscibility, suppresses crystallization, and forms onephase systems. Behavior of styrene copolymer mixtures with vinylphenylhexafluoromethyl carbynol was studied for such polymers as poly(vinyl acetate), poly(methyl methacrylate), poly(ethyl methacrylate), poly-n-(butyl methacrylate), poly(methyl vinyl ether), poly-2,6-dimethyl-1,4-phenylene oxide, polycarbonate based on bisphenol A, styrene copolymer with acrylonitrile, as well as with amorphous and solid polyesters and polyamides [193]. For these systems, hydrogen bonding influences the miscibility of components, which has been confirmed by measurements of the glass transition temperature, as well as by FTIR-spectroscopy. Ref. [165] represents a detailed investigation of the miscibility of this polymer with a series of aliphatic polyamides, such as nylon-6,12 and N,N’-dimethyl-substituted nylon-6,12. The miscibility criterion was again assumed to be general glass transition temperature for the mixture, therewith, the polymers were used, for which the glass transition temperature is significantly different from that for polystyrene and copolymer. For example, the glass transition temperature of nylon-6,12 is 46°C, and the melting point is estimated in the range of 206–215°C. To estimate the influence of the crystallinity degree on miscibility, besides nylon-6,12, N,N’-dimethyl-substituted nylon-6,12 was used, as well as copolymers with different concentration of it. The main conclusions made according to the results of ref. [165] are that hydrogen bonds between components of the mixture are formed and these bonds dissociate at heating and occur again at cooling down. Therewith, the introduction of a small amount of carbonyl groups to polystyrene improved the miscibility of such immiscible polymers as polystyrene and polyamide. Consequently, the copolymer under consideration may be a compatibilizer. Ref. [192] represents the study of the miscibility of substituted phenol condensed resins with poly(methyl methacrylate) (PMMA). The following resins were studied: OH

R

n

where R = H; t-butyl; NO2; Cl. This work indicates again that formation of the hydrogen bonds between components of the mixture plays a significant role in miscibility. Thermodynamic parameters of dissociation of hydrogen bonds, such as enthalpy and entropy, were determined. The most significant influence is caused by such substituents as NO2 and Cl. All mixtures of these phenol resins with poly(methyl methacrylate) displayed the single glass transition temperature that meant that they are miscible well. Therewith, the dependences of the glass transition temperature on the composition were corresponded to three different cases: 1. The glass transition temperature of mixtures is higher than the mean glass transition temperature. 2. The glass transition temperature of mixtures is always lower than the mean glass transition temperature.

627

3. Dependence of the glass transition temperature on the composition is of the Sshape in relation to the mean dependence. The authors of ref. [192] suggest description of the mixture behavior appropriate to the cases 1 and 2 by the following correlation: Tg = W1Tg1 + W2Tg2 + qW1W2,

(A-5-1)

where Tg1 and Tg2 are the glass transition temperatures of polymers 1 and 2, respectively; W1 and W2 are their weight parts; the parameter q may be interpreted as the contribution of hydrogen bonds, which may be considered as pseudo-crosslinks. Therewith, the value of q characterizes intensity of the hydrogen bonding. The experiments showed that when NO2 and t-butyl are used as substituents, the values of q are negative and approximately equal by the absolute value. If substituents are H and Cl, then the values of q are positive (all the above-said is true at substitution of an aromatic cycle in the para-position). Consequently, mixtures of phenol resins possessing t-butyl and NO2-groups with poly(methyl methacrylate) display the behavior corresponding to the second case. When there is no substitution, the behavior of the system corresponds to the third case. Finally, when Cl is the substituent, behavior of the mixture corresponds to the first case. For the third case, the S-shape of dependence of the glass transition temperature Tg on the composition may be described by the following correlation: Tg =

W1Tg1 + kW2Tg2 W1 + kW2

+ qW1W2 ,

(A-5-2)

which is the most general one compared with expression (A-5-1). Thereafter [190], correlation (A-5-2) was applied to description of the dependence of the glass transition temperature on the weight part of the components for mixtures of substituted phenol resins (see above) with such polymers as poly(ethyl methacrylate) and poly(methyl methacrylate) F and t-butyl being substituents on the phenol resin, and behavior of the mixtures based on non-substituted phenol resin was also studied. All three cases described above were obtained, and all parameters of equation (A-5-2) were found. Studied in refs. [170] and [171] was the phenomenon of hydrogen bonding between macromolecules in mixtures of polymers by the FTIR-spectroscopy, and using the Patterson and Robald theory [173] and by obtaining diagrams with the lowest threshold temperature of dissolution. The solubility and miscibility of poly(ethyl oxazoline) (

N CH2

CH2

)n

C2H5C O were studied; poly(ethyl oxazoline) is the isomer of poly-N,N’-dimethylacrylamide (

CH2

CH

)n

O CN(CH3)2

628

To estimate the miscibility of poly(ethyl oxazoline) with other polymers, two series of experiments were performed. In the first series, the films based on mixtures of pairs of polymers were obtained, one of which was poly(ethyl oxazoline). In the second series of experiments, complexes based on the same pairs of polymers were obtained. These complexes were obtained by mixing polymeric solutions with further separation of residue, its drying in vacuum during a long time to a constant mass. It was found that the composition of the complex differs from that of the initial mixture, the composition of the complex being correspondent to the ratio of polar groups leading to a strong intermolecular interaction. The glass transition temperature of poly(ethyl oxazoline) mixed with polyacrylic acid is below the additive values, whereas for the complexes, the glass transition temperature is above them. The authors associate this with the formation of a network of physical bonds in the case of complexes. The miscibility of poly(vinyl methyl ether) with styrene copolymers with methyl methacrylate [136] was also studied. The threshold composition of the copolymer, at which it is miscible with poly(vinyl methyl ether), was found. Such copolymer must contain about 60% (mol) of polystyrene. Phase diagrams and socalled ‘windows of miscibility’ for these mixtures were obtained. Besides the glass transition temperature, the thermal stability of mixtures was also studied [221] (on the example of poly-p-hydroxystyrene mixtures with poly(vinyl pyrrolidone) and poly(ethylene oxazoline)). It was found that during heating a small loss of polyhydroxystyrene mass (6%) in the temperature range of 200–250°C is caused by the cross-linking reaction leading to formation of ether bonds. Importance of hydrogen bonds formation between chains of polymers is also noted. Intermolecular complexes may be formed directly during polymerization [135]. For example, this is manifested in photopolymerization of acrylic acid, in which poly(ethylene oxide) is dissolved. The glass transition temperature of the complexes exceeds not only the glass transition temperature of mixtures, but also glass transition temperatures of the original components. These complexes are dissolved in such solvents as dimethylformamide and dimethylsulfoxide, and definitely swell in water and methanol; however, they do not swell in dioxane. If the number of groups able to form hydrogen bonds is decreased by copolymerization of acrylic acid with methyl methacrylate, the ability to complex formation is preserved, although it is somewhat reduced. Thermal oxidation also depends [191] on the formation of hydrogen bonds between chains of polymers (for example, for mixtures of poly(vinyl methyl ether) and modified polystyrene). Modified polystyrene represented a styrene copolymer containing 2.5% (mol) of hexofluoro-2-propylstyrene, i.e. it contained hydroxyl groups inclined to formation of hydrogen bonds. As mentioned many times above, this circumstance provided for improved miscibility of the components in the mixture. However, in addition, phenol groups in the copolymer caused an increase of the system resistance to thermal oxidation, i.e. these groups acted as antioxidants. This was expressed in an increase of the induction period of poly(vinyl methyl ether) thermal oxidation, and the rate of the process decreased. The complex formation described above was also observed between poly-N,N’-dimethylacrylamide and phenoloformaldehyde resin [218]. The complexes were precipitated from solutions in acetone, ethyl acetate and dioxane. Therewith, as before, the composition of these complexes corresponded to the molar ratio of the components. The glass transition temperature of complexes was higher than the glass transition temperatures of the original components. Poly(dimethyl acrylamide) also formed complexes with

629

p-methoxyphenoloformaldehyde resin, therewith the glass transition temperature increases significantly compared with that of each of the components [216, 217]. In ref. [162] were synthesized interpenetrating networks (IPN) based on miscible polymers – poly-1-hydroxy-2,6-methylphenylene and poly(methyl methacrylate). Two types of cross-linked agents were used at various temperatures: hexamethylene tetramine and 1,3-dioxolane. As indicated in the cited work, the intensity of hydrogen bonding in mixtures and IPN is determined by variation of the cross-linking temperature and decrease of the concentration of groups able to form hydrogen bonds. The concentration of these groups was varied by using methyl methacrylate copolymer with styrene. Using FTIR-spectroscopy, it was shown that to preserve miscibility in these mixtures, it is necessary to ensure that the value of intermolecular interaction, stipulated by hydrogen bonds, is not lower than a definite threshold value. Hydrogen bonding influences the phase behavior of mixtures of polymers [163]. Methyl methacrylate copolymers with styrene and phenoloformaldehyde resin, in which hydroxyl groups are partially methylated, were chosen as objects for such investigation. Miscibility diagrams were composed and so-called ‘windows of miscibility’ were found where full miscibility and microphase separation were observed in dependence on temperature and concentration of one of the components. Ref. [222] studied the miscibility of mixtures of homopolymers with copolymers. The first pair represented a mixture of poly-4-hydroxystyrene with n-butyl acrylate copolymer with t-butyl methacrylate. The mixtures mentioned are miscible, when butyl acrylate concentration in the copolymer is 64% or higher. The second pair represented poly-t-butyl acrylate and styrene copolymer with 4hydroxystyrene. For this pair, the ‘window of miscibility’ existed at 4-hydroxystyrene concentration in copolymer between 28 and 66% (mol). The glass transition temperature of miscible mixtures of poly-t-butyl acrylate and styrene copolymer with 4-hydroxystyrene is significantly lower than the additive values and, which is of special interest, it is extremely weakly dependent on the mixture composition, being approximately equal to the glass transition temperature of copolymers themselves. Such behavior may be explained only by the formation of hydrogen bonds between components of the mixture, which is confirmed experimentally by IR-spectroscopy methods. Future development of these ideas may be observed in ref. [116], in which hydrogen bonding of IPN, obtained from a miscible polymeric mixture of poly-1hydroxyl-2,6-methylenephenylene and poly(methyl methacrylate), was studied. Copolymers of methyl methacrylate and styrene were also used in order to decrease the amount of carbonyl groups. To obtain IPN, various cross-linking agents were used, such as hexamethylene tetramine and 1,3-dioxolane. Cross-linking was performed at various temperatures, by which the intensity of hydrogen bonding in IPN was varied. The miscible mixture of the two polymers displayed thermal reversibility in relation to hydrogen bonding. Semi-IPN and IPN prepared at temperatures above the glass transition temperature of the mixture contained no initial amount of hydrogen bonds after cooling down to room temperature; but when poly(methyl methacrylate) copolymer with styrene is used instead of pure poly(methyl methacrylate) (i.e. when the amount of carbonyl groups is reduced), semi-IPN did not form a single phase at a significant decrease of the concentration of these groups. However, semi-IPN and IPN synthesized at comparatively low temperatures (below the glass transition temperature of the mixture), preserved high

630

level of hydrogen bonds amount compared with the ones, synthesized at high temperatures, and the single phase [196]. In ref. [186], the authors turned to new objects, such as polybenzimidazoles and poly-4-vinylpyridine. The main object of investigation was poly-2,2’-(mphenylene)-5,5’-bibenzimidazole

NH

NH

N

N

C

C n

All mixtures of different compositions displayed the single glass transition temperature that testified about their miscibility of components and, therewith, the glass transition temperature was above the additive values. As in the previous works, the authors explain this by the formation of hydrogen bonds taking place according to the scheme: N

N

C

C N

N H

H

N

)n The formation of hydrogen bonds is confirmed by experimental FTIRspectroscopy. The main practical conclusion which can be drawn on the basis of the works cited is that miscibility can be improved by introduction of a small amount of functional groups, hydroxyl ones, for example, into one of the components, which lead to the formation of hydrogen bonds between polymers – the mixture components. Therewith, domains of various size may be formed, and to decrease their size it is enough, for example, to introduce 4.4% (mol) of hydroxyl groups into polystyrene so that it would become miscible with poly-n-butyl acrylate. Preliminary investigations of these regions of relaxation and the size of domains by the NMR method were performed in ref. [158]. In studies [159, 178, 195, 207, 223], these investigations were continued. Complexes based on poly-4-hydroxystyrene and poly-N,N’-dimethyl acrylamide were studied by the NMR 13C method with cross-polarization and sample rotation at the magic angle. The size of inhomogeneities determined by this method was found to be equal to ≈ 2.5 nm [207]. Further on, this investigation was performed for IPN. It is found that, in this case, the size of aggregates is smaller than 2.2 nm [195]. The influence of PMMA microtacticity on its miscibility with a styrene copolymer with vinyl phenol was studied by the NMR method [159]. It was found that syndiotactic PMMA is miscible more efficiently with the copolymer mentioned and formed a single phase in a wide range of mixture compositions based on both (

CH CH2

631

methyl methacrylates. As indicated by the NMR method, for most composites, the size of microinhomogeneities is about 2 nm. Investigations of this kind have also been carried out with poly-4-vinylphenyl dimethylsilanol and its copolymers with styrene [178, 185]. In the present case, a significant influence of hydrogen bonding between phenolic and phosphate groups was also observed, as indicated by IR-spectroscopy, NMR 31P and NMR 13C methods [224]. Studied in ref. [137] were mixtures of poly(ethylene oxide) and poly(butyl methacrylate) with modified poly(butyl methacrylate) containing groups, able to form hydrogen bonds [179 – 184]. Introduction of 4-hydroxy-4,4-bis-3-fluoromethylbutyl group CH3 Si

O

(CH2)3 F3C C

CF3

OH n even into a siloxane polymer possessing a low surface energy makes it possible obtaining mixtures miscible with poly(ethylene oxide) and poly(butyl methacrylate). Estimated in ref. [151] is the parameter of the polymer–polymer interaction based on the study of diffusion of water in the mixtures. In all cases, this parameter became more negative, which indicated better miscibility. Correlations between the diffusion coefficient and the specific volume of the polymer were found. It should be noted [194] that functionalization of polystyrene at the sacrifice of introduction of fluoralkylcarbonyl or hydroxyl groups in it improves the miscibility of polystyrene with other polymers and increases its thermal stability, oxidation resistance, and decreases combustibility; this is evident in its mixtures with other polymers. The miscibility of a series of polyamides with other polymers was studied [128, 138, 157]. In ref. [138], poly-p-phenylene terephthalamide sulfonyl was chosen as the test sample: HN

NH CO SO3H

CO n

Based on its mixtures with poly(vinyl pyrrolidone), poly-4-vinylpyridine and polyvinyl alcohol, the so-called molecular composites were obtained, in which the rigid-chain polyamide sulfonyl was the reinforcing element. A significant influence of hydrogen bonding between elements of the molecular composite was detected. Therewith, for mixtures with poly(vinyl pyridine) and IPN, the glass transition temperature was below the additive values that, according to the authors, testified about a small number of contacts between macromolecules. An attempt was also made to modify nylon-6 by preparing its mixtures with a small amount of phenoloformaldehyde resin [157]. Addition of phenoloformaldehyde resin in amounts of 1–2% increases the elasticity coefficient and decreases water absorption. Therewith, larger spherulites were produced. Increase of the phenoloformaldehyde resin content in the composite induces no improvement of properties. Consequently, it is concluded that the miscibility of nylon-6 with

632

phenoloformaldehyde resin is rather restricted and falls within the range up to 3% of phenoloformaldehyde resin. The aim of the work [128] was study of the mechanism of polymer-analogous reaction between poly(trichlorobutadiene) (PTCB) and aliphatic diamines: t-butylamine, diethylamine and triethylamine, which model chemical processes proceeding in separate fragments of polymeric chains during PTCB interaction with branched poly(ethylene imine). With the help of FTIR methods and electronic spectroscopy, it was shown that when poly-1,1,2-trichlorobutadiene interacts with amines, hydrogen-bonded ionic complexes with the charge transfer are formed accompanying reactions of allyl chlorine substitution by amino group and dehydration. The contribution of each of these processes to the total conversion of functional groups of the polymer depends on amine nature (the N-substitution degree) and the type of solvent. The primary and secondary amines are more inclined to form stable hydrogen-bonded complexes with polymers, whereas the tertiary amines cause mostly dehydrochlorination of the polymer and formation of polyene sequences of different length. Dehydrochlorination prevails in dioxane, and substitution and complex formation – in chloroform. Hence, for more objective prediction of the miscibility of polymers with each other, as well as for analyzing the reasons for miscibility, special attention should be paid not only to the properties of individual components, but also to the specific intermolecular interaction between them. As the results of numerous works indicate, there are several ways of improving the miscibility of polymers: 1. Selection of polymeric pairs or modification of polymers, which are performed for strong intermolecular interaction occurring between heterogeneous polymeric chains (for example, hydrogen bonding). This problem will be analyzed in detail below. 2. The second way concludes in performing chemical reactions between components of the mixture that finally leads to obtaining of so-called interpolymers, described in detail in ref. [215]. 3. The third way concludes in introducing compatibilizers into the system, i.e. lowmolecular and high-molecular compounds possessing functional groups, which strengthen the specific intermolecular interaction between chains. Copolymers may also be used as compatibilizers,. Let us discuss in more detail the problems associated with strengthening of the specific intermolecular interaction between mixed polymers. If such an interaction does not occur, the glass transition temperature of a homogeneous mixture of miscible polymers is calculated from equation (IV.57). It contains the glass transition temperatures of homopolymers based on the components 1 and 2, the values of which may be taken as both calculated and experimental for estimating the glass transition temperature of the mixture. In another form, equation (IV.57) is reduced to expression (IV.55), which contains sets of constants for the components 1 and 2, associated with the energy of intermolecular interaction. Suppose now that hydrogen bonding occurs in the case, polymer 2 is added to polymer 1. In this case, constant bh = –140⋅10–3 Å3K–1, which characterizes the   contribution of hydrogen bonds, must be introduced to the value  ∑ ai ∆Vi + ∑ b j  j  i 1 for the component 1. For this case from equation (IV.55), we obtain:

633

    α1  ∑ ∆Vi  + α 2  ∑ ∆Vi   i 1  i 2 Tg = , (A-5-3)     α1  ∑ ai ∆Vi + ∑ b j + 2α 2bh  + α 2  ∑ ai ∆Vi + ∑ b j  + 2α1α 2 ⋅ 0.03 j j  i 1  i 2 because a part of repeat units of the polymer 1 appeared bonded to the component 2 by hydrogen bonds. This equation was deduced on the basis of the assumption that two repeat units are linked by hydrogen bonds, one of them being belonged to the polymer 1, and the second – to the polymer 2. Taking into account equation (IV.57) and the expression α1 = (1 – α2), it should be written down that

Tg =

(1 − α 2 ) ∑ ∆Vi     ∑ ∆Vi  1 (1 − α 2 )  i Tg,1

  + α 2  ∑ ∆Vi   i 1  i 2 ,    ∑ ∆Vi   i 2 + 2(1 − α 2 )α 2bh + α 2 + 2(1 − α 2 )α 2 ⋅ 0.03 Tg,2

(A-5-4)

where Tg,1 and Tg,2 are the glass transition temperatures (calculated or experimental) for the components 1 and 2, respectively. Let us now analyze the dependence of the glass transition temperature on the mixture composition, reflected by equations (A-5-3) and (A-5-4). Three different cases will be considered: 1) The Van-der-Waals volumes of repeat unit of polymers 1 and 2 are approximately     equal:  ∑ ∆Vi  ≈  ∑ ∆Vi  .  i 1  i 2 2) The Van-der-Waals volume of repeat unit of the polymer 1 is significantly lower     than for the polymer 2:  ∑ ∆Vi  >  ∑ ∆Vi  .  i 1  i 2       Initial values of  ∑ ∆Vi  ,  ∑ ∆Vi  , Tg,1, Tg,2,  ∑ ai ∆Vi + ∑ b j  , and j  i 1  i 2  i 1    ∑ ai ∆Vi + ∑ b j  for the mixtures corresponded to all three cases mentioned are  i  j  2 shown in Table A-5-1. Indicated in Figure A-5-1,a are dependences of the glass transition temperature of mixtures on the content of component 2 for the case, when      ∑ ∆Vi  ≈  ∑ ∆Vi  . Therewith, these values vary in a wide range. When the Van i 1  i 2   der-Waals volume of the repeat units is low, the value of  ∑ ai ∆Vi + ∑ b j  is also j  i 2

634

low, therewith, the cases are considered when the glass transition temperature is practically the same for both components of the mixture. Since the value bh, which characterizes the influence of hydrogen bonds on Tg, is quite high, it may be observed from equations (A-5-3) and (A-5-4) that the smaller is the Van-der-Waals volume, the more the glass transition temperature exceeds the value appropriate to the usual case, at which additional specific interaction between components is absent. This affects the run of Tg dependences on α2, indicated in Figure A-5-1,a. When the Van-der-Waals volume of repeat units of both components increases, the effect of additional interaction decreases, and the glass transition temperature of the mixture is just a little higher than the value of Tg calculated by equations (IV.55) and (IV.57). Table A-5-1 Initial values of parameters for calculation of the glass transition temperature of miscible mixtures of homopolymers             Number of  ∆Vi  ,  ∆Vi  , , L ∆'L + -M  , , L ∆'L + -M  , ∑ ∑       Figure curve in      i 1  i 2 M M  L   L  Figure A-5-1 3 3 3 –1 3 –1 Å Å ÅK ÅK 260 293 115 110 A-5-1a 1 588 665 260 250 2 814 931 360 350 3 1041 1197 460 450 4 543 279 240 105 A-5-1b 1 769 279 340 105 2 995 279 440 105 3 1222 279 540 105 4 260 598 115 225 A-5-1c 1 260 904 115 340 2 260 1170 115 440 3 260 1436 115 540 4 Note: Tg,1 = 376 K; Tg,2 = 442 K.

∑

∑

∑

∑

    Figure A-5-1,b is appropriate to the case, when  ∑ ∆Vi  >  ∑ ∆Vi  . In this  i 1  i 2 case, influence of the additional hydrogen bonding decreases, because the total energy of dispersion interaction significantly exceeds the energy of hydrogen bonds. Such situation also appears in the cases, when the excessive intermolecular interaction between components at their mixing is the dipole–dipole interaction, occurred owing to the presence of polar groups in the repeat unit. In this case, the value bh in equations (A-5-3) and (A-5-4) is substituted by the value bd:

635

Figure A-5-1. Dependence of the glass transition temperature Tg on concentration of the second component α2 for miscible mixtures of two polymers when formation of hydrogen













bonding between them takes place: a)  ∑ ∆Vi  ≈  ∑ ∆Vi  ; b)  ∑ ∆Vi 
 ∑ ∆Vi  ; numbers on curves correspond to the  i 2  i 1  i 2

numbers in the curves shown in Table A-5-1. The curves 1’– 4’ correspond to the situation when no additional hydrogen bonding between the components takes place.

636

    α1  ∑ ∆Vi  + α 2  ∑ ∆Vi       i 1  i 2 Tg = ;         α1  ∑ ai ∆Vi + ∑ b j + 2α 2 bd  + α 2  ∑ ai ∆Vi + ∑ b j  + 2α1α 2 ⋅ 0.03 j j  i 1  i 2 

Tg =

  + α 2  ∑ ∆Vi     i 1  i 2 .    ∆V  ∑ i   i 2 + 2(1 − α 2 )α 2 ⋅ 0.03 + 2(1 − α 2 )α 2 bd + α 2 Tg,2

(A-5-5)



(1 − α 2 ) ∑ ∆Vi     ∆V  i ∑   1 (1 − α 2 )  i Tg,1

(A-5-6)

    When  ∑ ∆Vi  ≈  ∑ ∆Vi  , the influence of additional intermolecular  i 1  i 2 interaction on the dependence of Tg on the composition is also displayed, but it appears significantly lower than at occurrence of hydrogen bonds between components (Figure A-5-2,a). The reason is that the value bd, characterizing influence of the dipole–dipole interaction on the glass transition temperature, is lower by the absolute value than the value bh. If the Van-der-Waals volume of the component 2 is significantly higher than that of the component 1, positive deviation of Tg values from the average values also takes place, however, the effect is not so high as in the case of occurrence of hydrogen bonds (Figure A-5-2,b). If the Van-der-Waals volume of the repeat unit of the component 1 is much higher than of the component 2, the influence of additional intermolecular interaction is not so high, and dependences of the glass transition temperatures on the composition are quite close to those calculated by equation (IV.55), i.e. with no regard to additional intermolecular interaction between components. This is clearly indicated in Figure A-5-2,c. It is common knowledge that besides the dependences of glass transition temperatures on the composition of the mixtures with maxima (curve 1) and minima (curve 2), the S-shaped dependences are encountered quite often (curve 3) (Figure A5-3). This is associated with the fact that one of the components of the mixture represents a copolymer containing a limited number of polar groups, able to form hydrogen bonds. Let us consider this situation in more detail. Suppose that a copolymer contains a limited amount of repeat units capable of hydrogen bonding (copolymer 2). For example, copolymer 2 may be presented in the form: (CH2

CH)m

(*)

(CH2

CH)n

OH (**)

637

Figure A-5-2. Similar to the situation in Figure A-5-1 but with occurrence of additional dipole–dipole interaction between components.

638

Let us designate the molar part of the repeat unit (**) as β. Suppose that the counter-polymer (polymer 1) is able to form hydrogen bonds with the repeat unit (**), contained in the copolymer 2. Applying these designations, equations (A-5-3) and (A5-4) are reduced to the following forms: 

Tg =



(1 − α 2 ) ∑ ∆Vi  

1

i

+

  (1 − α 2 ) ∑ ai ∆Vi + ∑ b j  + 2(1 − α 2 )α 2 2α 2 βbh + j  i 1

→

  + α 2  ∑ ∆Vi     i 2 → ;   + α 2  ∑ ai ∆Vi + ∑ b j  + 2(1 − α 2 )α 2 ⋅ 0.03   j  i 2





( − α  ) ∑ ∆'  

%J = ( − α 

   ∑ ∆'   ) L

L

%J

L

L

;

(A-5-7)

+



+ ( − α  )α  α  β- + α 

   ∑ ∆'   

K

→

L

L

%J

+

.

(A-5-8)

  + α   ∑ ∆'    → + ( − α  )α  ⋅   L

L

Figure A-5-3. Schematic representation of typical deviation of the glass transition temperature from its average values for the mixtures of miscible polymers (see text).

As above, let us discuss a series of cases: 1) The Van-der-Waals volume of the repeat unit is approximately the same. Initial values of all parameters necessary for the calculation are shown in Table A-5-2. During calculation, let us vary content of the component (**) for the copolymer 2. Calculation results are shown in Figure A-5-4,a. Clearly, the part of the

639

components (**) able to form hydrogen bonds is quite moderate and, therewith, S-shaped dependences of the glass transition temperature of the mixtures on the composition are formed. These dependences were observed in many works (refs. [180, 192, 193, 209]). Table A-5-2 Initial values of parameters for calculating the glass transition temperature of miscible (Tg,1 = 376 K, Tg,2 = 442 K) mixtures of homopolymer (1) and copolymer (2)           , Å3K–1   , Å3K–1  ∆V  , Å3  ∆V  , Å3 , ' , ' ∆ + ∆ + i i ∑ ∑ L L L L M M             i 1  i 2 M M  L   L 

∑

110

115

∑

293

∑

∑

260

Figure A-5-4. Dependence of the glass transition temperature Tg on concentration of the second component α2 for miscible mixtures of homopolymer and copolymer (see text) when: a) hydrogen bonding between components exists; b) dipole–dipole interaction between components prevail.

2) This case corresponds to formation of strong dipole–dipole interactions between copolymer 2 and polymer 1.

640

For calculation of the glass transition temperature, appropriate equations are deduced from equations (A-5-7) and (A-5-8):

  − α  ) ∑ ∆'  +   %J = →   ( − α  ) ∑ , ∆' + ∑ -  + ( − α  )α  α  β- +  

(



L

L

L

L

M

L

G

M

;   + α   ∑ ∆'     →   + α   ∑ , ∆' + ∑ -  + ( − α  )α  ⋅        ( − α  ) ∑ ∆'  +   → =      ∑ ∆'   ∑ ∆'     + + ( − α  )α  α  β- + α  ( − α  ) 

(A-5-9)

L

L

L

L

%J

L

M

M

L

L

L

L

L

L

%J

G

%J

(A-5-10)

  + α   ∑ ∆'    →  + ( − α  )α  ⋅   L

L

The calculation results obtained by equations (A-5-9) and (A-5-10) are indicated in Figure A-5-4,b. Calculated dependences of Tg on the part of copolymer 2 were obtained under various parts of the component (**) in the copolymer. It should be noted that occurrence of the S-shape of Tg dependence on the composition is displayed only in the case, when the copolymer 2 contains a significant part of the component (**). However, in all the cases, these dependences differ from these obtained with no regard to occurrence of an additional dipole–dipole interaction between components of the mixture. In relation to variations of the glass transition temperatures occurred as a result of excessive intermolecular interaction between components, the calculated data indicate that these interactions are of a significant importance. The values of Tg differ from those, when no additional intermolecular interaction occurs. Note also the important circumstance that all equations (A-5-3) – (A-5-10) applied to the analysis of the glass transition temperature dependence on the mixture composition displays no one ‘fitting’ parameter and, hence, all calculations are performed on the basis of the chemical structure of the mixture components. Let us consider behavior of a series of particular mixtures of two miscible polymers. The first of them represents a mixture of poly-n-butyl methacrylate (PBMA) with styrene copolymer with 4-vinylphenyl dimethylsilanol (St-VPDMS) [180]:

641

(CH2

CH)m

H3C

(CH2

CH)n

Si CH3 OH

Firstly, it is necessary to calculate glass transition temperatures for St-VPDMS copolymer at different concentration of VPDMS. Such calculations were performed by equation (IV.55), and their results are presented in Table A-5-3. Good coincidence of calculated and experimental data is observed. For further calculations of glass transition temperatures of PBMA mixtures with the given copolymer, it is necessary     to know values of  ∑ , ∆' + ∑ -  and  ∑ , ∆' + ∑ -  determined       !  $9 '!$ from equation (IV.55). It is also necessary to determine the same values for copolymers of all compositions. These values are also shown in Table A-5-3. They were used for future calculation of the glass transition temperature of a series of PBMA and St-VPDMS mixtures of different compositions. Indicated in Figure A-5-5 are the calculation results for two mixtures in the form of dependences of the glass transition temperature on the composition. These dependences for miscible mixtures containing St-VPDMS-34 and St-VPDMS-9 were obtained by equation (A-5-7). For every mixture, quite good coincidence with the experimental data is observed (see Figure A-5-5,a and b). L

L

L

M

M

L

L

L

M

M

Table A-5-3 Parameters of copolymers of styrene with vinylphenyldimethylsilanol Tg (exp.), ºC Designations The part of Tg (calc.), ºC   ∆Vi ,   VPDMS, , L ∆'L + -M × 3  Å  L  % (mol) M   3 3 -1 ×10 , Å K PS 100 105 103 110 293 PBMA 100 29 19 148 516 PVPDMS-2 1.9 97 103 111 295 PVPDMS-4 4.1 98 103 113 301 PVPDMS-9 8.7 98 103 116 309 PVPDMS-P 11.4 99 103 117 311 PVPDMS-18 18.2 101 104 122 324 PVPDMS-34 33.9 115 109 133 348 PVPDMS-60 60.0 121 122 151 382 PVPDMS-100 100 153 178 418 

∑

∑

∑

Moreover, let us analyze dependence of Tg on composition for PBMA mixture with St-VPDMS-9 with the help o equation (A-5-8). Therewith, let us also introduce experimental data into this equation. Consequently, we obtain a good coincidence of calculated and experimental data (see Figure A-5-5,c). Note that glass transition temperatures of mixtures are below the average values, when concentration of modified styrene (i.e. St-VPDMS) in the mixture is low. In the case, when concentration of this component in the mixture increases, glass transition

642

temperatures exceed the average values. Such exceeding is explained by formation of a great amount of hydrogen bonds between components at their mixing.

Figure A-5-5. Dependence of the glass transition temperature Tg on the mole fraction of copolymer α2 for miscible mixtures of PS with VPDMS/PBMA: a) PVPDMS-34; b) PVPDMS-9. 1 – calculated curve; 2 – experimental dependence; 3 – linear dependence.

Let us now consider behavior of another mixture obtained at the mixing of poly-(2,2’-m-phenylene-5,5’-bibenzimidazol) (PBI): N

N

NH

NH

and poly-4-vinylpyridine:

643

[CH2

CH]

N These mixtures were studied in ref. [186]. It has been indicated that hydrogen bonds are formed between residues of 4-vinylpyridine and NH-groups in PBI. This is the reason that homogeneous mixtures based on these two polymers are formed. Experimental dependences of the glass transition temperatures on the composition of these mixtures, taken from ref. [186], are indicated in Figure A-5-6. Glass transition temperatures of the mixtures exceed values of Tg for the original components. Calculated dependences of Tg on composition, determined by equation (A-5-8), are also indicated in Figure A-5-6. It is obvious from this figure that experimental points fit well the calculated curve, when the molar fraction of PBI in the mixture does not exceed 0.3. Deviation of the experimental points from the calculated curve at high concentration of PBI is associated with the onset of poly-4-vinylpyridine degradation at heating over 375°. Note one more time that all calculations are performed by the equations containing no ‘fitting parameters. Hence, all the results are obtained only on the base of chemical structure of the components of the mixture.

Figure A-5-6. Dependence of the glass transition temperature Tg on the composition α2 for miscible mixtures of poly(vinyl pyridine) with poly(benzimidazole). 1 – calculated curve; 2 – experimental dependence; 3 – linear dependence.

Let us make some conclusions from the above analysis. In the case of miscible mixtures of two homopolymers, the dependence of the glass transition temperature on the composition of the mixture may obtain different forms /shapes/. If the Van-derWaals volumes of the repeat unit of homopolymers are approximately equal, and no additional strong intermolecular interaction occurs between the components, the glass transition temperature falls below the average values. If the Van-der-Waals volume of

644

the unit of homopolymer 1 is significantly smaller than that of homopolymer 2, positive deviations of the glass transition temperature from the average value take place even if the additional intermolecular interactions are absent. But if such interactions take place, a positive deviation of Tg values from the average values always takes place. In the case of homopolymer mixtures with a copolymer containing a limited amount of polar groups, capable for strong intermolecular interaction with other components (dipole–dipole interaction, hydrogen bonds), dependences of Tg on the composition are S-shaped. All the mentioned features of behavior of such miscible mixtures may be described with the help of the equations mentioned above, which allow estimation of the properties of the mixtures based on the chemical structure of the components. It is self-evident that the present approach cannot pretend to be general, and more general investigations are required to take into account the influence of various specific interactions and fine features of the structure of components of mixtures on their thermomechanical behavior.

Appendix 6. On formation of super-molecular structures in amorphous polymers

1 Scheme of formation of the super-molecular structure The experimental data obtained up to the present time, as well as theoretical investigations of polymers enable us to appoint a scheme of the formation of supermolecular structures and, yielding from this scheme, to make an attempt in future to set a connection between the chemical structure of a polymer, its super-molecular structure and physical properties [236]. The question about super-molecular structures and their forms was originally formulated in ref. [237]. Further on, various models of super-molecular structure appeared [238, 239], which allow an explanation of a series of properties of amorphous polymers in solution, melt and solid state. Simultaneously with model ideas, numerous experiments with obtaining super-molecular structure by various methods were performed, with the method of electron microscopy being the chief method. The most typical situation in amorphous polymers observed is the picture of globules the sizes of which correspond to aggregates of tens and hundreds of macromolecules. Let us dwell on problems of super-molecular structure formation and description of this process with the help of an analytical apparatus, developed in refs. [240 – 242]. Before passing to the essence of the problem, let us note in brief the main results of these works, which will be necessary for us for future discussion. Suggested by Lifshitz in ref. [240] was the equation: gˆψ = Λexp{µ*(n)/RT}Ψ, n = ψ2exp{µ*(n)/RT}, N = ∫ nd 3 r ,

(A-6-1) (A-6-2)

where gˆ is the integral operator; gˆψ = ∫ g (x − x′)ψ (x′)d 3 x′ ; g(x – x′) is the

conditional probability of existence of two units in points x and x′, respectively; ψ and Λ are the characteristic function and the characteristic value of equation (A-6-1), respectively; n(x) is the function of the smoothed density which defines the macroscopic state of the polymeric globule; µ* is the chemical potential of the system of broken chains; N is the total number of units of the macromolecule. Besides description of the ‘coil – globule’ transition, this equation allows analysis of the structure of various physical factors (temperature, solvent quality, interaction with the solvent). Basing on the analysis of solutions of equation (A-6-1), a phase diagram of the system of interacting particles of the polymeric macromolecule in solution was composed (Figure A-6-1), which, further on, will be widely used for explaining the formation of the super-molecular structure. As the ‘starting state’, consider a diluted solution of a polymer, in which overlapping of coils is absent, and a monomacromolecular transition is possible. It may be either a diluted solution, specially prepared for this purpose, or a solution of propagating chains of the polymer in the medium in which synthesis proceeds. The synthesis may proceed both in the monomer medium and in the medium of a specially

646

selected solvent (then, in the first case, the amount of macromolecules formed at the onset of the reaction will be low, and the solution may be considered diluted). The solution temperature T will be lower than some critical temperature Tc (which will be determined below), but is greater than the triple point T (Figure A-6-1). Then, macromolecules with molecular mass above the BA line (Figure A-6-1) will transit into the globular state with a dense center and loose ‘periphery’, and macromolecules with the molecular weight below the BA line will remain in the coil state.

Figure A-6-1. Phase diagram of a system of interacting particles (beads) of the chain in solution. EDC lines separate the area of globule without periphery, EDBA – globules with periphery, CBA – the coil. T is the temperature of the triple point; Tcr is the critical temperature of broken chains. Figure A-6-2. Scheme of formation of the initial element of super-molecular structure: 1, 2 – centers of globules of macromolecules; 3, 4 – peripheries of globules of macromolecules; 5 – bond globule (or coil).

To solve the task set, let us limit by the volumetric approximation when the density of a macromolecule at the nucleus–periphery interface changes jump-like to zero (periphery density). Let us discuss an interaction of two such globules with the periphery when they approach each other due to diffusion motion or sedimentation (interaction of coils is out of interest for us, because in this case either globules with a periphery may appear, if the total number of units in coils will appear above the coil– globule transition on the phase diagram, or a coil with higher molecular weight is formed, i.e. the problem is reduced to the same cases, which will be discussed below). When peripheries of globules of two macromolecules interpenetrate, units of peripheries will interact with each other. Therewith, the following variants are possible. If the total number of units in peripheries under given temperature is above the coil–globule phase transition line (Figure A-6-1), a bond globule with periphery is formed (Figure A-6-2). If the total number of units in peripheries is low and appears below the phase transition line, a bond coil is formed at the capture of periphery units of one globule by periphery units of another one, which at a future decrease of temperature transits either to the bond globule with the periphery or to the bond globule without the periphery (Figure A-6-1). Hence, in any case, the initial element forming the super-molecular structure will be two globules connected with each other by a globule or a bond coil. Depending on the size of the globule center and bond globule (or coil), these elements of super-molecular structure in the limit form two most typical types of elements of the super-molecular structure.

647

If a bond globule (coil) is small compared with nucleus of globules of two initial macromolecules, i.e. r ξ1, i.e. at |Ka2| < 1, the atom existing in the fields of two neighboring atoms will possess only one state of equilibrium. When ξ2 < ξ1, i.e. |Ka2| > 1, the atom existing in the field of two neighboring atoms possesses two states of equilibrium. Therewith, if all three atoms are of the same type, or the atom located in the point ξ = 1 interacts with similar (but of a different type, than in the point ξ = 1) atoms located in the points ξ = 0 and ξ = 2, the difference of energies of potential pits in points ξ 2′ and ξ 2′′ (the difference in energies of rotary isomers) ∆E = 0. But if the atom located in the point ξ = 1 interacts with different atoms located in points ξ = 0 and ξ = 2, then ξ1 − ξ 2′ ≠ ξ 2′′ − ξ1 and ∆E ≠ 0 (Figure A-6-7). Summing up potentials, we will proceed from the condition that positions of the maximum of the potential Φ(ξ) of the left and the right atoms coincide (although this condition is not obligatory).

( ) ( )

Figure A-6-7. Potential of interaction of the given atom (ξ1 = 1) with two neighboring atoms (ξ = 0 and ξ = 2) under two different conditions: ξ2 > ξ1 (a) or ξ2 < ξ1 (b).

Hence, when |Ka2| > 1, summation of potentials (A-6-14) will give two states of equilibrium for every atoms, which is typical of systems of the order–disorder type. Systems of similar type display a phase transition of the second kind [267]. To provide transitions of atom from one state of equilibrium into another, the presence of defects (of the disclination type) in the polymer is necessary, the size of which (angular values) may be determined via coefficients of molecular packing of amorphous and crystalline states. When |Ka2| < 1, summation of potentials (A-6-14) will give only one state of equilibrium for each atom, which is typical of regular systems of the crystal type. In such systems, the phase transition of the first order takes place [267]. Let estimate the value β basing on the following ideas. According to formula (A-6-10), K = 1 βl lRgl−m . If assume that a ~ 2 Å (this corresponds to two Van-der-

(

)

(

)

Waals radii of hydrogen atom), and Rgl-m ≈ 20 Å, then at Ka2 = 4 βl 20l ~ 1, β2/3 ≅ l ,β –1

2/3

(

)

≅ 1 lun. nper . For the globule, nper ~ 24 [94], β

2/3

≅ 1/(5lun.), lun. ~ 3 Å, β ≅

0.45, i.e. is approximately equal to the half of the periphery thickness. That is why, R1 in expression (A-6-10) may be presented in the following form: R1 = 0.5lun. nper . If nper > nf or nper > ngl (where nf and ngl are the numbers of units in the bond

665

hyperboloid in the case of fibrillar or globular super-molecular structure [94]), the polymer exists in the crystalline state. On the base of data from ref. [94], let us determine

(Ka ) (Ka ) 2

a

2

c

l =  c  la

  

3

2

n  =  c   na 

3

4

= 3 4 ≅ 2.3 . 3

1

Since (Ka2)c = 1, (Ka2)a = 2.3 and ξ2 ≅

≅ 0.7. The value ξ2 is appropriate to − Ka 2 the size of the molecular defect and may be estimated via the coefficient of molecular packing in amorphous, ka, and crystalline, kc, state by the relation [94]:ξ2 = (kc – ka)1/3. Usually in the crystalline state, the mean packing coefficient kc = 0.74, and in the amorphous one ka = 0.68; then ξ2 ≅ 0.45. Let us now determine the size of amophone3. For scattering of X-rays or electrons on the globule–macromolecule to be fully isotropic, it is necessary that the whole surface of the globule is overlapped by cross-sections of the rotation hyperboloid with radius R2, i.e. 4πRgl2 −m = NπR22 . N=

Rgl2 −m R22

=

4 Rgl−m l

=4

M mol ~ 40 , ndet

L2a = 4 NRgl2 −m ~ 160Rgl2 −m , Na ~ 12Rgl-m ~ 240 Å. The cross size of the element of the super-molecular structure in a polymer fibril approaches by the order of value the size of amorphone estimated above. That is why the fibril may be approximated as a tube possessing the radius of amorphone and filled with amorphones along the generatrix. In the globule of the super-molecular 4 4 structure, the amount of globules–macromolecules equals πRgl3 = N m πRgl3 -m , 3 3 Nm =

Rgl3 Rgl3 -m

3

 5 ⋅ 10 2   ~ 16 ⋅ 103 , ~   ⋅ 2 10  

Nm ~ 400 , Na m

where Nm is the number of globules–macromolecules forming the globule of the super-molecular structure; Nam is the number of globules–macromolecules forming the amorphone. Hence, the globule of the super-molecular structure contains ~400 amorphones. Given here were statistical estimates of amorphone. Determining the number of amorphones in the globule of the super-molecular structure, it was suggested that it has the spherical shape. In reality, to determine its shape, it is necessary to find, from the condition of dense packing of globules in the element of the super-molecular structure, the shape of the bordering surface providing isotropic scattering of X-rays 3

The assumption used is excessive and guarantees fully isotropic scattering; more precise solution of the problem requires determination of the amount of cross-sections and their projections appearing at overlapping of bond hyperboloids under condition of formation of element of the super-molecular structure.

666

or electrons on globules–macromolecules. This sort of problems may be solved by a computer. The model of the super-molecular structure considered enables to refine the physical meaning of elements of the nonlinear mechanical model of polymeric substances, suggested in ref. [87]. This model is depicted in Figure A-6-8. According to this model, relaxation processes are described by the spectrum of relaxation times, which contains two main times (short and long) and a number of other relaxation times dependent on these two main times. In the right part of Figure A-6-8 shown the globule–macromolecule and radial lines connecting the center O of the globule– macromolecule with canters of neighboring globules–macromolecules. Let us separate the typical element, deformation of which determines the deformation behavior of the whole polymeric substance. In Figure A-6-8, this element is marked by the dotted line. Two thresholds may be indicated in the mentioned element: one threshold (OA) includes a bond hyperboloid, and another one (OB) does not include it. Therewith, OA ≠ OB, but taking into account the small thickness of the periphery, it may be assumed that OA ≈ OB, i.e. the supposition about equal lengths of elements in the nonlinear mechanical model made in ref. [87], may be assumed to be true.

Figure A-6-8. Element of super-molecular structure (right) and nonlinear mechanical model of polymeric body appropriate to it (See text).

Let us estimate the angle β between the axis lines of elements of the supermolecular structure (pairs of bonded globules). This may be made proceeding from the following ideas. In the case of spatial contacts, β = 4π/n, where n is the number of globules present in the first spherical layer near the present globule–macromolecule of the radius Rgl-m. Let us determine the value of n from the following expression: 2 Rgl−m + 2 Ri )3 − Rgl3 −m R (  Rgl−m   + 12 gl−m , n= = 8 + 6

Ri3

 R   i 

Ri

where Ri is the radius of the i-th globule present in the spherical layer near the globule of radius Rgl-m. In the general case, Rgl-m/Ri is a random value, because Ri may obtain values depended on molecular mass and molecular-mass distribution. Let us estimate values of n and β from different border cases. When Rgl-m/Ri = 1, n = 26, β = π/6; Rgl-m/Ri → 0, n = 8, β = π/2;

667

Rgl-m/Ri → ∞, n → ∞, β = 0. Suggesting these cases to be equally probable, let us calculate the value of β as 〈 β〉 =

1π π  2π .  + + 0 = 3 6 2  9

Hence, 〈β〉 corresponds to Rgl-m/Ri ~ 1 (more accurate, to Rgl-m/Ri = 0.63). The model of the super-molecular structure suggested allows complete definition of the physical meaning of relaxation mechanisms of the Alexandrov– Lazurkin elements, participating in the nonlinear model: one mechanism associated with long relaxation times takes place in bond hyperboloids and may be described with the help of the order–disorder system in the isomeric approximation by Volkenstein. The second mechanism with shorter relaxation times is analogous to the mechanism associated with stagnation of internal rotation and is developed in the globule–macromolecule itself (the Bresler–Frenkel mechanism). So, one of the main relaxation times (the short one) is typical of the globule of super-molecular structure of a positive curvature (corresponds to the time in ferroelectric of the mixing type), and the second one is typical of the bond hyperboloid with a negative curvature (long time in the system of the order–disorder type). The time and frequency dependences of polymer behavior in the transitional region can be described satisfactorily with the help of the Isakovich–Chaban [268, 269] and Irzhak–Rozenberg–Rostiashvili [270] models. In the one-dimensional case, it follows from these models that the main relaxation process is stipulated by the mutual diffusion of five to seven atoms. In the case of the model of the suggested super-molecular structure, these regions of rearrangement of atoms may be concretely defined – they must proceed in the bond hyperboloids.

669

References

1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30.

31.

A.P. Alexandrov, Proc. I and II Conf. on High-Molecular Compounds, Moscow-Leningrad, Izd. AN SSSR, 1945, pp. 49-59. (Rus) O.V. Anulov, G.V. Baryishnikov, N.I. Shimanova, N.M. Mestechkina, and V.D. Shcherbukhin, Appl. Biochem. And Microbiol., 1995, vol. 31(1), pp. 87-91. (Rus) P.U. Arifov, S.A. Tishin, A.V. Shevchenko, and V.A. Tishin, Vysokomol. Soedin., 1987, vol. B29(1), pp. 59-63. (Rus) A.A. Askadskii, Physicochemistry of polyarylates. Moscow, Khimia, 1968, 214 p. (Rus) A.A. Askadskii, Deformation of polymers. Moscow, Khimia, 1973, 448 p. (Rus) A.A. Askadskii, Structure and properties of heat-resistant polymers. Moscow, Khimia, 1981, 320 p. (Rus) A.A. Askadskii, Mechan. Comp. Mater., 1987, No. 3, pp. 403-409. (Rus) A.A. Askadskii, Vysokomol. Soedin., 1989, vol. A31(10), pp. 2141-2148. (Rus) A.A. Askadskii, Mechan. Composite Mater., 1990, No. 6, pp. 963-977. (Rus) A.A. Askadskii, V.A. Arslanbekov, T.A. Andryushchenko, Yu.I. Matveev, and A.L. Blumenfeld, Vysokomol. Soedin., 1989, vol. A31(8), pp. 1616-1623. (Rus) A.A. Askadskii, R.B. Banyavichus, Z.S. Vikhauskas, A.I. Marma, and A.L. Blumenfeld, Vysokomol. Soedin., 1988, vol. A30(8), pp. 1684-1689. (Rus) A.A. Askadskii, V.A. Beloshenko, K.A. Byichko, V.V. Shaposhnikova, A.V. Samoryadov, O.V. Kovriga, S.N. Salazkin, V.A. Sergeev, V.G. Slobodina, and Ya.V. Genin, Vysokomol. Soedin., 1994, vol. A36(7), pp. 1143-1147. (Rus) A.A. Askadskii, A.L. Blumenfeld, E.G. Galpern, and A.L. Chistyakov, Vysokomol. Soedin., vol. A36(7), pp. 1143-1147. (Rus) A.A. Askadskii, K.A. Byichko, O.V. Kovriga, S.V. Tsutsuran, R.B. Shleifman, and V.V. Kurashev, Vysokomol. Soedin., 1991, vol. A33(11), pp. 2477-2486. (Rus) A.A. Askadskii, and M.P. Valetskii, Mechan. Composite Mater., 1990, No. 3, pp. 441-446. (Rus) A.A. Askadskii, and I.I. Vointseva, Vysokomol. Soedin., 1987, vol. A29(12), pp. 2654-2669. (Rus) A.A. Askadskii, E.G. Galpern, T.P. Matveeva, A.L. Chistyakov, and G.L. Slonimskii, Vysokomol. Soedin., 1987, vol. A29(11), pp. 2433-2440. (Rus) A.A. Askadskii, E.G. Galpern, G.V. Surov, V.V. Bulatov, G.L. Slonimskii, and V.V. Korshak, Vysokomol. Soedin., 1989, vol. B31(4), pp. 308-317. (Rus) A.A. Askadskii, L.M. Goleneva, and K.A. Byichko, Vysokomol. Soedin., 1995, vol. A37(5), pp. 829-841. (Rus) A.A. Askadskii, V.V. Kazantsva, O.A. Melnik, K.A. Byichko, A.A. Sakharova, G.L. Slonymskii, and T.M. Frunze, Vysokomol. Soedin., 1988, vol. A30(6), pp. 1285-1293. (Rus) A.A. Askadskii, A.I. Kitaigorodskii, and G.L. Slonimskii, Vysokomol. Soedin., Vysokomol. Soedin., 1975, vol. A17(10), pp. 2293-2300. (Rus) A.A. Askadskii, and A.F. Klinskikh, Plasticheskie Massy, 1998, No. 4, pp. 29-33. (Rus) A.A. Askadskii, and A.F. Klinskikh, Vysokomol. Soedin., 1999, vol. A41(1), pp. 83-85. (Rus) A.A. Askadskii, and O.V. Kovriga, Vysokomol. Soedin., 1991, vol. A33(9), pp. 1945-1955. (Rus) A.A. Askadskii, L.K. Kolmakova, A.A. Tager, G.L. Slonymskii, and V.V. Korshak, Vysokomol. Soedin., 1977, vol. A19(5), pp. 1004-1013. (Rus) A.A. Askadskii, and V.I. Kondrashchenko, Vysokomol. Soedin., 1997, vol. A39(10), pp. 16251634. (Rus) A.A. Askadskii, V.M. Litvinov. A.A. Zhdanov, and G.L. Slonymskii, Vysokomol. Soedin., 1985, vol. A27(11), pp. 2408-2414. (Rus) A.A. Askadskii, and Yu.I. Matveev, Chemical structure and physical properties of polymers. Moscow, Khimia, 1983, 248 p. (Rus) A.A. Askadskii, Yu.I. Matveev, G.L. Slonymskii, and V.V. Korshak, Doklady AN SSSR, 1978, vol. 238(3), pp. 592-595. (Rus) A.A. Askadskii, Yu.I. Matveev, A.V. Pastukhov, B.A. Rozenberg, T.I. Ponomareva, N.A. Shchegolevskaya, and A.S. Marshalkovich, Vysokomol. Soedin., 1983, vol. A25(1), pp. 56-71). (Rus) A.A. Askadskii, Yu.I. Matveev, and T.P. Matveeva, Vysokomol. Soedin., 1988, vol. A30(12), pp. 2542-2550. (Rus)

670

32. A.A. Askadskii, Yu.I. Matveev, and M.S. Motevosyan, Vysokomol. Soedin., 1990, vol. A32(10), pp. 2157-2166. (Rus) 33. A.A. Askadskii, M.S. Motevosyan, and G.L. Slonymskii, Dep. VINITI, No. 6949-C, Dep. IEOC October 2, 1985, Moscow, 26 p. (Rus) 34. A.A. Askadskii, M.S. Motevosyan, and G.L. Slonymskii, Vysokomol. Soedin., 1987, vol. A29(4), pp. 753-760. (Rus) 35. A.A. Askadskii, A.V. Pastukhov, and A.S. Marshalkovich, Vysokomol. Soedin., 1984, vol. A26(1), pp. 160-171. (Rus) 36. A.A. Askadskii, S.N. Prozorova, and G.L. Slonymskii, Vysokomol. Soedin., 1976, vol. A18(3), pp. 636-647. (Rus) 37. A.A. Askadskii, and T.R. Razmadze, Vysokomol. Soedin., 1991, vol. A33(5), pp. 1141-1148. (Rus) 38. A.A. Askadskii, T.R. Razmadze, S.N. Salazkin, V.A. Sergeev, A.V. Samoryadov, K.A. Byichko, O.V. Kovriga, T.M. Babchinitser, and A. Varada Ragulu, Vysokomol. Soedin., 1991, vol. A33(6), pp. 1239-1250. (Rus) 39. A.A. Askadskii, A.A. Sakharova, O.A. Melnik, and V.V. Kazantseva, Vysokomol. Soedin., 1997, vol. A39(7), pp. 1160-1165. (Rus) 40. A.A. Askadskii, and G.L. Slonymskii, Vysokomol. Soedin., 1971, vol. A13(8), pp. 1917-1919. (Rus) 41. A.A. Askadskii, G.L. Slonymskii, and A.I. Kitaigorodskii, Vysokomol. Soedin., 1974, vol. A16(2), pp. 424-430. (Rus) 42. A.A. Askadskii, G.L. Slonymskii, Yu.I, Matveev, and V.V. Korshak, Doklady AN SSSR, 1975, vol. 224(3), pp. 612-615. (Rus) 43. A.A. Askadskii, G.L. Slonymskii, Yu.I, Matveev, and V.V. Korshak, Vysokomol. Soedin., 1976, vol. A18(9), pp. 2067-2074. (Rus) 44. A.A. Askadskii, G.V. Surov, V.V. Nemchinov, A.L. Blumenfeld, and Z.S. Vikhauskas, Vysokomol. Soedin., 1989, vol. A31(6), pp. 1320-1327. (Rus) 45. A.A. Askadskii, G.V. Surov, V.A. Pankratov, Ts.M. Frenkel, A.A. Zhdanov, L.I. Makarova, A.S. Marshalkovich, and L.G. Radchenko, Vysokomol. Soedin., 1990, vol. A32(7), pp. 1517-1527. (Rus) 46. A.A. Askadskii, G.V. Surov, V.A. Pankratov, Ts.M. Frenkel, L.I. Makarov, A.A. Zhdanov, I.V. Blagodetskikh, and A.V. Pastukhov, Vysokomol. Soedin., 1990, vol. A32(7), pp. 1528-1534. (Rus) 47. A.A. Askadskii, G.V. Surov, A.S. Marshalkovich, V.V. Dvalishvili, V.A. Pankratov, and Ts.M. Frenkel, Mechan. Composite Mater., 1991, No. 1, pp. 3-8. (Rus) 48. A.A. Askadskii, S.A. Tishin, V.V. Kazantseva, and O.V. Kovriga, Vysokomol. Soedin., 1990, vol. A32(12), pp. 2437-2445. (Rus) 49. A.A. Askadskii, S.A. Tishin, M.I. Tsapovetskii, V.V. Kazantseva, O.V. Kovriga, and V.A. Tishin, Vysokomol. Soedin., 1992, vol. A34(12), pp. 62-72. (Rus) 50. Yu.S. Barash, J. Exper. And Theor. Phys., 1980, vol. 79(6), pp. 2271-2281. (Rus) 51. G.M. Bartenev, and Yu.V. Zelenev, Physics and Mechanics of Polymers. Moscow, Vysshaya Shkola, 1983, 391 p. (Rus) 52. G.M. Bartenev, and S.Ya. Frenkel, Physics of polymers. Ed. A.M. Elyashevich, Leningrad, Khimia, 1990, 432 p. (Rus) 53. G.M. Bartenev, and A.G. Barteneva, Relaxation properties of polymers. Moscow, Khimia, 1992, 383 p. (Rus) 54. A.Z. Varisov, Yu.N. Kuznetsov, E.P. Prokopiev, and A.I. Filipiev, Uspekhi Khimii, 1981, vol. 50(10), pp. 1892-1923. (Rus) 55. S.V. Vinogradova, S.N. Salazkin, G.Sh. Chelidze, G.L. Slonymskii, A.A. Askadskii, K.A. Bychko, L.I. Komarova, I.V. Zhuravleva, and V.V. Korshak, Plasticheskie Massy, 1971, No. 8, pp. 10-13. (Rus) 56. S.V. Vinogradova, V.A. Pankratov, Ts.M. Frenkel, L.F. Larina, L.I. Komarova, and V.V. Korshak, Vysokomol. Soedin., 1981, vol. A23(6), pp. 1238-1243. (Rus) 57. M.V. Volkenstein, Molecular optics. Moscow-Leningrad, Gos. Izd. Tekhn. I Teor. Lit., 1951, 744 p. (Rus) 58. M.V. Volkenstein, Configuration statistics of polymeric chains. Moscow-Leningrad, Izd. AN SSSR, Leningrad dept., 1959, 466 p. (Rus) 59. B. Vunderlich, and G. Baur, Heat capacity of linear polymers (Transl. From Engl. And Germ.). Moscow, Mir, 1972, 238 p. (Rus) 60. Hemicelluloses. Ed. V.S. Gromov and M.S. Dudkin, Riga, Zinatne, 1991, 488 p. (Rus)

671

61. Yu.K. Godovskii, Thermophysical methods of polymers study. Moscow, Khimia, 1976, 216 p. (Rus) 62. Yu.K. Godovskii, Thermophysics of polymers. Moscow, Khimia, 1982, 280 p. (Rus) 63. V.E. Gul, Colloid. Zh., 1953, vol. 15(3), pp. 170-177. (Rus) 64. L.V. Gurvich, G.V. Karachentsev, V.N. Kondratiev, Yu.A. Lebedev, V.A. Medvedev, V.K. Potapov, and Yu.S. Khodeev, Energies of chemical bonds break. Ionization potentials and affinity to electron. Moscow, Nauka, 1974, 351 p. (Rus) 65. G.I. Gurevich, Zh. Tekhn. Fiz., 1947, vol. 17(12), pp. 1491-1502. (Rus) 66. V.G. Dashevskii, Conformation of organic molecules. Moscow, Khimia, 1974, 432 p. (Rus) 67. B.A. Dogadkin, and V.E. Gul, Doklady AN SSSR, 1950, vol. 70(6), pp. 1017-1019. (Rus) 68. M.M. Dubinin, Surface and porosity of adsorbents. In: Main Problems of the theory of physical adsorption. Proc. I-st All-Union Conf. on Theor. Problems of Adsorption. Moscow, Nauka, 1970, pp. 251-269. (Rus) 69. N.S. Enikolopov, and S.A. Volfson, Chemistry and technology of polyformaldehyde. Moscow, Khimia, 1968, 279 p. (Rus) 70. I.G. Zedginidze, Planning of experiment for study of multi-component systems. Moscow, Nauka, 1976, 390 p. (Rus) 71. P.I. Zubov, Mechanism of formation of protein jellies. Doctor Thesis, Moscow, L.Ya. Karpov SICPI, 1949, 174 p. (Rus) 72. P.I. Zubov, Yu.I. Matveev, A.A. Askadskii, and T.A. Andryushchenko, Vysokomol. Soedin., 1980, vol. A22(6), pp. 1347-1358. (Rus) 73. A.A. Iliushin, and B.E. Pobedrya, Grounds of mathematical theory of thermal viscoelasticity. Moscow, Nauka, 1970, 280 p. (Rus) 74. V.A. Kabanov, Doklady AN SSSR, 1970, vol. 195(2), pp. 402-405. (Rus) 75. A.I. Kitaigorodskii, Organic crystallochemistry. Moscow, Izd. AN SSSR, 1955, 558 p. (Rus) 76. V.S. Klimenkov, V.A. Kargin, and A.I. Kitaigorodskii, Zh. Fiz. Khim., 1953, vol. 27(8), pp. 1217-1227. (Rus) 77. M.I. Kornfeld, Elasticity and strength of liquids. Moscow-Leningrad, Gos. Izd. Tekhn. Teor. Lit., 1951, 108 p. (Rus) 78. V.V. Korshak, Heterochain structure of polymers. Moscow, Nauka, 1977, 301 p. (Rus) 79. V.V. Korshak, S.V. Vinogradova, G.L. Slonymskii, V.A. Pankratov, A.A. Askadskii, Ts.M. Frenkel, L.F. Larina, and K.A. Bychko, Vysokomol. Soedin., 1981, vol. A23(6), pp. 1244-1251. (Rus) 80. V.V. Korshak, and A.A. Askadskii, Doklady AN SSSR, 1986, vol. 289(6), pp. 1412-1416. (Rus) 81. V.V. Korshak, G.L. Slonymskii, A.A. Askadskii, A.L. Rusanov, T.V. Lekae, and M.S. Matevosyan, Vysokomol. Soedin., 1989, vol. A31(1), pp. 34-39. (Rus) 82. V.G. Krasovskii, N.A. Sadovskii, O.B. Gorbatsevich, A.M. Muzafarov, V.D. Myakushev, M.N. Il’ina, I.I. Dubovik, T.V. Strelkova, and V.S. Papkov, Vysokomol. Soedin., 1994, vol. A36(4), pp. 714-720. (Rus) 83. E.S. Krongauz, N.M. Belomoina, A.A. Askadskii, V.V. Kazantseva, K.A. Bychko, G.L. Slonymskii, and V.V. Korshak, Vysokomol. Soedin., 1986, vol. A28(7), pp. 1473-1478. (Rus) 84. A.S. Kuzminskii, and L.V. Borkova, Zh. Fiz. Khim., 1958, vol. 32(9), pp. 2051-2060. (Rus) 85. L.D. Landau, and E.M. Lifshits, Theoretical physics. Vol. 8. Electrodynamics of continuum. 2nd Ed., improved and added by E.M. Lifshits and L.P. Pitaevskii, Moscow, Nauka, 1982, 623 p. (Rus) 86. L.D. Landau, and E.M. Lifshits, Theoretical physics. Vol. 7. Elasticity theory. 4th Ed., Moscow, Nauka, 1987, 246 p. (Rus) 87. Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soedin., 1981, vol. A23(6), pp. 1347-1357. (Rus) 88. Yu.I. Matveev, A.A. Askadskii, I.V. Zhuravleva, G.L. Slonymskii, and V.V. Korshak, Vysokomol. Soedin., 1981, vol. A23(9), pp. 2013-2026. (Rus) 89. Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soedin., 1982, vol. A24(6), pp. 1295-1303. (Rus) 90. Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soedin., 1985, vol. A27(11), pp. 2357-2362. (Rus) 91. T.P. Matveeva, Yu.I. Matveev, and A.A. Askadskii, Mechan. Composite Mater., 1986, No. 2, pp. 201-206. (Rus) 92. Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soedin., 1986, vol. A28(7), pp. 1365-1372. (Rus) 93. Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soedin., 1989, vol. A31(3), pp. 617-622. (Rus)

672

94. 95. 96. 97. 98. 99. 100. 101. 102. 103. 104. 105. 106. 107. 108. 109. 110. 111. 112. 113.

114. 115. 116. 117. 118. 119. 120. 121. 122. 123. 124. 125. 126.

Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soedin., 1989, vol. A31(3), pp. 526-532. (Rus) Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soedin., 1994, vol. A36(3), pp. 436-443. (Rus) Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soedin., 1993, vol. A35(1), pp. 63-67. (Rus) M.S. Matevosyan, A.A. Askadskii, and G.L. Slonymskii, Vysokomol. Soedin., 1987, vol. A29(4), pp. 761-767. (Rus) A.M. Muzafarov, E.A. Rebrov, and V.S. Papkov, Uspekhi Khimii, 1991, vol. 60(7), pp. 15961612. (Rus) A.F. Nikolaev, Synthetic polymers and plastics on their base. 2nd Ed., Moscow-Leningrad, Khimia, Leningrad dept., 1966, 768 p. (Rus) R.S. Norkina, S.I. Sokolov, and N.A. Shchegolevskaya, Izv. VUZov, Khimia i Khim. Tekhnol., 1964, vol. 7(4), pp. 645-650. (Rus) V.A. Pankratov, A.A. Askadskii, M.M. Patsuria, Yu.S. Kochergin, S.V. Vinogradova, G.L. Slonymskii, and V.V. Korshak, Vysokomol. Soedin., 1977, vol. A19(1), pp. 142-148. (Rus) G.L. Slonymskii, V.V. Korshak, S.V. Vinogradova, A.I. Kitaigorodskii, A.A. Askadskii, S.N. Salazkin, and E.M. Belavtseva, Vysokomol. Soedin., 1967, vol. A9(2), pp. 851-854. (Rus) G.L. Slonymskii, V.V. Korshak, A.I. Mzhelskii, A.A. Askadskii, Ya.S. Vygodskii, and S.V. Vinogradova, Doklady AN SSSR, 1968, vol. 182(4), pp. 851-854. (Rus) G.L. Slonymskii, and V.O. Shestopal, Vysokomol. Soedin., 1978, vol. A20(8), pp. 1712-1721. (Rus) G.L. Slonymskii, and A.A. Askadskii, Vysokomol. Soedin., 1986, vol. A28(5), pp. 1014-1022. (Rus) T.A. Speranskaya, and L.N. Tarutina, Optical properties of polymers. Leningrad, Khimia, Leningrad dept., 1976, 136 p. (Rus) A.A. Tager, M.V. Tsilipotkina, and A.I. Suvorova, Doklady AN SSSR, 1958, vol. 120(3), pp. 570-572. (Rus) A.A. Tager, and L.K. Kolmakova, Vysokomol. Soedin., 1980, vol. A22(3), pp. 483-496. (Rus) B.Ya. Teitelbaum, Thermomechanical analysis of polymers. Moscow, Nauka, 1979, 234 p. (Rus) S.A. Tishin, V.A. Tishin, and B.A. Shpilevskii, Mechan. Composite Mater., 1990, No. 1, pp. 3-8. (Rus) S.A. Tishin, Appl. and Tech. Exper., 1990, No. 5, pp. 171-174. (Rus) Yu.S. Urzhumtsev, and R.D. Maksimov, Prognosis of deformation of polymeric materials. Riga, Zinatne, 1975, 416 p. (Rus) Achievements in the field of synthesis of elementorganic polymers. pp. 143-231. V.V.Korshak, A.I. Kirilin et al.; Ed. V.V. Korshak, Nesmeyanov’s Institute of Organo-Element Compounds, AS USSR. Moscow, Nauka, 1988, 319 p. (Rus) R.F. Feinman, Statistic mechanics: the course of lectures. (Transl. From Engl.) Ed. Prof. D.N. Zubarev, 2nd Ed., Moscow, Mir, 1978, 407 p. (Rus) M.V. Tsilipotkina, A.A. Tager, O.V. Nechaeva, A.V. Vasiliev, L.M. Bykova, S.M. Bulygina, V.A. Vasnev, and S.N. Salazkin, Vysokomol. Soedin., 1972, vol. A14(9), pp. 2053-2057. (Rus) V.I. Sharkov, N.I. Kuibina, and Yu.P. Solovieva, J. Appl. Chem., 1965, vol. 35(5), pp. 11191128. (Rus) V.I. Sharkov, N.I. Kuibina, and Yu.P. Solovieva, J. Appl. Chem., 1967, vol. 40(11), pp. 26092611. (Rus) V.I. Sharkov, and N.I. Kuibina, Chemistry of Hemicelluloses. Moscow, Lesnaya Promyshlennost’, 1972, 440 p. (Rus) V.O. Shestopal, Phys. Solids, 1970, vol. 12(1), pp. 291-294. (Rus) A. Einstein, Collection of scientific works. Vol. 3. Works on kinetic theory, theory of radiation and grounds of quantum mechanics. Moscow, Nauka, 1966, 631 p. (Rus) Experimental methods in adsorption and molecular chromatography. Ed. A.V. Kiselev and V.P. Dreving, Moscow, Izd. Moscow Univ., 1973, 433 p. (Rus) Encyclopedia of polymers. Vol. I. 1043 p., Moscow, Sov. Enciklop., 1972. (Rus) P. Arifov, S. Vasserman, and S. Tishin, Phys. Stat. Sol. A-Appl. Res., 1987, vol. 102(2), pp. 565570. A.A. Askadskii, Physical properties of polymers. Encyclopedia of Fluid Mechanics. Vol. 9. Polymer Flow Engineering. Ed. N.P. Cheremisinoff, 1990, pp. 103-147. A.A. Askadskii, Analysis of the structure and properties of high-crosslinked polymer networks. Chemistry Review, vol. 16, part 3, Harwood Academic Publishers, 1992, 120 p. A.A. Askadskii, E.G. Galpern, I.V. Stankevich, and A.L. Chistyakov, Computer simulation of polymers with predetermined physical properties. J. Biochem. Kinet., 1992, vol. 2(4), pp. 225232.

673

127. A.A. Askadskii, A.E. Shvorak, T.M. Frenkel, T.M. Babshinitzer, C.A. Bychko, O.V. Kovriga, V.A. Pankratov, A.V. Rajulu, J. Appl. Polymer Sci., 1995, vol. 55(8), pp. 1173-1183. 128. A.A. Askadskii, Physical properties of polymers, prediction and control. Gordon and Breach Publishers, Amsterdam, 1996, 333 p. 129. A.A. Askadskii, and L.M. Goleneva, Macromolecular Symposia “Nano-Structures in Polymer Systems”, 1966, vol. 106(9), April, pp. 9-17. 130. G.O. Aspinal, Constitution of plant cell wall Polysaccharides. Encyclopedia of Plant Physiology, Ed. W. Tanner and E.A. Loewus, Berlin, etc., Springer Verlag, 1981, vol. 13B. Plant Carbohydrates, 11, Extracellular Carbohydrates, pp. 5-8. 131. M. Bank, J. Leffmgwell, and C. Thies, Macromolecules, 1971, vol. 4(1), pp. 43-46. 132. R.G. Beaman, J. Polym. Sci., 1952, vol. 9(5), pp. 470-472. 133. J. Bicerano, Prediction of polymer properties. New-York, Marcel Dekker Inc., 1996, 528 p. 134. F.J. Calleja, J. Serna, J. Vicente, and M.A. Segovia, J. Appl. Phys., 1985, vol. 58(1), pp. 253-259. 135. F.-L. Chen, E.M. Pearce, and T.K. Kwei, Polymers, 1988, vol. 29(12), pp. 2285-2289. 136. Y.Y. Chien, E.M. Pierce, and T.K. Kwei, Macromolecules, 1988, vol. 21(6), pp. 1616-1619. 137. E.Y. Chu, E.M. Pearce, T.K. Kwei, T.F. Yeh, and Y. Okamoto, Makromol. Chem., Rapid Commun., 1991, vol. 12(1), pp. 1-4. 138. Y.K. Dai, E.Y. Chu, Z.S. Xu, E.M. Pearce, Y. Okamoto, and T.K. Kwei, J. Polym. Sci., Part A, Polym. Chem., 1994, vol. 32, pp. 397-400. 139. M.A. de Araujo, R. Stadler, and H.-J. Cantow, Polymer, 1988, vol. 29(12), pp. 2235-2243. 140. M. Eldrup, D. Lightbood, and J.N. Sherwood, Chem. Phys., 1981, vol. 63(1-2), pp. 51-58. 141. R.F. Fedors, Polymer Eng. and Sci., 1974, vol. 14(2), pp. 147-154. 142. P.J. Flory, Faraday Disc. Chem. Soc., 1979, No. 68, pp. 14-25. 143. F.M. Fowkes, Indust. Eng. Chem., 1964, vol. 56(12), p. 40. 144. T.G. Fox, and P.J. Flory, J. Appl. Phys., 1950, vol. 21(6), pp. 581-591. 145. T.G. Fox, and S. Loshaek, J. Polym. Sci., 1955, vol. 15(80), pp. 371-390. 146. R.J. Gaylord, B. Joss, J.T. Bendler, and E.A. di Marzio, Brit. Polymer J., 1985, vol. 17(2), pp. 126-128. 147. L.A. Girifalco, and R.J. Good, J. Phys. Chem., 1957, vol. 61(7), pp. 904-909. 148. R.J. Good, L.A. Girifalco, and G.A. Kraus, J. Phys. Chem., 1958, vol. 62(11), pp. 1418-1421. 149. R.J. Good, and L.A. Girifalco, J. Phys. Chem., 1960, vol. 64(5), pp. 561-565. 150. J.L. Gordon, Cohesive energy density. Encyclopedia of Polymer Science and Technology, vol. 3, New-York, John Wiley and Sons, Inc., 1965, pp. 833-862. 151. T.C. Gsell, E.M. Pearce, and T.K. Kwei, Polymer, 1991, vol. 9, pp. 1663-1674. 152. A.M. Gupta, and C.W. Macosko, Macromolecules, 1993, vol. 26(10), pp. 2455-2463. 153. J.-L. Halary, F.C. Ben Larbi, P. Oudin, and L. Monnerie, Macromol. Chem., 1988, vol. 189(9), pp. 2117-2124. 154. R.A. Haldon, and R. Simha, J. Appl. Phys., 1968, No. 39, pp. 1890-1898. 155. A.E. Hamielec, M. Eldrup, O.E. Mogensen, and P. Jansen, J. Macromol. Sci., 1973, vol. 9(2), pp. 305-337. 156. C.K. Hu, and G.R. Gruzalsk, Phys. Rev., 1983, vol. B27(1), pp. 1-8. 157. W. Huang, K.J. Zhu, E.M. Pearce, and T.K. Kwei, J. Appl. Sci., 1993, vol. 48, pp. 563-573. 158. L. Jong, E.M. Pearce, T.K. Kwei, and L.C. Dickinson, Macromolecules, 1990, vol. 23(24), pp. 5071-5074. 159. L. Jong, E.M. Pearce, and T.K. Kwei, Polymer, 1993, vol. 34(1), pp. 48-55. 160. G. Kanig, J. Polym. Sci., part C, 1967, pp. 1957-1964. 161. H.-L. Kim, T.K. Kwei, and E.M. Pearce, Hydrogen bonding interaction in Interpenetrating polymer network. In: Contemporary Topics in Polymer Science, vol. 6 (Ed. B. Culberison), Plenum, New York, 1989, pp. 687-697. 162. H.-L. Kim, E.M. Pearce, and T.K. Kwei, Macromolecules, 1989, vol. 22(8), pp. 3374-3380. 163. H.-L. Kim, E.M. Pearce, and T.K. Kwei, Macromolecules, 1989, vol. 22(8), pp. 3498-3500. 164. P. Kindl, and G. Reiter, Phys. Stat. Sol. A – Appl. Res., 1987, vol. 104(2), pp. 707-713. 165. D.L. Kotzev, E.M. Pearce, and T.K. Kwei, J. Appl. Polym. Sci., 1984, vol. 29, pp. 4443-4448. 166. M. Kryszewski, J. Jachwicz, M. Malanga, and O. Vogl, Polymer, 1982, vol. 23(2), pp. 271-276. 167. K. Kun, and R. Kunin, J. Polymer Sci., 1964, vol. B2, p. 587. 168. T.K. Kwei, T. Nishi, and R.F. Roberts, Macromolecules, 1974, vol. 7(5), pp. 667-674. 169. T.K. Kwei, and H.L. Frisch, Macromolecules, 1978, vol. 11(6), pp. 1267-1271. 170. T.K. Kwei, E.M. Pearce, and B.Y. Min, Macromolecules, 1985, vol. 18(11), pp. 2326, 2327. 171. T.K. Kwei, E.M. Pearce, F. Ren, and J.P. Chen, J. Polym. Sci., Part B, Polym. Phys., 1986, vol. 24(7), pp. 1597-1609.

674

172. W.A. Lee, and G.J. Knight, Brit. Polymer J., 1970, vol. 2(2), pp. 73-80. 173. P. Lin, C. Clash, E.M. Pearce, and T.K. Kwei, J. Polym. Sci., Part B, Polym. Phys., 1988, vol. 26, pp. 603-619. 174. Y.-H. Lin, Macromolecules, 1984, vol. 17(12), pp. 2846-2856. 175. Y.-H. Lin, Macromolecules, 1986, vol. 19(1), pp. 159-168. 176. Y.-H. Lin, Macromolecules, 1991, vol. 19(1), pp. 168-173. 177. Y.-H. Lin, Macromolecules, 1991, vol. 24(19), pp. 5346-5350. 178. S. Lu, E.M. Pearce, and T.K. Kwei, Macromolecules, 1993, vol. 26(4), pp. 3514-3518. 179. S. Lu, E.M. Pearce, and T.K. Kwei, J. Polym. Sci., Part A, Polym. Chem., 1994, vol. 32, pp. 2597-2601. 180. S. Lu, E.M. Pearce, and T.K. Kwei, J. Macromol. Sci., Pure Appl. Chem., 1994, vol. A31(11), pp. 1535-1560. 181. S. Lu, M.M. Melo, J. Zhao, E.M. Pearce, and T.K. Kwei, Macromolecules, 1995, vol. 28(14), pp. 4908-4913. 182. S. Lu, E.M. Pearce, and T.K. Kwei, Polymer Eng. Sci., 1995, vol. 35(13), pp. 1113-1116. 183. S. Lu, E.M. Pearce, and T.K. Kwei, Polym. Adv. Tech., 1996, vol. 7, pp. 553-559. 184. S. Lu, E.M. Pearce, and T.K. Kwei, J. Polym. Sci., Part A, Polym. Chem., 1996, vol. 34, pp. 3163-3172. 185. D. Luo, E.M. Pearce, and T.K. Kwei, Macromolecules, 1993, vol. 26(23), pp. 6220-6225. 186. S. Makhija, E.M. Pearce, T.K. Kwei, and F. Liu, Polym. Eng. Sci., 1990, vol. 30(13), pp. 798801. 187. B.D. Malhotra, and R.A. Pethrick, Eur. Polym. J., 1983, vol. 19(6), pp. 457-459. 188. J.E. Mark, and J.L. Sullivan, J. Chem. Phys., 1977, vol. 66(3), pp. 1006-1011. 189. R.L. Miller, and R.F. Boyer, J. Polymer Sci., Polymer Phys. Ed., 1984, vol. 22(12), pp. 20432050. 190. K. Ogawa, F. Tanaka, J. Tamura, K. Kadowaki, and K. Okamura, Macromolecules, 1987, vol. 20(5), pp. 1174-1176. 191. H. Park, E.M. Pearce, W.H. Starnes, and T.K. Kwei, J. Polym. Sci., Part A, Polym. Chem., 1990, vol. 28, pp. 1079-1089. 192. J.R. Pennacchia, E.M. Pearce, T.K. Kwei, B.J. Bulkin, and J.-P. Chen, Macromolecules, 1986, vol. 19(4), pp. 973-977. 193. E.M. Pearce, T.K. Kwei, and T.K. Min, J. Macromol. Sci. – Chem., 1984, vol. A21(8,9), pp. 1181-1216. 194. E.M. Pearce, and T.K. Kwei, J. Macromol. Sci. – Chem., 1991, vol. A28(11,12), pp. 1207-1212. 195. E.M. Pearce, and T.K. Kwei, Polym. Solutions, Blends and Interfaces, 1992, pp. 133-149. 196. E.M. Pearce, T.K. Kwei, and S. Lu, Polym. Adv. Techn., 1994, vol. 5, pp. 600-602. 197. W.A. Prest, and R.S. Porter, J. Polym. Sci., Part A-2, Polym. Phys., 1972, vol. 10(9), pp. 16391647. 198. K. Schmidt-Rohr, J. Clauss, and H.W. Spiess, Macromolecules, 1992, vol. 25(12), pp. 3273-3277. 199. H.A. Schneider, and H.J. Brekner, Polymer Bull., 1985, vol. 14(2), pp. 173-178. 200. H.A. Schneider, and B. Leikauf, Thermochim. Acta, 1987, vol. 114(1), pp. 165-170. 201. B.L. Schuerman, Int. Conference St-Petersburg – Moscow, May 18-26, 1995, OL70. 202. A. Shefer, and M. Gottlieb, Macromolecules, 1992, vol. 25(15), pp. 4036-4042. 203. A.R. Shultz, and B.M. Gendron, J. Appl. Polymer Sci., 1972, vol. 16(2), pp. 461-471. 204. A.R. Shiltz, and A.L. Young, J. Appl. Polym. Sci., 1983, vol. 28(5), pp. 1677-1684. 205. R. Simha, J. Chem. Phys., 1962, vol. 37(5), p. 1003. 206. P.A. Small, J. Appl. Chem., 1953, vol. 3(2), pp. 71-80. 207. T. Suzuki, E.M. Pearce, and T.K. Kwei, Polymer, 1992, vol. 33(1), pp. 198-201. 208. T.E. Timell, Wood hemicellulose. Adv. In Carbohydrate Chem., New York, 1964, vol. 19, pp. 247-302. 209. S.P. Ting, E.M. Pearce, and T.K. Kwei, J. Polym. Sci., Polym. Lett., 1980, vol. 18(3), pp. 201209. 210. S.P. Ting, B.J. Bulkin, and E.M. Pearce, J. Polym. Sci., Part A, Polym. Chem., 1981, vol. 19(6), pp. 1451-1473. 211. S.A. Tishin, E.S. Bakaev, and B.A. Shipilevskij, Plaste und Kautschuk, 1991, Heft 4, SS. 45-49. 212. D.A. Tomalia, A.M. Noylor, and A.W. Doddard, Angew. Chem., 1990, vol. 29(2), pp. 138-175. 213. M.M. Vaidya, K. Levon, and E.M. Pearce, J. Polym. Sci., Part B, Polym. Phys., 1995, vol. 33, pp. 2093-2108. 214. D.W. Van Krevelen, Properties of polymers. Third Edition, Elsevier, Amsterdam, 1990, p. 875.

675

215. I.I. Vointseva, and A.A. Askadskii, Interpolymers (paired polymers). Chemistry reviews, Soviet scientific reviews. Vol. 16, part 2, Harwood Academic Publishers, Chur-Reading, Paris, Philadelphia, Tokyo, Melbourne, 1991, p. 86. 216. L.F. Wang, E.M. Pearce, and T.K. Kwei, J. Polym. Sci., Part C, Polym. Lett., 1990, vol. 28, pp. 317-321. 217. L.F. Wang, E.M. Pearce, and T.K. Kwei, J. Polym. Sci., Part B, Polym. Phys., 1991, vol. 29, pp. 619-626. 218. T.P. Yang, E.M. Pearce, T.K. Kwei, and N.L. Yang, Macromolecules, 1989, vol. 22(4), pp. 18131818. 219. X. Yang, P.C. Painter, M.M. Coleman, E.M. Pearce, and T.K. Kwei, Macromolecules, 1992, vol. 25(8), pp. 2156-2165. 220. A.F. Yee, R.J. Bankert, K.L. Ngai, and R.W. Rendell, J. Polymer Sci., 1988, vol. 26(12), pp. 2463-2483. 221. K.J. Zhu, E.M. Pearce, and T.K. Kwei, J. Appl. Polym. Sci., 1989, vol. 37(2), pp. 573-578. 222. K.J. Zhu, S.F. Chen, T. Ho, E.M. Pearce, and T.K. Kwei, Macromolecules, 1990, vol. 23(1), pp. 150-154. 223. H. Zhuang, E.M. Pearce, and T.K. Kwei, Macromolecules, 1994, vol. 27(22), pp. 6398-6403. 224. H. Zhuang, E.M. Pearce, and T.K. Kwei, Polymer, 1995, vol. 36(11), pp. 2237-2241. 225. M. Doi, and S.F. Edwards, J. Chem. Soc. Faraday Trans. II, 1978, vol. 74(10), p. 1818. 226. M. Doi, J. Polym. Sci., Polym. Phys. Ed., 1983, vol. 21(5), p. 667. 227. M.J. Doi, J. Polym. Sci., Polym. Phys. Ed., 1980, vol. 18(5), p. 1005. 228. M. Doi, and S.F. Edwards, The Theory of Polymer Dynamics, Oxford Univ. Press, 1986. 229. D. Richter, B. Farago, R. Bitera, L.J. Fetters, J.S. Huang, and B. Ewen, Macromolecules, 1993, vol. 26(4), p. 795. 230. S. Wu, J. Polym. Sci., Polym. Phys. Ed., 1989, vol. 27(4), p. 723. 231. K. Iwata, and S.F. Edwards, J. Chem. Phys., 1989, vol. 90(8), p. 4567. 232. Yu.I. Matveev, and A.A. Askadskii, Vysikomol. Soedin., 1993, vol. A35(1), p. 63. (Rus) 233. A.V. Vologodskii, A.V. Lukashin, M.D. Frank-Kamenetskii, and V.V. Anshelevich, Zh. Eksper. I Teor. Fiz., 1974, vol. 66(6), p. 2153 (Rus); M.D. Frank-Kamenetskii, A.V. Lukashin, and A.V. Vologodskii, Nature, 1975, vol. 258(3), p. 398; Frank-Kamenetskii, and A.V. Vologodskii, Uspekhi Fiz. Nauk, 1981, vol. 139(4), p. 641. (Rus) 234. A.A. Askadskii, A.I. Kitaigorodskii, and G.L. Slonimskii, Vysokomol. Soedin., 1975, vol. A17(10), p. 2293. (Rus) 235. A.A. Askadskii, and Yu.I. Matveev, Chemical Structure and Physical Properties of Polymers, Moscow, Khimia, 1983. (Rus) 236. M. Nakato, T. Nakagama, Y. Nakamura, and S. Wakatsuki, Kinetics of Chain Aggregation of Poly(Methyl Methacrylate) in Isoamyl Acetate, J. Chem. Phys., 1999, vol. 110(5), pp. 2711-2716. 237. V.A. Kargin, A.I. Kitaigorodskii, and G.L. Slonymskii, Colloid. Zh., 1957, vol. 19(2), pp. 131. (Rus) 238. G.S.Y. Yeh, Pure and Appl. Chem., 1972, vol. 32(1/2), pp. 65. 239. S.A. Arzhakov, N.F. Bakeev, and V.A. Kabanov, Vysokomol. Soed., 1973, vol. A15(5), pp. 1154. (Rus) 240. I.M. Lifshitz, Zh. Experim. I Teor. Fiz., 1968, vol. 55, vol. 6(12), pp. 2408. (Rus) 241. I.M. Lifshitz, and A.Yu. Grosberg, Zh. Exper. I Theor. Fiz., 1973, vol. 65(6 – 12), pp. 2399. (Rus) 242. A.Yu. Grosberg, and A.R. Khokhlov, In: Problems in Solid-state Physics, Ed. A.M. Prokhorov, A.S. Prokhorov, Moscow, Mir, 1984, 368 p. (Rus) 243. T.M. Birstein, ans O.B. Ptyitsin, Conformations of Macromolecules, Moscow – Leningrad, Nauka, 1964, 391 p. (Rus) 244. G.L. Slonimskii, V.V. Korshak, S.V. Vinogradova, A.I. Kitaigorodskii, A.A. Askadskii, S.N. Salazkin, and E.M. Belavtseva, Vysokomol. Soed., 1967, vol. A9(2), pp. 402. (Rus) 245. A.P. Khokhlov, In: Model Approach in Statistic Mechanics, Moscow, Izd. MSU, 1979. (Rus) 246. T.M. Birshtein, A.M. Skvotsov, and A.A. Sariban, Vysokomol. Soed., 1977, vol. A19(1), pp. 63. (Rus) 247. S.R. Rafikov, V.P. Budtov, and Yu.B. Monakov, Introduction into Physicochemistry of Solutions of Polymers, Moscow, Nauka, 1978, 328 p. (Rus) 248. A.A. Askadskii, and Yu.I. Matveev, Chemical Structure and Physical Properties of Polymers, Moscow, 1983, 248 p. (Rus) 249. T.P. Matveeva, Yu.I. Matveev, and A.A. Askadskii, Mechanics of Composite Materials, 1986, No. 2, pp. 201. (Rus) 250. A.A. Askadskii, and Yu.I. Matveev, Doklady AN SSSR, 1986, vol. 290(1), pp. 135. (Rus)

676

251. Yu.A. Matveev, and A.A. Askadskii, Vysokomol. Soed., 1987. (Rus) 252. A.A. Askadskii, A.S. Marshalovich, T.P. Matveeva, A.V. Pastukhov, and G.I. Sidorova, Mechanics of Composite Materials, 1983, No. 5, pp. 906. (Rus) 253. S.Ya. Frenkel, Introduction into Statistic Theory of Polymerization, Leningrad, 1965. (Rus) 254. E.B. Zhulina, and T.M. Birstein, Vysokomol. Soed. 1986, vol. A28(12), pp. 2589. (Rus) 255. P. de Jen, Ideas of Scaling in Physic of Polymers, 1982, Moscow, 368 p. (Rus) 256. I.M. Lifshits, Uspekhi Fiz. Nauk, 1979, vol. 127(3), pp. 353. (Rus) 257. L.D. Landau, and E.M. Lifshits, Statistic Physics, 1964, Moscow, 568 p. (Rus) 258. G.Z. Gershuni, and E.M. Zhukhovskaya, Convective Stability of Incompressible Liquid, 1972, Moscow, 392 p. (Rus) 259. M. Kleman, and J.E. Sados, Phys. Letters, 1979, vol. 40, p. 569; J.F. Sados, and R. Mosseri, Phys. Mag., 1982, vol. B45, p. 467. 260. M. Kleman, J. Phys., 1982, vol. 43, p. 1389. 261. D.R. Nelson, Phys. Rev. Letters, 1983, vol. 50, p. 982. 262. V.N. Novikov, Zh. Eksper. I Teor. Fiz., 1984, vol. 87, No. 3(9), p. 1080. (Rus) 263. Yu. I. Matveev, and A.A. Askadskii, Vysokomol. Soed., 1986, vol. A28(7), p. 1365. (Rus) 264. A.A. Askadskii, and Yu.I. Matveev, Doklady AN SSSR, 1986, vol. 290(1), p. 135. (Rus) 265. R. Grigorovici, Amorphous and Liquid Semiconductors, 1974, New York, 320 p. 266. N.V. Efimov, Mathematical Encyclopedia, 1984, vol. 4, p. 163. (Rus) 267. A. Brus, and R. Kauli, Structure Phase Transitions, 1984, Moscow, 408 p. (Rus) 268. Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soed., 1989, vol. A31(3). (Rus) 269. Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soed., 1981, vol. A23(6), p.1347. (Rus) 270. M.A. Isakovich, and I.A. Chaban, Zh. Eksper. I Teor. Fiz., 1966, vol. 50(5), p. 1343. (Rus) 271. I.A. Chaban, Doctor Thesis, Moscow, N.N. Andreev Acoustic Institute, 1984, 324 p. (Rus) 272. V.G. Rostiashvili, A.R. Nekhoda, and V.I. Irzhak, Fluctuation Theory of Relaxation and Dynamic Properties of Amorphous Polymers in the Area of Glass Transition, 1985, Chernogolovka, 324 p. (Rus) 273. L.E. Nielsen, Mechanical Properties of Polymers, Reinhold, New York, 1962. 274. R.F. Boyer, Rubber Chem. Technol., 1963, vol. 63, p. 1303. 275. J.H. Sewell, Royal Aircraft Establishment, Farnborough, Hants. UK, Unpublished report. 276. L. Turunen, Kunststoffe, 1962, vol. 52, p. 672. 277. R.H. Wiley, and G.M. Brauer, J. Polym. Sci., 1948, vol. 3, p. 647. 278. P.L. Magagnini, Chim. Ind. (Milan), 1967, vol. 49, p. 1041. 279. W.J. Jackson, T.F. Gray, and J.R. Caldwell, J. Appl. Polym. Sci., 1970, vol. 14, p. 685. 280. O.G. Lewis, "Physical Constants of Linear Homopolymers", Springer-Verlag, 1968. 281. B.G. Ranby, K.S. Chan, and H. Brumberger, J. Polym. Sci., 1962, vol. 58, p. 545. 282. A. Quach, and R. Shima, J. Appl. Phys., 1971, vol. 42, p. 4592. 283. H.G. Killian, and E. Jenckel, in: K.A. Wolf (Ed.), "Struktur und Physikalisches Verhalten der Kunststoffe", Springer-Verlag, 1962, p. 176. 284. G.A. Gordon, J. Polym. Sci., 1971, vol. A-2(9), p. 1693. 285. S.C. Temin, J. Polym. Sci., 1965, vol. 9, p. 471. 286. R.F. Boyer, Changements de Phases, Soc. Chim. Phys., Paris, 1952, p. 383. 287. W.G. Barb, J. Polym. Sci., 1959, vol. 37, p. 515. 288. S.Y. Chuang, S.J. Tao, and J.M. Wilkenfeld, 1972, vol. 43, p. 737. 289. J.N. Gayles, and W.L. Peticolas, Light Scattering Spectr. Solids, Proc. Intern. Conf., 1968, Ed. G.B. Wright, Springer-Verlag, New York, 1969, p. 715; Chem. Abstr., 1970, vol. 72, p. 22089z. 290. B.M. Grieveson, Polymer, 1960, vol. 1, p. 499. 291. D.W. Brown, and L.A. Wall, J. Polym. Sci., 1969, vol. A-2(7), p. 601. 292. G. Allen, J. McAinsh, and G.M. Jeffs, Polymer, 1971, vol. 12, p. 85. 293. IUPAC, "Nomenclature of Organic Chemistry", Sections A and B, Third Edit., Sect. C, Second Edit., London, Butterworths, 1969. 294. J.M. Augl, and J.V. Duffy, J. Polym. Sci., 1971, vol. A-1(9), p. 1343. 295. G.F.L. Ehlers, and K.R. Fisch, Appl. Polym. Symp., 1969, vol. 8, p. 171. 296. V.V. Korshak, V.M. Mamedov, G.E. Golubkov, and D.R. Tur, Vysokomol. Soedin., 1970, vol. B12, p. 57. (Rus) 297. R.N. Johnson, A.G. Farnham, R.A. Glendinning, W.F. Hale, and C.N. Merriam, J. Polym. Sci., 1967, vol. A-1(5), p. 2375. 298. J.K. Gilham, and M.B. Roller, Polym. Eng. Sci., 1971, vol. 11, p. 295. 299. W.M. Edwards, and I.M. Robinson, US Pat. 2,710,853, 14 June 1955. 300. K.W. Doak, Modern Plastics Encyclopedia, 1967, vol. 45(1A), p. 14.

677

301. J.M. Barton, and J.P. Crichley, Polymer, 1970, vol. 11, p. 212. 302. S.L. Cooper, A.D. Mair, and A.V. Tobolsky, Textile Res. J., 1965, vol. 35, p. 1110. 303. J.H. Freeman, L.W. Frost, G.M. Bower, and E.J. Traynor, Conf. Structural Plastics, Adhesives, Filament Wound Composites, WPAFB, Dayton, Ohio, 1962, vol. 1, p. 30. 304. G.A. Bernier, and D.E. Kline, J. Appl. Sci., 1968, vol. 12, p. 593. 305. A.D. Mair, M.C. Shen, and A.V. Tobolsky, AD 604010, 1964, "High temperature polymers: HFilm and SP-Polymer", ONR Tech. Rept. RLT-83. 306. C.E. Sroog, J. Polym. Sci., 1967, vol. C16, p. 1191; data quoted from W.E. Tatum, L.E. Amborski, C.W. Gerow, J.F. Heacock, and R.S. Mallouk, Electrical Insulation Conf., Chicago, 1963. 307. A.V. Sidorovich, and Ye.V. Kuvshinskii, Polym. Sci. USSR, 1968, vol. 10, p. 1627; (Transl'n of Vysokomol. Soedin., 1968, vol. A10, p. 1401. (Rus)). 308. W. Wrasidlo, and J.M. Augl, J. Polym. Sci., 1969, vol. A-1(7), p. 321. 309. G.A. Progany, Polymer, 1970, vol. 11, p.66. 310. J.M. Augl, J. Polym. Sci., 1970, vol. A-1(8), p. 3145. 311. W.Wrasidlo, J. Polym. Sci., 1970, vol. A-1(8), p. 1107. 312. W. Wrasidlo, and J.M. Augl, J. Polym. Sci., 1969, vol. B7, p. 281. 313. P.W. Morgan, J. Polym. Sci., 1964, vol. A2, p. 437. 314. J.P. Critchley, V.C.R. McLoughlin, J. Thrower, and I.M. White, Brit. Polym. J., 1970, vol. 2, p. 288. 315. I.M. Dolgopol'skii, Kauchuk i Rezina, 1971, vol. 30(2), p. 31. (Rus) (transl'n in Soviet Rubber Technol., 1971, vol. 30(2), p. 38). 316. G.L. Brode, ACS Polym. Preprints, 1965, vol. 6, p. 626. 317. R.G. Beaman, J. Appl. Polym. Sci., 1965, vol. 9, p. 3949. 318. A. Schiller, J.C. Petropoulos, and C.S.H. Chen, J. appl. Polym. Sci., 1964, vol. 8, p. 1699. 319. M.E. Baird, G.T. Goldsworthy, and C.J. Creasey, J. Polym. Sci., 1968, vol. B6, p. 737. 320. M.E. Baird, J. Polym. Sci., 1970, vol. A-2(8), p. 739. 321. A.B. Thompson, and D.W. Woods, Trans. Faraday Soc., 1956, vol. 52, p. 1383. 322. H.A. Vogel, J. Polym. Sci., 1970, vol. A-1(8), p. 2035. 323. Z. Dobkowski, B. Krajewski, and Z. Weilgosz, Polim. Tworz. Wielk., 1970, vol. 15, p. 428. 324. R.F. Clash, and L.M. Runkieweiz, Ind. Eng. Chem., 1944, vol. 36, p. 279. 325. K.E. Perepelkin, Mekh. Polim., 1971, vol. 5, p. 790. (Rus) 326. G.P. Mikhailov, A.I. Artyukhov, and V.A. Polym. Sci. USSR, 1969, vol. 11, p. 553 (transl'n of Vysokomol. Soedin., 1969, vol. A11, p. 553). 327. F.E. Wiley, Ind. Eng. Chem., 1942, vol. 34, p. 1052. 328. W.J. Feast, W.K.R. Musgrave, and N. Reeves, J. Polym. Sci., 1971, vol. A-1(9), p. 2733. 329. N.H. Reinking, A.E. Bamabeo, and W.F. Hale, J. Appl. Polymer Sci., 1963, vol. 7, p. 2153. 330. J. Lai, and G.S. Trick, J. Polym. Sci., 1970, vol. A-1(8), p. 2339. 331. A.S. Hay, and R.F. Clark, Macromolecules, 1970, vol. 3, p. 533. 332. A.R. Blythe, and G.M. Jeffs, J. Macromol. Sci., 1969, vol. B3, p. 141. 333. D.J. Marks, Thesis, Manchester, Univ., 1961. 334. G.Allen, C. Booth, S.J. Hunt, C. Price, F. Vernon, and R.F. Warren, Polymer, 1967, vol. 8, p. 406. 335. P.G. Wapner, (supervisor: W.C. Forsman), PhD. Thesis, Univ. Pennsylvania, 1971; via Diss. Abstr. Intern., 1971, vol. B32, p. 2332. 336. N. Doddi, W.C. Forsman, and C.C. Price, Macromolecules, 1971, vol. 4, p. 648. 337. H. Schnell, L. Bottenbruch, G. Darsow, and K. Weirauch, Brit. 1,400.00, 15, Jan. 1969. 338. P.E. Wei, and P.E. Butler, J. Polym. Sci., 1968, vol. A-1(6), p. 2461. 339. V. Frosini, E. Butta, and M. Calamia, J. Appl. Polym. Sci., 1967, vol. 11, p. 527. 340. F.S. Dainton, D,M, Evans, F.E. Hoare, and T.P. Meila, Polymer, 1962, vol. 3, p. 271. 341. D.J.H. Sandiford, J. Appl. Chem., 1958, vol. 8, p. 188. 342. K.-H. Helwege, J. Hennig, and W. Knappe, Kolloid Z.-Z. Polym., 1962, vol. 186, p. 29. 343. K.-H. Helwege, R. Hoffman, and W. Knappe, Kolloid Z.-Z. Polym., 1968, vol. 226, p. 109. 344. M. Barccaredda, E. Butta, and V. Frosini, Eur. Polym. J., 1966, vol. 2, p. 423. 345. A. Nagai, T. Ishibashi, and M. Takayanagi, Rept. Progr. Polym. Phys. (Japan), 1967, vol. 10, p. 341. 346. A.I. Marei, Ye.A. Sidorovich, G.Ye. Novikova, and E.I. Rodina, Polym. Sci. USSR, 1968, vol. 10, p. 630 (transl'n of Vysokomol. Soedin., 1968, vol. 10, p. 542 (Rus)). 347. J.A. Faucher, and J.V. Koleske, Polymer, 1968, vol. 9, p. 44. 348. W.G. Miller, and J.H. Saunders, J. Appl. Polym. Sci., 1969, vol. 13, p. 1277. 349. Yu.K. Godovskii, and Yu.S. Lipatov, Polym. Sci. USSR, 1968, vol. 10, p. 34 (transl'n of Vysokomol. Soedin., 1968, vol. 10, p. 32 (Rus)).

678

350. A. Conix, J. Polym. Sci., 1958, vol. 29, p. 343. 351. R.H. Gobran, and M.B. Berenbaum, ACS Meeting 13, April 1958; via E.R. Bertozzi, Rubber Chem. Technol., 1968, vol. 41, p. 114. 352. A.V. Tobolsky, and W.J. MacKnight, in: H.F. Mark and E.H. Immergut (Eds.), "Polymer Reviews", vol. 13: Polymeric Sulfur and Related Polymer, Interscience, 1965, p. 35. 353. G. Williams, Trans. Faraday Soc., 1963, vol. 59, p. 1397. 354. B.E. Read, Polymer, 1962, vol. 3, p. 529. 355. A. Mele, A. Delle Site, C. Bettinali, and A. Di Domenico, J. Chem. Phys., 1968, vol. 49, p. 3297. 356. J.L. Zollinger, J.R. Throckmorton, S.T. Ting, R.A. Mitsch, and D.E. Elrick, J. Macromol. Sci., 1969, vol. A3, p. 1443. 357. W.A. Lee, Royal Aircraft Establishment, Farnsborough, Hants., UK - Unpublished results. 358. P. Johncock, M.A.H. Hewins, Royal Aircraft Establishment, Farnborough, Hants., UK Unpublished report. 359. N.H. Reinking, A.E. Bamabeo, and W.F. Hale, J. Appl. Polymer Sci., 1963, vol. 7, p. 2135. 360. K. Fujimoto, Chem. High Polym. (Japan), 1961, vol. 18, p. 415. 361. J. Heijboer, Brit. Polym., 1969, vol. 1, p. 3. 362. A.H. Willbourn, Kolloid Z. - Z. Polym., 1965, vol. 201, p. 20. 363. R.G. Saba, J.A. Sauer, and A.E. Woodward, J. Polym. Sci., 1963, vol. A1, p. 1483. 364. J.J. Stratta, F.P. Reding, and J.A. Faucher, J. Polym. Sci., 1964, vol. A2, p. 5017. 365. F.B. Cramer, and R.G. Beaman, J. Polym. Sci., 1956, vol. 21, p. 237. 366. W.W. Schartz, and R.D. Lowrey, J. Appl. Polym. Sci., 1967, vol. 11, p. 553. 367. P. Johncock, and P.A. Grattan, Royal Aircraft Establishment, Farnborough, Hants., UK Unpublished report. 368. P. Johncock, and J.D. Lee, Royal Aircraft Establishment, Farnborough, Hants., UK - Unpublished report. 369. A.T. DiBenedetto, and K.L. Trachte, J. Appl. Polym. Sci., 1970, vol. 14, p. 2249. 370. E. Butta, Matter, Plastics, Elastomers, 1969, vol. 35, p. 1411. 371. P.A. Gratten, V.C.R. McLoughlin, and W.A. Lee, Royal Aircraft Establishment, Farnborough, Hants., UK - Unpublished data. 372. L.W. Breed, R.L. Elliot, and M.E. Whitehead, J. Polym. Sci., 1967, vol. A-1(5), p. 2745. 373. L.T.C. Lee, and E.M. Pearce, J. Polym. Sci., 1971, vol. A-1(9), p. 557. 374. K. Saotome, and H. Komoto, J. Polym. Sci., 1966, vol. A-1(4), p. 1475. 375. J.C. Mileo, B. Sillion, and G. De Gaudemaris, Compt. Rend., 1969, vol. C268, p. 1949. 376. M.E.B. Jones, and I. Goodman, Brit. Pat. 1,128,807, 2, Oct. 1968. 377. D. Brown, M.E.B. Jones, and W.R. Maltman, J. Polym. Sci., 1968, vol. B6, p. 635. 378. V. Frosini, M. Pasquini, and E. Butta, Chim. Ind., 1971, vol. 53, p. 140. 379. E. Butta, S. de Petris, V. Frosini, and M. Pasquini, Eur. Polym. J., 1971, vol. 7, p. 387. 380. G.F.L. Ehlers, R.C. Evers, and K.R. Fisch, J. Polym. Sci, 1969, vol. A-1(7), p. 3413. 381. B.E. Jennings, M.E.B. Jones, and J.B. Rose, J. Polym. Sci, 1967, vol. C16, p. 715. 382. M.E.A. Cudby, R.G. Feasey, B.E. Jennings, M.E.B. Jones, and J.B. Rose, Polymer, 1965, vol. 6, p. 589. 383. J.E. Kurz, J.C. Woodbrey, and M. Ohta, J. Polym. Sci., 1970, vol. A-2(8), p. 1169. 384. H. Schnell, Ind. Eng. Chem., 1959, vol. 51, p. 157. 385. A.N. Perepelkin, and P.V. Kozlov, Polymer Sci. USSR, 1966, vol. 8, p. 56 (transl'n of Vysocomol. Soedin., 1966, vol. 8, p. 56 (Rus)). 386. F.P. Reding, J.A. Faucher, and R.D. Whitman, J. Polym. Sci., 1961, vol. 54, p. S56. 387. L.J. Garfield, J. Polym. Sci., 1970, vol. C30, p. 561. 388. H. Schnell, "Chemistry and Physics of Polycarbonates", 1964, Interscience, New York, Chap. III. 389. B.F. Malichenko, V.I. Feoktistova, and A.E. Nesterov, Vysokomol. Soedin., 1969, vol. B11, p. 543. (Rus) 390. E.N. Elam, J.C. Martin, and R. Gilkey, US Pat. 3,313,777, 11 April, 1967 (Brit. 962,913). 391. W. Gawlak, R.P. Palmer, J.B. Rose, D.J. Sandford, and A. Turner-Jones, Chem. Ind., 1962, vol. 25, p. 1148. 392. A.A. D'Onofrio, Brit. Pat. 1,011,283, 24 Nov., 1965. 393. O.V. Smirnova, El Said Ali Kasan, I.P. Losev, and G.S. Kolesnikov, Polymer Sci. USSR, 1965, vol. 7, p. 557 (transl'n of Vysokomol. Soedin., 1965, vol. 7, p. 503 (Rus)). 394. H. Schnell, Angew. Chem., 1956, vol. 68, p. 633. 395. US Patent 3,546,165, Dec. 8, 1970, assigned to P.W. Morgan. 396. D. Stefan, H.L. Williams, D.R. Renton, and M.M. Pintar, J. Macromol. Sci., 1970, vol. B4, p. 853. 397. D.W. McCall, and D.R. Falcone, Trans. Faraday Soc., 1970, vol. 66, p. 262.

679

398. S. Matsuoka, and Y. Ishida, J. Polym. Sci., 1966, vol. C14, p. 247. 399. F. Krum, and F.H. Muller, Kolloid. Z., 1959, vol. 164, p. 81. 400. G.P. Mikhailov, and M.P. Eidel'nant, Vysokomol. Soedin., 1960, vol. 2, p. 287. (Rus) 401. J. Bussink, J. Heijboer, and J.A. Prins (Ed.), " Physics of Non-Crystalline Solids", Proc. Intern. Conf., Delft, 1964, p. 388, North Holland Publishing Co., Amsterdam, 1965. 402. B. von Falkai, and W. Rellensmann, Makromol. Chem., 1964, vol. 75, p. 112. 403. E.V. Gouinlock, E.J. Quinn, H.W. Marciniak, and R.R. Hindersinn, IUPAC Preprints, Intern. Symp. Macromol. Chem., Toronto, Sect. A13.3, 1968. 404. H.G. Weyland, C.A.M. Hoefs, K. Yntema, and M.J. Mijs, Eur. Polym. J., 1970, vol. 6, p. 1339. 405. T. Takekoshi, ACS Polym. Preprints, 1969, vol. 10, p. 103. 406. G. Bier, Adv, Chem. Ser., 1969, vol. 91, p. 612. 407. A. Conix, IUPAC Preprints, Intern. Symp. Macromol. Chem., Montreal, Sect. D39, 1961; via O.G. Lewis, "Physical Constants of Linear Homopolymers", Springer-Verlag, 1968. 408. C.S. Marvel, and C.H. Young, J. Amer. Chem. Soc., 1951, vol. 73, p. 1066. 409. W.A. Lee, and B. Stag, Royal Aircraft Establishment, Farnborough, Hants, UK, TR 71,223, 1971. 410. V.C.R. McLoughlin, J. Thrower, M.A.H. Hewins, J.S. Pippett, and M.A. White, Royal Aircraft Establishment, Farnborough, Hants, UK, TR 70,160, 1970. 411. I.N. Duling, US Pat. 3,436,376, April 1, 1969. 412. H.J. Kolb, and E.F. Izard, J. Appl. Phys., 1949, vol. 20, p. 564. 413. Y. Wada, J. Phys. Soc. (Japan), 1961, vol. 16, p. 1226. 414. I.M. Ward, Textile Res. J., 1961, vol. 13, p. 650. 415. L. Mandelkern, G.M. Martin, and A. Quinn, J. Res. Nat. Bur. Std., 1957, vol. 58, p. 137. 416. G. Farrow, J. McIntosh, and I.M. Ward, Makromol. Chem., 1960, vol. 38, p. 147. 417. J.G. Smith, C.J. Kibler, and B.J. Sublett, J. Polym. Sci., 1966, vol. A-1(4), p. 1851; values from R.M. Schulken, R.E. Boy, and R.H. Cox, J. Polym. Sci., 1964, vol. C6, p. 17. 418. I.M. Dolgopol'skii, Kh.A. Dobina, V.S. Fikhteingol'ts, S.A. Kamysheva, M.I. Sinaiskaya, L.G. Balashova, and R.V. Zolotareva, Polymer Sci. USSR, 1967, vol. 9, p. 1723 (transl'n of Vysokomol. Soedin, 1967, vol. A9, p. 1536 (Rus)). 419. E.V. Gouinlick, C.J. Verbanic, and G.C. Schweiker, J. Appl. Polym. Sci., 1959, vol. 1, p. 361. 420. W.R. Griffin, Rubber World, 1957, vol. 136, p. 687. 421. G.C. Schweiker, and P. Robitschek, J. Polym. Sci., 1957, vol. 24, p. 33. 422. J.H. Sewll, Royal Aircraft Establishment, Farnborough, Hants, UK, unpublished results. 423. I.J. Goldfarb, and R. McGuchan, AD 697987, 1987. 424. R.C. Evers, and G.F.L. Ehlers, J. Polym. Sci., 1969, vol. A-1(7), p. 3020. 425. A Conix, Ind. Eng. Chem., 1959, vol. 51, p. 147. 426. V. Frosini, and G. Vallebona, Chim. Ind., 1970, vol. 52, p. 499. 427. C.S. Marvel, and J.H. Johnson, J. Amer. Chem. Soc., 1950, vol. 72, p. 1674. 428. S.M. Somerville, and I.M. White, Royal Aircraft Establishment, Farnborough, Hants, UK, TR 66345, 1966. 429. I.M. White, M.A.H. Hewins, and S.M. Somerville, paper presented at 2nd Intern. Symp. Organosilicon Chem., Univ. Bordeaux, July 9-12, 1968. 430. W.A. Lee, and I.H. Sewell, Royal Aircraft Establishment, Farnborough, Hants, UK, unpublished results. 431. W.A. Lee, and F. Pinchin, Royal Aircraft Establishment, Farnborough, Hants, UK, unpublished results. 432. French Pat. 1,175,362, 1959; Brit. Pat. 863, 704, 1961, via G.F.L. Ehlers, R.C. Evers, and K.R. Fisch, J. Polym. Sci, 1969, vol. A-1(7), p. 3413. 433. W.M. Eareckson, J. Polym. Sci., 1959, vol. 40, p. 399. 434. V.V. Korshak, S.V. Vinogradova, C.L. Slonimskii, Ya.S. Vygodskii, S.N. Salazkin, A.A. Askadskii, A.I. Mzhel'skii, and V.P. Sidorova, Polym. Sci. USSR, 1968, vol. 10, p. 2395 (transl'n of Vysokomol. Soedin., 1968, vol. A10, p. 2058 (Rus)). 435. W.A. Lee, I.M. White, and F. Pinchin, Royal Aircraft Establishmant, Farnborough, Hants, UK, unpublished results. 436. K.A. Gol'dgammer, G.G. Pimenov, A.I. Maklakov, V.V. Korshak, S.V. Vinogradova, P.M. Valetskii, and A.N. Baskakov, Vysokomol. Soedin., 1968, vol. A10, p. 821 (Rus); (transl'n of Polym. Sci. USSR, 1968, vol. 10, p. 953). 437. R.L. Combs, and R.G. Nations, J. Polym. Sci., 1970, vol. C30, p. 407 (unpublished results of T.F. Gray).

680

438. V.V. Korshak, G.L. Berestneva, S.V. Vinogradova, A.N. Baskakov, and P.M. Valetskii, Polymer Sci. USSR, 1968, vol. 10, p. 2300 (transl'n of Vysokomol. Soedin., 1968, vol. A10, p. 1984 (Rus)). 439. S.S. Karapetyan, A.Ya. Yakubovich, and I.L. Knunyants, Polym. Sci. USSR, 1964, vol. 6, p. 1718 (transl'n of Vysokomol. Soedin., 1964, vol. 6, p. 1550 (Rus)). 440. J.E. McIntyre, and E.C. Pugh, Brit. Pat. 838,986, 1960. 441. K. Saotome, and H. Komoto, J. Polym. Sci., 1967, vol. A-1(5), p. 119. 442. W.J. MacKnight, M. Yang, and T. Kajiyama, ACS Polym. Preprints, 1968, vol. 9, p. 860. 443. D.J. Lyman, J. Heller, and M. Borlow, Makromol. Chem., 1965, vol. 84, p. 64. 444. M.A. McCall, J.R. Caldwell, H.G. Morre, and H.M. Beard, J. Macromol. Sci., 1969, vol. A3, p. 911. 445. P.D. Schumann, E.C. Stump, and G. Westmoreland, J. Macromol. Sci., 1967, vol. B1, p. 815. 446. Yu.A. Yuzhelevskii, E.G. Kagan, A.L. Klebanskii, I.A. Zevakin, and A.V. Kharlamova, Vysokomol. Soedin., 1969, vol. B11, p. 854. (Rus) 447. M.S. Paterson, J. Appl. Phys., 1964, vol. 35, p. 176. 448. K.A. Andrianov, T.K. Dzhashiashvili, V.V. Astakin, and G.N. Shumakavo, Vysokomol. Soedin., 1968, vol. B10, p. 766. (Rus) 449. K.A. Andrianov, and S.E. Yakushkina, Vysokomol. Soedin., 1962, vol. 4, p. 1193. (Rus) 450. V.C.R. McLoughlin, and P.A. Grattan, Royal Aircraft Establishment, Farnborough, Hants, UK, TR 71224, 1971. 451. R.E. Burks, and J.L. Greene, N68-16509; Southern Res. Inst. Rept., 25, 1967. 452. J.A. Empen, and J.K. Stille, in: N.G. Gaylord (Ed.), "Macromolecular Synthesis", 3, Wiley, New York, 1969, p. 15. 453. Polymer Handbook, Eds. J. Brandrup, E.H. Immergut, and E.A. Grulke, Associate Eds. A. Abe, and D.R. Bloch, 4th Edition, 1999, Wiley, New York. 454. A. Nicco, J.P. Machon, H. Fremaux, J.Ph. Pied, B. Zindy, and M. Thiery, Eur. Polym. J., 1970, vol. 6, p. 1427. 455. R.S. Nevin, and E.M. Pearce, J. Polym. Sci., 1965, vol. B3, p. 487. 456. W.J. Middleton, H.W. Jacobson, R.E. Putnam, H.C. Walter, D.G. Pye, and W.H. Sharkey, J. Polym. Sci., 1965, vol. A3, p. 4115. 457. V.A. Engelhardt; report in Chem. Eng. News, 1965, vol. 43, p. 80. 458. W.H. Sharkey, W.J. Middleton, H.W. Jacobson, O.S. Acker, and H.C. Walter, Chem. Eng. News, 1963, vol. 41, p. 46. 459. J.A. Empen, and J.K. Stille, in: N.G. Gaylord (Ed.), "Macromolecular Synthesis", 3, Wiley, New York, 1969, p. 53. 460. C.C. Price, and E.A. Blair, J. Polym. Sci., 1967, vol. A-1(5), p. 171. 461. R.M. Fitch, and D.C. Helgeson, J. Polym. Sci., 1969, vol. C22, p. 1101. 462. M. Morton, R.F. Kammereck, and L.J. Fetters, Brit. Polym. J., 1971, vol. 3, p. 120. 463. H. Komoto, Rev. Phys. Chem. (Japan), 1967, vol. 37, p. 112. 464. J. Pellon, J. Polym. Sci., 1963, vol. A1, p. 3561. 465. C.G. Overberger, and J.K. Weise, J. Amer. Chem. Soc., 1968, vol. 90, p. 3538. 466. H.G. Buhrer, and H.-G. Elias, Makromol. Chem., 1970, vol. 140, p. 41. 467. M.E.B. Jones, SPE Tech. Papers, 15, 27th ANTEC, Chicago, 1969, p. 453. 468. G. Jarrett, and M.E.B. Jones, Brit. Polym. J., 1970, vol. 2, p. 229. 469. H.Wexler, Makromol. Chem., 1968, vol. 115, p. 262. 470. R.G. Beaman, and F.B. Cramer, J. Polym. Sci., 1956, vol. 21, p. 223. 471. J.H. Magill, J. Polym. Sci., 1965, vol. A3, p. 1195. 472. B.Ke, and A.W. Sisko, J. Polym. Sci., 1961, vol. 50, p. 87. 473. Y.Nishijima, J. Selki, and T. Kawai, Rept. Progr. Polym. Phys. (Japan), 1967, vol. 10, p. 473. 474. V. Frosini, and E. Butta, J. Polym. Sci., 1971, vol. B9, p. 253. 475. D.C. Prevorsek, R.H. Butler, and K.H. Reimschuessel, J. Polym. Sci., 1971, vol. A-2(9), p. 867. 476. K. Schmieder, and K. Wolf, Kolloid Z., 1953, vol. 134, 149. 477. H. Komoto, Rev. Phys. Chem. (Japan), 1967, vol. 37, p. 105. 478. K. Saotome, and H. Komoto, J. Polym. Sci., 1966, vol. A-1(4), p. 1463. 479. H. Komoto, and K. Saotome, Chem. High Polymers (Japan), 1965, vol. 22, p. 337; Chem. Abstr., 1965, vol. 56, p. 15045f. 480. G. Champetier, and J.P. Pied, Makromol. Chem., 1961, vol. 44/46, p. 64; Chem. Abstr., 1962, vol. 56, p. 1584c. 481. B.S. Marks, and G.C. Schweiker, J. Polym. Sci., 1960, vol. 43, p. 229. 482. D.A. Holmer, J. Polym. Sci, 1968, vol. A-1(6), p. 3177.

681

483. J.C. Mileo, B. Sillion, and G. De Gaudemaris, Compt. Rend., 1969, vol. C268, p. 2007. 484. J.B. Jackson, Polymer, 1969, vol. 10, p. 159. 485. L.C. Glover, and B.J. Lyons, ACS Polymer Preprints, 1968, vol. 9, p. 243. 486. G.A. Kuznetsov, V.D. Gerasimov, L.N. Fomenko, A.I. Maklakov, G.G. Pimenov, and L.B. Sokolov, Polym. Sci. USSR, 1965, vol. 7, p. 1763 (transl'n of Vysokomol. Soedin., 1965, vol. 7, 1592 (Rus)). 487. G.S. Kolesnikov, O.Ya. Fedotova, V.V. Trezov, and V.N. Kuz'micheva, Polym. Sci. USSR, 1968, vol. 10, p. 2612 (transl'n of Vysokomol. Soedin., 1968, vol. 10, p. 2248 (Rus)). 488. E. Bessler, and G. Bier, Makromol. Chem., 1969, vol. 122, p. 30. 489. N.S. Nametkin, N.V. Ushakov, and V.M. Vdovin, Polym. Sci. USSR, 1971, vol. 13, p. 31 (transl'n of Vysokomol. Soedin., 1971, vol. A13, p. 29 (Rus)). 490. N.S. Nametkin, V.M. Vdovin, and V.I. Zav'yalov, Doklady Akad. Nauk SSSR, 1965, vol. 162, p. 824. (Rus) 491. F.S. Model, G. Redl, and E.-G. Rochow, J. Polym. Sci., 1966, vol. A-1(4), p. 639. 492. F.S. Model, and E.G. Rochow, J. Polym. Sci., 1970, vol. A-2(8), p. 999. 493. N.S. Nametkin, V.M. Vdovin, and V.I. Zav'yalov, Polym. Sci. USSR, 1965, vol. 7, p.836 (transl'n of Vysokomol. Soedin., 1965, vol. 7, p. 757 (Rus)). 494. M. Morton, J. Elastoplastics, 1971, vol. 3, p. 112. 495. E. Jenckel, Kolloid Z., 1942, vol. 100, p. 163. 496. M.L. Dannis, J. Appl. Polym. Sci., 1959, vol. 1, p. 121. 497. R.H. Gerke, J. Polym. Sci., 1954, vol. 13, p. 295. 498. R.H.Gerke, J. Polym. Sci., 1954, vol. 13, p. 295. 499. W. Marconi, A. Mazzel, G. Ligni, and M. Bruzzone, J. Polym. Sci., 1967, vol. C16, p. 805. 500. D.I. Relyea, H.P. Smith, and A.N. Johnson, 1967, AD 657675. 501. W.R. Brown, and G.S. Park, Paint Technol., 1970, vol. 42, p.16. 502. F. Haas, K. Nutzel, S. Pampus, and D. Theisen, Rubber Chem Technol., 1970, vol. 43, p. 1116. See also Kautschuk Gummi Kunststoffe, 1970, vol. 23, S. 502. 503. M. Takeda, K. Tanaka, and R. Nagao, J. Polym. Sci., 1962, vol. 57, p. 517. 504. I.A. Livshits, L.M. Korobova, and E.A. Sidorovich, Mekh. Polim., 1967, vol. 4, p. 596. (Rus) 505. C.G. Overberger, L.H. Arond, R.H. Wiley, and R.R. Garrett, J. Polym. Sci., 1951, vol. 7, p. 431. 506. W. Marconi, A. Mazzei, S. Cucinella, and M. Cesari, J. Polym. Sci., 1964, vol. B2, p. 4261. 507. I.A. Livshits, and L.M. Korobova, Dokl. Akad. Nauk SSSR, 1958, vol. 121, p. 474. (Rus) 508. G. Dall'asta, and P. Scaglione, Rubber Chem. Technol., 1969, vol. 42, p. 1235. 509. K.J. Clark, A.T. Jones, and D.H. Sandford, Chem. Ind., 1962, vol. 47, p. 2010. 510. G. Natta, F. Danusso, and G. Moraglio, J. Polym. Sci., 1957, vol. 25, p. 119. 511. K.R. Dunham, J. Vandenberghe, J.W.H. Faber, and L.E. Contois, J. Polym. Sci., 1963, vol. A1, p. 751. 512. G. Natta, Rend. Accad. Nazi. Lincei. Ser., 1958, vol. 8, p. 24; via Ref. 223. 513. S.F. Kurath, E. Passaglia, and R. Pariser, J. Appl. Phys., 1957, vol. 28, p. 499. 514. F.P. Reding, J.A. Faucher, and R.D. Whitman, J. Polym. Sci., 1962, vol. 57, p. 483. 515. H.-G. Elias, and O. Etter, J. Macromol. Sci., 1967, vol. A1, p. 943. 516. W.H. McCarty, and G. Parravano, J. Polym. Sci., 1965, vol. A3, p. 4029. 517. G.L. Taylor, and S. Davison, J. Polym. Sci., 1968, vol. B699. 518. S.T. Barsamyan, A.S. Apresyan, V.I. Kleiner, and L.L. Stotskaya, Soviet Plastics, 1968, vol. 3, p. 17 (transl'n of Plasticheskie Massy, 1968, vol. 3, p. 13 (Rus)). 519. R.E. Kelchner, and J.J. Aklonis, J. Polym. Sci., 1970, vol. A-2(8), p. 799. 520. A. Abe, and T. Hama, J. Polym. Sci., 1969, vol. B7, p. 427. 521. M. Takayanagi, Pure Appl. Chem., 1970, vol. 23, p. 151. 522. M. Baccaredda, and E. Butta, Chim. Ind. (Milan), 1962, vol. 44, p. 1228. 523. A.V. Tobolsky, "Properties and Structure of Polymers", 1960, Wiley, New York. 524. R.A. Jackson, S.R.D. Oldland, and A. Pajaczkowski, J. Appl. Polym. Sci., 1968, vol. 12, p. 1297. 525. J.P. Kennedy, W. Naegele, and J.J. Elliott, J. Polym. Sci., 1965, vol. B3, p. 729. 526. O.E. Van Lohuizen, and K.S. De Vries, J. Polym. Sci., 1968, vol. C16, p. 3943. 527. A.E. Woodward, Trans. N.Y. Acad. Sci., 1962, vol. 24, p. 250. 528. A.E. Woodward, J.A. Sauer, and R.A. Wall, J. Polym. Sci., 1961, vol. 50, p. 117. 529. J.H. Griffith, and B.G. Ranby, J. Polym. Sci., 1960, vol. 44, p. 369. 530. R.W. Penn, Trans. Soc. Rheol., 1963, vol. 3, p. 416. 531. W.A. Hewett, and F.E. Weir, J. Polym. Sci., 1963, vol. A1, p. 1239. 532. F.E. Karasz, H.E. Bair, and J.M. O'Reilly, Polymer, 1967, vol. 8, p. 547. 533. T.P. Melia, and A. Tyson, Makromol. Chem., 1967, vol. 109, p. 87.

682

534. I. Kirshenbaum, R.B. Isaacson, and M. Druin, J. Polym. Sci., 1965, vol. B3, p. 525. 535. N. Kawasaki, and M. Takayanagi, Rept. Progr. Polym. Phys. (Japan), 1967, vol. 10, p. 337. 536. R.G. Quynn, and B.S. Sprague, J. Polym. Sci., 1970, vol. A-2(8), p. 1971. 537. A.A. Miller, J. Polym. Sci., 1968, vol. A-2(6), p. 249. 538. G. Gianotti, G. Dall'asta, A. Valvassori, and V. Zamboni, Makromol. Chem., 1971, vol. 149, p. 117. 539. A.Turner, and F.E. Bailey, J. Polym. Sci., 1963, vol. B1, p. 601. 540. J.P. Kennedy, and R.M. Thomas, Macromol. Chem., 1963, vol. 64, p. 1. 541. J.P. Kennedy, and R.M. Thomas, Macromol. Chem., 1962, vol. 53, p. 28. 542. J.P. Kennedy, J.J. Elliott, and B. Groten, Macromol. Chem., 1964, vol. 77, p. 26. 543. G. Gianotti, and A. Capizzi, Eur. Polym. J., 1968, vol. 4, p. 677. 544. G.M. Pogosyan, G.A. Zhamkochyan, and S.G. Matsoyan, Arm. Khim. Zh., 1969, vol. 22, p. 364. (Rus) 545. G.M. Pogosyan, L.M. Akopyan, E.V. Vanyan, and S.G. Matsoyan, Vysokomol. Soedin., 1971, vol. B13, p. 242. (Rus) 546. W. Kern, W. Heitz, M. Jager, K. Pfitzner, and H.O. Wirth, Makromol. Chem., 1969, vol. 126, p. 73. 547. G.M. Pogosyan, L.M. Akopyan, E.V. Vanyan, and S.G. Matsoyan, Vysokomol. Soedin., 1970, vol. B12, p. 142. (Rus) 548. K.R. Dunham, J.W.H. Faber, J. Vandenberghe, and W.F. Fowler, J. Appl. Polym. Sci., 1963, vol. 7, p. 897. 549. R. Kosfeld, Kolloid Z., 1960, vol. 172, p. 182. 550. K.H. Illers, Z. Elektrochem., 1961, vol. 65, p. 679. 551. G.M. Pogosyan, T.G. Karapetyan, and S.G. Matsoyan, Vysokomol. Soedin., 1971, vol. B13, p. 228. (Rus) 552. E.C. Chapin, J.G. Abrams, and V.L. Lyons, J. Org. Chem., 1962, vol. 27, p. 2595. 553. G.S. Kolesnikov, and G.M. Pogosyan, Izv. Akad. Nauk SSSR, Otd. Khim. Nauk, 1958, vol. 2, p. 227. 554. C.G. Overberger, C. Frazier, J. Mandelman, and H.F. Smith, J. Amer. Chem. Soc., 1953, vol. 75, p. 3326. 555. T.E. Davies, British Plastics, 1959, vol. 32, p. 283. 556. G.M. Pogosyan, T.G. Karapetyan, and S.G. Matsoyan, Vysokomol. Soedin., 1970, vol. B12, p. 463. (Rus) 557. G.S. Kolesnikov, Izv. Akad. Nauk SSSR, Otd. Khim Nauk, 1959, p. 1333. (Rus) 558. K.R. Dumham, J. Vandenberghe, J.W.H. Faber, and W.F. Fowler, J. Appl. Polym. Sci., 1963, vol. 3, p. 1531. 559. Brit. Pat. 609,482, 1 Oct. 1948. 560. S. Krause, J.J. Gormley, N. Roman, J.A. Shetter, and W.H. Watanabe, J. Polym. Sci., 1965, vol. A3, p. 3573. 561. J. Thrower, and M.A.H., Royal Aircraft Establishment, Farnborough, Hants, UK, TR 70056, 1970. 562. R.A. Abdrashitov, N.M. Bazhenov, M.V. Vol'kenstein, A.I. Kol'tsov, and A.S. Khachaturov, Vysocomol. Soedin., 1963, vol. 5, p. 405; (transl'n in Polymer Sci. USSR, 1963, vol. 4, p. 1066); Z. Phys. Chem., 1962, vol. 220, p. 413. 563. F. Danusso, and G. Polizzotti, Makromol. Chem., 1963, vol. 61, p. 157. 564. K. Tanaka, O. Yano, S. Manu, and R. Nagao, Rept. Progr. Polym. Phys. (Japan), 1969, vol. 12, p. 379. 565. R.A. Abdrashitov, N.M. Bazhenov, M.V. Vol'kensthtein, A.I. Kol'tsov, and A.S. Khachaturov, Polym. Sci. SSSR, 1964, vol. 6, p. 2074; (transl'n of Vysocomol. Soedin., 1964, vol. 6, p. 1871). 566. US Pat. 2,651,627, 8 Sept. 1953. 567. G.M. Pogosyan, G.A. Zhamkochyan, R.A. Stepanyan, and S.G. Matsoyan, Arm. Khim. Zh., 1969, vol. 22, p. 915. (Rus) 568. Polaroid Corp., Offic. Sci. Res. Dev. Rept. No. 4417, p. 246, Feb. 1945. 569. V. Frosini, and P.L. Magagnini, Eur. Polym. J., 1966, vol. 2, p. 129. 570. V. Frosini, and E. Butta, Mater. Sci. Eng., 1970, vol. 6, p. 274. 571. E. Rovira, and A. Eisenberg. Unpublished results quoted by: M.C. Shen, and A. Eisenberg in: "Progress in Solid State Chemistry", Ed. by H. Reiss, 1966, vol. 3, Pergamon Press, New York, p. 407; reprint in Rubber Chem. Technol., 1970, vol. 43, p. 95. 572. G.T. Kennedy, and F. Morton, J. Chem. Soc., 1949, p. 2383. 573. L.C. Corrado, J. Chem. Phys., 1969, vol. 50, p. 2260.

683

574. W. Hodes, American Cyanamid Co. Unpublished results quoted by O.G. Lewis in "Physical Constants of Linear Homopolymers", Springer-Verlag, 1968. 575. G.S. Kolesnikov, and G.M. Pogosyan, Izv. Akad. Nauk SSSR, Otd. Khim. Nauk, 1962, p. 2098; Chem. Abstr., 1963, vol. 58, p. 8047a. 576. L.A. Utracki, and R Simha, Makromol. Chem., 1968, vol. 117, p. 94. 577. M. Bank, J. Leffingwell, and C, Thies, Macromolecules, 1971, vol. 4, p. 43. 578. M. Baccaredda, P.L. Magagnini, G. Pizzirani, and P. Giusti, J. Polym. Sci., 1971, vol. B9, p. 303. 579. E.C. Eberlin. Unpublished values quoted by Ref. 44. 580. E.C. Eberlin, unpublished data quoted by O.G. Lewis, "Physical Constants of Linear Homopolymers", Springer-Verlag, 1968. 581. C.E. Rehberg, and C.H. Fisher, Ind. Eng. Chem., 1948, vol. 40, p. 1429. 582. C.E. Rehberg, W.A. Faucette, and C.H. Fisher, J. Am. Chem. Soc., 1944, vol. 44, p. 1723. 583. J.A. Shetter, J. Polym. Sci., 1963, vol. B1, p. 209. 584. J.A. Monahan, J. Polym. Sci., 1966, vol. A-1(4), p. 2381. 585. G. Pizzirani, and P.L. Magagnini, Chim. Ind. (Milan), 1968, vol. 50, p. 1218. 586. V.P. Shibayev, B.S. Petrukhin, Yu.A. Zubov, N.A. Plate, and V.A. Krgin, Polym. Sci. USSR, 1968, vol. 10, p. 258. 587. F.A. Boyer, and J.F. Abere, J. Polym. Sci., 1955, vol. 15, 537. 588. G.P. Mikhailov, and V.A. Shevelev, Polym. Sci. USSR, 1967, vol. 9, p. 2762 (transl'n of Vysokomol. Soedin. 1967, vol. A9, p. 2442 (Rus)). 589. F.A. Bovey, J.F. Abere, G.B. Rathmann, and C.L. Sandberg, J. polym. Sci., 1955, vol. 15, p. 520. 590. A.S. Khachaturov, N.M. Bazhenov, M.V. Vol'kenstein, I.M. Dolgopol'skii, and A.I. Kol'tsov, Soviet Rubber Technol., 1965, vol. 24(12), p. 9 (transl'n of Kauchuk i Rezina, 1965, vol. 24(12), p. 6 (Rus)). 591. A.G. Pittman, B.A. Ludwig, and D.L. Sharp, J. Poym. Sci., 1968, vol. A-1(6), p. 1741. 592. W.R. Sorenson, and T.W. Campbell, "Preparative Methods of Polymer Chemistry", 2nd Ed., 1968, p. 248. 593. E.P. Otocka, and T.K. Kwei, Macromolecules, 1968, vol. 1, p. 401. 594. J.R. Constanza, and J.A. Vona, J. Polym. Sci., 1966, vol. A-1(4), p. 2659. 595. F. Wuerstlin, in: H.A. Stuart (Ed.), "Die Physik der Hochpolymeren", Springer, Berlin, 1955, Chap. 11. 596. R.A. Haldon, and R.Simha, J. Appl. Phys., 1968, vol. 39, p. 1890. 597. A.V. Tobolsky, and M.C. Shen, J. Phys. Chem., 1963, vol. 67, p. 1886. 598. S.S. Rogers, and L. Mandelkern, J. Phys. Chem., 1957, vol. 61, p. 985. 599. E.A.W. Hoff, D.W. Robinson, and A.H. Willbourn, J. Polym. Sci., 1955, vol. 18, p. 161. 600. J. Lal, and G.S. Trick, J. Polym. Sci., 1964, vol. A2, p. 4559. 601. G. Williams, and D.C. Watts, Trans. Faraday Soc., 1971, vol. 67, p. 2793. 602. W.M. Lee (advisers: F.R. Eirich and B.R. McGarvey), Dissertation, Polytechn. Inst., Brooklyn, 1967: via Diss. Abs., 1967, vol. B28, p. 1897. 603. E.N. Rostovskii, and L.D. Rubinovich, Vysokomol. Soedin., Karb. Vys. Soedin., Sb. Statei, 1963, p. 140. (Rus) 604. M.C. Chen, J.D. String, and F.J. Matusik, J. Macromol. Sci., 1967, vol. B1, p. 15. 605. J. Janacek, and J.D. Ferry, J. Macromol. Sci., 1971, vol. B5, p. 219. 606. F. Lednicky, and J. Janacek, J. Macromol. Sci., 1971, vol. B5, p. 335. 607. H. Ochiai, H. Shindo, and H. Yamamura, J. Polym. Sci., 1971, vol. A-2(9), p. 431. 608. A.K. Schulz, J. Chim. Phys., 1956, vol. 53, p. 933. 609. N.N. Aylward, J. Polym. Sci., 1970, vol. A-1(8), p. 319. 610. T.I. Borisova, Vysokomol. Soedin., 1970, vol. A12, p. 932 (Rus) (transl'n in Polymer Sci. USSR, 1970, vol. 12, p 1060). 611. G.M. Chetyrkina, T.A. Sokolova, and M.M. Koton, Vysokomol. Soedin., Vsesoyuz. Khim. Obshchestvo im. D.I. Mendeleeva, 1959, vol. 1, p. 248; Chem Abstr., 1959, vol. 53, p. 23059i. 612. B.E. Tate, Adv. Polym. Sci., 1967, vol. 5, p. 214 (Unpublished results of Charles Pfizer and Co. Inc.). 613. J.B. Kinsingr, J.R. Panchak, R.L. Kelso, J.S. Bartlett, and R.K. Graham, J. Appl. Polym. Sci., 1965, vol. 9, p. 429. 614. B.Wesslen, and R.W. Lenz, ACS Polym. Preprints, 1970, vol. 11, p. 105. 615. J.A. Powell, and R.K. Graham, J. Polym. Sci., 1965, vol. A-1(3), p. 3451. 616. J.A. Powell, and R.K. Graham, J. Polym. Sci., 1965, vol. A-1(3), p. 3451. 617. V.A. Kargin, and T.I. Sogolova, Zh. Fiz. Khim., 1949, vol. 23, p. 540. (Rus) 618. H.D. Anspon, and J.J. Baron, WADC Tech' 1 Report 57-24, Pt. 1, 1957, Pt. 11, 1958; via ref. 616.

684

619. H. Yuki, K. Hatada, T. Nijnomi, M. Hashimoto, and J. Ohshima, Polym. J. (Japan), 1971, vol. 2, p. 759. 620. R.A. Haldon, W.J. Schell, and R. Simha, J. Macromol. Sci., 1967, vol. B1, p. 759. 621. D.S. Otto, Vinyl Technol. Newsletter, 1968, vol. 5, p. 20. 622. W.J. Schell, R. Simha, and J.J. Aklonis, J. Macromol. Sci., 1969, vol. A3, p. 1297. 623. W.J. Schell, Thesis, Univ. S. California, 1969; via Diss. I Abstr. Intern., 1969, vol. B30, p. 2120. 624. L. Fishbein, and B.F. Crowe, Macromol. Chem., 1961, vol. 48, p. 221. 625. E.J. Vandenberg, R.F. Heck, and D.S. Breslow, J. Polym. Sci., 1959, vol. 41, p. 519. 626. C.E. Schildkecht, S.T. Gross, H.R. Davidson, J.M. Lambert, and A.O. Zoss, Ind. Eng. Chem., 1948, vol. 40, p. 2104. 627. G.M. Pogosyan, E.S. Avanesyan, and S.G. Matsoyan, Arm. Khim. Zh., 1971, vol. 24, p. 694. (Rus) 628. G. Pizzirani, P. Magagnini, and P. Giusti, J. Polym. Sci., 1971, vol. A-2(9), p. 1133. 629. J.D. Hoffman, J. Amer. Chem. Soc., 1952, vol. 74, p. 1696. 630. R.F. Boyer, J. Appl. Phys., 1954, vol. 25, p. 825. 631. F.P. Reding; private communication to Ref. 946. 632. J.D. Hoffman, and J.J. Weeks, J. Polym. Sci., 1958, vol. 28, p. 472; J. Res. Nat. Bur. Std., 1958, vol. 60, p. 465. 633. T. Nakajima, and S. Saito, J. Polym. Sci., 1958, vol. 31, p. 423. 634. A. Nishioka, J. Polym. Sci., 1959, vol. 37, p. 163. 635. F. Krum, Kolloid Z., 1959, vol. 165, p. 77. 636. K.-H. Illers, and E. Jenckel, Kolloid Z., 1959, vol. 165, p. 84. 637. M. Baccaredda, and E. Butta, J. Polym. Sci., 1960, vol. 44, p. 421. 638. A.W. Meyers, V. Tammela, V. Stannett, and M. Szwarc, Mod. Plast., 1960, vol. 37, p. 139. 639. N.G. McGrum, J. Polym. Sci., 1962, vol. 60, p. 53. 640. A.H. Scott, D.J. Scheiber, A.J. Curtis, J.L. Lauritzen, and J.D. Hoffman, J. Res. Nat. Bur. Std., 1962, vol. 66A, p. 269. 641. E. Passaglia, J.M. Crissman, and R.R. Stromberg, ACS Polym. Preprints, 1965, Vol. 6, p. 590. 642. J.D. Hoffman, G. Williams, and E. Passaglia, J. Polym. Sci., 1966, vol. C14, p. 173. 643. J.M. Crissman, and E. Passaglia, J. Polym. Sci., 1966, vol. C14, p. 237. 644. I.I. Perepechko, and L.A. Bodrova, Vysokomol. Soedin., 1968, vol. B10, p. 148. (Rus) 645. I.I. Perepechko, L.A. Kvacheva, L.A. Ushakov, A.Ya. Svetov, and V.A. Grechishkin, Soviet Plastics, 1970, vol. 8, p. 39; (transl'n of Plasticheskie Massy, 1970, vol. 8, p. 43 (Rus)). 646. G.S. Kolesnikov, and M.G. Avetyan, Izv. Akad. Nauk SSSR, Otd. Khim. Nauk, 1959, p. 331. (Rus) 647. D.W. Brown, and L.A. Wall, ACSPolym. Preprints, 1966, vol. 7, p. 1116. 648. E.M. Sullivan, E.W. Wise, and F.P. Reding, US Pat. 3,110,705, 12 Nov. 1962. 649. J.A.E. Kail, Polymer, 1965, vol. 6, p. 535. 650. H. Van Hoorn, Rheol. Acta, 1971, vol. 10. P. 208. 651. H. Hopff, and M.A. Osman, Angew. Makromol. Chem., 1969, vol. 6, p. 39. 652. M. Kinoshita, T. Irie, and M. Imoto, Makromol. Chem., 1967, vol. 110, p. 47. 653. P.L. Magagnini, and V. Frosini, Eur. Polym. J., 1966, vol. 2, p. 139. 654. A.R. Monahan, Macromolecules, 1968, vol. 1, p. 408. 655. M.A. Osman, and H.-G. Elias, J. Macromol. Sci., 1971, vol. A5, p. 805. 656. T.S. Reid, D.W. Codding, and F.A. Bovey, J. Polym. Sci., 1955, vol. 18, p. 417. 657. H.C. Haas, E.S. Emerson, and N.W. Schuler, J. Polym. Sci., 1956, vol. 22, p. 291. 658. G. Pizzirani, and P.L. Magagnini, J. Appl. Polym. Sci., 1967, vol. 11, p. 1173. 659. H. Hopff, and M.A. Osman, Makromol. Chem., 1970, vol. 135, p. 175. 660. H. Hopff, and M.A. Osman, Makromol. Chem., 1971, vol. 143, p. 289. 661. J.A. Price, M.R. Lytton, and B.G. Ranby, J. Polym. Sci., 1961, vol. 51, p. 541. 662. K.A. Movsisyan, G.T. Ovanesov, and K.A. Gasparyan, Uch. Zap. Erevan. Univ. Estestv. Nauk, 1980, vol. 2, p. 140. (Rus) 663. Y.K. Sung, D.E. Gregonis, G.A. Russell, and J.D. Andrade, Polymer, 1978, vol. 19(11), p. 1362. 664. L. Gargallo, and M. Russo, Makromol. Chem., 1975, vol. 176(9), p. 2735. 665. J.M.G. Cowie, Z. Haq, and I.J. McEwen, J. Polym. Sci., Polym. Lett. Ed., 1979, vol. 17(12), p. 771. 666. S.L. Malholtra, P. Lessard, and L.P. Blanchard, J. Macromol. Sci. A: Chem., 1981, vol. 15(1), p. 121. 667. S.L. Malholtra, P. Lessard, and L.P. Blanchard, J. Macromol. Sci. A: Chem., 1981, vol. 15(2), p. 279.

685

668. S.L. Malhotra, P. Lessard, and L.P. Blanchard, J. Macromol. Sci. A: Chem., 1981, vol. 15(8), pp. 1125, 1577. 669. J.A. Bergfjord, R.C. Penwell, and M. Stolka, J. Polym. Sci., Polym. Phys. Ed., 1979, vol. 17(4), p. 711. 670. Polymer Handbook, Eds. J. Brandrup, E.H. Immergut, and E.A. Grulke, Associate Eds. A. Abe, and D.R. Bloch, 4th Edition, 1999, Wiley, New York. 671. U. Gaur, and B. Wunderlich, Macromolecules, 1980, vol. 13(6), p. 1618. 672. S.L. Malhotra, P. Lessard, and L.P. Blanchard, J. Macromol. Sci., Chem., 1981, vol. A15(2), p. 301. 673. W. Wrasidlo, Macromolecules, 1971, vol. 4(5), p. 642. 674. H. Aida, and H. Senda, Fukui Daigaku Kogakubu Kenkyu Hokoku, 1980, vol. 28(1), p. 95. 675. C.G. Seefried Jr., and J.V. Koleske, J. Polym. Sci., Polym. Phys. Ed., 1975, vol. 13(4), p. 851. 676. Same as ref. 1172. 677. E. Sorta, and A. De Chirico, Polymer, 1976, vol. 17(6), p. 348. 678. E.Sorta, and A. De Chirico, Polymer, 1976, vol. 17(4), p. 348. 679. The same as ref. 678. 680. K.H. Illers, Polymer, 1977, vol. 18(6), p. 551. 681. Same as ref. 680. 682. J.M. Barrales-Rienda, Ramos J. Gonzalez, and M. Sanchez. (Same as ref. 1196). 683. S.Wu, J. Appl. Polym. Sci., 1992, vol. 46, p. 619. 684. S.J. Bai, M. Dotrong, and R.C. Evers, J. Polym. Sci., Part B: Polym. Phys., 1992, vol. 30, pp. 1515. 685. M. Scandola, G. Ceccorulli, and M. Pizzoli, Macromolecules, 1992, vol. 25, p. 6441. 686. S. Koizumi, K. Tadano, Y. Tanaka, T. Shimidzu, S. Kutsumizu, and Yano, Macromolecules, 1992, vol. 25, p, 6563. 687. T. Narasimhaswamy, S.C. Sumathi, and B.S.R. Reddy, J. Polym. Sci., Part A: Polym. Chem., 1992, vol. 30, p. 2165. 688. S.S. Murthy, J. Polym. Sci., Part B: Polym. Phys., 1993, vol. 31, p. 475. 689. J.M.G. Cowie, and S. Miachon, Macromolecules, 1992, vol. 25, 3295. 690. D. Zaldivar, C. Peniche, A. Bulay, and J. San Roman, J. Polym. Sci., Part A: Polym. Chem., 1993, vol. 31, p. 625. 691. E. Jabbari, and N.A. Peppas, Macromolecules, 1993, vol. 26, p. 2175. 692. E.M. Cavalcante, and M. Campos, Synth. Met., 1993, vol. 57, p. 4918. 693. V.I. Bondar, Yu.M. Kukharskii, Y.P. Yampol'skii, E.Sh. Finkelshtein, and K.L. Makovetskii, J. Polym. Sci., Part B: Polym. Phys., 1993, vol. 31, p. 1273. 694. E. Espi, M. Alberdi, and J.J. Iruin, Macromolecules, 1993, vol. 26, p. 4586. 695. K.L. Ngai, and C.M. Roland, Macromolecules, 1993, vol. 26, p. 6824. 696. A.R. Khokhlov, and I.Ya. Erukhimovich, Macromolecules, 1993, vol. 26, p. 7195. 697. W.-Y. Chiang, and J.-Y. Lu, J. Appl. Polym. Sci., 1993, vol. 49, p. 893. 698. H. Kumazawa, J.-S. Wang, K. Naito, B. Messaoudi, and E. Sada, J. Appl. Polym. Sci., 1994, vol. 51, 1015. 699. S.-J. Chang, and H.-B. Tsai, J. Appl. Polym. Sci., 1994, vol. 51, p. 999. 700. M. Mourgeus-Martin, A. Bernes, and C. Lacabanne, J. Therm. Anal., 1993, vol. 40, p. 697. 701. D.M. Petrovic-Djakov, J.M. Filipovic, Lj.P. Vrhovac, and J.S. Velickovic, J. Therm. Anal., 1993, vol. 40, p. 741. 702. C.L. Choy, K.W. Kwok, W.P. Leung, and F.P. Lau, J. polym. Sci., Part B: Polym Phys., 1994, vol. 32, p. 1389. 703. X. Zhang, M. Shomoda, and A. Toyoda, J. Polym. Sci., Part B: Polym. Phys., 1994, vol. 32, p. 1399. 704. G. Muller, and R. Stadler, Macromolecules, 1994, vol. 27, p. 1555. 705. C.K. Park, C.S. Ha, J.K. Lee, and W.J. Cho, J. Appl. Polym. Sci., 1994, vol. 53, p. 967. 706. C.C. Cypcar, P. Camelio, V. Lazzeri, L.J. Mathias, and B. Waegell, Macromolecules, 1996, vol. 29, p. 8954. 707. F. Koopmann, A. Burgath, R. Knischka, J. Leukel, and H. Fey, Acta Polym., 1996, vol. 47, p. 377. 708. A. Brunacci, J.M.G. Cowie, R. Ferguson, J.L.G. Ribelles, and A.V. Garayo, Macromolecules, 1996, vol. 29, p. 7976. 709. S. Matsuoka, J. Therm. Anal., 1996, vol. 46, p. 985. 710. D.D. Deppe, A. Dhinojwala, and J.M. Torkelson, Macromolecules, 1996, vol. 26, p. 3898. 711. F. Koopmann, and H. Frey, Macromolecules, 1996, vol. 29, p. 3701. 712. Y. Yuan, A. Siegmann, and M. Markis, J. Appl. Polym. Sci., 1996, vol. 60, p. 1475.

686

713. Y. Ding, and A.S. Hay, Macromolecules, 1996, vol. 26, p. 4811. 714. D. Li, and J. Brisson, Macromolecules, 1996, vol. 29, 868. 715. M. Chen, and H.W. Gibson, Macromolecules, 1996, vol. 29, p. 5502. 716. L.F. Brown, J.I. Scheinbeim, and B.A. Newman, Ferroelectrics, 1995, vol. 171, p. 321. 717. C.-P. Yang, and J.-H. Lin, J. Polym. Sci., Part A: Polym. Chem., 1996, vol. 29, p. 1943. 718. A. Spyros, and R.H. Marchessault, Macromolecules, 1996, vol. 29, p. 2479. 719. H. Takeno, S. Koizumi, H. Hasegawa, and T. Hashimoto, Macromolecules, 1996, vol. 29, p. 2440. 720. S.S. Wu, D.S. Kalika, R.R. Lamonte, and S. Makhija, J. Macromol. Sci., Part B: Phys., 1996, vol. 35, p. 157. 721. E. Perez, R. Benavente, A. Bello, J.M. Perena, and V.L. VanderHart, Macromolecules, 1995, vol. 28, p. 6211. 722. E. Perez, Z. Zhen, A. Bello, and R. Benavente, Polymer, 1994, vol. 35, p. 4794. 723. J.S. Kollodge, and R.S. Porter, Macromolecules, 1995, vol. 28, p. 4089. 724. H. Abe, I. Matsubara, Y. Doi, Y. Hoi, and A. Yamaguchi, Macromolecules, 1994, vol. 27, p. 6018. 725. K.H. Yoon, S.C. Lee, and O.O. Park, Polymer Journal, 1994, vol. 26, p. 816. 726. K. Osaki, T. Inoue, E.-J. Hwang, H. Okamoto, and O. Takiguchi, J. Non-Cryst. Solids, 1994, vol. 172/177, p. 838. 727. R.A. Huijts, and A.J. De Vries, "International Journal of Polymeric Materials", 1993, vol. 23, p. 231. 728. E.G. Kiparisova, T.A. Bykova, B.V. Lebedev, T.I. Guseva, K.A. Mager, and Yu.G. Gololobov, Vysokomol. Soed., 1993, vol. A35(6), p. 615. (Rus) 729. T.A. Bykova, E.G. Kiparisova, B.V. Lebedev, T.I. Guseva, K.A. Mager, and Yu.G. Gololobov, Vysokomol. Soed., 1991, vol. A33(12), p. 2602. (Rus) 730. T.A. Bykova, E.G. Kiparisova, B.V. Lebedev, K.A. Mager, and Yu.G. Gololobov, Vysokomol. Soed., 1991, vol. A33(3), p. 614. (Rus) 731. T.A. Bykova, E.G. Kiparisova, B.V. Lebedev, N.G. Senchenya, K.A. Mager, and Yu.G. Gololobov, 1993, vol. A35(1), p. 13. (Rus) 732. T.I. Guseva, Yu.P. Kvachev, N.G. Senchenya, and Yu.G. Gololobov, Russian Polymer News, 1997, vol. 2(3), p. 11. 733. N.G. Senchenya, M.D. Suchkova, K.A. Mager, T.I. Guseva, and Yu.G. Gololobov, Vysokomol. Soed., 1990, vol. B32(7), p. 524. (Rus) 734. W.A. Lee, and R.A. Rutherford, In: Polymer Handbook, 2nd Ed., J. Brandrup and E.H. Immergut (Eds.), Wiley, New York, p. III-139. 735. W.S. Bahary, D.I. Sapper, and J.H. Lane, Rubber Chem. Technol., 1967, vol. 40, p. 1529. 736. G.S. Trick, J. Appl. Polym. Sci., 1960, vol. 3, p. 253. 737. G.C. Eastmond, and J. Paprotny, J. Mater. Chem., 1996, vol. 6, p. 1459. 738. T. Takekoshi et al., J. Polym. Sci., Polym. Chem. Ed., 1980, vol. 18, p. 3069. 739. G.C. Eastmond, J. Paprotny, and I. Webster, Polymer, 1993, vol. 34, p. 2865. 740. V.S. Papkov et al., J. Polym. Sci., Polym. Chem. Ed., 1984, vol. 22, p. 3617. 741. C.L. Beatty, and F.E. Karasz, J. Polym. Sci., Polym. Phys. Ed., 1975, vol. 13, p. 971. 742. A. Matsumoto, K. Mizata, and T. Otsu, J. Polym. Sci., Polym. Chem. Ed., 1993, vol. 31, p. 2531. 743. K.R. Dunham, J. Vandenberghe, J.W.H. Faber, and W.F. Fowler, J. Appl. Polym. Sci., 1963, vol. 7, p.143. 744. A. Anton, and H.C. Beachel, J. Polym. Sci., 1969, vol. B7, p. 215. 745. B.F. Malichenko, E.V. Shedul'ko, and Yu.Yu. Kercha, Vysokomol. Soedin., 1967, vol. A9, p. 2482 (Rus) (transl'n in Polym. Sci. USSR, 1967, vol. 9, p. 2808). 746. Yu.Yu. Kercha, L.I. Ryabokon', and B.F. Malichenko, In: Synthesis and Physico-Chemistry of Polyurethanes, Yu.S. Lipatov (Ed.), Naukova Dumka, Kiev, 1968, p. 198. (Rus) 747. J.B. Alexopoulos, J.A. Barrie, J.C. Tye, and M. Fredrickson, Polymer, 1968, vol. 9, p. 56. 748. K.E. Polmanteer, and M.J. Hunter, J. Appl. Polym. Sci., 1959, vol. 1, p. 3. 749. C.C. Price, and E.A. Blair, J. Polym. Sci., 1967, vol. A-1(5), p. 171. 750. T.G. Bassiri, A. Levy, and M. Litt, J. Polym. Sci., 1967, vol. B5, p. 871. 751. I.N. Markevich, S.I. Beilin, M.P. Teterina, G.P. Karpacheva, and B.A. Dolgoplosk, Dokl. Akad. Nauk SSSR, 1970, vol. 191, p. 362. (Rus) 752. R.J. Schaffhauser, M.G. Shen, and A.V. Tobolsky, J. Appl. Polym. Sci., 1964, vol. 8, p. 2825. 753. M. Kaufman, and A.F. Williams, J. Appl. Chem., 1951, vol. 1, p. 489. 754. B. Vollmert, and H.Haas, Brit. Pat. 1,116, 933, June12, 1968. 755. J.H. Prager, R.M. McCurdy, and C.B. Rathmann, J. Polym. Sci., 1964, vol. A2, p. 1941. 756. R.H. Wiley, and G.M. Brauer, J. Polym. Sci., 1949, vol. 4, p. 351.

687

757. E.F. Jordan, G.R. Riser, B. Artymyshyn, W.E. Parker, J.W. Pensabene, and A.N. Wridley, J. Appl. Polym. Sci., 1969, vol. 13, p. 1777. 758. L. Gargallo, and M. Russo, Makromol. Chem., 1975, vol. 176(9), p. 2735. 759. J. Ballesteros, G.J. Howard, and L. Teasdale, J. Macromol. Sci., Chem., 1977, vol. A11(1), p. 39. 760. A. Matsumoto, K. Mizuta, and T. Otsu, Macromolecules, 1993, vol. 26, p. 1659. 761. A.J. Milton, and A.P. Monkman, J. Phys. D: Appl. Phys., 1993, vol. 26, p. 1468. 762. G. Muller, and R. Stadler, Macromolecules, 1994, vol. 27, p. 1555. 763. P. Skoglund, and A. Fransson, J. Polym. Sci., Part B: Polym. Phys., 1994, vol. 32, p. 1999. 764. E. Perez, Z. Zhen, A. Bello, and R. Benavente, Polymer, 1994, vol. 35, p. 4794. 765. Yu.K. Govodskii, and Yu.S. Lipatov, Vysokomol. Soedin., 1968, vol. 10, p. 323. (Rus) 766. Polymer Handbook, J. Brandrup, E.H. Immergut, and E.A. Grulke Eds., A. Abe, and D.R. Bloch Associate Eds., 1999, 4th edition, Wiley, New York. 767. Yu.I. Matveev, and A.A. Askadskii, Vysokomol. Soed., 1994, vol. B36(10), pp. 1750-1755. (Rus) 768. A.I. Bachinskii, Izbrannye Trudy, 1960, Moscow. (Rus) 769. V.V. Shaposhnikova, S.N. Salazkin, V.A. Sergeev, I.V. Blagodatskikh, L.V. Dobrovina, A.A. Sakunts, and S.A. Pavlova, Izvestiya Akademii Nauk, Ser. Khim, 1996, No. 10, pp. 2526 – 2530. (Rus) 770. V.V. Shaposhnikova, A.A. Askadskii, S.N. Salazkin, V.A. Sergeev, A.V. Samoryadov, A.P. Krasnov, V.V. Kazantseva, and B.S. Lioznov, Vysokomol. Soedin., 1997, vol. A39(4), pp. 713 – 719. (Rus) 771. V.V. Shaposhnikova, S.N. Salazkin, K.I. Donetskii, G.V. Gorshkov, A.A. Askadskii, K.A. Bychko, V.V. Kazantseva, A.V. Samoryadov, A.P. Krasnov, B.S. Lioznov, O.V. Afonicheva, N.A. Svetlova, A.S. Kogan, and A.S. Tkachenko, Vysokomol. Soedin., 1999, vol. A41(2), pp. 217 – 225. (Rus) 772. M. Doi, J. Polym. Sci., Polym. Phys. Ed., 1983, vol. 21(5), p. 667; 1980, vol. 18(5), p. 1005.

689

Subject Index

A Acetone 454 Acid, -, acetic 454 -, butyric 454 -, isophthalic 70 -, isovaleric 454 -, polyacrylic 422 -, sebacic 70 -, n-valeric 454 Alcohol polyvinyl 9, 39, 70 Aldehyde(s) 532 Amide(s) 533 Amine(s) 533 Amino group 632 Angle tangent -, of dielectric losses 86 -, of mechanical losses 86 Anharmonic oscillator 405 Anhydride, -, polysebacic acid 473 Aniline phthalein 70 Aniline phthalein polypyromellitimide 70 Anisotropy, -, polarizability 426 Annihilation -, positrons 52 Arabinogalactane 599 Arabinoglucuronoxylane 597 Arsenic 17 Artifact(s) 509 B Barrier, -, energetic 88 -, potential 88 Benzene 454, 516 – 518 Benzoyl peroxide 560 Birefrigrance 426 Bispheno-A-polycarbonate 70, 87, 449, 625 Bisphenol 358, 555 Bond(s) hydrogen 63, 101, 399, 588 intrachain 588 intermolecular 101, 399 interchain 588 intraunit 588 physical 102 Van-der-Waals 101 Boron 17, 63 Bromine 17 Bromobenzene 454 Butanale 454 Butylethyl ether 454

n-Butanol 454 t-Butyl 626, 627 n-Butylacetate 454 t-Butylamine 644 Butyl acrylate 621 Butyl methacrylate 621 C Carbon 17, 63, 399 Chlorine 17, 64 Chlorobenzene 454 Chloroform 516 Coefficient bond elasticity 459 deformation-optical 426, 427 depolarization 446 diffusion 480 of heat capacity increase 562 of elasticity of rotary-isomeric subsystem 459 of linear expansion 59, 60 of molecular packing 29 – 34 of molecules packing in the surface layer 530 of oscillator anharmonism 405 of packing, partial 398 of the reaction equation, stoichiometric 103 of the repeating unit friction 62 oscillator elasticity 405 partial 62 Poisson 427 segment friction 385 stress-optical 426, 427 volumetric expansion 59, 60, 63 weight 460 Conformation of macromolecules 88, 497 Connection cylinder(s) 524 Connective globules 524 Constant, Boltzmann 88 equilibrium 103 Morse potential 457 reaction rate 477 universal gas 89 Constant(s) (increments), -, fragments 567 – 568 -, linear chains 342 -, network cross-linked point 342 -, self (Van-der-Waals) volume 17 -, strong intermolecular interaction 63 -, weak intermolecular interaction 63 Contraction 47 Coordination bonds 10 Copolymer alternating 12

690

block-copolymer 12 grafted 13 of n-butyl acrylate with tert-butyl methacrylate 629 statistical of styrene with acrylonitrile 626 of styrene with divinylbenzene 14 of styrene with hexafluorine-2propylstyrene 628 of styrene with 4-hydroxystyrene 628 of styrene with methyl methacrylate 629 of styrene with 4-vinylphenyl dimethylsilanol 630 of styrene with vinylphenylhexafluoromethylcarbiol 625 Compatibilizer 632 Creep -, mechanical 441 -, optical 441 of polymer 475 Criterion miscibility 547 solubility 513, 514 Cross-linked point -, cross-linked chains 14, 343 -, four-functional 345 -, isocyanurate 469 -, network 346 -, trifunctional 337, 345 Curve dilatometric 58 recovery 56 stress relaxation 56, 496 thermogravimetric 78, 79 with saturation 555 Cyclohexane 454 Cyclohexanol 454 Cyclohexanon 454

D Debye pattern 589 n-Decane 454 Defects in the form of branchings 375 hanged chains 375 isolated loop 375 Degradation, -, thermal 78 -, thermooxidative 78 Degree -, cross-linking 363 -, polymerization 520 Dendrimer(s) 333 Density -, real 45 -, seeming 45

of cohesive energy 504, 512 of polymer 18 Diamond 353 1,2-Dibromoethane 454 Diamyl ether 454 Dibutyl ether 454 Dielectric constant 418, 447 Dielectric(s) 447 Diethyl ether 454 Diethylamine 632 Diethylketone 454 Diisoamyl ether 454 Diisocyanate 467 Diisopropyl ether 454 Difference of main normal stresses 427 of run, optical 427 Diffusion, -, Fick’s 479 -, kinetic units 475, 479 -, relaxants 475, 479 Dimer 560 1,3-Dioxolane 629 Dipropyl ether 454 Domain(s) 471 E Elastomer networks 456 Energy -, anharmonic oscillator, free 405 -, chemical bonds dissociation 409 -, cohesive 504, 538, 555 -, dipole-dipole interaction 62 -, dispersion interaction 595 -, free 61 -, heat 89 -, hydrogen bonds 61 -, interaction activation 494 -, intermolecular interaction 61 -, internal 88 -, low-temperature gamma-transition, activation 595 -, particle 89 -, relaxants interaction 495 -, rotary isomers, difference 459 -, rotation 88 -, surface 469 -, transition 88 Entropy 89, 475 Epoxy resin 14 Equation -, Arrhenius 103 -, Boltzmann 88 -, Boltzmann-Volterra 475 -, chemical kinetics 103 -, Clausius-Mossotti 418, 446 -, Fick 503 -, Flory 72 -, Fulcher-Tamman 75

691

-, Kargin-Slonymskii 74 -, Lorenz-Lorentz 418 Ethanale 454 Ethanol 454 Ether -, butyethyl 454 -, diamyl 454 -, dibutyl 454 -, diethyl 454 -, diglycidyl 358 -, diisoamyl 454 -, diisopropyl 454 -, polyvinylethyl 69 -, polyvinylisobutyl 405 -, polyvinylmethyl 69, 628 Ethyl acetate 454 Ethyl cellulose 449 Ethylbenzene 454 Ethylbromide 454 Ethylformate 454 2-Ethylhexyl acrylate 621 Ethyliodide 454 Ethylpropionate 454 F Fibrils 524 Fluorine 17, 61 Formamide 534 Force constant 409 Fragments -, basic 602 -, intercrosslinked, mean 347 -, linear 343 -, network, repeating 345 Frequency -, D-line of sodium 446 -, oscillation, natural 89 Front-factor 456 Function -, memory 476 -, response 613 G Galactouronane 598 Gibbs triangle 383 Glass transition mechanical 85 structural 85 temperature interval 91 Globule 509 Glucomannan 599 H Halogen-containing compound(s) 530 Heat capacity 562 Height of the sphere segment 17 Hemicellulose 589

n-Heptane 454 n-Heptylacrylate 621 Hexagonal packing 528 Hexamethylene tetramine 629 n-Hexane 454 n-Hexanol 454 Hydrocarbons -, monosubstituted, unsaturated 11 -, substituted, saturated 11 Hydrogen 17, 63 I Interaction cylinder 457 Interaction, -, chemical 16 -, dipole – dipole 61, 101 -, dispersion self 61 -, dispersion weak 61 -, intermolecular (physical) 16, 607 -, intermolecular strong 61 -, intramolecular 607 Iodine 17 Isobutanol 454 cis-Isomer 11 Isomer(s) 11, 320 Isopentane 453 Isopropylbenzene 454 J Joining of units -, anomalous (“head-to-head”, “tailto-tail”) 10 normal (“head-to-tail”) 10 K Ketone(s) 533 Kinetic unit 87, 475 L Law (rule), -, additivity 405 -, Il’ushin 494 -, Laplace 511, 524 -, mass action 103 -, Maxwell 447 -, molar parts, Zhurkov’s 105 -, Wertheim 426 Length, -, chemical bond 17 -, Cune segment 385 -, intermolecular radius 17 -, wave 418 Lifetime, -, intermediate component 52 of atom, settled 89 of long living component 51, 52

692

-, positron 51 Lifetime spectrum of positron(s) 51 Long-living component intensity 52 Lorentz correction 418 M Macrodiisocyanates 468 Macromolecule branched 13 flexible 73 linear 13 rigid 73 Main principal stress(es) 427 Mechanism glass transition 87 of relaxation process 87 of sorption, relaxation 497 relaxation 54, 55 swelling, relaxation 497 Melting enthalpy 398 entropy 398 point 398 Memory function 477 Metha-, para-phenylene diamine 109 Methanol 454 Method absorption, equilibrium 43 calorimetric 83, 85 capillary condensation 43 dilatometric 45, 83, 85 DSC 626 electron microscopy 469 electron spectroscopy 632 extrapolation 398 Foukes 535 Fourier-transformation 630 IR-spectroscopy 626, 630 neutron scattering 509 NMR, 13C NMR, 31P NMR 630, 631 of atomic approaches 76 of atomic constants 584 of deformations freezing 439 of dynamic mechanical analysis 86, 469 of experiment design 612 of gradient tubes 45 of dynamic tests 83 of least squares 108 of local Lorentz field 417, 418 of mercury porometry 43 of miscibility diagrams 587 of polymerization in solution 45 of registration of positron lifetime spectra 51 of small-angle X-ray scattering 509 of X-ray photoelectronic spectroscopy 469

optical 83 photocreep 443 photoelasticity 439 polarization-optical 439 polycondensation 45 positrons annihilation 43 pycnometric 45 reverse variable step 496 Runge-Cutt, numerical 482 Simpson 496 thermogravimetric 79 thermomechanical 66, 78 Methyl acetate 454 Methyl formate 454 Methyl methacrylate 628 Methylethylketone 454 4-O-Methylglucuronoxylane Methyliodide 454 Microdomain(s) 471 Microphase 471, 547 Miscibility of polymers 547, 625 Mobility translation 102 vibration 102 Modulus elasticity 79, 86, 440, 460, 474 equilibrium 456 of cross-linked points 460 of linear fragments 460 relaxation 494 rubbery 79 storage 473 Molecular mass of chain 385 of cross-linking bridges 350 of cross-linking point 347, 350 of intercross-linking point fragment 456 of linear chain between cross-linking points 348 of polymer 555 of segment 71 of the repeating unit 35 of unit neighboring to the crosslinking point 347 Moment dipole 595 magnet 445 Monomers bifunctional 14 disubstituted 11 polyfunctional 14 N N,N’-dimethylacrylamide 630 N,N’-dimethyl-substituted Nylon-6,12 626 Naphthalene 454 Network(s) high cross-linked 343

693

less cross-linked 343 Nitrile acetate 455 butyrate 455 isoheptanate 455 pentanate 455 propionate 455 Nitrobenzene 518 – 520 Nitrogen 17, 63, 505, 563 Nitroethane 454 Nitromethane 454 1-Nitropropane 454 2-Nitropropane 454 n-Nonane 454 n-Nonyl acrylate 454 Number -, coordination 64 -, repeating units in a segment 385 Nylon-6 626 O n-Octane 454 n-Octanol 454 Oscillator 446 Osmotic pressure 497 Oxygen 17, 63, 399

P Parachor of atom 527 of frequency 527 n-Pentane 453 n-Pentanol 454 Perfluorocompound 532 Permeability 595 Phase transition -, the first kind 87 -, the secondary kind 87 Phenolic resins 626 Phenoloformaldehyde resin 10, 607, 631 Phenolphthalein 70 Physical state -, glassy 29, 41, 67 -, rubbery 41, 67 -, viscous flow 67 Polarizability 446, 595 Polarization, atomic 418 deformational 447 electronic 418, 446 microscopic 446 orientational 418, 447 1,2-Polybutadiene 37 1,4-Polybutadiene 68, 449 1,4-Polyisocyanurate(s) 439 1,4-Polyisoprene 68, 449

1,4-cis-Polybutadiene 37 1,4-cis-Polyisoprene 37 1,4-trans-Polybutadiene 37 Poly(α,α,α,α-tetrafluorine-p-xylylene) 449 Poly(α-methyl styrene) 449 Poly(α-vinyl naphthalene) 449 Poly(β-vinyl naphthalene) 449 Poly(1,1,2-trichlorobutadiene) 632 Poly[1,1-cyclohexane bis(4-phenyl)carbonate] 449 Poly[1,1-ethane bis(4-phenyl)carbonate] 449 Poly(1,4-cyclohexylidene dimethylene terephthalate) 449 Poly(1-butene) 449 Poly(1-hydroxy-2,6-methylphenylene) 629 Poly(1-hydroxyl-2,6-methylenephenylene) 629 Poly[2,2’-(m-phenylene)-5,5’bibenzimidazole] 450 Poly(2,6-dimethyl-1,4-phenylene oxide) 449, 625 Poly(3,4-dichlorostyrene) 449 Poly[4,4’-diphenoxy di(4-phenylene)sulfone] 450 Poly[4,4’-isopropylidene diphenoxy di(4phenylene)sulfone] 450 Poly[4,4’-sulfone diphenoxy di(4-phenylene) sulfone] 450 Poly(4-hydroxy styrene) 629 Poly(4-methyl-1-pentene) 449 Poly-4-methylpentene-1 38, 404, 424 Poly(4-vinyl pyridine) 631, 642 Polyacetylene 9 Polyacrylamide 72 Polyacrylonitrile 72, 450 Polyamide 9, 38, 75, 109, 399, 405, 537 Polyamide 6,6-α-isomer 38, 537 Polyamide 6,6-β-isomer 38 Polyamide based on sebacic acid and anilinephthalein 70 Polyamidophenylquinoxaline(s) 320 Polyarylate F-1 74 Polybenzimidazole(s) 582 Polybenzoxazole 484 Polybutadiene 449 Poly(butyl acrylate) 69 Poly(butyl methacrylate) 625, 449 Polycarbonate 582 Polycarbonate based on bisphenol A 70, 87, 449, 625 Polychloroprene 37, 41 Poly(chloro-p-xylylene) 449 Poly(chlorotrifluoroethylene) 449 Poly(cyclohexyl methacrylate) 449 Poly(dimethyl siloxane) 68, 449 Polyester(s) based on secacic acid and phenolphthalein 70 isophthalic acid and phenolphthalein 70 Polyether(s) 9, 468

694

Poly(ether ether ketone) 449 Poly(ether ketone(s)) 449 Poly(ether sulfone(s)) 449 Poly(ethyl α-chloroacrylate) 449 Poly(ethyl methacrylate) 69, 449 Poly(ethyl oxazoline) 627 Polyethylene 9, 449 Poly(ethylene adipate) 38 Poly(ethylene isophthalate) 38 Poly(ethylene oxazoline) 628 Poly(ethylene oxide) 9, 537, 625 Poly(ethylene terephthalate) 70, 450 Polyformaldehyde 537 Poly(hexamethylene adipamide) 450 Poly(hexamethylene sebacamide) 449 Poly(hexamethylene terephthalate) 37 Poly(hexyl methacrylate) 69 Polyimide 69 Poly(isobutyl methacrylate) 449 Polyisobutylene 69, 449 Polyisoprene 449 Polymer chains -, branched 12, 13 -, cross-linked 14 -, linear 13 -, main 13 Polymer structure -, fibrillar 524 -, globular 523 -, macroporous 44 -, microporous 43 -, nodular 509 -, porous 43 -, supermolecular 509 Polymeric unit, -, elementary 10 -, repeating 10 Polymers amorphous 34, 46, 84 atactic, irregular 11 branched 13 carbochain 9, 10 cardo-type structure 514 chelate 10 crystalline 46, 84 dendrite 13, 335 elementorganic 9, 10 erythro-diisotactic 12 glassy-like 68 globular, amorphous 510, 520 gradient 465, 472 heat-resistant 68, 514 heterochain 10 heteromodular 465 homo- 35 inter- 15 isotactic 11 isotropic, amorphous 520 ladder 15 network 10, 608

non-globular, amorphous 510 non-polar 538 optically sensitive 426 oriented 524 partially crystalline 34, 84 polar 538 rigid-chain 73 rubber-like 68 semi-crystalline 45, 46, 84 star-like 335 stereoregular 11 syndiotactic 11 treo-diisotactic 12 Poly(m-chlorostyrene) 449 Poly(methyl α-chloroacrylate) 450 Poly(methyl acrylate) 69 Poly(methyl methacrylate) 69, 449, 626, 629, 630 Polymethylidene phthalide 46 Poly(N,N’-dimethyl acrylamide) 627 Poly[N,N’-(n,n’oxydiphenylene)pyromellitimide] 450 Poly(naphtoylene benzimidazole) 68 Poly(n-butyl acrylate) 68, 629 Poly(n-butyl methacrylate) 36, 626, 640 Poly(n-butyraldehyde) 41 Poly(n-propyl methacrylate) 36 Poly(N-vinyl carbazole) 449 Poly(o-methyl styrene) 449 Poly(oxy-2,2-dichloromethyl trimethylene)449 Poly[oxy(2,6-diphenyl-1,4-phenylene)] 449 Polyolefins 582 Polyoxadiazole 9, 484 Polyoxymethylene 39 Poly(p-chlorostyrene) 449 Poly(phenyl quinoxaline) 514 Poly(phenyl sylsesquioxane) 15 Polyphenylene 9 Poly(phosphonitrile chloride) 9 Poly(p-hydroxybenzoate) 450 Poly(p-hydroxystyrene) 628 Polypropylene 9, 37, 449 Poly(propylene oxide) 40 Poly(p-xylylene) 449 Polystyrene 69, 449 Polysulfide(s) 582 Polysulfone(s) 582 Poly(t-butyl methacrylate) 629 Poly(tert-butyl acrylate) 629 Poly(tetramethylene adipate) 405 Poly(tetramethylene oxide) 405 Poly(tetramethylene terephthalate) 449 Polytetrafluoroethylene 39, 50 Poly[thio(p-phenylene)] 449 Poly(trichlorobutadiene) 15 Poly(trimethylene adipate) 405 Polyurethane(s) 9, 582 Poly(vinyl acetate) 69, 450 Poly(vinyl alcohol) 70 Poly(vinyl butyral) 449

695

Poly(vinyl chloride) (PVC) 39, 69, 449, 537 Poly(vinyl cyclohexane) 449 Poly(vinyl fluoride) 39, 537 Polyvinylmethyl ether 69 Polyvinylethyl ether 69 Poly(vinyl pyrrolidone) 426, 628 Poly(vinyliden chloride) 449 Pore(s) distribution by sizes 43 specific surface 43 total volume 43 Porosity factor 45 Potential chemical interaction 409 Lennard-Jones 406 Morse 409 Principal strains 427 Process of adhesive wetting 511 of copolymerization 12 of creep 475 of desorption 500 of microphase separation 470 of polymerization 46 of stress relaxation 475 of swelling 497 of syneresis 403 Propanal 454 n-Propanol 454 n-Propyl acetate 454 Pyromellitic dianhydride 70 R Rate of diffusing particle 497 of system cooling 91 of system heating 91

-, of the method of constants 585 Segment -, molecular mass 72, 73 Cune 385 mechanical 73 of macromolecule 51 Silicon 17, 63 Simplex lattice 613 Size of bond, typical 459 of crystallites 398 of solvent, typical 513 typical 385 Solubility criterion 513 -, Hildebrand parameter 504 Sorbate 44, 45 Sorbent 44, 45 Spherical segment height 17 Square (surface) of interaction cylinder 457 Van-der-Waals, of atom 459 Steric factor 103, 588 Structural element 89 Styrene 454 Sub-micropore(s) 50 Substituent, side 73 Substitution, -, metha- 63 -, ortho- 63 -, para- 63 Sulfonated polyamide 631 poly(p-phenylene terephthalamide) 631 Sulfur 17, 63 T

Reaction of polycyclotrimerization 15, 468 of trimerization 15 of urethane formation 468 Refraction molar 448 molecular 418 of atoms, by Eizenlor 419 of atoms, specific 418 Relaxant(s) 475 Relaxation of microdefects 55 stress 475 Rubber, -, butadiene 514 -, isoprene 514 -, synthetic 10 S Scheme -, additive 527

Teflon 51 Temperature (point) -, critical 405 -, dissolution, lowest critical 627 -, flow 67 -, glass transition 36, 66, 589 -, intensive thermal degradation 408 -, melting 398 -,onset of intense thermal degradation 408 -, phase transition 406 Tension interfacial 510 surface 510 Theory (concept, rule) -, Flory- Haggins 520 -, Iliushin 494 -, Patterson and Robard 627 -, rotary-isomeric 521 -, Simha-Boyer 60 -, Volkenstein-Ptytsin 90

696

-, Zhurkov 101

Vector,

Unsaturated hydrocarbons disubstituted 11 monosubstituted 11

-, electric field intensity 445 -, electric induction 445 -, polarization 445 Viscosity, -, shear, Newtonian 385 -, system 75 Volume empty 17 fluctuation 42 free 42 molar 17 of atom 17 of defect 457 of end groups 555 of expansion 42 of ideal crystal 44 of interaction cylinder 457 of the repeating unit 17 self (real) 17 specific 17 total molar 17 Van-der-Waals, free 17 Van-der-Waals, of polymer 557 Van-der-Waals, of the repeating fragment of the network 344

V

W

Value,

Wisevesser formula 585 Work of adhesion 510

Tests, -, thermogravimetric 78 -, thermomechanical 78 -, X-ray structural 79 with periodical loading 84 Thermodynamic function 87 probability 88 Time, -, observation 89 -, relaxation 51, 89 of transition from the glassy state into the rubbery state 88, 89 Tin 17 Toluene 454 2,4-Toluylenediisocyanate 468, 472, 473 Trans-isomer 11 Triethylamine 632 Trimer 568 U

-, defect 457 -, mechanical segment 73 Van-der-Waals, -, radius of atom 17, 457 – 459 -, surface of atom 459 -, volume of atom 17 – 29, 453 – 455, 457 – 459

X m-Xylene 454 o-Xylene 454 p-Xylene

454