Computational Materials Science of Polymers

711 Pages·2003·4.57 MB·English

by  A A Askadskii

COMPUTATIONAL MATERIALS SCIENCE
OF
POLYMERS
COMPUTATIONAL
MATERIALS SCIENCE
OF
POLYMERS
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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
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in any form or by any means, electronic or mechanical, including photocopy,
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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 In-
stitute 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 poly-
mers 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 proper-
ties 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) proper-
ties 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 3
Chapter I. Brief information on types of polymes and their chemical structure 9
Chapter II. Packing of macromolecules and polymers density 16
II.1. Increments method and basic physical assumption 16
Chapter III. Temperature coefficient of volumetric expansion 58
Chapter IV. Glass transition temperature of polymers 67
IV.I. Thermomechanical and other methods of evaluation of the glass
transition temperature of polymers 67
IV.2. Mechanism of glass transition 88
IV.3. Calculation of the glass transition temperature of linear polymers 108
IV.4. Influence of plasticization on the glass transition temperature of polymers 322
IV.5. Calculation of the glass transition 343
Chapter V. Temperature of transition into the viscous flow state for amorphous
polymers 385
V.1. Estimation of temperature of transition into the viscous flow state of
polymers 385
V.2. Dependence of Newtonian viscosity on molecular mass of polymer in a
wide range of its change 38
Chapter VI. Melting point of polymers 398
Chapter VII. Temperature of onset of intense thermal degradation of polymers 408
Chapter VIII. Optical and opto-mechanical properties of polymers 418
VI.1. Refractive index 418
VIII. 2. Stress-optical coefficient 426
Chapter IX. Dielectric constant of polymers and organic solvents 445
Chapter X. Equilibrium rubber modulus for polymer networks 456
X.1. Calculation of the equilibrium modulus 456
X.2. Heteromodular and gradient-modulus polymers 46
Chapter XI. Description of relaxation processes in polymers 475
XI.1. Stres relaxation 475
XI. 2. Sorption and sweling proceses 497
Chapter XI. Solubility of polymers 504
XII.1. Specific cohesive energy of organic liquids and polymers. Hildebrand
solubility parameter 504
XI.2. Solubility criterion 509
XII.3. Influence of molecular mass and degree of macromolecule orientation
on solubility 520
Chapter XIII. Surface properties of organic liquids and polymers 527
XI.1. Surface tension of organic liquids 528
XI.2. Surface tension of polymers 536
Chapter XIV. Miscibility of polymers 547
Chapter XV. Influence of the end groups on the properties of polymers 555
Chapter XVI. Thermophysical properties of polymers 562
XVI.1. Heat capacity 562
XVI.2. Thermal difusivity and heat conductivity 564
Chapter XVII. Molecular design and computer synthesis of polymers with
predermined properties 567
Appendix 1. Examples of solution of direct problems of polymers synthesis 589
Appendix 2. Examples of solving the reverse problem of polymer synthesis 602
Appendix 3. The example of solving the complex problem – analysis of the
chemical structure of phenol formaldehyde resin 607
Appendix 4. Application of the approach to multicomponent copolymers 621
Appendix 5. Influence of strong intermolecular interaction occurring between
two dissimilar polymers on their miscibility 625
Appendix 6. On formation of super-molecular structure in amorphous polymers 645
1. Scheme of formation of the super-molecular structure 645
2. Calculation method of evaluation of dimensions of elements of super-
molecular structure of polymers
3. Phase state of polymers as a result of formation of the super-molecular
structure by one-cavity bond hyperboloids 653

References 69
Index 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 above-
mentioned 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 (Van-
der-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 semi-
empirical, 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:

∑ ∆Vi
i
Tg = ,
∑ ai∆Vi + ∑b j
i j