Polymer Science and Technology Series
OLIGOMERIC STATE OF SUBSTANCES
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POLYMER SCIENCE AND TECHNOLOGY SERIES Polycyclic Aromatic Hydrocarbons: Pollution, Health Effects and Chemistry Pierre A. Haines and Milton D. Hendrickson 2009 ISBN: 978-1-60741-462-9 Advances in Polymer Latex Technology Vikas Mittal 2009 ISBN: 978-1-60741-170-3 Oligomeric State of Substances S. M. Mezhikovskii, A. E. Arinstein and R. Ya. Deberdeev 2009. ISBN: 978-1-60741-344-8
Polymer Science and Technology Series
OLIGOMERIC STATE OF SUBSTANCES
S.M. MEZHIKOVSKII, A.E. ARINSTEIN AND
R. YA. DEBERDEEV
Nova Science Publishers, Inc. New York
Copyright © 2009 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers’ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works. Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Mezhikovskii, S. M. Oligomeric state of substances / S.M. Mezhikovskii , A.E. Arinstein , R. Ya. Deberdeev. p. cm. Includes index. ISBN 978-1-61728-554-7 (E-Book) 1. Oligomers--Structure. I. Arinstein, Arkadii E. II. Deberdeev, R. Ya. III. Title. QD382.O43M494 2009 547'.7--dc22 2009006388
Published by Nova Science Publishers, Inc. New York
CONTENTS Preface of Editor
ix
Preface
xi
Preface by Authors Introduction
xiii xv
Part 1
Oligomers as the Object of Research: Basic Principles
1
Part 2
Homogeneous Oligomer Systems
49
Part 3
Heterogeneous Oligomer Systems
183
Conclusion
249
References
253
Index
255
OLIGOMERIC STATE OF SUBSTANCES The book gives an original interpretation of modern ideas about oligomers as substances which, due to their molecular structure, demonstrate specific statistical behavior different form that of monomers or polymers. The criteria provided in this book allow us to distinguish monomers, oligomers and polymers in homologous series. The book presents theoretical aspects of small-scale structure of oligomers, and supramolecular structure formation models for liquid oligomeric systems. Theoretical and experimental results of the studies on phase transitions and anomalies of physical and chemical properties which oligomer systems have are considered. The book is aimed at scientists of academic profile working in the filed of physics and chemistry of oligomers and polymers, at researchers and specialists engaged in the development and production of materials based on oligomeric and polymeric systems. The book will be useful for professors, postgraduates and students of chemical and biological departments of universities and academies.
PREFACE OF EDITOR “The Science should be Cheerful, Fascinating and Simple as well as Scientists” Prof. Piotr L. Kapitsa The Winner Noble Price, Institute of Physical Problems, Academy of Sciences of USSR, Moscow
Oligomers (synthesis, properties and applications) are very important part of polymer material science as well as chemical industry. For some reasons oligomers are even more broad then material science. If monomers are bricks of polymers and composites the oligomers are blocks of polymers and composites as well as very important class of organic compounds for different applications (synthesis, medicine, agriculture, additives for polymers etc.). The contributors of this book are pupils of Prof. Alfred Anisimovich Berlin (1912-1978) who was pioneer, leader and organizer of oligomer science and industry in Soviet Union. The co-authors of this manuscript are working in the field of oligomers already 40-50 years. So, they accumulated tremendous amount of information and knowledge in the field of oligomers (ideas, theories, applications). All of them are included in this book. I hope that this manuscript will be very useful for the students, scientists and engineers who are working in the field of oligomers, polymers, composites and nanocomposites as well as in the field of application of chemistry for the medicine and agriculture. The contributors and editor of this book will be very happy to receive from readers some comments which we can take in account in our job in future. Prof. Gennady Efremovich Zaikov Institute of Biochemical Physics Russian Academy of Sciences Moscow, Russian
[email protected]
PREFACE The initial title presenting the subject of this book was “Chemical Physics of Oligomers”, however, we finally preferred the one which you can see on the front page. We have made this change for a variety of reasons. The first reason (the first but not the most important one). The term “state” together with the terms “oligomeric” and “substance” is linguistically substantial. A state is “the condition, internal or external circumstances something or somebody is in” (S.I. Ozhegov, Russian language thesaurus). In this regard, the word combination “Oligomeric State of Substance” seems as justified as the usual term “aggregative state of substance” or other less common expressions as, for example, “plasma state of substance”. The second reason. The title “Oligomeric State of Substance” is within the terminology of leading figures in polymer science (V.A. Kargin, S.Ya. Frenkel et al.), who used the term “polymeric state of substance” very broadly (for more information see Introduction in this book). The third reason. Stating that oligomer is a condensed state of matter and it has specific properties we renounce the traditional attitude to oligomers as only raw materials for polymer industry and want to attract more fundamental attention to oligomeric systems not limited by material science only (you can see more details throughout this book). And the last reason. The pretentious title of this book can cause not only evident disapproval and even irritation of some specialists but also a sense of curiosity among other readers. The curiosity that some readers will feel can transform into their desire to read this book. We hope that these readers will join the exciting research process concerning chemical physics of oligomers. This book summarizes the results of theoretical and experimental research in thermodynamics, kinetics and structure of liquid oligomers. The research is based on ideas mainly developed by Professor Alfred Berlin who was one of the greatest chemists of the second half of the last century. Moreover, some research results included into this publication were obtained in other research centers, particularly by Professor V. Irgac, Professor G. Korolev, Academician Yu. Lipatov, Professor S. Papkov, Academician A. Chohlov, Professor A. Chalykh, Professor S. Entelis, Professor K. Dushek, Professor K. Kveiya, Professor R. Koniksveld, Professor S. Krauze and many others. The book gives an original interpretation of modern ideas about oligomers as substances which, due to their molecular structure, demonstrate specific statistical behavior different from the statistics of monomers and polymers. This is the principal difference between this
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publication and other books concerning oligomers. This statement also relates to another book written by one of the authors “Physicohimiya Reactionnosposobnih Oligomerov” (Physical Chemistry of Reactive Oligomers, in Russian), published in 1998. The book in your hands uses some experimental results and statements from the latter, but presents them in a broader, completed and more accurate way giving somewhere a fresh look. The authors tried to maximize the contribution of the most important experimental results discussed at the latest international conferences on chemistry and physical chemistry of oligomers. We express many thanks to all the authors whose original research results were systematized in this publication. In particular, we’d like to thank the following individuals, without whose contributions, and discussions this work would not be half as useful: Academician A. Berlin, Professor I. Eruhimovich, Professor V. Irgak, Professor G. Korolev, Professor V. Kuleznev, correspondent member of the Russian Academy of Sciences V. Kulichichin, Professor V. Lancov, Academician Yu. Lipatov, Professor L. Manevich, Professor Yu. Morozov, Professor V. Hozin, Professor А. Chalykh et al. We’d also like to express our thanks to Professor A. Oleinic and Professor V. Shilov who reject some ideas which the authors support. This rejection stimulated new theoretical and experimental research as well as speculation on these ideas. We appreciate this fact greatly. We would like to express our deepest gratitude to the reviewers who have done much to improve this publication: Academician Aleksander Berlin and Professor Valerij Kuleznev. Special thanks to the managing editor, Professor Vadim Irzhak who added a reasonable pragmatism to the style of somewhere too enthusiastic authors. The only case when the position of the editor was not considered convincing and was not shared by the authors was the title of this book. Note, it was impossible to provide a separate letter for every value or variable used in writing and editing this book (even taking all the letters in three alphabets). That’s why various formulas in different sections of this book contain identical symbols describing values different in meaning and nature. The physical interpretation of symbols is provided for every specific calculation to avoid confusion. We tried to make the style of this book easy enough for readers with different levels of preparation and various interests in science. Therefore, you can find some inevitable imperfections. In some cases we could not avoid repetitions and sometimes we lost the main line of strict and sequential style, especially in the second part of this book. This book is aimed at scientists of academic profile working in the field of physics and chemistry of oligomers and polymers. We suppose it will be interesting for researchers and specialists engaged in development and production of materials based on oligomeric and polymeric systems. This book will be useful for professors, postgraduate and graduate students of chemical and biological departments of universities and polytechnic institutes.
PREFACE BY AUTHORS This book was first issued in Russia in 2005 in just 700 copies and became an instant bestseller. There was no further replication of the book due to the state in Russian book publishing system. However, we were aware of fact that this book in Russian is not readily available to the world scientific community in any number of copies. That is why we want to express our gratitude to Professor Gennady E. Zaikov, who inspired us to engage in its translation into English and agreed to be a scientific editor. We are also thankful to Timur R. Deberdeev for his inestimable contribution into formatting of the English version. Authors submit this book for judgment of English-speaking readers understanding that some of its aspects are points of discussion. But they don't consider it as a disadvantage. On the contrary, discussion is a way to find the grains of a veritable knowledge. Another convincing argument for such point of view was a review of the book written by the outstanding Russian academician Yuriy Sergeevich Lipatov, who sent it to the authors shortly before his decease. There he wrote: «Let me congratulate you with your book as the outstanding contribution to the science of polymers. I say “polymers” because its content and importance exceeds area of oligomers. In some way, it is the encyclopedia of the modern chemistry of polymers. I know nothing equal to it during last decades. The book contains lots of new interesting ideas and original approaches, and I have greatly enjoyed reading it. It doesn’t mean that I accept everything written there, but it is irrelevant in this case. It is a point of discussion. You have clearly delivered me your view of oligomers as the specific class of substances and this point of view is uncontestable. The book is integral, everything is presented logically and in a proper sequence. I wish the number of copies were not so scanty because this publication must be acquired by any library, research institute and university dealing with chemistry». Authors hope that the imperfection of translation will not prevent scientists and professionals in polymer science and technology from taking an interest in this publication. S.M. Mezhikovskii N.N. Semenov Institute of Chemical Physic Russian Academy of Science, Moscow, Russia A.E. Arinstein Technion-Israel Institute of Technology, Israel R. Ya. Deberdeev Kazan State Technological University, Russia
INTRODUCTION “Can we speak of a polymeric state of substance?”, – this question is used as the title for a problem-oriented and prognostic publication by S. Frenkel [1]. The author’s opinion is rather categorical. Yes, we can, but only if the term “state of substance” describes a form of molecular condensation. The process of polymeric structure formation (defined as polymerization, polycondensation, addition or ring-opening polymerization) is a chemical reaction involving dispersion and application of electrostatic forces to small molecules in order to form covalent bonds, where Van der Waals distances are reduced to covalent bond lengths in macromolecules. This process is called condensation (lat. ‘condensatio’ – concentration, accumulation, compaction, compression [2]). This compaction (“chemical” monomer → polymer transition) results in the formation of a new condensed state of substance with absolutely new fundamental properties. These new polymeric properties (such as elasticity) can not be described using the classical theory of aggregative state transitions. Thus, Oligomeric State of Substance is a specific form of condensed matter, different from polymer. It emerges spontaneously from a group of molecules, each being characterized by a specific length and rigidity. The nature of this specific form of condensed state is not only based on chemical transformations of molecules but is also related to the structure of a single oligomer molecule. Conformational properties and/or the existence of electrostatic centers in these molecules result in the formation of dense aggregates with various lifetimes and anisotropies in spatial arrangement. The nature of oligomer molecules defines their natural tendency to self-organization, which can be described neither by aggregative nor by phase transition theory. Oligomer systems with specific properties are very important in many biological and technical applications. For example, some cell enzymes, peptide antibiotics, genes, hormones and many other bioactive substances are oligomers [3]. The expert estimations showed that by the beginning of the ХХI century over 60% of polymer products in the world market were either based on reactive oligomers or used them as principal components. The fundamental characteristic of oligomers as a specific condensed state of substance is supported in various cosmological theories [4, 5] where they are considered a constituent stage of chemical molecule evolution which leads to the formation of living matter. Thus, the core subject of this book is the theoretical and experimental verifications of the statements concerning specific properties of oligomers as a condensed state of substance.
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REFERENCES [1] [2] [3]
[4] [5]
Frenkel S.Ya., Fisika segodnya i zavtra. Prognozi nauki. (Physics today and tomorrow. Scientific predictions), Leningrad: Nauka, 1973, p. 176 (In Russian). Slovar’ inostrannih slov (Foreign words dictionary), edited by Lehin, I.V. and Petrov, F.N., Moscow: GIINS, 1954, p .348 (In Russian). Artuhov, V.G., et. al. Oligomernie belki: strukturno-funkcional’nie modifikacii i pol’ cub’edinichnih contactov (Oligomeric proteins: structure functional modifications and the function of subunit contacts), Voronezh: VSU, 1997. Goldanskii, V.G., et. al. Fizicheskaya himiya: Sovrem. problemi (Physical chemistry: present day problems), Moscow: Himiya, 1988, p. 198 (In Russian). Foks, R, Energiya i evolucia gizni na zemle (Energy and evolution of life on Earth), Moscow: Mir, 1992 (In Russian).
Part 1
OLIGOMERS AS THE OBJECT OF RESEARCH: BASIC PRINCIPLES ABSTRACT The discussion deals with the following issues: oligomers as the object of scientific research, classification principles of oligomer systems, their liquid state structure and thermodynamic aspects.
1.1. TERMINOLOGY, CONCEPTS AND DEFINITIONS 1.1.1. Briefly on The Subject The term “oligomer” (ολιγοζ meaning several or few, and μεροζ meaning part or repetition) was introduced into scientific terminology gradually. According to [1] particle “oligo-” was originally used in publications by I. Gelferich et al. in 1930 [2] to denote carbohydrates, containing 3 to 6 monose residues, oligosaccharides. Later on (1932 - 1938), the meaning of this term expanded to compounds with molecules comprising small numbers of monomers. For example, the term “oligonucleotide” was applied to compounds containing 8 to 10 nucleotide residues, and “oligopeptide” was applied to peptides containing about 10 amino acid residues [3]. In the course of time the meaning of the term “oligomer” expanded considerably and it was probably G. Danelio (1942) [4, 5] who used this term to describe any chemical substances in the intermediate position between monomers (low molecular weight compounds) and polymers (high molecular weight compounds). When considering the evolution of the term “oligomer” (and, to say, is still undergoing) [1, 6 - 11], it is necessary to note that the use of the other terms (sometimes earlier and sometimes later) for the description of these compounds can be seen in scientific literature. Some of these old-style terms (synthetic resins [12]) or special terms describing individual structural features of oligomers (macromers, low molecular weight polymers, pleinomers, telechelates, forpolymers, etc. [13–16]) are still used today. Each term is probably used within a sufficient logical or physical framework thus having the right to exist. But the usage of the aforementioned and similar terms is hardly reasonable at the present stage of scientific
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development. It results not only in terminological confusion but also in the omission of the core aspect: a huge group of chemical compounds called oligomers is deprived of the strictly defined physical meaning as a condensed state of substance with special properties. These special properties are primarily the fact that oligomers are much more inclined to form more or less anisotropic aggregates than polymers with similar chemical structures. It is these anisotropic aggregates that allow us to declare macroscopic oligomer properties to be unique [11, 13, 15–20].
1.1.2. Meaning of Term “Oligomer” There is a certain discrepancy in terminology and between certain definitions of the term “oligomer”. It has both objective and subjective reasons. Oligomers have long been considered undesirable by-products in the synthesis of high molecular weight compounds; therefore, the image of oligomer as a “bad polymer”* appeared. It can be well traced in various definitions of oligomers. For example, encyclopedia of 1964 [3] calls oligomers “low molecular weight polymers”. Paper [13] gives a more precise definition: “oligomers are low molecular weight polymers with molecular weight of about М=500–10000 mass units”. V. Kern [8] provides a more complete definition: “oligomers are low molecular weight homogeneous substances homological to polymers”. Even in 1970s some Japanese authors [21] stated that the term “oligomer” has a range of applications corresponding just to “polymer products with a low degree of polymerization”. Following this logical conclusion we could state on the same basis but with no less uncertainty that polymers are oligomeric products with a high degree of polymerization or a high molecular weight. One of the subjective reasons that lead us to such a skeptical attitude to oligomers as a possible object for fundamental research is the fact that in many definitions (see, e.g. [1,4,10]) the term “oligomer” is related to compounds taking an intermediate position between oligomers and polymers, where the word “intermediate” has some hint on indefiniteness and ambiguity in meaning that is, “neither fish nor flesh” (“neither beginning nor ending some classification chain”; “corresponding to none of the opposite phenomena” [23]). But if we accept this intermediate position of oligomers as some objective entity such as the one appearing when analyzing the state of aggregation of matter: liquid is an intermediate state of matter between gas and solid body*, the aspects we underline change drastically. Let’s accept a classical thesis: to give a definition is to make some conception a part of a broader one and to explain its meaning. It is clear that differences in various definitions of the term “oligomer” arise from the fact that, on the one hand, we choose different objects as a broader concept (polymer, monomer, matter, homologous series) and, on the other hand, from different approaches to choosing a characteristic feature (molecular weight, molecular size and linear length, number of monomeric links, distance between chain ends, molecular *
It is suitable to demonstrate some historical examples here: the XIXth century chemists looked at uncrystallizable and undistillable ‘resinous woods’, formed as products of chemical reactions (which appeared in most cases to be polymer-like substances) just as if they were worthless substances [22]. * Note, it is about pure analogy. Aggregative transition is always a usual first-order phase transition, opposite to monomer ↔ oligomer ↔ polymer transformations which are quite different from phase transitions in their classical meaning (see below).
Oligomers as the Object of Research: Basic Principles
3
volume, flexibility, physical properties, and etc.) describing the meaning of the term “oligomer” and defining its intermediate position between monomers and polymers. First of all let us note that “broader concepts” of “polymer” and “monomer” used in many definitions in general sense are equivalent to the term “oligomer”. In addition, the aforementioned essential features are always correlated but these links in meaning are not equivalent. Of course, the molecular weight of molecules in one homologous series does not always increase with the chain length growth, but the compound with the same chain length as the first one but belonging to another homologous series can bear an incommensurably lower or higher molecular weight. Some compounds such as cyclical molecules will pass the molecular weight test as oligomers according to the above given definition because their molecular weight is about hundreds and thousands of oxygen units but we should take care when using the term “chain length” (periodicity) for their description*). And at last, the usage of a physical property as a characteristic feature often leads to mismatch of numerical values of the chosen parameter taken as the results of experiments based on different methods. You can see these critical values vary depending on the experimental conditions even when the same methods are being used. All these facts make it impossible to develop a clear gradation on the basis of the known definitions: according to some test results some chemical compounds may fall into the class of oligomers but according to the other tests they can be considered either polymers or monomers. This is the source of a long-history view that, nevertheless, still exists in some minds about oligomers as something indefinite and multiple meaning. For example, oligomers are described as “unfinished polymers” (forpolymers) or “axelrath” monomers (macromonomers).
1.1.3. Development of “Oligomer” Term Formulations The definition proposed by the IUPAC Commission on the molecular nomenclature [24] made things clearer in the late 1970s - early 1980s of the last century: “Oligomer is a substance consisting of molecules formed by atoms of one or several types or atomic groups (constitutional units), The definition proposed by the IUPAC Commission on the molecular nomenclature [24] made things clearer in the late 1970s - early 1980s of the last century: “Oligomer is a substance consisting of molecules formed by atoms of one or several types or atomic groups (constitutional units), associated in a recurring way. Physical properties of oligomer change if one or several constitutional units are added or deleted”. The oligomeric molecule can be most commonly presented as
*
Don’t forget that the second essential part of the word oligomer - μεροζ – can be translated not only as “a part” but also as “a definition”.
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Y1
Y3 X1-X2 Y4
n
Y2
The n sum of constitutional units (Х1-Х2 …) of oligomeric molecule is also called an oligomeric block (OB). The Х1 and Х2 units can have the same (Х1 = Х2) or different chemical structures (Х1 ≠ Х2) or Х2 = 0. There are also end groups = у1, у2, у3, у4,...), whose chemical structures differ from chain monomers. The number of end groups can vary from 2 (Y1 and Y2 =1, Y3 = Y4=0) to more (Y1, Y2, Y3 and Y4 = 1), while end groups themselves can be the same (Y1 = Y2 = Y3 = Y4) or different (for example, Y1 = Y2 ≠ Y3 = Y 4) in an oligomeric molecule. The definition given above by IUPAC is considerably correct. The broader concept “oligomer” falls into is neither polymer nor monomer but a substance characterized by a structural feature. This definition forms the upper limit for the n number of oligomeric block constitutional units corresponding to the transition from oligomeric to polymeric state of the substance. Indeed, we can experimentally distinguish the fact of adding just one link to oligomeric block from n to n+1 because the change from Хn (oligomer) to a compound with Хn+1 blocks (polymer) never goes without changes of physical properties. Any further increase of oligomeric block length from n+1 to n+2 (a polymer with Хn+1 block changes into polymer with Хn+2 block) cannot be registered experimentally because polymers have identical physical properties within a small Δn. But IUPAC description is nevertheless short of accuracy for it doesn’t provide any considerable difference between the terms “oligomer” and “low molecular weight compound”. The fact is that when we go from Хn oligomeric block to Хn–1 block and further on, from Хn–1 (monomer) to Хn–2 (monomer) and etc., the change of physical properties can be experimentally registered (if we change the length of both oligomeric and monomeric molecular chains, physical properties will also change), so this method cannot help us to find the lower limit for the number of the nth oligomeric block constitutional units. This problem of uncertainty was solved by Alfred Berlin. His interpretation of gradation “monomer – oligomer – polymer” [25] is more accurate and physically justified. Analyzing the changes of partial values of various physical parameters Φ (for example, volatility, heat capacity, density, viscosity, melting and boiling temperatures, etc.) which characterize homologous series of organic compounds, А. Berlin defined three areas with considerably different dependence Φ on the n number of constitutional units. Their common but simplified graphical representation is shown in Figure 1.1.
Oligomers as the Object of Research: Basic Principles
5
Figure 1.1. Physical parameter Φ=f(n) (solid line) and increments of it’s value ΔΦ/Δn (df(n)/dn) (dashed line) of homologous series.
The first area which is characterized by linear function Φ=f(n), i.е. ΔΦ/Δn=const, corresponds to low molecular weight homologous, in other words, monomers (generally this linear function exists in some generalized coordinates {Y(Φ), n}, i.е. the function Y(Φ)=f(n), and ΔY(Φ)/Δn = const is linear.) The size of molecules within this homologous area is always less than the size of the segment which “limits” the Φ properties described by the classical physical chemistry laws [26, 27]. The second area represents a nonlinear dependence of the Φ parameter partial value increment on n, that is, ΔΦ/Δn≠const. In other words, the form of function Φ=f(n) describing a homologous series changes sharply when we reach a fixed number of constitutional units n. This is the lower limit of oligomeric area. In the upper limit of this area Φ does not depend on n any longer and its increment ΔΦ is equal to 0. But it is necessary to note that physical parameters Φ of the same homologous series or a physical parameter Φ in various homologous series can be described by different nonlinear functions f(n). The third area covers polymers with Φ independent from the chain length within small Δn, i.e. in this case ΔΦ/Δn=0. Though possessing a strictly logical structure, Berlin’s interpretation of the “oligomer” term definition still seems indefinite concerning the fact that many factors contribute to the boundary values of n. Indeed, theoretically estimated and experimentally obtained boundary values of n, showing that the substance belongs to this or that area (see, e.g. [28-42]) were proven to change even within one homological series depending on evenness or oddness of rows, branching or non-branching of the main chain, the nature of the end groups, as well as proven to depend on experimental methodology, or the physical parameter Φ chosen for registration, measurement conditions, test sensitivity and etc.
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It is necessary to note, most publications show that researchers’ attention was mainly attracted to the area of large n. For example, the study by V. Privalko [39] presents an analysis of molecular pack density (ρα) as the function of molecular weight (М) in homologous series of tetramethylenoxide, ethylenoxide and styrene with М ~ 5·102 - 106. While analyzing the regular behavior principles (see Figure 1.2) in areas with М > 103 based on three models (intermolecular packs, overlapping statistical coils and statistically collapsing macromolecules), the author comes to a conclusion that the last fact corresponds to experimental data. As for the unusual effects discovered for substances with М < 103, they are considered to be caused by the influence of the end groups.
Figure 1.2. Dependence of density ρα on a molecular weight of tetramethyleneoxide (1) and ethyleneoxide (2) homologues at 750С and styrene (3) at 250С.
Hansen and Hou [41] proposed a model describing the dependence of heat capacity (λ) on average polymerization degree (Р) of molecules taking their orientation into account (different degrees of interaction between neighboring links connected by chemical and physical bonds). They have theoretically proven that λ is proportional to Р1/2 for short length molecular chains, however, with the molecular length increase, the increment of λ rapidly falls down, and that corresponds to the experimental data presented in [41] for homologous series of n-methylenes and n-styrenes. A titanic work was done by G. Korolev and А. Il’in [28]. They carried out the analysis of melting (Tm) and boiling (Tb) temperatures behavior and coefficients of molecular packing Kp in homologous series (Кp = Na.Vv /M · d, where Na is Avogadro number, Vv is Van der Waals molecular volume, М is molecular weight, d is density) as functions of molecular size (its Van der Waals volume) for 5000 various organic compounds. This enormous amount of experimental data allows us to make the following conclusions: 1) for research with a wide range of values Vv analyzed, the absolute majority of curves corresponding to functions Тm ,Тb, Кp, = f (Vv), presented in [28], show us (i.e., see Figure 1.3) a definite existence of linear and non-linear functional areas predicted by А. Berlin; 2) deviations from the above shown functions (see Figure 1.3 again) are caused by such “disturbing” factors as symmetry (and
Oligomers as the Object of Research: Basic Principles
7
asymmetry) of the molecular structure depending on the symmetry or oddness of the molecular rows, the shielding effect of the side groups on the centers of intermolecular interaction, presence of hinged bridges (e.g., -О- link), facilitating compact packing of molecules, and etc. Paper [28] gives a detailed analysis of various factors contributing to the influence of molecular structure on intermolecular interactions.
(A)
(B) Figure 1.3. Dependence of molecular packing coefficient Кp at 200С on the Van-der-Vaals molecular volume Vv for homologous rows of organic compounds with linear aliphatic chains and various nature of end groups: 1- amides; 2- acids; 3 – anhydrides; 4 – alcohols; 5 – nitriles; 6 – iodides; 7 – esters; 8 – aldehydes; 8 – bromides; 9 – ketones; 11 – amines; 12 – chlorides; 13 – phtorides; 14 – alkyl oxides.
The fact that the n boundary values depend on experimental conditions is well demonstrated in papers [8,9] where X-ray scattering was used to find a lower limit between oligomers and low molecular weight compounds. The authors showed that the long period value for crystallizing homologues which is determined by the size of crystallites is a linear function of n, which grows with the molecular size, increases up to some limit of the n value depending on the homologous row nature. In the area above, the linear principle does not work, as the chain gets the ability to fold. The lower boundary of oligomeric (or pleinomeric, according to the original author’s terminology) area was assigned to the limit value n=n1min where a longer period value function of n starts to take a contribution from the molecular
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
chain flexibility parameter. But according to another experiment with nothing but a lower crystallization speed different from the previous research, the crystallization temperature was close to the melting point of the analyzed sample with narrow MWD, and the area where the longer period function of n for the same homologous series was linear extended up to the values n=n2min, where n2min>>n1min. The increase of the boundary value nmin was caused by the new experimental conditions which allowed us to permit thermodynamically the opportunity of straightened molecules crystallization even for potentially flexible and relatively long chain monomeric molecules. The existence of such thermodynamically permitted conditions in the previous experiment was forbidden kinetically. The given example, however, proves Berlin’s statement: the results of specific experiments always show us three well-defined areas of the curve Φ=f(n) independent of the boundary values N: linear dependence area, non-linear dependence area and the area, where material properties do not depend on the polymerization degree. Thus, the laws describing the change of chain growth properties in low molecular weight, oligomer and polymer systems are totally different. If we consider that the group of these three totally different areas defines the term “oligomer” and take the intermediate one for oligomeric state characterized by nonlinear function Φ (n), any homologous row will show us an oligomeric interval. Such a definition, however, still has various interpretations, because the boarders of oligomeric area in homologous rows are set by external conditions and physical test parameter Φ. But it is not unusual. This is what we should expect. A fundamental constant, such as the water boiling point, also depends on measurement conditions, e.g., on pressure. The dependence of the matter properties on the macromolecule length (or the number of chain links) was chosen as a core characteristic distinguishing homologous rows in this method. It is a principal choice. It proved to be effective and showed us the way to systematic analysis of the term “oligomer”. Further on, this approach [43] developed an attempt to go from statements to physical values for functions describing the dependence of physical properties characterizing compounds in homologous rows on the length of molecules. We have analyzed patterns of internal energy density change with the growth of the n polymerization (polycondensation) degree in highly diluted solutions of organic compounds with various values of n. The mass concentration of solution was set constant to make the total number of monomer units constant and independent of n. The logical conclusions of the analysis presented in [43] can be reduced to the following qualitative statements: the molecules in highly diluted solutions make following contributions to the internal energy of the system: 1. 2. 3. 4.
internal energy of molecules, which does not depend on n; interaction energy of molecules and solution media, which does not depend on n; molecular interaction energy, i.e. intermolecular energy, which depends on n; interaction energy of chain segments, which depends on n only within the specific values of n.
Indeed, if every link interacts only with its nearest monomer neighbors in the molecular chain, the number of internal degrees of freedom grows proportionally to the number of monomeric units, i.e. it depends linearly on the degree of polymerization. Therefore, internal
Oligomers as the Object of Research: Basic Principles
9
energy and interaction energy of every molecule will increase k times if we change the degree of polymerization k times. However, molecular concentration will be k times less for this degree of polymerization (assuming mass concentration of our solution is constant). As the corresponding contribution to the energy density is one molecule energy multiplied by molecular concentration, this value will remain constant. The interaction energy of molecules and solution media gives us the same results. The molecular interaction (pair interaction) energy contribution to the energy density is proportional to square concentration, collision probability and interaction energy of two molecules for a diluted solution within the gas approximation. The homologue molecules numeric concentration with a constant mass concentration is inversely proportional to the degree of polymerization n, and the collision probability is proportional to the multiplication of molecule volumes, i.e., squared degree of polymerization n2. Therefore, the squared concentration and collision probability multiplication are independent of the degree of polymerization. Thus, the pair interaction energy contribution to the system energy density depends only on the constant of the pair interaction proportional to the number of macromolecule constitutional units. Therefore, the homologue degree of polymerization shows contributions to the energy density so that its properties vary linearly with the internal energy change (see left area of Figure 1.1). Though this statement is true only for paired or neighboring interactions of chain links, it can be applied to almost any low molecular weight compound with a straight molecule. Any further increase of the chain length provides not only neighboring interactions but full intrachain contacts within one molecule due to inevitable bending deformations. Such a remote intrachain interaction effectively reduces the internal degrees of freedom and acts as a shield for interaction with other molecules and solution media. Therefore, the internal energy density depends less on the chain length due to all these factors and no longer corresponds to linear function (see middle area in Figure 1.1). Any further increase of the diluted molecule chain length promotes shielding effects (the same middle area in Figure 1.1). However, after a certain chain length, when the chain gets coiled, the chain length no longer influences the interchain interaction constant (see right area in Figure 1.1); this relates to the fact that a long enough chain can be described as a group of blobs (statistically independent real chain fragments) [44]. Thus we can reduce interaction between chains to interaction between blobs of different macromolecules. Because parameters of blobs, such as their size, depend only on chemical structure of the macromolecule and do not depend on chain length even at 1/n scale [44], the interchain interaction constant does not depend on chain length within the large values of n. The analysis of internal energy dependence on chain length for diluted and concentrated solutions and liquid melts of organic molecules gives us the same results. The most important statement in the previous discussion is that the remote intramolecular interactions (interactions within one chain) emerge. It is these interactions that shield interchain interactions and lead to deviation (decline) of Φ=f(n) dependence on linear function. These remote intrachain interactions between monomer (constitutional) units in a single molecule mark a transition from low molecular weight to oligomeric state of substance as n increases in a homologous row. Taking into account that this interaction is the result of bending deformations which can take place only in a relatively long macromolecule (for minimum chain length see next parts), it is reasonable and even natural to use a chain length parameter, but not, e.g., molecular weight, as the criterion of transition from low molecular
10
S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
weight to oligomeric state of the substance (though these parameters are equivalent in some cases). But we should also take into account the fact that, apart from chemical structure, the rigidity (or flexibility) of the chain is defined by the system temperature and surroundings as well. So the conclusion is inevitable and logical: “low molecular weight compound – oligomer” transition takes place at different chain lengths depending on various conditions. While “monomer – oligomer” transition boundary is set by remote intrachain interactions emerging with the increase of the chain length, “oligomer – polymer” transition corresponds to collapse into globular conformation with the increase of the n value. According to statistical physics of polymers this state is achieved only at some minimum chain length. Therefore “oligomer – polymer” transition can also be sufficiently well described in terms of chain length. These statements also show us that the lower and the upper boundaries of the oligomeric area depend on the condition the tested molecule is in. This dependence is not a disadvantage of the proposed method to define these boundaries, but a physical property of the condensed state of substance in the form of oligomer. Therefore, the chain length is the core parameter to determine the oligomeric area boundaries. A macromolecular chain is capable of bending and taking a globular conformation depending on the system temperature and conditions. All we need is to find a minimum length of molecules with statistical flexibility for the lower oligomeric area boundary, and globular macromolecules for the upper oligomeric area boundary. In paper [44] the authors applied theoretical analysis (described in [45]) of statistical conformations of a long macromolecule including the influence of chain rigidity in a model of orientation-correlated migration to estimate deformation and ability to form a coil for chains with various rigidity and length values. This fact allowed us to estimate the upper and lower boundaries of oligomeric area in homologous rows. The dependence of the mean-square molecular radius to chain length ratio (R2(n)/n) on the chain length was chosen as the parameter characterizing the bending and coil-forming abilities of the macromolecule. We also took into account the fact that apart from the molecular chemical structure, the rigidity (or flexibility) of chain is defined by the system temperature. The higher the temperature is, the more rigid is the chain, the lower the temperature is, the more flexible it is. Figure 1.4 shows the results given in [44]. Every curve consists of three areas similar to schematic dependencies presented in Figure 1.1. However, the boundaries of these areas change with the change of the system temperature: the temperature increase results in a smaller oligomeric area size and the chain length shift to smaller values of n. This example proves that the molecular length – rigidity correlation can serve as the main criterion for classification of homologous as monomers, oligomers or polymers and boundaries between these areas depend on different system parameters, such as the temperature.
Oligomers as the Object of Research: Basic Principles
11
Figure 1.4. Plot R2(n)/n versus n for various temperatures: T1 – 1, T2 – 2, T3 – 3 (T1
1.1.4. Oligomeric System as Statistical Ensemble Let us discuss another essential aspect of oligomer science. We have previously stated that statistical flexibility of macromolecules defines the transition between low molecular weight and oligomeric states of a substance. It means that oligomers though having molecules of middle size obtain some statistical properties. This viewpoint is evidently controversial. Statistical methods cannot be applied to an individual monomer molecule. We can use statistics to describe only large groups of molecules. The conventional approach shown in [36] assumes that an infinitely long individual polymer chain is an object of statistical analysis (polymer statistics usually varies in the range of 1/n) and this statistics works fine, if we take, e.g., Flory Gaussian. But it is always assumed that oligomers have a finite chain length. So can we use statistics to describe a molecule of oligomer? The answer was given in papers [45, 46]. If the number of elements in a system consisting of one oligomeric molecule cannot be considered infinite, let us take a system comprised of all constituent links in all oligomeric molecules and consider its number of elements infinite. The authors used the average of an entire ensemble instead of the group of monomer links (which is typical of a polymer molecule) in one infinite chain to describe statistic properties of a single oligomer molecule in this ensemble, i.e. its internal degrees of freedom. This physical meaning was used for averaging in [45] to get the curves shown in Figure 1.4. Papers [45,46] give many important conclusions. First, according to this approach, oligomer is a statistical object. Second, unlike polymers, oligomers do not show Gaussian statistics (even ideal hypothetic oligomeric molecules)*. Third, statistical properties of oligomers depend on both energy and statistical
*
It was Yu. Lipatov in 1977 who questioned the usage of Gaussian statistics to estimate oligomer system properties [11].
12
S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
properties of molecules. And, the last, oligomers are a group of oligomeric molecules but not a single molecule; this defines the bulk properties of oligomers. Let’s take a closer look at these statements. The scaling analysis of conformational properties showed that various orientation and correlation effects for chains with specific length/property ratio can be found for freely joined chains varying in rigidity (or flexibility) and length (in homologous rows) [46]. If we take into account the excluded volume parameter in these correlated systems within Onzager’s model of rigid rods, we can see critical concentrations of rods for microscopic areas (aggregates) with local orientational orderings of rods in the initially isotropic macroscopic system, which, therefore, have an increased density. This concentration depends on the row length. The density of rods packing in aggregates depends on regularity in their orientation. The size of such areas (orientational correlation length) is another characteristic of the system scale which must be compared both with the Kuhn segment size and macromolecular size. Three alternative correlations are possible: A) the correlation length parameter is lower than the Kuhn segment size, or the chain length. The system is a typical polymer with macroscopic properties not affected by microscopic local ordering. B) the correlation length parameter is higher than the Kuhn segment size or the chain length. A low chain length corresponds here to the systems with low-molecular weight elements. But the local ordering of the relatively long chains compared to their Kuhn segment length can change into macromolecular ordering and finally lead to liquid crystal state transition. C) the correlation length parameter is higher than the Kuhn segment size but lower than the chain length. The last alternative corresponds to oligomeric area where local ordering of segments in different chains influences their conformation beyond the Kuhn segment level, i.e., sets the entire system macroscopic properties. Further discussion on these statements is provided below (see Part 2.2). Note that the low-scale structure of oligomer systems (local orientational ordering areas) influences the macroscopic properties of the system and is the effect of collectivism in oligomeric molecules behavior. This structure corresponds only to a specific length/rigidity ratio. However, it is not only the molecular structure that influences the effective rigidity but also the environment and external conditions, such as temperature. Note another unusual fact: formation of oligomeric aggregates, that is, complication of the system structure by orientationally ordered structures, is stipulated not only by the energy consuming intermolecular interaction forces (such as dipole, hydrogen, coordination and other physical bonds) but also by the conformational statistical properties of oligomer molecules. These properties appear at specific length/persistent length ratio, which, in turn, means, that boundaries between low molecular weight, oligomeric and polymeric states are characterized by drastic changes in the statistical behavior of macromolecules. Since the spontaneous complication of the structure (or self-organization) is anti-entropic, oligomer systems are naturally inclined to the processes with the entropy drop (due to their statistical behaviour) which must be compensated by the internal system energy. Calculations carried out in [47] show that the entropy drop compensation by the positive energy efficiency is a specific feature of oligomers: the individual chains loose their free energy only if they
Oligomers as the Object of Research: Basic Principles
13
belong to a specific chain length range where all conformations are not equally probable but, instead, correlated, i.e., they are oligomers characterized by distance intramolecular interactions. It is these oligomer chains, if aggregating, that compensate the enthalpy drop by their internal energy. Therefore, a thermodynamic ensemble of molecules obtains a new specific group feature at the point of transition from low molecular weight to oligomeric state: inclination to form supramolecular structures, or orientationally ordered aggregates. This fact can not be stipulated by specific physical and chemical interactions. This feature disappears when we go from oligomers to polymers. This statement does not mean that: а) specific forces in oligomer systems (polar forces, hydrogen bonds and etc.) cannot lead to aggregation. They can – depending on the molecule chemical structure; b) supramolecular structures cannot be formed in polymer solutions and melts. They can, due to the same specific properties. All this means that the nature of supramolecular structures formation can be different for oligomer and polymer systems, though the statistical behavior of oligomers is an essential, sometimes dominating, factor of their aggregation. Therefore, we must take into account both energy and statistical properties of homologous molecules in order to obtain experimental or theoretical values of the criteria properties within the framework of the approach being discussed. It is based on homologous row differentiation according to the chain length. These properties do not describe a single oligomer molecule but the behavior of the entire ensemble. We cannot state in this case that a single oligomer molecule has essential physical features, instead, we consider them to be averaged in the effective oligomer molecules ensemble and affected, in their turn, by a single oligomer molecule structure. Hence, we cannot say that a single “oligomeric” molecule is the only carrier of oligomeric properties – they are extended beyond to their thermodynamic ensemble. In other words, the study of oligomers should not be limited by the study of a single molecule properties. We should analyze the thermodynamic properties of the whole oligomeric ensemble and kinetics of its advance to thermodynamic equilibrium to make the image complete. The last statement is discussed in separate chapters (see Parts 2.3 and 2.7).
1.2. CLASSIFICATION PRINCIPLES OF OLIGOMER SYSTEMS Thousands of natural and synthetic compounds can be considered oligomers according to the definitions given in the previous part. Various criteria for systematization according to different essential features [8,13,15,16,48,49] have been offered to describe this variety of oligomers. The part below provides the oligomers taxonomy according to [16].
1.2.1. Taxonomy of Oligomers 1. According to the Ability of Oligomers to Take or Not to Take Part in Chemical Reactions According to this feature oligomers are subdivided into two classes: а) reactive and b) non-reactive. This classification is rather relative, because various factors influence the reactivity of oligomers. For example, a chemical bond may be reactive within a specific
14
S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
temperature range and inert beyond its boundaries, a catalyst may initiate a chemical reaction in an oligomeric system, and may not in another system, and a functional group may interact with one component and may not interact with another one. The subject of interest is not abstract reactivity but the behavior of a specific oligomer in specific storage and processing conditions.
2. According to Chemical Nature of Oligomeric Blocks The gradation here is the same as the standard classification in polymer chemistry: а) carbon-chain, b) element-chain, c) heterogeneous chain, d) cyclic oligomers, and etc. Each class can include subclasses: oligoalkyls, oligodienes, oligoarylens, oligoalkylensulfides, oligosyloxanes. and etc. 3. According to the Chemical Nature of Functional Groups For example, а) vinyl, b) acryl, c) hydroxyl, d) epoxy (dlycidyle), e) carboxyle, f) isocyanates, g) maleinates, h) peroxide, i) amide, j) sulfoxide, and etc. (for more information, see Table 1.1). 4. According to Functionality Parameters This classification subdivides oligomers into the following groups: a) According to the number of functional groups in a molecule: zero- , mono-, bi-, three, tetra-, and multifunctional oligomers. Non reactive oligomers have no functional groups, while reactive oligomers have one, two, three, four, and etc. functional groups. b) According to the arrangement of functional groups in a molecule: Oligomers can contain chain-end functional groups in oligomeric backbone (telechelates), and branched functional groups (alternants). Oligomers can contain regularly (structurally regular oligomers) or statistically alternating functional groups. c) According to the FTD and MWD parameters. This classification requires average functionality fi, that is the number of functional groups in the i-th molecule, to be supplemented by weight average (fw) and number average (fn) functionalities (as weight-average (Мw) and number average (Мn) molecular weights, correspondingly). Oligomers are subdivided into: oligomers with strongly defined functionality and ideal ratios fw/fn =1, Мw/Мn≥1; oligomers with fn ∼ Мn and fw/fn ∼ Мw/Мn and oligomers with fw /fn > 1 и Мw /Мn > 1. 5. According to Curing Pattern This classification subdivides oligomers into two large classes: a) а) polymerization oligomers (PO): curing goes without any release of low molecular weight by-products; b) b) condensation oligomers (CO): low-molecular weight products do not release during polymerization reaction*. *
Some authors [44, 50] reject classical definitions of polymerization and polycondensation [51] and consider them as sequential addition chain – growing process Аn + А → Аn+1 where A stands for a monomer molecule (polymerization) and combination of chain blocks having free end valencies Аn + Аm → Аn+m (polycondensation).
Oligomers as the Object of Research: Basic Principles
15
Each class offers possible sub-classification according to the chain-growth mechanism (such as radical polymerization, ionic polymerization, addition polymerization, migratory polymerization, equilibrium and non-equilibrium polycondensation, and etc.) and according to initiation or activation mechanisms (peroxide, radiative, photonic and catalytic initiation or activation by specific curing agents). PO – subclass includes, for example, oligodienes, unsaturated oligoesters, oligoesterepoxides, urethane-forming and other oligomers with multiple bonds or reactive cyclic units. CO – subclass includes various phenol- and urea-formaldehyde, glyptal and carbamide oligomers, mercaptooligosulfides, oligosyloxanediols, and etc. This classification is also relative because any functional group can react according to various mechanisms depending on conditions (see below).
6. According to Topological Structure of the Cured Products This classification offers various criteria to describe the end structure topology. The most popular gradation of oligomers is based here on the structure of polymer products which can be linear (a), branched (b) or cross-linked (c). Oligomer functionality is, evidently, the cornerstone of this classification. 7. According to Relaxation State of the Cured Products This gradation offers two sub-classes of oligomers: oligomers forming elastomeric compounds (a) and stiff polymers (b). A typical first class representative is the so-called “liquid rubber” which is hydrocarbon or urethane oligomeric compound with the number of links about > 10-20 and various functional groups. Second sub-class includes short-chain and multifunctional oligomers such as oligoestermaleinatfumarates, oligoester acrylates and etc. Strict definition of these groups is rather complicated and distinction is mostly conditional because the relaxation state of polymers formed as curing products of oligomers belonging to each class is determined by the test (operation) temperature, curing pattern, polyreaction kinetics, initial product FWD, presence of additives (such as plasticizers) and many other factors. This classification also includes a specific group of the so-called “heat-resistant oligomers”. These oligomer compounds are, certainly, not heat-resistant (they are liquid or low-melt) but their curing products are highly thermal and heat-resistant. The reason is either that curing process leaves initial oligometic heat-resistant blocks unchanged (for example, oligosiloxane blocks or fragments with interconnections) or that chemical curing of oligomers results in formation of new energy-consuming compounds (polyaromatic, polyinterconnected and other structures) [52-57].
This approach puts ring-opening and free valence migration reactions into the category of polycondensation processes, although no by-products are formed here.
Table 1.1. Classification of Structurally Regular Oligomers [25]
Functional group (FG) structure
1 -ОН, -Н, -СООН, -NН2 -Hal (-Br, -Cl, -F) N
R
N
R/ ,
O CH CH2 ,
S CH
H N CH
CH2 ,
NCO*
and etc. N C NR
CH2 NCO* C
N
FG label
Oligomeric block (OB) nature
2
3
The label for a functional group of the cross-linking agent* (СL) 4
А
Oligoalkylene, oligodiene
D, E, F
-
Polyaddition
B
C
-
Onium polymerization
С
B
-
The same
O
With СА
5
6
Oligoalkylene oxide, Oligoarylene oxide, oligoalkylene sulfide
A, F or without СА
Polymerization of cycles
Polyaddition, polymerization
E
Oligoester, oligocarbonate, oligoamide, oligoimide
A, D or without СL
Polymerization of isocyanates, polycyclotrimerization
Polyaddition, ionic polymerization
2
3
4
5
6
F
Oligourethane, oligosiloxane, various copolymers
A, G or without СL
Multiple bond polymerization
Polyaddition, radical and ionic polymerization
O N
Without СL
D
,
, CH2=CRCOO-, HOOCCH=CHCOOROOCCH=CHCOO-, RC≡C1
Network formation mechanisms
Table 1.1. (Continued).
Y
O C N C O
O
,
H2 2HC C C O H H2 2HC C O C O H ,
N
-
A or without СL
Multiple bond polymerization
Polyaddition, chain polymerization
H
-
F
-
Polyaddition
2
3
4
5
6
I
-
F or without СL
-
Quasi-radical or donoracceptor polymerization
,
1 2HC C R
G
,
,
18
Oligomers as the Object of Research: Basic Principles
8. According to Preliminary Expertise There are other principles of classification which supplement the previous gradation system. They are less strongly determined but important for a preliminary expertise. For example, reactive oligomers can be also described in terms of their production volume as those produced in large amounts and in small amounts. The first group are oligomers which have “occupied” the world market. They are produced in amounts reaching hundreds of thousands or even millions of tons. These oligomers include unsaturated oligoesters, oligoester aleinates/fumarates and oligoester acrylates; different brands of epoxide oligomers and urethane-forming oligomers, phenolformaldehyde and phenol carbamide oligomers; liquid rubbers (mostly based on diene and isoprene), and etc. [15.58-70.75]. The second group comprises specialty oligomers such as, for example, allylic or peroxide oligomers, vinyl oligoesters, oligosulfides, the so called “thermally stable oligomers” and many other products [52-57, 64, 71-74]. The production of these oligomers is not large and depends on the current market demand. But these products mainly stimulate the development of aircraft and deep-water vehicle production, data transfer and storage and other industries of high priority.
1.2.2. Taxonomy of Oligomers Introduced by A. Berlin The taxonomy of regular structure oligomers, proposed by A. Berlin in one of his last works [25] is now of a growing importance. This taxonomy seems to be the most rational among other approaches to reactive oligomers classification as it is targeted at the finite structure of polymers and provides reasonable methodology for selection of oligomeric systems and their transformation into polymers. This taxonomy includes topological structure analysis for the cured oligomer, consideration of its functional groups chemical nature, evaluation of the role of the cross-linking (curing) agents molecular structure and prediction of a possible cross-linking mechanism. This classification, which, in fact, covers most of the discussed features, generalizes the variety of reactions that may be used to cure oligomers; moreover, it also makes it possible to specify limitations for the application of reactive oligomers in distinct technological processes. Table 1.1 gives an outline of classification suggested by A. Berlin. The first column lists the chemical structures of the functional groups of oligomers; these structures are united into classes, which are denoted by letters from A to J (column 2). Column 3 lists the main types of oligomeric blocks associated with the particular classes of oligomers. Column 4 lists the cross-linking (curing) agents, if those are used to extend and branch the chain or form a network. They are labeled by the symbols of the corresponding functional groups. Letter M denotes the non-reactive fragment between functional groups of the cross-linking agent molecule. Its chemical structure can be the same or differ from the structure of an oligomeric molecule. The last two columns describe the well-known or presumed mechanisms of oligomer curing without (column 5) or in the presence (column 6) of curing agents. The table is so illustrative and simple that there is actually no need to discuss it in detail. It provides a compact presentation of the well-known conventional laws of organic chemistry. That is why many trivial and nontrivial conclusions can be made logically and easily. For example, liquid oligomers can be converted to solid crosslinked polymers by different
Oligomers as the Object of Research: Basic Principles
19
mechanisms depending on the nature of the functional groups. By selecting appropriate methods of initiation, one and the same oligomer may be cured by different mechanisms and form various end structures. For example, curing of epoxide oligomers (class D, see column 2) can involve various Class А and Class Е compounds such as amines. But we can also use chemical reactions to open the epoxide ring which make the second curing component unnecessary. The table also shows that functionality of reactive groups can vary in different reactions. For example, double chemical bond F is bifunctional in polymerization reactions: every elementary chain-opening act is a starting point for two kinetic chains and, therefore, leads to formation of polymer networks. But the same chemical bond F is multifunctional in step growth polymerization (reactions involving Class А and Class G compounds): one labile atom migrates along the double chemical bond to form a linear reaction product. Another example: Epoxy group D, monofunctional in reactions with amino or carboxyl group A, whereas it is bifunctional in catalytic polymerization. The authors of [13] had to modify concepts [76] on average functionality f of reactive oligomers and to introduce a new concept of functionality in a distinct chemical reaction fr in addition to molecular functionality fi described above to take all these conclusions based on Table 1.1 into account. We must take it into account when calculating fw and fn. However, A. Berlin admitted in [25] that this table cannot be considered a completed classification. Nevertheless it provides a relatively completed presentation of chemical “opportunities” targeted at insertion of informational framework to raw oligomers with its further fixation in the finite polymer product. Thus, this scheme makes it possible to perform task-specific search of oligomers and procedures to be used for their conversion to polymers and, therefore, to make at least qualitative predictions on the structure of polymer materials.
1.2.3. Taxonomy of Oligomer Blends The terminology and taxonomy of polymer and, moreover, of oligomer blends (OB) has not been completely acquired yet [16]. Therefore, to evade possible misinterpretation, below we outline the physical implications of concepts referred to in this book. However, we do not claim that the definitions given below are comprehensive and perfect. A blend in which one of the components is an oligomer is referred to as an oligomer blend (OB). The second component of the blend may be represented by any low molecular weight, oligomeric, or high molecular weight compound. Note also that not every blend, containing an oligomer and any of the second components listed above, which can be formally (sic!) classified as an oligomer blend, can really be classified as OB. Indeed, the formal approach to identification of the majority of industrial oligomers represents them as OBs because almost all homologous oligomers show wide FWD and molecular weight distribution. Nevertheless, it is necessary to note that this approach is not always reasonable. Indeed, the formal approach would lead to a conclusion that many commercialized oligomer forms contain small amounts of low molecular weight “synthesis inhibitors” to avoid uncontrolled spontaneous reactions during storage and processing or being a part of a synthesis process or doped with small amounts of “storage inhibitors”. This would also be the case with oligomeric products doped with small amounts of initiators, catalysts, activators, and etc., added to the system before curing. The role of
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
these active additives is very important and, sometimes, decisive for the curing process in its chemical and kinetic aspect [15, 50, 77, 78]. The MWD and FWD of oligomers are also essential for the formation of cured polymer material topological structure [13, 50]. However, minimal dosage of the second component described above has almost no effect on the supramolecular and phase structure of liquid oligomer mixtures (unless otherwise specified). Therefore, we must consider primarily the features which make a significant thermodynamic contribution to supermolecular and phase structures of initial mixture to classify oligomer blends as mixable or unmixable. The principles of “individual” oligomers classification discussed in the previous chapter are, of course, applicable to oligomer blends. But they become much more complicated due to the multiplicity of subsystems. For example, oligomer blends can include following reactive components: PO + PO, CO + CO and PO + CO. Any subsystem can itself include variations of functional groups and oligomeric block of different nature, the length of oligomeric block and the number of functional groups etc. But there are some features that characterize only oligomer blends. First of all, they are the second component state (monomer, oligomer or polymer) and thermodynamic compatibility (or incompatibility) of blend components. We can most commonly subdivide oligomeric blends into three groups according to the first criteria: a) oligomer – monomer blends, b) oligomer – oligomer blends and c) oligomer – polymer blends.
Oligomer - Monomer Blends Among the vast number of oligomer-monomer blends let us mention those which are commercially important. These blends are primarily represented by the mixtures of oligoestermaleinatefumarates with various vinyl monomers (mostly styrene); these blends are commonly referred to as “polyester resins” [58-60]. This class of OB also includes epoxide compositions (blends of oligoester epoxides with amines or other monomeric curing agents) [50,61,62], some novolak phenolformaldehyde compositions cured by, for example, hexamethylenetetramine [66], oligosulfides – oxidants blends [74] and urethane composites (blends of oligoester- or oligodiene glycols with di- and triisocyanates) [63-65]. These types of blends are used in the majority (with only few exceptions) of commercial formulations (e.g., see [79-85]). Oligomer - Oligomer Blends These blends comprise systems of two main types. This first group includes oligomers differing in the nature of functional groups: acryl and epoxide, epoxide and isocyanate, metacryl and hydroxyl, metacryl and maleinate groups etc. One of these blends is used for preparation of simultaneous inter-penetrating networks (IPNs). The major requirement that these blends should satisfy is that the functional groups of each oligomer in the pair interact by different reactions; this must, therefore, eliminate the reactions between different chains [86-90]. On the contrary, other polyreactions with the same mechanisms are used to copolymerize different components. A popular industrial binder PN-609 based on a mixture of oligomaleinate/fumarates with oligoester acrylate (e.g, triethylene glycol dimethacrylate is another representative of oligomer-oligomer blends [15]. Oligoester acrylates are used instead of ecologically hazardous styrene to significantly accelerate curing of “polyester resins”. This
Oligomers as the Object of Research: Basic Principles
21
list can be continued by the blends of “liquid rubbers” containing epoxide or unsaturated functional groups with corresponding reactive oligomers. The curing process of such mixtures must desirably lead to elongation and (or) branching of a linear chain [81, 82, 90]. Another large group of oligomer-oligomer blends is represented by oligomers with different concentrations of identical functional groups and either identical or various oligomer blocks in different molecules. These blends are produced either by manual mixing of finished products [92] or by specific synthesis [75]. By varying the contents of different oligomer molecules in these compounds, we can control the properties of the blends and the rigidity of the resultant polymer products. For example, we can add mono- or bifunctional oligomers into high-viscous polyfunctional oligomer blends to produce compounds with lower viscosity and less fragile networks of cured oligomers. A typical example of this class of oligomeroligomer blends is provided by oligoester acrylate compounds of commercial brands D-20/50 (a 1:1 mixture of oligomer based on glycol and phthalic acid terminated by two methacrylic acid groups and pentaerythritol-based oligomer with eight methacrylic acid groups per oligomer molecule) and D-35 (a 35:65 w/w mixture of the same bifunctional oligomer and pentaerythritol-based oligomer with six methacrylic groups per molecule). There are other oligomer – oligomer blends of the same type (e.g., see reviews [17, 75, 85, 91, 92]).
Oligomer - Polymer Blends Application of this class suggests at least two extreme situations. In the first case an oligomer is added to modify a polymer (let us refer to this system as a polymer-oligomer blend). In the second case a linear polymer is added to a reactive oligomer in order to make the future network more elastic (referred to as an oligomer-polymer blend). In both cases, curing products are polymer-polymer blends, but their structures are totally different: they differ in the nature of dispersion medium and dispersion phase, morphological parameters, and etc. Polymer – oligomer systems are, in turn, divided into two subsystems differentiated by oligomer reactivity. A) Non-reactive oligomer. Oligomer acts as a common plasticizer when added to a linear polymer. Nonreactive oligomer plasticizer remains chemically intact in a resultant curing material and reduces its physico-chemical characteristics (first of all, a module) displaying a well-known Rebinder effect [98] unless anti-plasticization processes occur. High vapor tension (non-volatility and resultant ecological attractiveness) are the main advantages of such nonreactive oligomer plasticizers over common monomer plasticizers: we can select oligomer with a specific chemical structure [96, 97] which is more effective in comparison with its low molecular weight analogue in the same conditions. These advantages of oligomer plasticizers stipulate their successful commercial production [93, 94, 99]. B) Reactive oligomer. When a polymer is added to a reactive oligomer, the so-called “temporary plasticization” (a term used in technical documentation) takes place. During the initial processing stages of a polymer-oligomer blend (mixing of components, rolling, extrusion, etc.), the reactive oligomer acts as a common plasticizer (i.e., its effect is similar to that of nonreactive oligomer): it lowers the softening and flow temperatures, reduces the viscosity of the blend, and etc. However, during further processing after triggering the chemical reactions, the
22
S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev reactive oligomer (in contrast to its nonreactive analogue and low-molecular plasticizers) undergoes chemical transformations. There are two possible ways of reaction: either a network is formed with graft polymerization to a linear matrix or formation of such structures as “a snake in a cage” takes place. These objects perform a physical or chemical structural modification and eventually allow us to regulate the polymer substrate properties. Modification of final properties range for a cured system may depend on specific process conditions. Let us note, that the principle of “temporary plasticization” assumes a possibility of simultaneous physical and chemical modifications of linear polymers (in the same technological process) largely increasing practical opportunities to synthesize materials with predicted properties and to make the processing technology more efficient [77, 92, 99-108].
Compatibility of Components This feature subdivides oligomer blends into compatible (homogenious ≡ single-phase) and incompatible (heterogeneous ≡ two-or multi-phase) systems. Compatibility is obviously determined by chemical structure of components and system state parameters (such as temperature, pressure and concentration). Homogeneous Oligomer Blends can be homogeneous or heterogeneous at the supramolecular level of their structural organization. This structure itself can be isotropic or anisotropic. The reasons for structural heterogeneity of homogeneous liquids can vary very widely (see Parts 2.3 and 2.5). Heterogeneous oligomer blends are subdivided according to the size of dispersed particles (therefore, the classification used in colloidal chemistry of polymers is here applicable [98, 109, 110]), aggregative state of dispersion media or dispersion phase, temporary stability (or instability) of morphology, and etc. Many questions arise from this classification, and they have no definite answers at present. Further discussion on these problems is provided in further chapters in the third part of this monograph. All the above given classifications of oligomers and oligomer blends (as well as any of the other systems) are conventional and imperfect. Real systems are much more complicated than the proposed taxonomy. Therefore, all these principles and classifications of oligomers are subject to further detailing and improvement.
1.3. STRUCTURAL ORGANIZATION OF OLIGOMER BLENDS Description of oligomer systems usually involves their structural characteristics in initial state (before curing), intermediate state (during curing), and final product state (after curing). It is very important to choose a correct estimation parameter for these structures. As the term “structure” (“mutual alignment of incorporated elements” introduced in [111]) is too vague, it sometimes causes “science-like speculations” and incorrect conclusions. Therefore, it seems reasonable to correct terminology and general structural hierarchy used in physical chemistry of polymers [50, 112, 113] that is mainly suitable for oligomers.
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1.3.1. Structural Hierarchy Fundamental physical properties of any system (such as a polymer) are proven to be determined by its “main” constitutional subsystem. A macromolecule is this subsystem in polymers. Its chemical structure and, therefore, its conformation and configuration affect the structure of all higher levels of organization. Two levels of structural organization – molecular and supramolecular – are usually considered when discussing linear polymers [113-116].
Molecular Level It reflects the chemical structure of a system: chemical composition of repeating units, nature of co- valent bonds linking the units into a chain, nature of terminal and side groups, functionality, stereochemical structure (cis, trans, iso, syndio, etc.), arrangement of units in a chain (1-2, 1-4, head-to-tail), etc., which themselves determine thermodynamic parameters of a system such as the chemical affinity of components. Supramolecular Level It reflects the spatial arrangement of the system elements: nature and strength of physical bonds involved in intermolecular interaction, the extent of order in the arrangement of molecules or their segments (such as aggregation), distribution functions of aggregates according to their number and size (such as volume distribution) and etc. Intermolecular forces (hydrogen bonds, Van-der-Waals interactions, and etc.) contribution to packing of aggregates in liquid systems is supplemented by spontaneous volume fluctuations of molecular concentration. Cross-linked polymers require an additional topological level of structure [50] which is also used to describe oligomers. Topological Level This level reflects the MWD function, the distribution of network junctions (chemical and physical) with respect to their number and branching, distribution of interjunction chains in length, distribution of “internal” cycles with respect to their number and size, and etc. These three levels of structure cannot sufficiently describe blends and characterize objects in a wide range of state parameters. That is why a colloidal level of structure is introduced [98, 109, 110, 117-119]. Colloidal Level It is determined by thermodynamic parameters of the system components and described by phase state diagrams; distribution functions of dispersed particles with respect to their number and size (dispersity); component concentrations in corresponding phases; chemical nature of continuous and dispersed phases; kinetic morphological stability; phase inversion; interfacial phenomena; and etc. As we noted above, structural parameters are interrelated though belonging to different levels of structural hierarchy. For example, the structure of molecules affects conformation properties, packing in supramolecular structures and thermodynamic characteristics of the system which, in turn, determine its phase structure, particularly equilibrium concentrations
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
of components in coexisting phases. Reactive groups’ functionality and anisotropy of supramolecular elements affect curing kinetics and, therefore, are essential factors for branching of mesh-points and morphology parameters. The encyclopedia [112] provides three various features for classification of elements at any structural level: geometric, thermodynamic & kinetic.
Geometric Features a) absence or presence of far ordering. The maximum order level corresponds to a crystalline structure and the minimum level corresponds to an amorphous disordered structure. The supramolecular structure of crystallizing polymers has many forms and a hierarchy of levels (e.g., see [113, 120-124]). We have to stay beyond the level of problems in this publication to analyze it properly. Let us just note that polymer structure contains discrete elements; their size, shape and phase boundary remain unchanged during all the time of observation while fluctuating elements with these parameters do change during observation. b) absence or presence of close ordering. This feature is extremely important to describe amorphous and oligomer systems. For more information please see Part 2.3.2. Note that local areas (aggregates) with various molecular anisotropies can also appear in an oligomer system (see Part 1.1.3). These aggregates can be either discrete or fluctuating depending on stabilizing forces. Thermodynamic Features Discrete systems are thermodynamically stable, fluctuating systems are thermodynamically unstable. Note also the essential difference between oligomer blends based on reactive and noncreative oligomers. Indeed, the formation of all-level structures of a chemically cured product in reactive oligomer blends (polymer-polymer blend) occurs concomitantly with the permanent variation of the chemical structure of the components (at least one of them), whereas the formation of materials from non-reactive components (e.g. solid materials) is not accompanied by any chemical transformations. This means that during the cure of reactive oligomer blends, both thermodynamic parameters of the system as a whole and those, characteristic of each of the components, do vary. Because of this, the equilibrium, that is, thermodynamically stable values of the parameters belonging to different structural levels vary during the course of the process, whereas in nonreactive blends these parameters are the function of the parameters of state only and are specified from the very start of the process. Kinetic Features Structural transformations are kinetically described by two temporal parameters: 1) 1) transition time τ1 between two states or conformation of a structural element; 2) 2) the lifetime τ2 between formation and destruction of a structural element at certain conditions. Let us repeat that τ2 = ∞ for discrete structures, which are thermodynamically stable, while τ2 is finite for fluctuating systems. Various structural levels can have slightly different τ1. For example, consider a system with given state parameters. Aggregates will grow to their equilibrium size (that is, supramolecular
Oligomers as the Object of Research: Basic Principles
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level) within transition time τ1, but sometimes cannot reach equilibrium molecular anisotropy (that is, topological level). The “oligomer structure” concept is also differentiated by scale criteria [98,109,113,119,125]. Unfortunately, the scaling of oligomers is not unified yet. The most common starting points to analyze chemical structure of polymers are micro- and macrolevels. These levels can be considered both supramolecular and colloidal. The analysis range for supramolecular structure of crystallizible polymers comprises shapes and sizes of crystals and crystallites. Amorphous polymers and oligomers are characterized by the size of heterogeneities of various nature and names (see below). Colloidal level is mainly described by the scale parameters which are usual for colloidal chemistry [98,109]. The microscopic analysis of a polymer structure comprises link, chain and macromolecule sizes and various characteristics as arguments: contour length, distance between chain ends, volume, and etc.
1.4. SOME THERMODYNAMIC CHARACTERISTICS OF OLIGOMER SYSTEMS We need to consider at least four interrelated aspects to analyze the thermodynamics of oligomer systems: thermodynamic, kinetic, colloidal and methodological aspects. Thermodynamic aspect introduces applicable law of phase equilibrium and statistical thermodynamics to oligomer systems. Kinetic aspect is based on the fact that a system needs a certain time to reach equilibrium at various structural levels. Colloidal aspect correlates morphological stability (or instability) and phase boundary of oligomer systems with their macroscopic properties. Methodological aspect argues the reliability of results obtained using various phase structure analysis methods. These results are rather contradictory both because of different resolution of these methods and different interpretation of the term “phase” by various authors.
1.4.1. Thermodynamic Aspect Back in 1937, V.A. Kargin, S.P. Papkov, and Z.A. Rogovin showed that polymer solutions obey the rule of phase equilibrium, which is one of the fundamental laws of physical chemistry. Since then, there numerous attempts have been made to find an analytical relation between the molecular parameters of components and their mutual solubility. However, no serious generalizations were obtained for a long time. It was only the lattice model of liquid created by Flory [127] and Huggins [128] using the concepts of the Gibbs equilibrium thermodynamics, which analytically related a change in the free energy of mixing (AGm) or a change in the chemical potential (Δμ) to the equilibrium fraction of polymer in solution: ΔFc = kT (n1 ln υ1 + n2 lnυ2 + χ1 n1 υ1 υ2)
(1.1)
Δμ = μ1 - μ1° = RT [ln (1-υ2) + (1 - 1/x) υ2 + χ12]
(1.2)
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
where k is Boltzmann constant, R is universal gas constant, n1 and n2 are number of polymer and solvent molecules correspondingly, υ1 and υ2 are volume fractions of solvent and polymer, μ1 is a solvent’s chemical potential in a solution, μ1° is a pure solvent’s chemical potential, х is a number of fragments in a polymer molecule in a lattice (this parameter is similar to a degree of polymerization), χ1 is Flori – Huggins constant (interaction parameter), which describes an excess free energy of interaction per a solvent molecule. This outstanding theory stimulated research (see, for example, reviews [129-135] and their references). The results provide a quantitative correlation between molecular structure parameters of components, their mutual solubility and some properties of blends. For example, Scott [136] and Tompa [137] derived the equation for ΔFc as a function of solution temperature and molecular weight of components. Scott-Tompa’s approximation allows us to estimate the critical parameters of various blends depending on х: polymer-monomer, polymer-oligomer, oligomer-oligomer and etc. Taking a mixture of two low-molecular liquids, for example, where x1 and x2 are obviously close to 1, we get (χ1)cr=2. For polymer (x2→∞) dissolved in a low-molecular liquid (x1 ≈ 1) we get (χ1)cr=0.5. Oligomer – oligomer blends (for example, x1 and x2 ≈ 103) have (χ1)cr=0.01. Two polymers have x1 and x2 → ∞ and are, therefore, incompatible. Thus, it seems that distinct information about the degree of polymerization and the molecular structure of components allows us to calculate the critical parameters of the blend and make a conclusion about compatibility of this or that pair of components. Indeed, sometimes this rule works properly. But a comparison of experimental and theoretical results for a variety of objects has shown that this theory is not always right. The most striking examples of such a mismatch of results challenge fundamental aspects of this theory: there are several pairs of certainly compatible polymers [139,140] with χ1 as a function of concentration [133,138]. This is what the theory cannot predict. Various correlation factors and “more precise” definitions were added to initial a priori modeling and theoretical apparatus of the theory to overcome these or those mismatches of experimental data and predictions of the classical Flori-Huggins theory (and its many modifications [136, 137, 141, 142]). Particularly, the empirical parameter S, that is, “degree of mixing” was introduced to describe the so called “segmental” solubility of polymers [142]. The value S=1 was taken for a degree of mixing reaching molecular level. The area S<0 corresponds to the segmental dissolution. The area S>>1 corresponds to a phase separation. These attempts to make the theory “fit” experimental results are unnatural. They couldn’t overcome limitations of the initial lattice model which doesn’t take into consideration structural, first of all supramolecular characteristics of polymers. Flori has removed many classical theory version defects [143] from his modified thermodynamical theory of liquid blends, where he used the main aspects of the corresponding states model, which Prigozhin [144] had worked out for solutions. We will not go into details of this theory, which has been discussed, commented and further developed by many well-known scientists (see for example [129,131,132-135,145-149]). Let us just mention that the Flori theory has naturally taken into account some specific structural features of the real polymer solutions, such as change of component volumes during mixing, association of components and etc. The special appeal of a new theory was a nontrivial effect that could be naturally derived from it. Flori has theoretically proven that mixing of polymers can reduce the system entropy while increasing the number of its combinating units, because the aggregation degree of each
Oligomers as the Object of Research: Basic Principles
27
component molecule also increases. Thus, the introduction of combinatorial and noncombinatorial parts for a total entropy provides us with reasonable explanation and qualitative description of the real effects and in some cases reduction of a total entropy in blends through calculation of their concurrent contributions into entropy component of a free energy. Further development of thermodynamics of polymer systems involves concepts of fluctuation theory and scale invariance (scaling). Fundamental generalizations developed by I.Prigojin [144], I.M.Liphshits and his successors [150], S.Edwards [151,152], P. de Jan [149], R.Kennigsfeld [153] et.al [145-148] allowed us to obtain quantitative results for various polymer system types: [145-148] they provided quantitative description of various polymer systems: polymers with flexible and stiff chains, mono- and polydisperse polymers, polymers with low or high affinity of components, concentrated or diluted solutions, near or far from critical points, in metastable and phase-transition states etc. The state-of-the-art theory for thermodynamics of large molecules is presented in monograph of А.Е.Chalykh et. al. [134] and a successful compilation by V.I.Klenin [135]. The reasons for the fact that an oligomer molecule can be identified neither as a monomer molecule (it’s not a point object) nor a polymer molecule (we cannot take the average of all conformations) are provided above. Application of statistical physics methods to monomers is only possible for ensembles of monomer units. However, these methods can be applied to a single polymer molecule. A possibility to use statistical laws for a single monomer molecule is a subject of long-term discussion. Some authors [154,155] show that the calculated flexibility of oligomer molecules is close to that of vinyl polymers thus making it possible to use Gaussian ball model for oligomers. Other reports [156,157] postulate persistent model and provide calculations based on “fermicular chain” of Porada [158], which describes behaviour of molecules of any stiffness (flexibility) – from sticks to balls. The authors of all reports interpreted experimental results as a confirmation for their own conclusions. For example, the authors of [156] used Flori equation to calculate flexibility of oligoglycoadipinate and toluylenediizocyanate [143] (ho2 /M)1/2 = ([η]θ M/Φ)1/3 M1/2
(1.3)
where (ho2)1/2 is a chain size that doesn’t interact with solvent, [η]θ is a characteristic viscosity in θ - solvent, Ф is a constant, that is universal for polymers, М is a molecular weight. The parameters (ho2 /M)1/2 and [η]θ in this report were calculated by StockmayerFixmann equation [159] using experimental viscosity data of oligomer objects. In other research [154] viscosimetry and light scattering methods were used for oligopropyleneglycole homologues with the molecular weight М= 400 – 4000. It gives an explanation for the scattered light depolarization factor and viscosity coefficient dependence on molecular weight М and oligomer concentration provided that these compounds keep the shape of statistical ball for molecular weights less significantly than that of other known polymers. At last, authors in [38] use Porada method to calculate the root-mean-square distance between chain ends: ho2 = 2а [( L/а) -1 + е-L/a]
(1.4)
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
where “L” is the full chain length and “а” is the persistent chain length, and obtained а = 8 8,6 А° for oligoethyleneglycoladipinate, that is according to their report [38], shows that hydrodynamic behavior of oligomers is close to behavior of polymer Gaussian balls, which have weak hydrodynamic interaction. V.P. Privalko [39] analyses some limitations of the Gaussian ball model. He declares that Gauss approximation is inadequate for the description of the short-chain oligomer molecules giving various examplary illustrations. In particular, experimental data, provided in [160] for the functional dependence of the first member χ1 of the enthalpy component series expansion χн on molecular weight for polystyrene solutions in real solvents. The critical range of М~1,2 – 1,5 ·103 (it depends on a solvent) has proven to have extreme behavior of χ1 that goes beyond the limits within М~1,5 - 5·104. The author [39] explains these properties of the function χ1 on М as a transformation of macromolecular conformation from straight nonGaussian to Gaussian ball shape*. Please note, that these interpretations of similarities and differences in “structural” behavior of oligomer and polymer molecules were not based on direct structural research and object-oriented theoretical calculations but on indirect dynamic experiments and calculations where their results were used. That is why we should agree with Yu.S. Lipatov in his opinion based on the results of these experiments and the ones alike [11], that “hydrodynamic oligomer characteristics agree well with non-flowing Gaussian ball model, though oligomers are not Gaussian balls because their molecular chain is too short”. The statistical properties of oligomer systems are more specific than that of monomers due to additional degrees of freedom contributing oligomer flexibility and differ from properties of polymers because their chain is too short for a sufficient ball conformation. Therefore theories that have been developed and confirmed for low-molecular and highmolecular weight compounds cannot be identically applied to oligomers when their conformational properties are not considered. Part 2.2 provides some approaches to understanding the oligomer structure formation thermodynamics.
1.4.2. Kinetic Aspect High viscosities of polymers and different constants of diffusion and relaxation of components in oligomer and polymer blends are the factors which determine the difficulty of getting the equilibrium state of such systems which is attained at different velocities and at different structural levels. Therefore, the methods of sample preparation for testing and the conditions and duration of sample storage (i.e its prehistory) may affect the experimental results. This very circumstance may be the reason for the highly contradictory experimental data reported on the mutual solubility (compatibility) of components in polymer blends [129,162-166]. This is well illustrated by the results reported in [166] which demonstrate the inconsistency of estimation of thermodynamical compatibility by the initial transparency of *
V.N. Kuleznev proposes a rather interesting comment [161] to this and similar experiments. He believes that critical phenomena in oligomer blends can be observed in a specific structural transition within a stage of a partial layer separation of macromolecules, when double phase structure is partially formed but the interphase surface segments are still compatible. Such a combination of macromolecular incompatibility and segment interaction is an effect of intrinsic dualism of polymer molecules. Oligomers show no dualism.
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films (a proven method for estimation of compatibility). This method does not include relaxation kinetics because components can be thermodynamically compatible (incompatible) at various stages of experiment. Indeed, authors report that the films of a mixture comprising 70% oligovinylmethyl ether and 30% polystyrene obtained from solution in a common solvent (further removed), were transparent (that indicates compatibility of components) for 1.5-2 months after vacuum drying performed to delete the third component (mutual solvent), but got turbid when stored (mixture components become incompatible). Similar films containing 75% ether became turbid already in 5-8 days after preparation. Since no chemical processes occurred during the storage of both compositions (as it was reported), the initial transparency of the films cannot indicate thermodynamic compatibility of components. Indeed, if the optical densities of both films are measured in the first hours or days after preparation, we may conclude that both systems are compatible. Further testing of films in 10 days, for example, shows compatibility of the first sample and incompatibility of the second one. According to measures made 2 months later both blends look incompatible. This system is in fact partially compatible. Both blends are thermodynamically incompatible within a chosen range of state parameters (oligoester concentration is 70% and 75% correspondingly) and must go through a phase separation. But the phase separation process is rather longlasting in the first case due to insufficient concentration of the low-viscous component. That is why the system is non-equilibrium at certain moments. In other words a film is transparent for some period of time (system compatibility) due to not thermodynamical but not kinetic effect. S.P. Papkov shows similar law patterns [167] for systems with liquid crystal equilibrium: the transition into equilibrium state for a system of isotropic solution, crystal solvate and liquid crystal phase is long-lasting within a certain temperature range. These examples describe low segregation at the colloidal level. Other examples [168] describe processes of long-lasting equilibration: initially turbid blends become transparent in several months or even years due to low mutual diffusion rate. Therefore, thermodynamically compatible systems [118, 129,168] were considered incompatible. The examples shown above are more or less trivial because correct conditions and modes of check experiments easily prevent possible mistakes. However, equilibration processes at supramolecular and topological levels are less demonstrative and require further investigation [169-173]. They will be discussed below. Now we take a look at kinetic aspects of an equilibrium structure formation process in liquid oligomer systems. The macroscopically closed system can be presented as a group of microscopic subsystems (or system elements) changing matter and energy with other elements and environment during equilibration. These subsystems can be not only phase inclusions but also supramolecular structures such as concentration fluctuations with various temporal and spatial parameters. Various distribution functions are postulated for liquids: numeric, size and lifetime distribution – f(n), f(r) and f(τ0) correspondingly, which are Boltzmann, Gibbs distribution functions etc. [174-176] and amendments [176-178]. Distribution functions are, anyway, subject to change during relaxation period τi between initial system state (that is usually stochastic) f0 and equilibrium state (that doesn’t depend on initial conditions) fр. It’s not always possible to calculate f0(n,r,τ0) and fр(n,r,τ0) precisely so average values n, r, τ0 are used in practice.
30
S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev Relaxation rate is a function of many variables. The first one [175] is the scale factor: τi = L/νi,
(1.5)
where τi is the characteristic relaxation time, L is the linear size of a system, νi is the equilibration rate by ith parameter. Relaxation rate is evidently influenced by the system state parameters. An important factor for blends is the phase organization and viscosity of dispersion phase and dispersive media. In addition, possible mutual close- order orientation is also important for relaxation process when equilibration of non-spherical molecules is discussed. Equilibration time of a macroscopic system is usually calculated by the slowest relaxation process on a subsystem level. Let’s note another aspect which is principally important. The experimental methods used to study a system are chosen by the single fluctuation relaxation time (or its lifetime) or by the average relaxation time of all fluctuations: the value τ0 must not exceed the resolution of a method (device) t∗, and the average relaxation time τi to equilibrium is used to set exposure τe (observation time, that is a period between preparation of a sample and experimental registration of its properties) because τi must be less than τe. The low molecular weight liquid systems have very low relaxation times of concentration fluctuations to equilibrium state which are characterized by inequalities τ0 < τi and τi < τe. (Numerical evaluations and descriptions of specific cases are provided in [175,176]). Thus, fluctuation equilibration kinetics doesn’t imitate relaxation rate in a macroscopic system (possible exceptions are discussed on the basis of nonequilibrium thermodynamics [179-181]). Polymers are usually characterized by a broad range of relaxation times, some of them (the upper limit) considerably exceed (exponentially) the observation time [174], or τi >> τe. Thus we can’t get precise information on the influence of kinetics within a reasonable observation time though a polymer system doesn’t reach its equilibrium state. This problem is shown in lots of publications (see, for example [174,182-185]). However, liquid oligomers having considerably lower upper limit of relaxation times due to their molecular structure than that of polymers, but still higher than that of low-molecular liquids, may have fluctuation lifetimes and equilibration rates close to the experimental observation time: τ0 ≅ t∗, and τi ≅ τe. Therefore, more methods can be used to study oligomers correctly [186], however, on the other hand, macroscopic properties of oligomers may also depend on temporal and temperature (or generally energy) history of a system, because various initial conditions and deviations from the equilibrium state may precede registration of a certain physical property. This problem is not an exception for any oligomer blends but is a more common case for systems with a limited compatibility, which have significantly increased amplitudes and correlation radiuses of long-wave fluctuations in metastable state or around the critical point. Unfortunately, literature sources do not provide us with a common opinion (e.g., see Part VI of monograph [134]) on unambiguous experimental criteria to define whether the system is in a thermodynamical equilibrium by the time of a test. It’s not just a result of a limited methodological opportunities and incorrect interpretation of experimental results. Such a
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complication is stipulated by an objective aspect of the classical expression (1.5) with νi value of equilibration rate by the ith parameter. These values (rates) can be different for various tested criteria (parameters). Therefore, thermodynamic equilibrium of a macroscopic system is an effect of local equilibration processes at a subsystem level (structural hierarchies). In other words, concentration equilibrium in a system (molecular composition equilibrium) doesn’t correspond to the equilibrium number and size and especially inner structure (topological) distributions of supramolecular structures and completion of the phase separation process with stationary concentrations in contacting phases doesn’t characterize phase solution layering because of possible further coalescence and morphology system changes. All these aspects are evidently stipulated by thermodynamical equilibration kinetics. Further information on equilibration kinetics at various structural organization levels is presented in Parts II and III of this book.
1.4.3. Methodological Aspect The variety of experimental methods used in the study of thermodynamic compatibility of blended systems is based on four principles: 1) measurement of the wave properties (optical, electronic, X-ray methods etc.) of the system, 2) determination of its sorption capacity, 3) registration of the relaxation characteristics of the blend, 4) monitoring of the “third” component (label) properties, introduced into the system. The experimental methods can be also divided into four groups by their instrumentation, correspondingly [40,129,133,134,142,146,183-190]. Each method within a given group has its own advantages and disadvantages. For example, measurements of the optical density (light scattering, refraction, transmission etc.) of liquid systems cannot in principle provide information about particles less than <1000 А°, even if they are present in the system, the small-angle X-ray scattering cannot “see” particles greater than >1000 А°. According to the laws of optics we cannot differentiate between phase formations if the dispersion media and the disperse phase have close refraction factors. Therefore, even obviously heterogeneous systems may appear transparent in optical experiments. In addition, inclination of molecules to aggregation (formation of supramolecular heterogeneities) exerts a significant influence on a mutual solubility of components [191]. It is important to take all the characteristic structural parameters of molecular heterogeneities into account during the experiment. A typical mistake to be noted was apparently found for the first time by V.N. Kuleznev [118]. It is particularly often found in research which uses optical microscopy to estimate compatibility. Some authors describe any heterogeneity under microscope as an effect of phase formation. It’s not always like that. Any heterogeneity that the microscope’s lens reveals (even when artefacts are excluded) cannot prove that the second phase exists. The fact is: a single-phase blend can be heterogeneous and the size of some globular macromolecules (associates, concentration and density fluctuations), low molecular weight and oligomer molecules can be compared with the resolution of an instrument. These structures studied at the microscopic level can be erroneously considered heterophase particles. The fact is that thermodynamical properties of these heterogeneities, even interfaced, depend on quantity of a
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matter in the system and according to Gibbs phase definition these systems cannot be in the thermodynamical phase. An objective restriction for dynamic methods is the impossibility to estimate system phase structure in a broad temperature range: All the temperature transitions that these methods detect correspond to the structure of a sample formed in certain preparation conditions and “fixed” by freezing. Let’s note here that obtaining of contradictory experimental data by various scientists may also be stipulated by different “resolution” of methods defined by sample preparation methods. A systematic research [142] is an examplary case here, as it offers various methods to study compatibility in a certain blend: dynamic mechanical spectroscopy, young modulus and elasticity modulus temperature functions change, dielectric loss method and thermo optical characteristics. The results obtained by the various methods proved to correspond to different phase organizations (thermodynamically compatible or incompatible system or a system with limited compatibility). Indeed, according to certain methods the glass temperature Тс, had a single value equal to the average Тс of components, that is typical for a homogeneous system. Other methods registered two values of Тс similar to Тс of individual components, that is, a property of a system with incompatible components. And one of the methods has shown three peaks on a curve (one average and two individual values), thus demonstrating limited compatibility of a system. A system with limited compatibility can obviously be in single-phase or two-phase states depending on state parameters (thermodynamics) and its history (kinetics), so methods with various preparation techniques will register different states of this system. But a system cannot have both compatible and incompatible components as some authors [142] reasonably note. This problem is well prevented by a critical attitude to methods and correct analysis of experimental data. It is relevant to mention here the following note of A.E. Chalykh [134]: “the main contradictions in presentation of results* root in not their experimental background but interpretation and a strange desire of scientists to abstract from data obtained by other researches. The fact of contradictory experimental data is illusive and reflects the complexity of the studied systems”. It is essential that the relaxation rate is less than scanning rate by temperature when dynamic methods are used to estimate compatibility. The main obstacle in the study of critical phenomena in low molecular weight liquids was the difficulty to achieve a small ΔТ during experiment [175,192]. Finally, it was mentioned before that a correct experiment is possible only with τ0>t∗. G.V. Korolev [190] has estimated relaxation characteristics of various oligomer liquids (oligomers with different functional groups and capable of intermolecular interactions) with regard to lifetimes of forming associates τа. Having compared them with the resolution of t∗ various research methods lets us estimate in the first approximation applicability of specific methods for analysis of specific systems (see also Part 2.5).
*
Phase equilibrium data.
Oligomers as the Object of Research: Basic Principles
33
1.4.4. Colloidal Aspect In considering the process of cellulose acetate dissolution in chloroform during experimental investigation of polymer dissolution in low-molecular solvents, Papkov et al. [126] were the first to distinguish several states of the phase structure formation in polymer systems with limited compatibility and some low-molecular blends. The solution was transparent at the selected initial temperature and concentration. However, if the temperature goes below the critical point (its position depends on concentration) the system shows turbidity: phase disintegration (transition, separation) occurs. In this case an emulsion is formed. It is characterized by the number and size distribution of constituent particles which depends on phase separation mechanism, temperature decrease rate and etc. Then the system morphology starts to change. The same phase particles gradually aggregate, which finally leads to formation of two transparent layers: cellulose solution in chloroform (upper layer) and chloroform solution in a polymer (lower layer). This process is called phase layering. Later on, similar observation results were obtained for many polymer and oligomer systems [168]. The recent decades provided a successful solution for such theoretical problems as phase formation in polymer systems, formation of their disperse structure, phase layering and etc. These results have formed a subject of an independent science that is colloidal chemistry of polymers [109]. Colloidal chemistry can be used for the following processes in oligomer systems: а) formation of a heterogeneous structure during chemical curing of oligomers, b) formation of a heterogeneous structure in source oligomers. The first one goes beyond the subject of this book, the second one will be discussed in Part III of this monograph. Note here that oligomer systems are more complicated than polymer-polymer blends with a constant morphology of samples from the moment of their preparation. For example, the history of a sample has almost no effect on morphology [193,194] of heterogeneous polymer-oligomer systems with a dispersive media viscosity 8 - 10 decimal exponents lower than the dispersion phase – this effect is similar to properties of polymer-polymer blends. But during the phase inversion, when the low-viscous (in comparison with dispersion phase) polymer solution in oligomer becomes a dispersive media, the phase layering time decreases to the object observation time [195]. This effect must be considered when dealing with material science problems. The initial oligomer system morphology before curing has a direct impact on the structure of a polymer formed of cured oligomer blends [125, 196], so the morphology parameters are, therefore, of primary importance by the time of the chemical reaction activation mechanism initiation. This aspect is very important both for oligomer-oligomer and oligomer-polymer blends, which are characterized by morphologically unstable evolution in time. Both the phase layering rate and form of disperse particles distribution function evidently depend on various factors: the initial size of emulsion droplets, dispersive media viscosity, surface tension, presence of surfactants and etc. [109,118,125,168,197,198]. Unfortunately, these important problems of colloid chemistry stay entirely unapplied to reactive oligomer systems (see also Part 3.3).
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1.4.5. Compatibility and Phase Equilibrium In the “Encyclopedia of Polymers” the “compatibility of polymers” is determined as “a term that is commonly accepted in technological practice, which characterizes the ability of various polymers to form mixtures possessing satisfactory properties” [199]. Similar definitions are also given in some other monographs (see, for example, [118,119,200]). We will not stress the fact, that these definitions are formed conventionally, and just note that they can’t be used for oligomer systems because oligomers are used as materials not at their initial state but after certain transformations, so such characteristics as “satisfactory mechanic properties” is unacceptable here. The compatibility of oligomer systems, according to Krauze [129], is their ability to molecularly disperse on after contact that is formation of true solutions or, in other words, mixing at a molecular level. The mutual solubility of components is defined by thermodynamic constants and system state parameters. This characteristic is called * thermodynamical compatibility . There are thermodynamically compatible and incompatible systems and systems with limited compatibility. Systems are compatible if their components form solutions (components are dispersed at the molecular level) within a total concentration (0<С<100%) and mixing temperature**) range, that is, they have unlimited solubility. They are single-phase systems at any ratio of components. Solutions in these blends can, however, include various heterogeneities (deviations from ideal state that are represented by associates on a supramolecular level). If system components are totally insoluble and even do not swell (that is an exceptional case for oligomers), such systems are considered incompatible. Forced mixing of oligomers leads in this case to formation of heterogeneous (colloid) systems with every phase as an individual component. The dispersity in these heterogeneous systems is a function of many factors and, first of all, of the energy “injected” into a system. At last, there are systems with a pair of components in equilibrium which can be either compatible or form colloidal mixtures (emulsions, suspensions) of solutions with different concentration of initial components depending on temperature, pressure and the ratio of components. They are systems with limited compatibility components or, in other words, restricted compatible systems. The lion share of oligomer systems falls into this category. Components of systems with limited compatibility form true solutions within a certain range of concentrations and temperatures. When their dosage is beyond the limits of mutual solubility, colloidal systems of coexisting disperse phases are formed, where each phase is a solution. One of the components is in “excess” in the first phase and in “shortage” in another *
A certain period in polymer publications has been studied, when such characterizations as “technological”, “operational”, “mechanic”, “forced”, “segmental” etc. were added to the term “compatibility” to describe properties of thermodynamically incompatible polymers or polymers with a limited compatibility. In our opinion this differentiation doesn’t have a reasonable physical meaning. This problem has more than once been referred to in publications (see, for example [109,163]). Application of these “amendments” could be stipulated by kinetic aspects ignored during analysis of mixing and phase separation processes in polymer blends and failed attempts to provide “scientific” base under practical preparation methods of polymer blends with “satisfactory (?) properties”. ** This is a temperature range corresponding to practical storage, test and processing temperatures of oligomers. Such an interpretation is initially uncertain. First, these temperatures can differ by tens or hundreds degrees and be lower than glass or crystallization temperatures. Secondly, even single-component systems will have inevitable phase transition within a broad temperature range.
Oligomers as the Object of Research: Basic Principles
35
one. Equilibrium concentrations of components in coexisting phases, which are identical to mutual solubility boundaries, can be found on the phase state diagram. Each solution in coexisting phases has a unique degree of deviation from ideal state i.e. has its own level of supramolecular ordering. The presence of heterogeneities in solutions does not mean that these solutions are in heterogeneous state after the second or even the first order phase transition. It doesn’t even stand for microphase separation, as it sometimes stated. Let’s not discuss other opinions [109] and just note that a phase is by the classical Gibbs definition [201] “a combination of homogeneous system components with the same composition, physical and chemical properties, that doesn‘t depend on a quantity of matter and has an interface separating it from other system parts”. Even if we take into account the amendment by A.V. Rakovskiy [26], that led to subdivision of thermodynamic variables into “field” and “density” [202] types and states that “the physical properties are thermodynamical if they can be described by state parameter functions (volume, pressure, temperature and concentration functions) and by them only”, we’ll see that a phase still has two essential features: a) its properties do not depend on the quantity of matter in a phase (or the ratio of components) and b) presence of interface. According to Gibbs, only a combination of these features is the necessary and sufficient condition for the existence of a phase. These features only simultaneously combined can mean that the thermodynamic phase is formed instead of other heterogeneous liquids. That is why various supramolecular heterogeneities in oligomer liquids such as aggregates, associates or cybotactic groups are not “microfhases”. The term “micro” can be used here, but the term “phase” in inapplicable on the basis of Gibbs approximation. The compatibility of oligomers has been subject to investigation for more than 60 years, but it got a kind of a systematized research only in recent decades [129,133-135,165,203207]. Complete phase diagrams and experimental temperature and concentration dependencies for χ12, ΔН1, Δμ1 and other thermodynamic parameters for a broad range of oligomer systems were obtained only in recent years. The majority of them are systematized in the monograph [134]. Literature sources provide few examples of single-phase oligomer systems with unlimited compatibility of components within real processing temperature range. The examples include oligomer - monomer systems (for example oligoestermaleinefumarate - styrene, epoxyglycedyle ester – amine and oligodiol – castor oil blends etc.), oligomer - oligomer systems (for example, oligobutadieneurethanemetacrylate - n-methylene-dimetacrylate blends within n = 1-10, various molecular weight oligoesterepoxyde blends (340 - 7150), oligoesterdieneisocyanate – oligoglycole blends etc.) and even polymer - oligomer systems (butadiene-nitrile rubber - trioxyethylenedimetacrylate). The majority of oligomer blends are systems with limited compatibility, i.e. forming true solutions within a limited range of concentrations and test temperatures. Phase state diagrams provide quantitative information on the limits of mutual solubility of components [60,82,118,129,134,165,170,206-214]. The experimental phase diagrams of oligomer systems will be discussed in the third part of this book. This part of the monograph has its own tasks so we’ll concentrate on some general statements necessary for a logical representation of the data below. Figure 1.5 illustrates conditional phase state diagram in temperature (Т) – oligomer dosage (С) coordinates that is a generalization of experimental phase diagrams known for various oligomer systems [134,170,208-214]. The areas I and II of a single-phase system state
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
in Figure 1.5 are limited by binodal (solid curve). The area between binodal and spinodal (dashed curve) corresponds to the metastable system state (III). The area under spinodal is a two-phase system state (V). Single-phase and two-phase states of a system are stable, so no phase transitions occur within С and Т limiting areas I, II and V when state parameters vary. A characteristic feature of a system in metastable state [89] is that even infinitesimal change of state parameters (ΔТ and ΔС) leads to the phase transition and moves this system into one of stable areas, i.e. when ΔТ and ΔС ≠ 0 the metastable system becomes either single-phase or two-phase and stable. The structure of a solution in the metastable state around the critical point (area IV in Figure 1.5) has much denser fluctuation concentrations with larger correlation radius and lifetimes than in other states.
Figure 1.5. Conditional phase diagram of oligomer blended system and the chart of structure of solutions with shortage (I) and exceed (II) of oligomer before (I – II) and after (II – I) phase inversion point. III – metastable area, IV – area of UCST, V – two-phase state area; ω’b and ω”b – oligomer concentrations on the left and right branches of a binodal, ω’s - oligomer concentration on the left branch of a spinodal Т=Т1; С1 – oligomer dosage; Сi – oligomer dosage at the phase inversion point. •schematic presentation of an oligomer molecule; │ - schematic presentation of an polymer molecule
Oligomer systems are typically described by phase diagrams of an amorphous equilibrium according to classification by S.P. Papkov [168,206]. Sometimes amorphouscrystalline equilibrium [134,165] is observed [134,165]. The majority of oligomer system phase diagrams is asymmetric and has upper critical solubility temperature* (UCST). *
There are some unique systems, such as oligopropyleneglycole and oligoethyleneglycoleadipinate blends with both upper and lower critical temperatures registered [215].
Oligomers as the Object of Research: Basic Principles
37
The first one is stipulated by the fact that oligomer solubility limit in the second component in the area I (this component can be a monomer, oligomer or polymer) is far beyond the equilibrium concentration of the second component in oligomer (area II). This, in turn, explains merging of right bimodal and spinodal branches for some oligomer systems, i.e. oligomer concentrations in the oligomer excess area (the right part of the phase diagram) on binodal and spinodal are quite similar: ω”B ≈ ω”С. The existence of the upper critical layering temperature leads to permanent increase of mutual solubility of components with growth of temperature. As Figure 1.5 shows, a system remains a single-phase one within oligomer concentration С ≤ ω’B where ω’B is an oligomer concentration corresponding to the Т1 point at the left branch of a binodal at the conventionally chosen temperature Т1 = Const (it can be a blend storage temperature for example). An oligomer solution is formed in a second blend component at this point (these solutions are also called oligomer - weakened). If an oligomer dosage С ≥ ω”B, where ω”B, is an oligomer concentration at Т1 corresponding to a point at the right branch of a bimodal, the system is also a single-phase one, but this solution is enriched with oligomer, thus it is a solution of the second component in oligomer. The increase of oligomer dosage: С > ω’B moves the system into a metastable area which ends at С = ω’С, that corresponds to oligomer concentration at the left branch of a spinodal Т1. Further increase of concentration: С > ω’С leads to phase separation and formation of a two-phase system. Let’s note again that these phases are not individual components according to some publications. This system is formed by interfaced solutions of one component into another with oligomer concentration varying significantly. In this case a blend of two true solutions is formed within ω’С ≤ С ≤ ω”С. These solutions are: a) solution I with oligomer concentration ω’B and b) solution II with oligomer concentration ω”B. Let’s pay attention to another important detail. The oligomer dosage С always corresponds to its concentration in single-phase systems in weight (ω), volume (φ) or molar (ν) parts, and weight concentration ω increases when the С dosage grows. However, the concentration of an oligomer in components of two- phase systems is always constant when Т = const and has a value ω’B and ω”B, correspondingly. Increase of the total oligomer content in the blend within ω’С ≤ С ≤ ω”С and Т = const doesn’t lead to any changes of phase solution concentrations, but changes the volume ratio of dispersion and dispersive phases, which is in fact a phase inversion. This process is shown in the upper section of Figure 1.5. As we can see, at С < Сi , where Сi is the dosage of oligomer in the inversion point, the dispersive phase is solution I, while at С > Сi the dispersive phase is solution II.
CONCLUSION The criteria setting the boundaries of oligomeric state in homologous rows of organic substances has been proposed. The “monomer – oligomer transition” occurs through the longrange intramolecular interaction of constituent monomer units at the threshold chain length (the lower boundary). Longer chain obtains coil conformation at some length according to laws of statistics. This is the upper boundary for an oligomeric state. The statistics of
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
oligomers differs from the Gauss statistics. Oligomers prove to be a special condensed state of substance with specific properties.
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[194] T.D. Mal'chevskaja. Dis. ...Kand. Khim. Nauk. M.:Nifkhi, 1980. [195] S.M. Mezhikovskijj. // Dokl. i Vsesojuz. Konf. “Smesi Polimerov” (Reports of The i All-Union Conference “Polymer Blends”). Ivanovo. 1986, P.15. [196] S.M. Mezhikovskijj. // Vysokomolek. Soed., 1987. T.29 A, No 8, C.1571. [197] S.M. Mezhikovskijj. Nekotorye Problemy Fizikokhimii Polimer-Oligomernykh Sistem i Kompozitov Na Ikh Osnove (Some Aspects of The Physical Chemistry of PolymerOligomer Systems and Related Composites). -Chernogolovka: Oikhf AN SSSR, 1986 (in Russian). [198] V.V. Shilov, Ju. S. Lipatov. // Fizikokhimija Mnogokomponentnykh Polimernykh System (Physical Chemistry of Multicomponent Polymer Systems). Kiev: Naukova Dumka, 1986. V.2. P.25 (in Russian). [199] ”Sovmestimost' Polimerov”. // Ehnciklopedija Polimerov (“Compatibility of Polymers”. // Polymer Encyclopedia). - M.: Sov. Ehnciklopedija, 1977, V.3, P.433 (in Russian). [200] V.E. Gul', A.E. Penskaja, N.A. Zanemonec, T.A. Zanina. // Vysokomolek. Soed., 1972, T.14A, No 2, S. 291. [201] Dzh. Gibbs. Termodinamicheskie Raboty (Works on Thermodynamics). -M.: Goskhimizdat, 1950 (in Russian). [202] M. Fisher. // Ustojjchivost' i Fazovye Perekhody (Stability and Phase Transitions). -M.: Mir, 1973, P. 275 (in Russian). [203] A.A. Tager, L.K. Kolmakova. // Vysokomolek. Soed.,1980, V.22 A, №3, P. 483. [204] Tager A.A., Fizikokhimija Polimerov (Physical Chemistry of Polymers). – M.: Khimija, 1978 (in Russian). [205] V.P. Volkov, G.F. Roginskaja, A.E. Chalykh, B.A. Rozenberg. // Usp. Khimii, 1982, V.51, No 10, P.1733. [206] Papkov S.P. Ravnovesie Faz V Sisteme Polimer-Rastvoritel' (Phase Equilibrium in A Polymer – Solvent System).- M.: Khimija, 1981 (in Russian). [207] Chalykh A.E. Diagrammy Fazovykh Sostojanijj Polimernykh System (Phase State Diagrams of Polymer Systems). – M.: Ifkh RAN, 1995 (in Russian). [208] G.F. Roginskaja. Dis. ... Kand. Khim. Nauk. Chernogolovka: Oikhf AN SSSR, 1983. [209] A.V. Kotova. Dis. ... Kand. Khim. Nauk. M.: Ikhf AN SSSR, 1988. [210] N.N. Avdeev. Dis.... Kand. Fiz.-Mat. Nauk. M.: Ifkh RAN, 1990. [211] T.B. Repina. Dis. ... Kand. Khim. Nauk. M.: Mgkhtu, 1995. [212] Shamalijj O.N. Dis. ... Kand. Khim. Nauk. M.: Ifkh RAN, 1995. [213] Andreeva N.P. Dis. ... Kand. Khim. Nauk. M.: Ikhf RAN, 2003. [214] Bukhtev A.E. Dis.... Kand. Khim. Nauk. M.: Ifkh RAN, 2003. [215] Ju. S. Lipatov, A.E. Nesterov, T.D. Ignatova. // Dokl. AN SSSR, 1975, T.222, №3, S. 609; 1975, T.224, No 4, S. 634.
Part 2
HOMOGENEOUS OLIGOMER SYSTEMS ABSTRACT Reasons of a molecular inhomogeneity in synthetic oligomer systems have been considered. The scaling analysis of a small – scale structure for a chain with limited length and finite bending rigidity has been carried out. Special consideration is given to the supramolecular structure of oligomers at the basis of associate – sybotactic models of liquid.
2.1. MOLECULAR HETEROGENEITY OF OLIGOMERS Despite their chain complexity, natural biological macromolecules are complicated individual compounds [1-3]. The molecular structure of synthetic oligomers is heterogeneous; it is characterized by distribution according to their molecular weight and functionality; typical of co-oligomers is distribution according to their composition [1] as well. Molecular heterogeneity of synthetic oligomers is conditioned by the random character of their formation process and by the side reactions during their synthesis. These side reactions result in the formation of deficient molecules; in some commercial products the content of the latter may reach the content of the target molecules [1,2,4-11]. Therefore, one of the major tasks in the physical chemistry of oligomers is the analysis of the molecular heterogeneity of some reactive oligomers. Many achievements in this field are due to the research of S. Entelis and his school [1,2,5,9]. Recent years have given special significance to these achievements because of the discoveries in the field of critical chromatography [2].
2.1.1. Molecular Weight Distribution Functions Molecular weight heterogeneity of oligomers is characterized by the parameters common for all polymers [12-15]: polydispersity index Mw /Мn, ratio Мz / Mw, and heterogeneity -1
coefficient of Schultz (Mw/Мn,) . In the physical sense, the latter is the relative dispersion of molecular weight distribution.
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
The Мn average number molecular weight can be described as the ratio of oligomer weight and the number of molecules n: Мn = (n1 M1 + n2 M2 +....) /(n1 + n2 + ....) = =Σ ni Mi /Σ ni
(2.1)
the Mw average number molecular weight can be described as 2
Mw = ∑ ni Mi / ∑ ni Mi = ∑ ϖi Mi
(2.2)
Mz is the average number molecular weight, Mz can be described as 3
2
(2.3)
Mz = ∑ ni Mi / ∑ ni Mi
where ni is the number of molecules with molecular weight Mi; ni = ϖi / Mi on condition that Σ ni Mi =1; ϖi is the mass fraction of molecules with molecular weight Mi. Unlike polymers, characterized by continuous functions of molecular weight distribution, oligomers are characterized by discrete functions. This means that while for polymers the numeric molecular weight distribution (М)ΔМ represents the numeric fraction of molecules with molecular weight from М to М+ΔМ, for oligomers, it represents the numeric fraction of molecules with molecular weight Mi, this fraction corresponds to a certain degree of polymerization. The same rule works for the mass molecular weight distribution of oligomers ϖ(M) which represents the mass fraction of molecules with exactly fixed molecular weight Mi. Analytically speaking, molecular weight distribution of oligomers is usually described by the three types of distribution functions: Flory, Schultz, and Poisson. The most probable distribution (Flory distribution) can be described as the function of polymerization degree (r) for mass fraction W(r) of the reacted functional groups (λ) W(r)= rλ
r-1
2
(2.4)
(1-λ)
or for the mole fraction r as measure n(r) n(r) = λ
n-1
(1-λ)2
(2.5)
In some cases the most probable distribution can be presented as αM
W(M)=M α-2 e-
αM
and n(M)= α e-
,
(2.6)
where α=1/М for mass and numeric functions of molecular weight distribution. A typical characteristic of the most probable distribution is the constancy of the average molecular weights ratio Мz : Mw : Мn = 3:2:1.
Homogeneous Oligomer Systems
51
Poisson distribution describes oligomers with narrow molecular weight distribution: n(r) = е
-rn
r
[(rn ) / r!],
(2.7)
where rn – is the average number degree of polymerization. For this type of molecular weight distribution function, Mw / Мn = 1 +1/rn. Molecular weight distribution of oligomers in the range between the narrow (Poisson) and the most probable (Flory) distribution can be described by the G -distribution of Schultz, which can be analytically expressed by equation k+1
n(M)= [(α
k
) / G(k+1)] M e
-αM
,
(2.8)
where G(k) – is the gamma-function, parameters α and k can be described as k+1 = Мn / (Mw - Мn ) and α = (k+3) / Мz = (k+2) Mw. With this molecular weight distribution, the average molecular weights are connected to each other by ratio Мz : Mw : Мn = (k+3) : (k+2) : (k+1). You can see that at k=0 we get the most probable Flory distribution, and at bigger values of k we get Poisson distribution, typical of oligomers with narrow molecular weight distribution. Table 2.1 shows data on correlation between the methods of different oligomers synthesis and their molecular weight distribution functions. Table 2.1. Dependence of Molecular Weight Distribution Function Type on Method of Oligomer Synthesis [1] Type of Function
Poisson
Schultz
Method of Synthesis
Oligomer
Anionic step-growth oligomerization
Oligo-ethylene oxide
Anionic oligomerization Cationic oligomerization Radical oligomerization Anionic oligomerization with slow chain initiation or transfer Cationic oligomerization Oligocondensation
Flory
Cationic oligomerization Destruction with interchain exchange
Oligo-propylene oxide Oligobutadiene Vynyl oligomers
Molecular weight range 2 10 - 4.104 2 3 10 - 2.10 102 - 2.104 5
102 - 10 3 102 - 2.10
Oligo-alkylene oxides Oligobutadiene 102 - 104 Oligo-styrene and other vinyl 102 – 104 oligomers 3 Oligo-alkylene oxides 102 - 10 3 Complex oligoesters 102 - 5.10 Oligoesterepoxides
102 - 2.103
Oligotetramethylene oxide
102 - 10
Oligosulfides
102 - 104
4
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
As noted in [1], the analysis of molecular weight distribution parameters is a reliable instrument for the investigation of oligomerization process kinetics and mechanisms. Comparison of theoretical (for the chosen model of oligomerization) and experimental functions of molecular weight distribution and their compliance (or non-compliance) can serve as the measure of understanding the reaction mechanisms in the reactive environment, and, naturally, serve as the instrument to regulate the process of synthesis.
2.1.2. Functional Type Distribution Molecular (or structural) functionality f is the number of functional groups within the composition of one molecule of the given chemical compound. If some of the compound functional groups are not active within the conditions of a certain chemical reaction, we can use the concept of practical, or real functionality fр = f - f0., where f0 is the number of functional groups, which are non-reactive within the conditions of the given reaction. Naturally, fр < f. Molecules, which have no reactive groups, are called non-functional. Oligomers with f = 1; 2; 3 and etc., are, correspondingly, mono-, bi-, tri-, and etc., functional. We can distinguish oligomers according to the number and nature of reactive functional groups. Both characteristics determine the type of functionality. Together with molecular weight distribution, oligomers can be characterized by their distribution according to the types of functionality. The concept and term of functionality type distribution were first introduced into science by S. Entelis [1]. Functionality type distribution shows the relative content of molecules with different molecular functionality in the oligomer product. For reactive oligomers this is one of the most important physical and chemical characteristics. For quantification of functionality type distribution, similarly to molecular weight distribution, we use concepts of average number fn and average mass fw functionalities: fn = ∑ ni fi / ∑ ni 2
fw = ∑ ni fi / ∑ ni fi
(2.9)
where ni = pi /Mi is the number of moles of i -molecules with molecular weight Mi and functionality fi, their mass is pi . For average functionalities, as well as for f, we can use the concept of average realized functionality. The value of fn by itself doesn’t give final information about the polydispersity of oligomers according to functionality and doesn’t characterize their functionality type distribution. For example, fn=2 seems to be an ideal characteristic of bifunctionality, however, no strict bifunctionality of all molecules may occur, this value being the result of averaging: mono- and tri-functional molecules may exist in the system in equal share. Ambiguity may also occur when using ratio fw / fn to characterize polydispersity according to functionality. The presence of non-functional molecules (f=0) in the system does influence the value of fn, however, it does not influence the value of fw. For this reason, the
Homogeneous Oligomer Systems
53
functionality type distribution functions can be shown as mass, numeric and integral distribution curves, correspondingly, ni fi - fi; ni - fi and ∑ ni fi - fi. It has already been mentioned above (see Part 2.1.1), that the usage of functionality type distribution and molecular weight distribution values gives us an opportunity to divide all the existing reactive oligomers into three groups. Table 2.2 shows coefficients of polydispersity for these three types of oligomers, and all the possible reasons of functionality type distribution in them. Table 2.2. Polydispersity Coefficients of Oligomer Systems According to Parameters of Molecular Weight Distribution and Functionality Type Distribution. [16-18] Type Numbe r
Oligomer Formula
Polydispersity Coefficient
Possible Reasons of Functionality Type Distribution
Mw / Мn ≥ 1 1
Deficiency in functionality fw / fn ≥ 1 fn ∼ Мn
2 fw / fn ∼ Mw / Мn
A 3
Mw / Мn ≥ 1
A A
fw / fn ≥ 1
Deficiency in functionality; Molecular weight Molecular weight distribution; content distribution
The above given table requires explanation. Oligomers of the first type with a strictly defined target functionality can ideally be characterized by functions fw / fn = 1 and Mw / Мn ≥1. However, in reality, fw / fn > 1, which can be explained by deficient molecules formation, along with the target ones, even in special synthesis, because of the side reactions, incompleteness of the process and other factors. Polyfunctional linear and branched oligomers with regular alternation of functional groups in chain (the second type) are characterized by linear dependence of molecular weight Mi on functionality fi; at fixed values of Мn, every value of Mw / Мn corresponds to a certain value of fw / fn. Polyfunctional linear or branched oligomers of the third type with non-regular alternation of functional groups in chain can have very different values of polydispersity according to molecular weight and according to functionality type; however, we always have fw / fn > 1 and Mw / Мn > 1.
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
2.1.3. Critical Chromatography of Oligomers Critical chromatography, which was discovered in 1980’s [19-21], is based on the fact that molecules are adsorbed due to phase transition. Unlike monomers adsorption, where typical thermodynamic limit is 1023 (Avogadro constant), polymers and oligomers adsorption involves a much fewer number of particles. The finiteness (numeric infinitesimal) in this type of chain systems blurs the point (e.g., temperature) of adsorption phase transition to the area, the width of which depends on the size of molecules. For small chains (oligomers), this point may reach several degrees. In this transition (critical) area, the properties of the system are practically the same as they are in the critical point, however, unlike the latter, the critical area is stable to the small changes of the external parameters. This makes it possible for the system of oligomer chain molecules to be present in the critical area for a comparatively long time, which is enough to study their characteristics, in particular, their molecular and structural heterogeneity of different parameters. In the succeeding years, due to papers [2224], theoretical fundamentals of polymers critical chromatography were developed. Their practical application allowed us to investigate experimentally the molecular heterogeneity of the commercial oligomers main classes, obtain the functions of their heterogeneity according to their composition, functionality, and etc. This unique instrumental method has other practical applications (it can be used to study all the stages of polymerization process, mechanisms of destruction and depolymerization processes and etc.), yet for the problems addressed in this monograph, the results of research on oligomer systems molecular heterogeneity are of primary interest. They have been described in a number of papers (e.g., see [25-27]) and systematized in the doctoral thesis of A. Gorshkov [2]. The present work addresses only several examples. Figure 2.1 shows a chromatogram of oligopropelyne oxide adsorption critical regime, which was obtained on the basis of trifunctional glycerin. This chromatogram reflects the possible variety of the end –OH groups of this oligomer. Figure 2.1 gives the results of epoxide oligomers classification according to the types of functionality in the critical regime, and the bivariate function of their heterogeneity in the coordinates of molecular weight distribution and functionality type distribution. This reflects the composition of epoxide oligomer linear molecules with different end groups.
2.2. SMALL SCALE OLIGOMER STRUCTURE: THEORETICAL ASPECTS During the macromolecules statistics investigation (e.g., see [3,15,28-31]), the question of relation between the conformational states of molecules and their chain length was one of the major problems. Naturally, in case of component chain links variation, the molecules from oligomer area were also investigated. However, the interests of the scientists were mainly focused on the analysis of macromolecular systems with a huge number of Kuhn segments in the chain. We started to use statistical methods for a purposeful study of molecular-structural distribution in oligomer systems much later [34-48]. It followed from these papers that comparatively short molecules, possessing finite rigidity (it is this type of molecules that can be oligomeric) show the peculiarities of statistical behavior, which, in the long run, determines the specific properties of oligomer systems.
Homogeneous Oligomer Systems
55
In particular, for polymer systems, the scale of oriented-correlated areas is much smaller than the usual size of polymer coils, and, therefore, these areas do not have a strong influence on the conformational statistics of polymer molecules. For oligomer systems, however, the scale of correlated areas can influence the size of oligomer molecules. Hence, these orientedcorrelated areas, the result of local anisotropy of oligomer molecules, do influence the state of oligomer molecule.
Figure 2.1. Chromatogram of branched oligopropylene oxide in a critical mode, reflecting various types of end OH – groups.
Moreover, when describing the statistical properties of the comparatively short molecules, the asymptotic limit used to describe the infinitely long chains, is too rough to be an approximation. Non-Gaussian character of oligomer macromolecules conformations statistics is to be taken into account. These two circumstances make the statistical properties of oligomer macromolecules differ strongly from the properties of polymers. This fact influences the macroscopic properties as well. Following is the analysis of some (of the above-quoted) theoretical papers which do prove this statement.
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
2.2.1. Small Scale Structure of Limited Length Chain with Finite Bending Rigidity (Scaling Estimations) Publications [37,38] give the results of scaling estimation of the possible influence of small scale structure of a liquid oligomer system, composed of limited length and rigidity macromolecules, on its macroscopic properties. Following are some results of this study. A coil-type flexible polymer chain has a low density structure; the longer the chain, the lower is the volume density of the substance [3]. In fact, the volume of the freely-jointed chain with chain links number N and size a, has the value of Vch ~ a3N 3ν (1/3 < ν < 3/5), while the volume of the chain itself equals a3N. If the chain possesses certain rigidity, persistent length (Kuhn segment) is to be introduced, and the chain is to be considered freely-jointed, made up of Kuhn segments. The volume of this chain will be much larger:
Vch ~ (lK )3 ( N nK )3ν = (anK )3 ( N nK )3ν = a 3nK3( 1− ν) N 3ν
(2.10)
where N – is the number of chain links; lK=anK – is the length of a Kuhn segment, containing nK number of chain links; a – is the length of one chain link; for a globe ν = 1/3, for a Gaussian coil ν = 1/2, for a swollen coil ν = 3/5. Substance density in a single coil (density given in units of excluded volume) decreases with the increase of the Kuhn segment length as well as with the increase of the chain length: 3 ρ ch ~ a N ~
VK
1
, 1 < 3v < 3.
(2.11)
nK3(1−ν ) N 3ν −1
As the substance density in melt is close to one (Θ ∝ 1, 1 – Θ << 1) and depends neither on the length of the Kuhn segment nor on the chain length, there can be, in fact, an M number of chains in the volume of the chain Vch, the number of chains can be calculated according to the following ratio:
M ~ ΘnK3(1−ν ) N 3ν −1 , 1 < 3v < 3.
(2.12)
We can find the volume of a Kuhn segment in the volume of the given chain:
VK =
Vch ~ (anK )3 ( N nK )3ν −1 = a 3nK3( 1− ν)+1 N 3ν −1 N nK
(2.13)
This volume Vk (ellipsoid with axes L1 ~ anK, L2,3 = LK ~ anK(N/nK)(3ν – 1)/2 = anK3(1– ν )/2 (3ν – 1)/2 N ) is to be filled with M rods, the length of which is lK=anK , and their diameter is a ; they are the Kuhn segments of different chains. The calculated concentration of these rods is:
Cn ∞ M VK ~ Θ a3nK
(2.14)
Homogeneous Oligomer Systems
57
As the Kuhn segments of different chains are statistically independent, the situation studied is equivalent to the well-known model of rigid rods. When the excluded volume is considered within the framework of Onsager model [49], the system is considered to possess critical concentration Ckr, where the system obtains orientational ordering. The value of this critical concentration is determined by the length and diameter of the rods:
Ckr ~ 1 alK2 ∞ 1 a3nK2 ,
Θkr ~ 1 nK
(2.15)
For rigid chains, with a large length of the Kuhn segment, the system density exceeds the critical density, and the rods orientations (Kuhn segments of different chains) in the given ellipsoid correlate, i.e. a “string” of the relatively straight chain segments appears. The width of this “string” corresponds to the size of the orientationally ordered area; this size is neither the size of the Kuhn segment, nor the size of the polymer molecule itself. In other words, the system appears to have another characteristic scale – the scale of the orientational correlation of polymer chain segments Lkor.
(A)
(B) Figure 2.2. Functional type distribution of epoxyoligomer in a critical mode (a) and its 2-D function of heterogeneity «functionality – MW» (b).
58
S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
In order to access this new scale we can apply a plane perpendicular to the direction of the Kuhn segment of the chain (Figure 2.3). When we use this plane to cut the ellipsoid corresponding to the Kuhn segment of the chain, a circle is to be formed. When this circle crosses the rods (Kuhn segments of different chains) within the volume studied, a system of points appears, their concentration has the order of Cp ∞ Θ/a2, and the average distance between them is Δ ∞a/Θ1/2.
Figure 2.3. Plain section of ellipsoid, perpendicular to the Kuhn segment of a sample chain. Dots mark intersection of this plane with other Kuhn segments in a sector rested on a circular arc with a length Δ, where Δ is an average distance between intersection points of Kuhn segments with a cutting plane.
If we take unitary vectors for each one of the points, where the direction of the vectors coincides with the rod direction for the given point, we can get a secondary chain, the properties of which are almost the same as the properties of a rigid polymer chain, because the orientations of the two neighboring rods, and, therefore, secondary chain links, correlate. The correlation function of the chain links orientation along this chain is [50]:
⎛ ⎞ ⎡ (l Δ )Δ ⎤ ⎡ ⎤ = exp ⎢− nΔ ⎥ g (l ) ~ exp⎜ − l ⎟ = exp ⎢− ⎥ L L L ⎝ kor ⎠ ⎣ ⎣ kor ⎦ kor ⎦
(2.16)
where n – is the number of chain links or the number of rods between the two given rods in the radius sector LK and arc Δ (Δ ∝ a/Θ1/2 – is the average distance between the “points”), and Lkor – is the distance from the Kuhn segment of the given chain, for this very distance the orientations of the Kuhn segments of different chains do not depend on the given chain Kuhn segment orientation. For the two neighboring “links” (rods) at n = 1, correlation function is expressed through the angle of the relative orientation between them, this angle is determined by the density of their packing Θ. The required dependence 〈cosθ(Θ)〉 can be calculated using the Onsager model, modified in [51] for the case of high rods concentration:
Homogeneous Oligomer Systems
g (1) = cos θ (Θ) ≈ 1 − [ln(1 − Θ)nK ]− 2
59 (2.17)
Expansion of the correlation function (1.7) in a series at n = 1 (2.18)
⎡ ⎤ a g (1) = exp ⎢ − Δ ⎥ ≈ 1 − Θ Lkor ⎣ Lkor ⎦
Taking into account (2.17) we can find the required correlation length Lkor, which shows the distance from the chosen Kuhn segment where the orientational effects stop:
Lkor ~
a [ln(1 − Θ)]2 nK2 Θ
(2.19)
This new scale of the system – correlation length Lkor – appears as the result of collective interchain interactions. Its comparison with the two other characteristic system scales: characteristic area size, corresponding to one Kuhn segment – LK ∝ anK(N/nK)(3ν – 1)/2 = anK3(1– ν )/2 (3ν – 1)/2 N , and characteristic size of the whole chain – Rch ∝ anK(N/nK)ν = anK1–ν Nν, allows us to access the microstructure of the whole system and its influence on the system properties. If Lkor < LK, i.e., the size of the ordered area does not exceed the characteristic size of the area, corresponding to one Kuhn segment, then the effects of local ordering do not appear when averaging the scale over this size. This means that the local ordering of the Kuhn segments in different chain characteristic of the rigid chain polymer systems does not influence the macroscopic properties of the polymer system as a whole. In this case, introduction of a persistent length (Kuhn segment) allows us to consider the polymer chain freely-jointed. This situation is possible in case the Kuhn segment length is short enough compared to the whole chain length, i.e.:
nK ≤ ln (1 − Θ )
− 3ν4+1
N
1− 3ν2+1
(2.20)
In other words, if inequality (2.20) is accepted, the macromolecular system is a classical polymer system and no specific properties related to the finiteness of the macromolecules length can appear in this system. If Lkor > Rch, i.e., the size of the ordered area exceeds the size of the polymer coil, then the local ordering of the Kuhn segments of different chains results in cardinal reconstruction of the molecule state: its “polymer” degrees of freedom get ‘frozen” and its properties get closer to the properties of the low molecular weight compounds. Certainly, these types of systems possess specific properties of their own which are related to the high anisotropy of the molecules. In particular, liquid crystal regulation can take place in these systems. A system can be considered to be of this type in case the Kuhn segment length is large enough:
nK ≥ ln (1 − Θ)
− 2
ν +1 N
1− 1
ν +1
(2.21)
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
And, finally, we consider the case when the size of the regulated area is larger than the characteristic size of the area corresponding to one Kuhn segment but does not exceed the characteristic size of the whole chain: LK < Lkor < Rch. It is with this ratio of the system characteristic scales that the local ordering of the Kuhn segments of different chains does influence the conformational structure of the macromolecule in the scale bigger than the Kuhn segment, i.e., it can influence the macroscopic properties of the whole system. This kind of influence appears on condition that the length of the Kuhn segment is large enough, however, it is considerably shorter than the whole chain length:
ln (1 − Θ )
− 3ν4+1
N
1− 3ν2+1
≤ nK ≤ ln (1 − Θ )
− ν 2+1
N
1− ν 1+1
(2.22)
The scaling analysis, which has been carried out, can be considered a theoretical basis for some of the statements given in Part 1.1.3. In fact, depending on the ratio between the length and the effective rigidity of the molecules, the system can behave very differently. For the case (2.20), when the chain length is much larger than the Kuhn segment length, the system behaves as a classical polymer. For another case (2.21), the system may either have a low molecular weight (if the chain length is not big enough) or the system may obtain a liquid crystal state, or a polymer crystal state, when the effective rigidity of the chains is so large that the Kuhn segment length almost reaches the whole chain length. The intermediate situation, described in (2.22), corresponds to the oligomer systems; their properties are neither the properties of the low molecular weight compounds nor the properties of polymers. In this case, the local structural ordering is determined not only by the architecture (ratio between the length and flexibility of molecules), but also by the environment, that is, the exterior conditions, e.g. temperature. At certain conditions this ordering can influence the macroscopic properties of the oligomer system. Note, that the above given scaling analysis took into account only steric interaction between the chains. As this type of interaction is typical of all the macromolecular systems studied, no matter what their chemical nature is, the conclusions made can be applied to the whole class of oligomer systems; the tolerance used is not principal as all the other possible types of interactions, conditioned by the chemical structure of the compound [52] (see Part 1.1.2.), usually intensify the effects discussed. Thus, from the scaling analysis we can conclude: a spontaneous appearance of areas with local orientational ordering is possible in oligomer systems. These small-scale structures, which can influence the macroscopic properties of the system, are the result of collectivism in statistical behavior of oligomer molecules. Their appearance is possible only at a certain ratio of molecular chain length and rigidity which usually corresponds to the oligomer area. It is not only the architecture of the molecules, but also the environmental and exterior conditions that determine their effective rigidity.
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61
2.2.2. Oligomer Chain Statistics Depending on Length, Interlink Rigidity and Temperature The simplest model to describe conformational states of the long linear molecules is the model of an ideally flexible (phantom) polymer chain which is a chain of freely-jointed rigid rods with the length of l0 [3]. The orientations of the two neighboring chain links do not depend on each other. If the chain possesses interlink rigidity and the two neighboring links orientations correlate, we can introduce the concept of persistent length, or the concept of the Kuhn segment (a chain segment Δl, which has no memory of the orientation at the start). If the length of the Kuhn segment Δl equals the length of the new “rough molecule” elementary chain link, then the conformational states statistics for the molecule possessing a certain interlink rigidity can be described in the terms of absolutely flexible molecules. This approach is not suitable for oligomers, because it describes flexible and long molecules. As for the macromolecules possessing a certain interlink rigidity, this approach can be used only in case the length of the molecule has a great number of Kuhn segments. Typically, oligomer molecules are either not long enough or they are too rigid (in the latter case the Kuhn segment is too long). That is why the statistics of oligomer molecules conformational states differs from the statistics of long polymer chains. Special methods are to be used to describe oligomer molecules. These methods take into account finiteness (relative shortness) of the chain length, interlink rigidity, influence of the end groups on the state of the chain as a whole, conformational states of the internal links, and etc. Papers [36-38] show an attempt to describe the oligomer molecules conformations statistics taking into account the above listed requirements on the basis of the latticed model of orientational self-correlated wanderings [53-60]. Unlike the absolutely flexible chains model, where the wandering steps are independent, this model considers the macromolecular interlink rigidity, which assumes the dependence of the next step direction on the previous step direction. The ideology given in [37, 38] is as follows. The directions of each one step of wandering are not equiprobable. Therefore, probabilities of direction choice at each of the wandering steps on the lattice depending on the previous step direction are to be introduced. They are: • • •
probability to move in the same direction equals α+(T ); probability to move in a perpendicular direction equals α⊥(T ); probability to turnover 180° equals α−(T ).
These conditional probabilities are determined by the chain rigidity, and, in general, depend on the temperature (see below). Information on the spatial distribution of the molecular weight is contained in the distribution function G(Rn , n), which determines the probability that the n link of the chain, the beginning of which was at the origin of coordinates, after wandering in all the possible directions x, y and z, appeared to be in the lattice node with coordinates Rn ≡{Rnx = l0 mx , Rny = l0 my , Rnz = l0 mz }. At n = N distribution function G(RN , N) determines the probability of the fact that the chain end has shifted relative to its beginning by vector RN . This distribution
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function G(RN , N) is calculated as the result of averaging on all the possible wandering trajectories:
(
)
(2.23)
N ⎛ ⎞ G R N , N = δ ⎜ R N − l0 ∑ e(n) ⎟ , ⎝ ⎠ n
N here l0 ∑ e( n) – is the vector connecting the beginning and the end of the chain, e(n) − is n the vector corresponding to the lattice edge where the leap at the n step of wandering occurs (the same vector e(n)≡e(l) corresponds to the n chain link, l = l0n, l0 − is the length of the lattice edge, corresponding to the length of one chain link), and brackets
...
mean
averaging on all the possible wandering trajectories. When averaging out the left part of the equation (2.23), there appear interesting analogies with the Ising chain as well as the Dirac equation (in the imaginary time) for a relative quantum mechanical particle (mathematical details are described in detail in [38]). The results show that when the end rigidity of the macromolecule is taken into account, it distribution function G(Rn , n) does not appear to be Gaussian, even if the chain length tends to infinity. After the transition to the continuous limit (the chain length l = l0n), the expression for the desired distribution function (in Fourier presentation on coordinates в) is as follows: ⎡ (1 − θ )(1 − E )l ⎤ 1 − E ⎡ (1 − θ )(1 + E )l ⎤ ~ G(p, l ) = 1 + E exp⎢− ⎥ − 2 E exp⎢− ⎥ 2E 2 θ l 2θ l0 0 ⎣ ⎦ ⎣ ⎦
where
(2.24)
2 E = 1 − l02p 2 2θ (1 + θ ) 3(1 − θ ) , θ = α+ – α– – is the parameter characterizing
the chain rigidity (θ = 0 corresponds to the absolutely flexible chain, and θ = 1 – corresponds to the rigid rod). From expression (2.24) it follows that even at asymptotically large chain length, distribution function is not Gaussian, which in Fourier presentation looks as follows:
(
~ GГ (p, l ) = exp − p 2l0l 6
)
(2.25)
If, however, the macromolecule rigidity is negligibly small (this means that parameter θ → 0), and it is possible to factor the function root E in the following row:
2 E ≈ 1 − l02p 2 θ (1 + θ ) 3(1 − θ ) , it appears that the first summand in the right part of the
equation (2.24) transforms into an expression which fully coincides with the Gaussian distribution function (2.25), and the second summand in the right part (2.24) at sufficiently large molecule length l tends to zero. Thus, the statistics of oligomer macromolecules conformations appears to be nonGaussian. However, a preliminary distribution function analysis of macromolecules possessing end rigidity shows that the conformations statistics of these chains is always nonGaussian irrespective of their length. Nevertheless, it is well known that the approximation of
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Gaussian statistics works well for polymer (i.e., sufficiently long) chains. For these reasons it is very important to find the chain length and the conditions at which the non-Gaussian character of macromolecules conformations statistics and the same parameters at which Gaussian approximation is enough are to be taken into account. In order to answer the given question, paper [36] gives an analysis of the dependence of the root-mean-square size of the molecules with the end interlink rigidity (square of the distance between the beginning and the end of the chain) on chain length l=l0N and its “effective rigidity” θ, which, in its turn, depends on temperature T . Using (2.24) it is easy to calculate: 2 ~ 1 + θ ⎧⎪ 1 − exp(− l lкор ) ⎫⎪ = l0l ⎨1 − R 2 (l ) = − ∂ 2 G (p, l ) ⎬ 1 − θ ⎪⎩ l lкор ∂p ⎪⎭ p =0
(2.26)
where correlation length lкор = [2θ /(1 – θ )]l0, and the parameter of “effective rigidity” θ = α+ – α– depends on temperature (T ), i.e. θ ≡ θ (T ). There are two possible extreme cases: bending rigidity of the chain is small, which corresponds to condition θ << 1, and bending rigidity of the chain is large, which corresponds to condition 1 – θ ≡ ε << 1. At small values of θ (θ << 1, i.e. κ /T << 1) and at large values of l dependence (2.26) becomes linear, i.e. it corresponds to Gaussian coil:
R 2 (l ) ≈ l0l ⋅ (1 − lкор l ).
(2.27)
At θ close to 1 (1 –θ ≡ ε << 1, i.e. κ /T >> 1), and comparatively small values of l (l ≤ l0/ε) the obtainable dependence describes a practically rigid rod:
R 2 (l ) ≈ l 2 {1 − ε l 3l0 }.
(2.28)
However, even at θ close to 1, and rather large values of l (κ /T >> 1, 1 –θ = ε << 1, 2 l >> l0/ε) the squared dependence 〈R 〉 on l transforms asymptotically into a linear one
R 2 (l ) =
1+θ l0l = lK l 1−θ
(2.29)
which corresponds to chain transformation into a Gaussian coil. 2 Here we introduced value lК = 〈R 〉/l = [(1 + θ )/(1 – θ )]l0, which, by definition, represents the Kuhn segment of a macromolecule (the number of chain links in the Kuhn segment: nК = (1 + θ )/(1 – θ )). Note that the Kuhn segment length lК differs from correlation length lкор. This difference is related to transformation to the continuous limit. However, at small values of chain rigidity (θ << 1), all its characteristics practically do not depend on the
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correlation length, and at 1 –θ = ε << 1 (rigid molecule) both values practically coincide (the difference is infinitesimal ε). 2 Dependencies (2.26) 〈R 〉 on l for some values of parameter θ (θ = 0.1; 0.5; 0.9; 0.99) are given in Figure 2.4. Note that for curves 1 and 2 asymptotic form is typical (2.27), and for curves 3 and 4 − (2.28).
Figure 2.4. Dependence of the mean square size of a chain 〈R2〉 on the chain length N = l /l0 at θ = 0,1 − 1; 0,5 − 2; 0,9 − 3; 0,99 − 4.
If we consider the chain length which only insignificantly exceeds the Kuhn segment (includes 2-3 Kuhn segments) as the criterion to neglect the non-Gaussian character of conformations statistics, then it appears that up to the value of θ = 0.4, the value of nК ≈ 1, and we can use the Gaussian statistics practically for any chain length. It is only at θ = 0.9 that the value of nК ≈ 10, i.e. limits of the chain length appear. Nevertheless, it is well known that for a flexible chain, Gaussian statistics works even for very short chains (3–4 chain links), and, it seems that the same criterion should work for the chains possessing a certain bending rigidity. It has experimentally been proven, however, that for the chains with a relatively small rigidity, there is a certain interval in homologous rows in which the system properties are not the properties of low molecular weight compounds, yet, it is wrong to say that the properties of these compounds are not the properties of polymers. This contradiction can be resolved if we use another criterion of the chain length estimation. This is to be the length at which we may neglect the non-Gaussian character of 2 conformational statistics. The scale at which the dependence of 〈R 〉 on N transforms into a 2 linear one can be chosen as this kind of criterion. In this case 〈R 〉 can be represented as a power function with the exponent depending on the chain length. It is clear that at small values of chain length this value may be equal to 2, and at very large values of chain length it may be equal to 1. The chain length at which this value does not exponentially differ from 1
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65
is taken as critical length lГ, starting with which the chain conformational statistics can be considered Gaussian (i.e. this scale of lengths can be considered as the boundary between oligomers and polymers). The required value can be found through calculating the logarithmic derivative of the mean square of the chain size by chain length logarithm: (∂ln〈R2〉)/∂lnN. This dependence is given in Figure 2.5. Figure 2.5 shows that the second criterion gives significantly larger values of critical chain length lГ than the first criterion based on the estimation of the Kuhn segment lК. It appeared that at θ = 0.1 the value of nГ = lГ/l0 ≈ 10, at θ =0.25 − nГ = lГ/l0 ≈ 15, at θ =0.5 − nГ = lГ/l0 ≈ 20, and at θ =0.75 and θ = 0.9 − nГ = lГ/l0 > 100. The second criterion is preferable if we consider it connected with the scale at which polymer chain statistics becomes Gaussian.
Figure 2.5. Dependence of a logarithmic derivative of a mean square chain size with respect to the 2 chain length logarithm (∂ln〈R 〉)/∂lnN on the chain length N = l /l0 at θ = 0.1 − 1; 0,25 − 2; 0,5 − 3; 0,75 − 4; 0,9 − 5.
The dependence of the chain bending rigidity parameter θ on temperature can be derived from the following [38]. Because orientations of the neighboring chain links are not equiprobable and they correspond to the valence angles of the monomer chemical bond, their relative statistic weights are determined by the energy difference between the states Δε , and transformation from one relative orientation to another one is active through overcoming a certain energy barrier ΔE. At the same time, the statistical flexibility of the chain is determined by the difference in energy minima Δε of the corresponding valence angles, and the dynamic flexibility of the chain is determined by the height of the energy barrier between these states ΔE. If ΔE << Δε, and ΔE ~ T, then macromolecules are in an equilibrium conformational state and their statistical properties are determined by statistical flexibility. If we have a reverse
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inequality ΔE >> Δε, then the mechanism of dynamic rigidity prevails, and the macromolecule may be in non-equilibrium conformational state. It is obvious, that the turn of the two neighboring chain links through the angles of π/2 and π is determined by activation energies E1 and E2 (E1<E2). The question is whether these energies E1 and E2 correspond to the energy difference between the conformational states of the chain links, or the energy barriers between them are not essential for this case. Taking into account the fact that macroscopic properties of macromolecular systems are usually determined by the statistical rigidity of the chains, it is much more natural to interpret energies E1 and E2 as energy differences between the conformational states of the chain links. With this interpretation, probabilities αi (α+; α−; α⊥) are proportional to exp(–Ei /T), and the temperature dependence of parameter θ is determined by the difference of energies E1 and E2:
θ (T ) =
1 − exp(− E2 T ) , 1 + 4 exp(− E1 T ) + exp(− E2 T )
(2.30)
In extreme cases of high and low temperatures, when, correspondingly, E1,2/T << 1 and E1,2/T >> 1, we receive
θ (T ) ≈ E2 6T ,
E2 T << 1,
(2.31a)
and
θ (T ) ≈ 1 − 4 exp ( − E1 T ) , E2 T > E1 T >> 1.
(2.31b)
Using expressions (2.31), we find the macromolecule mean square sizes at high temperature and low temperature limits:
R 2 ( N ) ≈ l0l{1 − E2 3Tl}, E2 T << 1,
(2.32a)
R 2 (l ) ≈ l 2 {1 − 4l exp(− E1 T ) 3l0 },
(2.32b)
and
E1 T >> 1.
It should be noted that at high temperatures deviations of the macromolecule size from the Gaussian coil size is inverse to temperature T, yet, at low temperatures, deviations of the macromolecule size from the straight linear rod depends on the temperature much stronger, that is exponentially. It means that with the growth of the temperature, rigid molecule quickly looses its straight linear characteristic; however, it acquires the Gaussian coil form only at sufficiently large temperatures. The above given analysis provides a theoretical justification of the statements which were declared in Part 1.1.3. In particular, it has been shown that the conformational states statistics of the chains which possess the end interlink bending rigidity can differ strongly from the
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Gaussian statistics. Moreover, the non-Gaussian character of the macromolecule conformational statistics exists even in case when the dependence of the average size of this coil coincides with the Gaussian coil size: 〈R2(l)〉 ~ l. It should be underlined once again that this only seems to be a contradiction. It is obvious that in case of the smallest scale, the spatial function of molecular weight distribution differs from the Gaussian function. However, if this distribution can be averaged at the scale of the “straight” sections of the chain, then the spatial distribution of these “elementary” links can be considered Gaussian. The size of these “straight” sections of the chain can be easily estimated: in terms of the occasional wanderings model, the number of links in this section is equal to the average number of steps before the first turn
n = 1 ⋅ (α + + α − ) + 2 ⋅ (α + + α − )2 + 3 ⋅ (α + + α − )3 + ... = d α+ + α− , = (α + + α − ) ∑ z n = 2 dz n z =α +α ( − α − α ) 1 + − + −
(2.3)
and, therefore, the desired length is equal to
lпр =
(α + + α − )l0 . (1 − α + − α − )2
(2.34)
In the order of magnitude, this length coincides with the chain length lГ, where the dependence of the mean square size of the macromolecule on its length becomes linear (see Figure 2.5 and comments to it). This characteristic size of the macromolecule significantly exceeds the Kuhn segment size, traditionally calculated as the ratio between the mean square size of the macromolecule and its length (see (2.29)) or as the correlation length in the exponentially damped function of orientations correlation. Using ratio (2.34) we can estimate the number of chain links making the straight line section of the chain. For example, at the given values of parameters α+ + α− = 0.9 this section has 90 chain links. If α+ >> α− , then θ = α+ – α− ~ α+ + α− = 0.9. Figure 2.5 shows that the dependence 〈R2(l)〉 becomes linear at the same value of N, while the calculation according to formula nК ≈ 〈R2(l)〉/l gives a lower value (see comments to Figure 2.5). Therefore, if we use an expression like (2.34) as the criterion to estimate the characteristic scale of the macromolecule, where we can start to neglect the chain length rigidity, and if this very scale is used as the Kuhn segment, it will be much more adequate to the physical meaning of this concept than the usually applied criterion based on the exponential infinitesimal of the correlation function. The non-Gaussian character of the chain links can appear in two cases: if the resolution of the device (characteristic scale of the sensing electrode interaction with the molecule), used to estimate the polymer molecule state is smaller than the Kuhn segment; if the chain length is comparative to this scale or exceeds this scale insufficiently. It is these molecules that can be considered oligomers. There is also another important conclusion that follows from the above given analysis. It is not only physical and chemical properties of individual molecules, but also their
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temperature that can determine low molecular weight, oligomer or polymer state of the compound. Parameter θ depends on the temperature exponentially, thus the length of the Kuhn segment can also change strongly with the change of the temperature. As the result, a compound which behaves like a flexible chain polymer at a certain temperature may change its properties and become an oligomer with the decrease of the temperature. A reverse situation is also possible, when with a sufficient increase of the temperature, a typical oligomer starts behaving like a flexible chain polymer. On the other hand, temperature transitions like oligomer ↔ polymer are not obligatory for all the substances. Physical and chemical properties of some molecules may have no transition of this kind in the range of the temperature from polymer (oligomer) melting to destruction.
2.2.3. Orientational Ordering of Oligomer Molecules: Influence of Environment Scaling estimations given in Part 2.2.1, have shown that concentrated rigid chain polymer or oligomer systems always possess a local orientational ordering, which, at certain conditions, can result in orientational self-ordering of the system as a whole. In the approximation of the average field, paper [38] shows the conditions at which these systems obtain orientational ordering, and transformations which occur between the ordered and nonordered states. Following is the analysis of some results of this research, concerning the peculiarities of this phenomenon conditioned by the specifics of the oligomer systems. These results do not only confirm but also add to the scaling estimations of the local anisotropy influence in oligomer systems on their macroscopic properties. The approach taken in [38] is based on the same background of the model of orientationally correlated wanderings which could describe the non-Gaussian conformational statistics of oligomer chains (see Part 2.2.2). The behavior of a sample chain in the environment of the ones alike is studied. During the spatial placing of this sample chain, the orientation of each one of its links is influenced by the orientation of the neighboring links along the chain as well as the orientation of the links of the neighboring chains. In case of a two-dimensional space, the degree of the system orientational ordering is characterized by the order parameter which is defined as the difference between the share of the monomer links nx and ny, oriented along the directions of x and y (ni = Ni/N, N = ΣNi , i = x, y):
η = nx − n y =
Nx − N y Nx + N y
.
(2.35)
If all the links of the polymer chains are oriented along the x direction then the order parameter η = 1; if they are oriented along the y direction then η = –1, and if the system as a whole is isotropic then η = 0. (Note that with this definition of the system orientational ordering, when every link is not a vector, but a director, a high degree of ordering can denote absolute straightening of the chain as well as formation of a folded structure.) The influence of the environmental orientation means that the probability of the direction choice at every step of wandering corresponding to the next chain link, can be renormed, and,
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in this case, it depends not only on the properties of the chain itself, but also on the environmental orientation: • • •
probability to move in the same direction α+(T ) equals α+(T ) + δ+(η, T ); probability to move in a perpendicular direction α⊥(T ) equals α⊥(T ) – (δ+(η, T ) + δ– (η, T ))/2; probability to turn through the angle of π α–(T ) equals α–(T ) + δ–(η, T ).
Functions δ±(η) grow monotonously in the interval (–1, 1), and at the boundaries of this interval at η = 0 – they satisfy the conditions
⎧− α ± , ⎪ δ ± (η ) = ⎨0, ⎪α ± γ , ⎩ ⊥
η = −1, η = 0, η = 1,
(2.36)
the first one of which means that it is impossible to keep the orientation in the y direction, and the last one means that it is impossible to turn through the angle of 90°, if the environment is oriented in the x direction. As the value of α± + δ±(η) has a probability meaning, at any η the condition to be satisfied is 0 ≤ α± + δ±(η) ≤ 1. Parameterγ, determining the ratio between the straight line and the folded conformations of the chain in the highly oriented state satisfies the inequality – (α+ + α⊥) ≤ γ ≤ α– + α⊥. The basic idea of the system orientational state is to determine the share of the sampling chain links nx(η) and ny(η), oriented along directions x and y, depending on the orientational state of the environment (on the value of the order parameter η), within the model of orientationally self-correlated wanderings on the regular lattice. If the order parameter (in accordance with definition (2.35)) is expressed through the values of nx(η) and ny(η), a self-consistent equation is found which relates the order parameter η to the functions of δ±(η):
η=
β (η ) − β (−η ) 4α ⊥ − [β (η ) + β (−η )]
(2.37)
where β(η) = δ+(η) + δ-(η) – is a function which monotonously increases in the interval (–1, 1), at the boundaries of this interval at η = 0 function β+(η) satisfies the conditions (see boundary conditions for function δ±(η))
⎧− (1 − 2α ⊥ ), ⎪ β (η ) = ⎨0, ⎪2α , ⎩ ⊥
η = −1, η = 0, η = 1.
(2.38)
Note that parameterγ, determining the ratio between the straight line and folded conformations of the chain in the highly oriented state is not present in the self-consistent
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equation (2.37). This can be explained by the fact that the degree of the system orientational ordering is determined just by parallelism or perpendicularity of the chain links to the isolated direction, while parallel or antiparallel relative orientations of the two links are considered equivalent. Within the phenomenological study, the apparent view of the function β(η) is unknown, therefore it is represented as expansion to the degrees according toη. With this expansion polynomial to the 4th degree is enough:
[
β (η ) = 12 (1 − a )η − (1 − 4α ⊥ )(1 − b)η 2 + aη 3 − (1 − 4α ⊥ )bη 4
]
(2.39)
where a and b are parameters which characterize the ordering influence of the environment. Taking into account (2.39), equation (2.38) takes on form:
η=
η (1 − a + aη 2 ) 4α ⊥ + (1 − 4α ⊥ )η 2 (1 − b + bη 2 )
(2.40)
Depending on the values of parameters a, b and α⊥, equation (2.40) can have from three up to five physical solutions, where three solutions correspond to the isotropic state of the system (η1 = 0), and two solutions correspond to the full orientational ordering of the system (η2,3 = ±1). They satisfy the equation (2.40) at any values of parameters a, b and α⊥. At some values of parameters a, b and α⊥, however, the equation (2.40) has two other non-trivial solutions
η± = ±
a − (1 − 4α ⊥ ) , which correspond to the partially ordered states. (1 − 4α ⊥ )b
When analyzing the stability of the equation (2.40) solutions, it was estimated that at b > 0 states η± are unstable, state η1 = 0 is stable at a > 1 – 4α⊥, and states η2,3 = ±1 are stable at a < (1 – 4α⊥)(1 + b). This means that at b > 0 and 1 – 4α⊥ < a < (1 – 4α⊥)(1 + b) both isotropic and fully ordered states are stable, unstable states η± are between them, i.e. a typical situation of bistability is to be here (see Figure 2.6, b > 0). At b < 0 we get a quite different picture: states η± are stable, state η1 = 0 is stable at a > 1 – 4α⊥, and states η2,3 = ±1 are stable at a < (1 – 4α⊥)(1 + b). The regions where the nonordered and ordered states are stable do not overlap; in the transition region the degree of the system ordering smoothly changes from minimal to maximal or, vise versa, from maximal to minimal. This means that at b < 0 the transition from the ordered state into the non-ordered state (and back) is not uneven like at b > 0, but smooth at a certain end interval of the parameters values (see Figure 2.6, b < 0). In case the width of the transition interval changes to zero, the reconstruction of the system state takes place as a jump (see Figure 2.6, b = 0). Parameters α⊥ and a can change depending on the exterior conditions, for example, if the system temperature changes. Both the effective rigidity of the chain (parameter α⊥), and the ordering influence of the environment (parameter a) are the functions of temperature. It is natural to suppose that α⊥(T ), changes from 0 at (T = 0) to 1/4 (at T =→ ∞) according to the Arrhenius law: (4α⊥(T ) = exp(–Eж/kT )), and a(T ) obeys the same law, but with a different activation energy (a(T ) = exp(–Eор/kT )); the value of 1 – a(T ) decreases from 1 to 0 with the
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increase of the temperature. Corresponding bifurcational diagrams, where the control parameter is the dimensionless temperature τ = kT/Eж, Eор = Eж/2, and parameter b = ±0.3 or 0, are given in Figure 2.6 (b > 0, b < 0 and b = 0).
Figure 2.6. Bifurcation diagrams for the order parameter, which characterizes orientation ordering of a system at b=0,3>0 (bistability is observed in the temperature range τ1 - τ2), b=–0,3<0 (smooth transition between ordered and disordered states occurs in the temperature range τ1 - τ2), b = 0 (jump-like transition occurs between ordered and disordered states). The guiding parameter is a dimensionless temperature τ=kT/El. Stable states are marked with solid lines, unstable states are marked with dashed lines.
The same study has been done for a three-dimensional case. The peculiarity of the threedimensional state makes one scalar order parameter not enough to describe the degree of ordering. That is why we used the shares of monomers ni = Ni/N, oriented along directions x, y and z (ΣNi = N, i = x, y, z) as order parameters; for these values the normalization requirement is valid nx + ny + nz + = 1. For the three-dimensional space within the model of orientationally self-correlated wanderings on the regular cubic lattice we determined the share of the sample chain links nx(η), ny(η) and nz(η), oriented along directions x, y and z depending on the orientational state of the environment. As the result, we obtained a system of self-consistent equations, the solutions of which describe the orientational state of the system. Graphically the system of stationary states can be presented on the plane nx + ny + nz = 1, where a regular triangle has been cut; it corresponds to the region of physical values of parameters 0 ≤ ni ≤ 1 (see Figure 2.7).
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Figure 2.7. State diagram of a three-dimensional system. a – isotropic (I) state; b – transition to the cholesteric ordering; c – cholesteric (Ch) state; d – transition to nematic ordering; e – nematic (N) state; • – stable state, ° – unstable state
The meaning of the obtained solutions is as follows. Unlike a two-dimensional system where only one transition (rigid or smooth) occurs, a three-dimensional system has a cascade of transitions. If the links of the macromolecules were initially in the non-ordered state, with the change of conditions they start getting oriented parallel to a certain plane. No orientational order can be observed in the plane itself, i.e. this situation is similar to the cholesteric state. Only when almost all the links of the macromolecules take an orientation parallel to a certain plane, orientational ordering in the plane takes place: the links start to line up along a certain director in the plane of cholesteric ordering. As the result, the system moves to a fully orientationally ordered state similar to nematic. The type of transition (rigid or smooth) that is realized at the first and second stages of ordering depends on the values of coefficients in the self-consistent equations. Among these coefficients are two linearly independent parameters after all conditions are satisfied (like conditions (2.36) or (2.38)).
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73
Note that the stage mechanism which can be used for the ordering of a three-dimensional system (first, a plane ordering, and then a complete ordering) makes the question of kinetic accessibility of the ordered states solved, though partially. Thus, within the model of orientationally correlated wanderings an isotropic at high temperatures system turns into a highly-oriented state with the decrease of the temperature. The transition described here, unlike the usual one, possesses a peculiarity. Usually, a system consisting of anisotropic elements turns into an anisotropic state with the decrease of the temperature because of the tendency towards ordering conditioned by the steric limits and/or by the orienting interaction of anisotropic elements. This tendency prevails over the disordering entropic factors. For the case studied here, an additional ordering factor appears, that is, the increase of the chain effective rigidity and, therefore, anisotropy of the system elements with the decrease of the temperature. As the result, we can obtain a liquid crystal system with the decrease of the temperature in a fully isotropic system. Although the study carried out here is not absolutely complete, it allows us to make a number of important conclusions. First, besides the phase transition of the 1st type (rigid appearance of the anisotropic phase), the 2d type transition is also possible. For oligomer systems this fact is essential. The 2d type transition systems are characterized by the following phenomenon. Correlated regions of finitesimal dimensions (the correlation radius is finitesimal) appear in the system before the point of transition into the ordered state. With the approach to the transition point the dimensions of these regions increase and in the very point they tend to infinity. In other words, the closer is the system to the transition point the more probable is the appearance of correlated regions in it, and the larger the dimensions of these regions are. Therefore, if the state parameters make the system not too far from the transition point, then orientationally correlated regions exist in the system even in the non-ordered state. In this book these regions are called cybotactic groupings. Second, it is well-known that the conditions of transition into the oriented state depend on the chain length [49,62-64]. For example, it has been shown that the transition into the rotational phase* occurs only in chains, the length of which is no more than 100-120 monomer units [64]. At the same time, the transition temperature decreases with the decrease of the chain length. This fact can be interpreted as follows: for long (polymer) chains (if the system does not possess any specific orienting interchain interactions) the mechanism of local orientationally ordered regions appearance is suppressed. It can be realized only for relatively short (oligomer) macromolecules. For very short chains the transition conditions are complicated (the transition temperature is lower), and, ceteris paribus, the tendency to local orientational ordering for the systems consisting of shorter chains is lower than for the systems consisting of longer chains. On the other hand, shorter chains are more mobile, and, from the kinetic point of view, the formation of orientationally correlated regions in them is *
According to Muller [61], rotational transitions are connected with the rotation of molecular chains around the “long axes”. Systems which consist of macromolecules possessing anisotropic bending rigidity and rotational degrees of freedom (“spin” of the chain around its axis which changes the direction of bending anisotropy) at certain conditions can move into the so-called “rotational phase”. The rotational phase is characterized by nematic ordering of the chain; rotational degrees of freedom remain ordered. It is the presence of non-correlated rotational degrees of freedom that differentiates the rotational phase of polymers from nematic. The rotational phase is characterized by a layer structure, where elongated macromolecules form monomolecular layers. The packing of the elongated chains in these layers as well as the packing of the layers themselves can be different, i.e. there are several types of rotational phases
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
more probable. As the result, these two factors, thermodynamic and kinetic, compete with one other, and, in macromolecular systems consisting of chains the lengths of which are not very large (and not very small), formation of locally oriented regions is possible. In other words, tendency to local orientational self-organization is peculiar not to all macromolecular compounds but only to relatively short homologues – oligomers.
2.2.4. Free Energy of Oligomer Molecules It has already been noted above (see Part 2.2.2) that the volume of the chain possessing a certain interchain rigidity is much larger than the corresponding volume of a flexible chain. Papers [3, 32, 65] show that if the Kuhn segment of the polymer molecule equals nК, than the size of the phantom chain (without the effects of the excluded volume) has the following order: 12
RRF ∝ l0 nk ⎛⎜ N nk ⎞⎟ ⎝
⎠
= l0 nk1 2 N 1 2 ∝ nk1 2 RFF
(2.41a)
and the size of the real (without self-intersection) chain is:
RRR ∝ l0 nk ⎛⎜ N nk ⎞⎟ ⎝
⎠
35
= l0 nk 2 5 N 3 5 ∝ nk 2 5 RFR
(2.41b)
The excess of the free volume inside the coil formed by molecules possessing interchain rigidity can be taken by the other chains. However, this leads to limits for certain conformations of the chains, and, therefore, the number of the degrees of freedom in the chain decreases. As the result, entropy of each of the chains decreases, which is thermodynamically unprofitable. Papers [66-68] describe this situation. It has been shown that entropic losses can be compensated by gain in energy. Within the model of orientationally correlated wanderings on a regular lattice, paper [67] considers a single phantom chain. The elastic energy of the chain is described as
H(N ) = κ
N ⎧ ⎪
∑ ⎨1−
n = 1⎪⎩
⎫
e( n) ⋅ e( n +1) ⎪ ⎬ ⎪ l02 ⎭
(2.42)
The symbols are the same as in Part 2.2.1: vector e(n)≡e(l ) corresponds to the nth chain link (l = l0 n, l0 − the length of the lattice edge, corresponding to the length of one chain link; the total chain length equals L = l0 ( N + 1)). Two neighboring chain links with the same orientation (the chain does not bend here) contribute nothing to the elastic energy of the chain. When calculating the potential energy of the chain bending this level equals zero.
which differ by the packing of the oriented chains as well as the orientation of the nematic ordering axis relative to the molecular layer plane. For details see [61-64]
Homogeneous Oligomer Systems
75
Further on the following symbols have been accepted: if the chain turns through the angle of π /2, the corresponding contribution to the elastic energy of the chain equals ε⊥ = κ; if the chain turns through the angle of π , it equals ε– = 2κ = 2ε⊥. Thus, if due to the molecule conformation, the chain turned n⊥ times through the angle of π /2; n– times through the angle of π, and n+ = N – n⊥ + n– times the chain kept its orientation, the elastic energy of the chain equals:
H ( N , n⊥ , n− ) = n⊥ε ⊥ + n−ε −
(2.43)
The share of conformations corresponding to the set value of elastic energy:
Z( N , H ) =
⎧ n ε +n ε ⎫ 1 ∑ [exp⎨⎩− ⊥ ⊥ T − − ⎬⎭ × N (2d ) {n+ , n⊥ , n− }
(2.44)
× δ ( n+ + n⊥ + n− − N )δ ( n⊥ ε ⊥ + n−ε − − H )], where d – is the dimension of space (d=2 on the plane and d=3 in the space), δ(n) = 1, if n = 0 and δ(n) = 0, if n ≠ 0, temperature T in energy units. Free energy F and chain entropy S are expressed through the value of Z(N, H) by a standard method:
F ( N , H ) = −T ln Z (n, H ), S ( N , H ) = ln Z (n, H ) + H T
(2.45)
After corresponding transformations (2.44) we received an expression for the free energy of the system F(NH):
F ( N , H ) = −T ln Z( N , H ) = − 0,5ln 2π + κn + 2 NT ln 2 − T (2 N + 0,5) ln(2 N ) + + T ( n + 0,5) ln n + T (2 N − n + 0,5) ln(2 N − n), where n = H/κ . The minimum of free energy (by parameter n) is achieved at n ≈ Fmin ( N ) = − κ + ln 2π + T ln( N 2) − 2 NT ln{[1 + exp(− κ T )] 2}. 2
(2.46)
2N , then: 1 + exp(κ T ) (2.47)
Expression (2.47) sets the value of free energy for the phantom rigid chain molecule in a thermodynamically equilibrium state. Prohibitions for self-intersections were taken into account and the chain was considered more rigid, i.e. an effective rigidity of the chain was introduced κ∗ > κ , which resulted in the increase of the Kuhn segment of the molecule studied. If ratio (2.41а) is presented as
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev 12
RR ∝ l0 nk* ⎛⎜ N nk* ⎞⎟ ⎝
⎠
n*К = nК ( N nК )
15
12
= l0 nk*
N1 2
12
n*К
and
= nК 2 5 N 3 5 − 1 2 ,
i.e.
> nК , we receive a new ratio (2.41б). Therefore, for a real chain in a
thermodynamically equilibrium state the value of free energy is expressed as ∗ ⎧ ⎫ FР ( N ) = − κ + ln 2π + T ln( N 2) − 2NT ln ⎨⎡⎢1 + exp⎛⎜⎝ − κ ∗ T ⎞⎟⎠ ⎤⎥ 2⎬. 2 ⎣ ⎦ ⎩ ⎭
(2.48)
connection between κ∗ and κ on condition κ >> T is κ ∗ = κ 4 5 ( NT )1 5 . If the molecules exist independently of each other, free energy for each of the chains is calculated through the ratio (2.48). If interactions start, e.g., an aggregate is formed, their free energy changes. This change is related to the increase of the excluded volume conditioned by the prohibitions for chains intersections. On the one hand, due to this prohibition for intersections with other molecules it is impossible to realize some conformations of the chains. This means that the number of the degrees of freedom for each of the chains decreases. In the expression of free energy (2.48) the number of the degrees of freedom is set by the number of the chain links (N ); prohibition for some of the conformations will result in the decrease of the N value. On the other hand, prohibitions for the intersections of the chains compensate the prohibitions for self-intersection, and a real chain behaves like a phantom chain. This means that the effective rigidity of the chain κ∗, introduced in (2.48) decreases with the increase in the number of chains within the aggregate. At a certain degree of aggregation, the rigidity coefficient κ∗ takes its initial value κ . With the further increase of the chains concentration in the coil, their effective rigidity starts increasing again. This phenomenon is connected with the fact that the chain consists of almost straight sections which, starting from a certain critical concentration, obtain a correlated orientation. The same thing happens when the steric limits are considered for a system of rigid rods of finite width [49] –orientational ordering of the straight line sections appears in the aggregate of the chains, different chain bends are to be synchronized. Thus, for a chain within the aggregate of molecules, free energy is expressed as (2.48), however, parameters N and κ∗ do change: ∗ FА ( N ) = − κ − δκ + ln 2π + T ln⎛⎜⎝ N − δN ⎞⎟⎠ − 2 2
(2.49)
⎧
⎫
⎩
⎭
⎡ ∗ ⎛ ⎞⎤ − 2( N − δN )T ln ⎪⎨ 1 ⎢1 + exp⎜⎜ − κ − δκ ⎟⎟ ⎥⎪⎬. T ⎠ ⎥⎦⎪ ⎝ ⎪ 2 ⎢⎣
Resolution of expression (2.49) in a line (considering the change of values N and κ∗ to be small, the first summands remain) gives:
Homogeneous Oligomer Systems ⎧ ⎡ ⎤⎫ FА ( N ) = Fт ( N ) − ⎪⎨ T − 2T ln ⎢ 1 ⎛⎜⎜1 + exp⎛⎜ − κ ∗ T ⎞⎟ ⎞⎟⎟⎥ ⎪⎬δN − ⎝ ⎠ ⎠⎦ ⎪⎭ ⎪⎩ N ⎣2 ⎝
77
(2.50)
⎧ ⎫ ∗ ⎛ ⎞ ⎪ 2 N exp⎜ − κ T ⎟ ⎪ ⎪ ⎝ ⎠ −⎨ − 1 ⎪⎬δκ *, 2⎪ ⎪ 1 + exp⎛⎜ − κ ∗ T ⎞⎟ ⎝ ⎠ ⎩⎪ ⎭⎪
where δN is always positive, and δκ∗, depending on the number of chains in the aggregate can be both positive and negative. It is essential that with the decease of parameters N and κ∗ free energy of the system decreases. Expression (2.50) shows that there are two positive summands in the brackets by which δN is multiplied, and the first summand in the brackets by which δκ∗ is multiplied is equal to the number of the Kuhn segments on the chain length according to the order of value, and it is always larger than 1/2. This is the way by which a limit is set to the length of the chain. Due to the entangling of the chains with one another, the effective value of parameter N always decreases, and parameter κ∗ decreases until the number of chains within one aggregate exceeds the critical value. Therefore, the formation of aggregates consisting of a limited number of chains is thermodynamically efficient. With the growth of the aggregate size, parameter κ∗ becomes positive. This positive sign of δκ∗ does not mean that further growth of aggregates becomes thermodynamically inefficient. Depending on the ratio between the value of effective decrease of parameter N and effective increase of parameter κ∗ this can be both efficient and inefficient thermodynamically. It follows from expression (2.50) that at κ∗/T >> 1 and not very large values of N (corresponding to oligomer state) with the increase of the temperature, thermodynamic equilibrium can shift to the increase of the finite size of the chain aggregates. Figure 2.8, where the dependence of value
[(
)]
T − 2T ln 1 1 + exp( − κ ∗ T ) 2 N y(T ) = 2N −1 1 + exp(κ ∗ T ) 2
characterizing the shift of thermodynamic equilibrium for aggregate formation with the change of the temperature, for different values of N, shows that the value of y(T) depends on the rigidity coefficient and the chain length. If y(T) decreases, then the aggregate formation becomes thermodynamically less efficient with the increase of the temperature; if y(T ) increases, then the aggregate formation becomes thermodynamically more efficient with the increase of the temperature.
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
Figure 2.8. The dependence of y(T) on Т at κ∗=10, N=150 and N=250.
2.3. SUPRAMOLECULAR STRUCTURE OF OLIGOMERS The probability of different supramolecular structures in oligomer liquids has been postulated in many papers (e.g., see [69-75]) with the purpose to explain the peculiarities of rheology, sorption, polymerization and other macroscopic properties of oligomers and oligomer mixtures. Depending on the experimental results obtained, supramolecular structures have been considered to possess different patterns which can explain some of these specific effects. Until present, however, the studies have been carried out without any quantitative consideration of the supramolecular structures formation kinetics, without any regard to their possible distribution according to their number, size, life cycles and etc. The analysis of the oligomer supramolecular structure as well as the analysis of any other level of any system structure (see Part 1.3) has to consider three factors: geometric (mutual arrangement of the system elements in the environment), thermodynamic (the stability of the system and minimization of free energy), and kinetic (the time of relaxation to equilibrium and the life cycle of a structural element) [76].
2.3.1. Geometric Image of Oligomer Supramolecular Structure For a liquid, the concept of supramolecular structure is much broader than the geometric image, it can be expressed only through the reflexion of the molecules thermal movement. Paper [77] stresses that the geometric image of the liquid can be expressed through the analysis of the dynamic set of configurations, generated by the particles of the system during their thermal movement. Here, the self-drift of the particle is to be taken into consideration as well as its correlation with the nearest environment. It is natural that at different time scales (e.g., at different expositions in the experiment), the structural characteristics of the liquid can
Homogeneous Oligomer Systems
79
appear to be different, that is, (in the sequence of “instant pictures”) the kinetic factor can become essential.
2.3.2. Short Range Order When speaking of the supramolecular structure of the liquid, the local (short range) order is to be concerned first of all. In arbitrary choice of the particle, the neighbors of its first and second coordination spheres are located at certain distances. The size of the particle is determined by the average number of neighbors and the particles packing in each of the spheres. The appearance of the order in the structure, according to the paradox definition [50,78], is a violation of the symmetry in the sense of the following example: an isotropic (homogeneous in all directions inside the body) liquid is more symmetric than the anisotropic one; the appearance of the local ordering results in violation of the symmetry of the macroscopic structure as a whole. The concept of the molecules local ordering in a liquid (in contrast to “no gas structure”) appeared in the 1920-ies, when Stuart introduced the notion of “cybotactic area” [79]. The ideology of the particles aggregation in the liquid systems has had a long history (see papers [73,77,80-82]), the attempts to express this idea quantitatively within the “colloidal approximation” go back to the works of Smolukhovsky [83] and Osvald [84]. The further development of the liquid state theory is connected with the works of Ya. Frenkel, J. Bernal et al. (e.g. see [73,80-82]). The local ordering in the macroscopic volume of the liquid shows itself as a structural inhomogeneity. This inhomogeneity is not a phase structure, because it does not have an interface. It can be an element of both homogeneous and heterogeneous structures. The reasons for the appearance of the structural inhomogeneity of the liquid and, of liquid oligomers, in particular, can be both energetic and statistic. Supramolecular structures can be generated in oligomer systems due to the strong dipole-dipole interactions, hydrogen or complementary group bonds, Van der Waals and dispersion forces of molecules interaction, phase transition, or the existence of random fluctuations of the particles thermal movement, the scale of the latter significantly increases in the metastable area and in the critical point as the result of the distance intramolecular interaction appearance (in case of fair ratio of length and flexibility of the molecule) and statistic flexibility of molecules. That is, supramolecular structures can be formed in oligomer systems due to the reasons of different nature; this fact determines different scales of different inhomogeneities lifetimes. According to Landau, the liquid inhomogeneities are considered to be certain structures characterized by a finite size and a finite lifetime [50]. Dimensional and time scales of these fluctuations can change in a very wide range [3,50,73,77,80,39,85]. Moreover, these fluctuations can vary in the degree of the local anisotropy: according to paper [50] the dimensional and orientational arrangements of particles in the environment inside the fluctuation are not equiprobable, the directions of orientation may be different in different fluctuations though belonging to the same macroscopic volume.
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
2.3.3. Terminology The classical physical chemistry (e.g., see [86]) uses the concepts of an associate (the same name particles of the А+А →2А, А+А+А → 3А types) and a complex (different name particles of the А+В→АВ, А+В+А→АВА, В+А+В→ВАВ types) to describe the structure of the low molecular weight non-electrolytes solutions. Papers on oligmers give many different terms to describe the supramolecular inhomogeneities; some of the terms have been borrowed from the classical chemistry vocabulary, the others have been newly introduced. The examples of these terns are as follows: agglomerates, aggregates, ensembles, associates (homo- or self-associates), blobs, domains, half-finished products, clusters, complexes (heteroassociates), micelles, segregates, cybotactic groupings, and etc. Each of these terms can be used; each of them bears a certain meaning. In order to describe the supramolecular structures of the oligomer systems, this book mainly uses the following terms: “aggregate”, “associate”, and “cybotactic grouping”. When describing the supramolecular structures of oligomers, the concept of “aggregate” is the most general, it includes both associative and cybotactic structures. The terms “associate” and “cybotactic grouping” concern the liquid state of oligomers, they describe different types of the long-living (commensurable with the experimental methods resolution) supramolecular structures (aggregates), which differ in the special location and molecules orientation inside the inhomogeneity of the liquid. As noted above, the term “cybotactic grouping” (χιβωτοζ - ark) was introduced in the 1920-ies [79], however, it was finally approved much later, thanks to the fundamental summaries of Ya.Frenkel [80]. Now this term is widely used in the descriptions of the structure of both traditional low molecular weight organic and metallic liquids [87]. Papers on polymers often use another term, “cluster” (bunch, swarm). This term is close to “cybotactic grouping”, however, the probability of spatial orientation of the primary particles of this structural element has not been taken into account here. For this reason, another term, “nematic cluster” has been introduced, which, as well as the word combination “anisotropic associate”, is sometimes used to denote the cybotactic areas of the liquid. These terms do reflect the physical meaning of the concept, however, they are too cumbersome. In order to differentiate the terms “associate” and “cybotactic grouping”, general and distinctive features can be used [80, 87-89]. General features: а) both structures are formed of the same name molecules, b) they are not the phase structures, c) their lifetime is longer than that of the average statistical fluctuations. The lifetime of the ith cybotactic grouping or the ith associate depends on the system composition and temperature; it is determine by the intermolecular interactions energy. Distinctive feature: cybotactic grouping are characterized by the different degrees of anisotropy in the spatial location of molecules; associates are always isotropic. At certain conditions associates can transform into cybotactic groupings and vice versa. The equilibrium macroscopic system possesses the following characteristic: the increase of ordering (aggregates formation, transfer associate → cybotactic grouping and etc.) in one area results in disordering in another area.
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81
2.3.4. Associative-Cybotactic Schematics of Oligomer Liquid Supramolecular Structure A macroscopic oligomer system can be presented as a sum of microscopic subsystems (system elements) which exchange the substance and energy with each other and with the environment. It is not only the phase enclosures but also the supramolecular structures like concentration fluctuations with different time and space parameters that can represent these subsystems. Hypothetically we can consider a variety of models of the liquid supramolecular structure (e.g. see [80-82]).
K1 K2 Figure 2.9. Schematic presentation of associate ↔ Cybotaxis transition.
K3
a)
b)
K4
Figure 2.10. Diagrams of Cybotaxis ↔ Cybotaxis transition with various degree of anisotropy (а) and spatial orientation (b).
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
K5
+
a)
+
b)
K6
Figure 2.11. Schematic presentation of addition (separation) of «disorganized» molecule to Cybotaxis (а) and associate (b)
a)
b)
c)
Figure 2.12. Schematic presentation of a cybotaxic structure model of oligomer liquid. >⎯< «disorganized» molecule of a telechelate oligomer; cybotaxises are contoured with a dashed line. Cybotaxic liquids can differ on the number of cybotaxises in a unit of volume (а and b), on the size of cybotaxises (а and c).
Homogeneous Oligomer Systems
83
Figures 2.9 – 2.12 show one of the possible schemes of the associate-cybotactic structure of the telechelatic oligomer liquid; the authors of this book accept this very scheme. The system is considered to consist of organized (aggregated) and non-organized molecules. The subsystem of aggregates, in its turn, can be divided into cybotactic groupings and associates. The direct and reverse transitions cybotactic grouping ↔ associate can occur at the same (k1 = k2) or at different (к1 ≠ к2 ) velocities (Figure 2.9). Cybotactic grouping can have different forms and degrees of anisotropy (Figure 2.10 а and b). The non-organized molecules can join or slip off aggregates (Figure 2.11). The aggregative liquids can have different life times of the aggregates, different numbers of aggregates in the same volume and different sizes of the aggregates (Figure 2.12).
2.4. THEORETICAL MODELS OF SUPRAMOLECULAR STRUCTURE FORMATION The peculiarities of the macroscopic properties (rheology, relaxation, diffusion, optical, sorption, and etc.), which were determined experimentally during the study of the oligomer systems (e.g., [90-101]), can be explained using the analogies with the quantitative models well known for the low molecular weight and polymer liquids, for example, the models of the liquid crystal state [102-106], the model of the “flickering clusters” [107, 108], and etc. [109113]. The explanations were often arbitrary, at the qualitative approximation level without any concern for the oligomer state specifics. Following are the considerations of some (of the many possible) theoretical models within the framework of the above given scheme (see Part 2.3.4 ), and, in some cases, these considerations provide a qualitative description of the aggregates formation kinetics, find the function of the aggregates distribution according to their size, the degree of the molecules anisotropy inside the aggregates, and predict the conditions at which the aggregative structure of oligomers can influence the macroscopic properties of the liquid oligomers.
2.4.1. Activation Model The following postulates make the basis of this theoretical model of the oligomer supramolecular structure formation [114-117]: • • •
•
the system consists of aggregates and “non-organized” molecules; there is a function of these aggregates distribution according to their number and size, it is determined by the preliminary history of the system; to reach a thermodynamically balanced function of these aggregates distribution according to their number and size, which does not depend on the initial conditions, the system is to overcome a certain energy barrier, determined by the nature of the components; the molecules activation (not in the chemical sense of the word), allowing them to form aggregates, occurs due to the thermal or mechanical (deformation) “injection” of energy into the system from the outside;
84
S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev •
• • •
the external mechanical influence or the temperature increase can result in the activation of the “non-organized” molecules only (not included into the aggregates), but it does not influence the aggregates themselves; it is only due to the activated “non-organized” molecules joining that the aggregates size increases; aggregates can not dissociate and molecules can not split off them; the number of aggregates does not change during the process.
The theoretical approach to the aggregation process in paper [114] is based on the modified model of Becker-During, proposed in [118] to describe the continuous radical polymerization:
u&n = − vkn un + vkn − 1un − 1 + qn + 1un + 1 − qn un ,
u&1 = −vk1u1 + q2u2 , ∞
∞
n =1
n=2
n ≥ 2,
(2.51) (2.52)
v& = − v ∑ kn un + ∑ qn un ,
(2.53)
where un − is the concentration of aggregates, which consist of the n number of molecules; v − is the concentration of the separate molecules (a separate molecule and an aggregate consisting of 1 molecule have different physical natures); kn − is the constant of the velocity of separate molecules addition to an aggregate of the n size; qn − is the constant of the velocity of separate molecules splitting off an aggregate of the n size. For this case, it is supposed that these constants do not depend on the aggregate size n. Within the above given limits, the formation kinetics of the aggregates distribution according to their size, is described by the following system of equations:
u&n = − kvun + kvun −1,
n ≥ 2,
u&1 = − kvu1,
(2.54) (2.55)
∞
⎛
∞
⎞
n =1
⎝
n=2
⎠
v& = − vk ∑ un + p⎜⎜ c − ∑ nun − v⎟⎟ ,
(2.56)
where un − is the concentration of aggregates, which consist of the n number of molecules; v − is the concentration of the activated molecules, including the ones inside the aggregates; k − is the constant of the velocity of an activated molecule addition to an aggregate; p − is the constant of the molecules activation velocity; c − is the full concentration of the molecules in the system, including the activated molecules and the molecules inside the aggregate; a dot above the symbol denotes the time derivative.
Homogeneous Oligomer Systems
85
The system of equations (2.54)–( 2.56) follows from equations (2.51)–(2.53) of the modified model of Becker-During, if qn ≡ 0, and a summand is added into equation (2.53), describing the process of the inert molecules activation. Using the formality of the generating function and introducing the function of two variables ∞
F ( z, t ) = ∑ z n un (t ).
(2.57)
∂ F ( z, t ) = ( z −1)kv(t )F ( z, t ). ∂t
(2.58)
n =1
or
the expressions for the w(t) function, related to the activated particles concentration v(t) by ratio dw(t)/dt = v(t) were obtained:
w(t ) =
c − Fz 0 ⎧⎪⎛ v0 kN ⎞ ⎟ 1− exp( − kNt )] − ⎨⎜⎜ p − c − Fz 0 ⎟⎠ [ kN ( p − kN ) ⎪⎩⎝
(2.59)
⎫ v0 ⎞ ⎛ 1− exp( − pt )]⎪⎬, − kF ⎜1− ⎟ [ ⎝ c − Fz 0 ⎠ ⎪⎭
where Fz0 = dF0(z)/dz, N =Σun = const − is the total number of aggregates in the system. For the concentration of aggregates: n um0 (2.60) un (t ) = exp − kw(t ) ∑ kw(t ) n − m, ( − )! n m m=1
[
]
[
]
as well as for
v( t ) =
c − Fz 0 ⎡⎛⎜ v kN ⎞⎟ ⎢ p− 0 exp( − kNt ) − ⎜ c − Fz 0 ⎟⎠ ( p − kN ) ⎢⎣⎝
(2.61)
v0 ⎞ ⎫⎤ ⎛ − p⎜1− exp( − pt )⎬⎥. ⎟ ⎝ c − Fz 0 ⎠ ⎭⎥⎦
2.4.2. Relaxation Model This model proposed in paper [119], unlike the activation model, considers the possibility of the aggregates growth as well as the possibility of their destruction. Apart from the first four postulates of the activation model, there are some additional conditions introduced. They take into account the peculiarities of relaxation and the equilibrium of the function of aggregates distribution according to their size:
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev •
on the way to equilibrium the distribution of the aggregates according to their size after the external influence changes due to separate activated molecules joining the aggregates and molecules splitting off the aggregates; the number of aggregates does not change in the course of the process, i.e. formation of new aggregates or dissociation of large aggregates does not occur; separate splitoff molecules can not serve as the basis for a new aggregate, they can only join the existing ones.
•
The relaxation kinetics of the earlier generated distribution of aggregates to the equilibrium state can be described by the above given system of equations (2.51)–(2.53) of the modified model of Becker-During, in which, for simplicity, it is supposed that the velocity constants of the activated particles joining to and splitting off the aggregates do not depend on the aggregate size, that is kn ≡ k and qn ≡ q. Then
u&n = −vkun + vkun −1 + qun +1 − qun,
n ≥ 2,
u&1 = − vku1 + qu2 ,
(2.62) (2.63)
∞
∞
n =1
n=2
v& = − vk ∑ un + q ∑ un ,
(2.64)
where, like in equations (2.51)−(2.53), un − is the concentration of aggregates, which consist of the n number of molecules; v − is the concentration of the activated molecules, including the ones inside the aggregates; k − is the constant of the velocity of an activated molecule addition to an aggregate; q − is the constant of the velocity of separate molecules splitting off an aggregate; a dot above the symbol denotes the time derivative. The system of equations (2.62)−(2.64) describes two processes: joining of the activated particles to the aggregates with the velocity constant k, and splitting of the active molecules off the aggregate with the velocity constant q. The are two conservation laws which correspond to the system of equations (2.62)− (2.64): ∞
∞
n =1
n =1
∑ un = N = const and ∑ nun = M = const,
(2.65)
where N − is the concentration of all aggregates in the system regardless of their size; M − is the concentration of the activated molecules in the system, including the ones inside the aggregates. Transformation of the system of equations (2.62)−(2.64) using the generating function F(z,t) (2.57) gives stationary solutions:
Homogeneous Oligomer Systems
Fc ( z ) =
vc =
zF0 zc , 1− z (1− F0 zc N )
(2.66a)
q ⎛⎜ F0 zc ⎞⎟ 1− , N ⎟⎠ k ⎜⎝
(2.66b)
⎡
⎤
⎣
⎦
2 ⎛ ⎞ F0 zc = N ⎢⎢ ⎜1 − k M ⎟ + 4 k N + 1 − k M ⎥⎥. q ⎥ q 2⎢ ⎝ q ⎠
⎛
unс = F0 zс ⎜⎜1 − ⎝
87
F0 zс ⎞ n − 1 ⎟ . N ⎟⎠
(2.67)
(2.68)
The analysis of these equations shows that the evolution of the aggregated system to thermodynamic equilibrium can have several stages. Their number depends on the ratio of constants of joining and splitting off. Note, that the possibility of the stage-by-stage relaxation of oligomer system was established during the analysis of the low-scale chain structure with a limited length and a finite bending rigidity within the orientational correlated wanderings (see Part 2.2.3).
2.4.3. Activation-Relaxation Model Paper [120] considers the model which takes into account the fact that the activation and relaxation processes can occur simultaneously. The additional postulates for this model are as follows: • • • •
activation of the inert molecules due to the external (e.g. thermal) influence occurs according to the Arrhenius mechanism with the velocity constant k; activated molecules can relax to their initial state; from a certain critical value Nкр of the average aggregate size N, the capacity to have free molecules joined grows sharply; thermal influence results in the changes of k and Ncr..
This situation can be described by a system of kinetic equations “uniting” the above given systems of equations (2.53)–(2.55) and (2.62)–(2.64):
u&n = − vkun + vkun − 1 + qun + 1 − qun , n ≥ 2,
(2.69)
u&1 = − vku1 + qu2 ,
(2.70)
v& = − vk ∑ un + q ∑ un + Pc − Rv,
(2.71)
n =1
n=2
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
c& = − Pc + Rv,
(2.72)
where k − is the constant of the velocity of activated molecules addition to an aggregate; q − is the constant of the velocity of separate molecules splitting off an aggregate; p − is the constant of the molecules activation velocity; R – is the constant of the oligomer active molecules relaxation; c – is the concentration of the inert molecules; v – is the concentration of the active molecules; un − is the concentration of aggregates, which consist of the n number of molecules. Using the generating function (2.57), equations (2.69) – (2.72) were transformed to a stationary state: Fst(z) =
zu1st , c = ( R P)vst , u1st = 1− ( k q)v st N , 1− ( k q) zvst st
[
]
(2.73)
These equations allow us to (with regard to the second law of conservation (2.65), with the view of Σ nun + v + c = M ) to find any of these values. In particular, the value of F1zst (stationary value ∂F/∂z at z = 1), can be determined from the ratio:
k( F ) q 1 − N = 1zst ( M − F1zst ), 1+ R P F1zst
(2.74)
This implies that the aggregation velocity constant k depends on the average aggregate size, proportional to their total weight F1zst . The analysis of solutions (2.73) and (2.74) has shown that with the increase of Т, depending on the increase or decrease of the ratio (k/q)/(1+R/P), the value of F1zst can both increase or decrease. In the first case, when, with the growth of the temperature, the fraction (k/q)/(1+R/P) increases, and the amplitude of the k constant change during the increase of F1zst is sufficiently high, three stationary states are possible in the system: two stable and one unstable. This situation can be called bistable. This non-trivial consequence of this model allowed us to give an adequate explanation of the viscosity hysteresis phenomenon which has been first found for the oligomer systems in paper [121].
2.4.4. Kinetic Model The above given models postulated that the number of aggregates does not change during the evolution of the oligomer system to equilibrium. The model proposed by V.Irzhak et al. [122], does not impose any limits to the number of aggregates.
Homogeneous Oligomer Systems
89
This model, like the model described in paper [120], assumes that the process of the stationary state achievement is realized due to the exchange of separate oligomer molecules between the aggregates*:
Here the i index denoted the aggregate size, i.e., the number of the oligomer Х1; pi and qi+1 are the constants of the molecules joining or splitting off the aggregates with the size of i and i +1, correspondingly. Within the model assumed, the aggregates restructuring can be described by the following system of differential equations: ∞ ∞ dx1 = − p1 ⋅ x12 − x1 ⋅ ∑ p j ⋅ x j +q 2 ⋅ x 2 + ∑ q j ⋅ x j dt j=1 j= 2 dx 2 = p1 ⋅ x12 − p 2 ⋅ x1 ⋅ x 2 − q 2 ⋅ x 2 + q 3 ⋅ x 3 dt .....
dx i = p i −1 ⋅ x1 ⋅ x i −1 − p i ⋅ x1 ⋅ x i − q i ⋅ x i + q i +1 ⋅ x i +1 dt ..... where хi – is the concentration of the aggregate Xi, j– is the summation index. The analytical solution of this system for the different values of i, p and q (an example is given in Figure 2.13) has shown that the time to reach the stationary value of concentration τст depends on the aggregate size; the total concentration of aggregates reaches the stationary value very quickly, the time is almost the same as for the aggregates with the size of х1. This indicates that, for oligomer systems, the stationary state in different properties can occur in different ways: for the properties depending on the total (quantitative) concentration of aggregates, it occurs earlier; for the properties depending on the size of the aggregates (e.g., mass concentration), it occurs much later.
*
Here, as well as earlier, it is natural to assume that the redistribution in oligomer systems occurs due to the transference of the separate molecules between the aggregates, i.e., the process well known in the theory of the phase transitions as the process of Slezov-Lifshitz [123] is realized. The velocity of the aggregates transference in the high-viscous environments as a whole, can not be compared to the velocity of the separate oligomer molecules movement.
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
Figure 2.13. Redistribution kinetic curves of concentration of aggregates with aggregate size i: 1(1), 2(2), 3(3), 4(4), 5(5), 10(6), 15(7), Σхi (8).
2.4.5. Liquid Drop Model Based on the liquid concentration model, proposed by Ya.Frenkel [80] and developed for the supercooled vitrescent substances in papers [124-126], V.Irzhak, proposed an original alternative of the drop model for oligomer systems [127]. This model allowed us to determine the dependence of the aggregates distribution function on the intermolecular interaction and the chain rigidity. According to Frenkel [80], the drops generated during the liquid condensation, can be considered as complexes: K A1 + A n −1 ←⎯→ An ,
therefore concentration аn of aggregate (drop) An
a n = Ka1a n −1 = ξ n / K , where
ξ = Ka1 =
1 + 2 Ka10 − 1 + 4 Ka10 2 Ka10
,
Homogeneous Oligomer Systems
91
K is the equilibrium constant, а10 is the total concentration of the elementary particles A1 in the system. The average aggregate size is
~ (1−ξ)-1. A consistent assembly of the aggregate, consisting of the cylindrical molecules has been considered. The value of the kinetic constants of the formation and destruction of the aggregate made up of two molecules is determined by the cohesion energy. The model assumes that the interaction between the aggregates and their dissociation into large fragments does not exist. The kinetics of this process can be described by the following system of equations:
da1 = −2k1a12 − ka1 ∑ f i a i + 2 k '1 a 2 + k' ∑ f i a i dt i=2 i=3 da 2 = k1a12 − k '1 a 2 − kf 2a1a 2 + k ' f 3a 3 dt da 3 = kf 2 a1a 2 − k' f 3a 3 − kf3a1a 3 + k ' f 4a 4 KK dt da n = kf n −1a1a n −1 − k ' f n a n − kf n a1a n + k ' f n +1a n +1 KK dt
(2.75)
where an is the concentration of aggregates, consisting of the n number of molecules; k1 and
k '1 are the constants of formation and dissociation for А2; k and k′ are the same constants for А3, А4,…Аn aggregates; k>>k1, k ' << k '1 ; fn is the parameter characterizing the number of “seats” of the n size aggregate and the number of molecules which are capable of splitting off this aggregate. It is assumed that these two reactions are characterized by one and the same value of parameter fn. An aggregate consisting of two elementary particles (a dimer) is formed according to the scheme:
The cohesion occurring between the particles in unstable: fn of the direct and reverse reactions is the same. Much more durable and favorable is the following bond:
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
The number of “seats” fn depends on the aggregate size n. It can be expresses by the formula
f n = 3,6( n − 0,92 )
(2.76)
When equilibrium occurs, the system (2.75) gives:
a2 =
k1 2 a1 = K1a12 k'1
a3 =
k f2 f a1a 2 = K1K 2 a13 KK k' f 3 f3
an = K
(2.77)
f n −1 f a Bξ n −1 a1a n −1 = K1K n − 2 2 a1n = 1 KK fn fn n − 0,92
К1 << К are the corresponding equilibrium constants,
B=
K1 , and ξ = Ka1 . 1,8K
Figure 2.14 shows the curves of the mass function of the aggregates size distribution
wn =
na n ∑ ia i
for different values of ξ. It can be seen that in the wide range of values n the
i exponential law works.
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93
Figure 2.14. Mass function wn of the size distribution of aggregates. ξ = 0,1(1), 0,3(2), 0,5(3), 0,7(4), 0,9(5) и 0,95(6).
The first frequency moment λ = 1
ξβ , where β=2. ∑ ia i ≈ 1 − ξ i=2
In the range of 0<ξ≤0.8
a 01 = a1 (1 +
4qξ2 ) 1− ξ
(2.78)
where q~B<1. The equation (2.78) allows us to determine the dependence of parameter ξ and the value of а1, that is, actually, the share of elements, included into the aggregates, on the equilibrium constants K1 and K. The curves of one of these functions are given in Figure 2.15 as an example.
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
Figure 2.15. Dependence of parameter ξ on equilibrium constants K1 and K. q=0,01(1), 0,05(2), 0,1(3), 0,15(4), 0,2(5), 0,25(6), 0,35(7) and 0,5(8).
As it can be seen, parameter ξ increases with the growth of K. Therefore, the exponent value in the function of the aggregates size distribution decreases, and the average aggregate size grows. The presence of dependencies a1(q,K) and ξ(q,K) allows us to determine the frequency moments λ = k
∑ ika i ,
i=2
the average aggregate size < R > = λ1 , and the distribution n
λ0
dispersion D = λ 2 − λ1 as the functions of the equilibrium constants. λ1 λ1 λ 0 The aggregate formation free energy takes into account the intermolecular interaction energy and the chain rigidity. The efficient intermolecular interaction is due to the rigid districts of the oligomer molecules. If ϕ is the share of the rigid chain links of all the oligomer chain links (1-ϕ is the share of the absolutely flexible fragments), then the value of the free energy is proportional to ϕ, and the equilibrium constant can be expressed as follows: K(ϕ) = It is obvious that with the increase of ϕ the equilibrium constant increases Kϕ. (K(ϕ=0)=1), and the distribution function changes as well.
Homogeneous Oligomer Systems
95
2.5. LIFETIMES OF SHORT RANGE ORDERING It has already been noted above that the short range ordering in the oligomer liquids can be formed due to the forces of different nature and different energy saturation. If the supramolecular structures are formed due to the thermal fluctuations, then, according to Ya.Frenkel [80], the liquid particle transfer from one equilibrium state into another one is an activation process, and the “settled” life time of the particle close to the equilibrium state is determined by the Arrhenius function of the temperature: τ = τ0 е w/kT,
(2.79)
where τ0 is the average length of the particle presence in this fluctuation until its decay or “split-off”, and w is the activation energy of the decay or split-off process. In the simplest case τ ∼ the atomic fluctuations period ≈ 10-12 s. It is natural that the lower is the 0
temperature, the higher is τ. For Т, corresponding to the liquid state of the system, the lowest boundary of τ usually does not exceed 10-7 - 10-9 s. If, however, in the process of the temperature decrease, and, for the mixed systems, in the process of the concentration decrease as well, the system finds itself in a metastable area, then the life time of the fluctuations increases significantly [128], and in the critical point τ → ∞ [73, 128,129]. Note two circumstances. On the one hand, the range of temperatures (and concentrations), corresponding to the critical point, is very narrow [129, 130], and it is very difficult “to get” into this range [73,128,130]. On the other hand, for oligomers characterized by the wide intermolecular distribution [1], in case of the molecules aggregation due to the weak forces, the probability of the life time increase of some fluctuations can multiply. This can be explained by the fact that for the polydisperse systems, as it has been shown in experiments of R.Koningsveld [131, 132] and proven in papers [133, 135], the local “critical” and “metastable” states can appear at any point of the phase diagram. The point is not about the macroscopic effects, but about the appearance of the local concentration fluctuations, the state of the latter can correspond to the “critical” and “stable” ones. This assumption, although not obvious, first, has a theoretical basis [136]; second, it has been proven by experiments [88,136-140]. It is for this purpose that it is used in many papers by many different authors to explain some peculiarities of the translation diffusion of oligomers [70], their rheological behavior [141,143,144], and the phase separation processes during curing [134,135,145] and etc. For example, the abnormal viscosity growth in natural rubberoligomer systems, connected with the appearance of the large-scale fluctuations, were experimentally proven only for the polydisperse components of the mixture [141]. Different is the situation during the oligomer aggregation due to the strong forces – dipole-dipole, hydrogen and other bonds. G.Korolev [142,146,147], within the ideology of the physical nets [147], analyzed the possibility of realization and registration of the interaction between the atomic groups within the molecule (intermolecular interaction centers), characterized by the different bonding energies (see Table 2.3).
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
Table 2.3. Bonding energy of intermolecular interaction centers formed by different atomic groups [146] Atomic group
Е, kcal/mole
Atomic group
Е, kcal/mole
10.8
4.3
7.6
3.6
7.3
3.6
6.6
1.5
6.3
0.7
4.4
0.5
Paper [146] considers the process of the molecules “bonding” into aggregates in analogy with [149,150] as the process of the equilibrium polycondensation. The difference is that unlike the chemical reactions of consistent addition, resulting in the formation of the stable (in real conditions) covalent bonds between the molecules, “physical polycondensation” results in the formation of the final product, characterized in the same conditions by the lability of the bonds between the intermolecular interaction centers. The mechanism of the bonds formation can be described by a simple scheme of reversible polycondensation: k
2→ G G + G ⎯⎯ 2
k
1 G2 ⎯ ⎯→ G+G
(2.80) (2.81)
where G is the atomic group – bearer of the intermolecular interaction centers, G2 is the intermolecular bond, k1 and k2 are constants of the velocities of dissociation and regeneration of the bond (direct and reverse processes). The life time of G2 is related to the monomolecular constant of the k1 bond dissociation velocity by the ratio [146]: τ= 0.69 / k1.
(2.82)
In its turn, k1 = k01е-Е1/RT,
(2.83)
Homogeneous Oligomer Systems 12
97
-1
where the value of k01 ≈ 10 s (frequency of the atomic groups fluctuations), and the value of Е1 is the energy of dissociation for the corresponding intermolecular interaction centers (see Table 2.3). τ obeys the Arrhenius law for the life time of the bonds, formed by the intermolecular interaction centers as well as for the thermal fluctuations. It is absolutely obvious that the more intermolecular interaction centers are used in the aggregate formation, the longer is its life time. If the molecule contains several intermolecular interaction centers, then τ grows with the increase of the chain length N. Calculations have shown [151] that the aggregate life time increases in a power dependence on the number of intermolecular interaction centers, the exponent of power grows with the increase of the interaction energy Е1 (see Figure 2.16). The life time of the aggregate is several times higher that that of a separate bond [152]. The estimations of R.Fox [153], indicate: the life time of the aggregate consisting of three intermolecular interaction centers is 1 s, while for each of the bonds this time is about 10-9 s.
Figure 2.16. Dependence of lifetime of aggregates τ1 on the chain length N at various binding energy E/kT: 0 (1); 0,5 (2); 1,0 (3); 1,5 (4); 2,0 (5).
Due to different reasons, it is not every intermolecular interaction center that takes part in the aggregate formation, an important characteristic of the oligomer supramolecular structure formation process is the equilibrium concentration of the intermolecular bonds υ, which grows with the decrease of the temperature to the limiting value of υ0, corresponding to the total content of all the potential intermolecular interaction centers, capable of bond formation. Paper [146] shows that υ/υ0 =(1+γ) –( (1+γ) -1)1/2,
(2.84)
98
S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev γ=k1/8k2υ0 =k01.ехр[(Е2 - Е1)/RT]/8k02υ0
(2.85)
where the value of υ/υ0 has the meaning of the equilibrium concentration level, the share of the potential intermolecular interaction centers transformation into the intermolecular bonds, k01, k02, Е1 and Е2 are the preliminary exponents and activation energies of the corresponding reactions. Since the oligomer molecule may have several (in general case, n) potential intermolecular interaction centers, υ = n.С, where С is the oligomer molecules concentration. Figure 2.17 shows the dependencies obtained in [146], with the dependence of υ/υ0 and τ on Е/Т. The comparison with the resolution of the different techniques (Table 2.4) allows us to determine a priori the applicability of the latter for the study of oligomers, containing the atomic groups capable of intermolecular interaction centers formation with the different values of Е1, at different temperature ranges and in different model conditions, corresponding to curves 1-3 in Figure 2.17.
Figure 2.17. Т/Е generalized dependence of the degree of aggregation (ν/ν0 ) (1-3) and the lifetime (τа) (4) of an aggregative bond. К01 /(К02 ν0): 103 (1), 105 (2) and 107 (3).
Homogeneous Oligomer Systems
99
Table 2.4. Temporary resolution of different experimental techniques [146] Technique
t∗, s
Efficiency of radical initiation ESR for a spin sensing electrode 3 cm range (without saturation transfer)
10
3 cm range (with saturation transfer)
5⋅10 - 10
2 cm range NMR for high resolution
≥ 4⋅10
impulse methods
10 - 10
Kinetic parameters of radical polymerization Relaxometry dielectrical
> 10
mechanical
>10 >1
-10
5⋅10
- 10
-11
-9
- 10
-8
: ∼ 10
-4
-10
-10
-6
Thermomechanics
-7
-5
-4
-6
10 - 10
-3
-1
An important detail is to be noted here (see Part 2.8.1). It follows from Figure 2.17 that in the temperature region of 20 - 80°С, the life time of aggregates formed by the intermolecular -5
interaction centers with the bond energy of 0.5 - 10 kcal/mole (see Table 2.3) equals < 10 -6
10 s. At the same time, the classical papers by A.Berlin and G.Korolyov [154] show different anomalies of the oligoesteracrylate initial polymerization velocity. These anomalies are considered to be conditioned by the existence of the “kinetically favorable orders” (in our terminology, cybotactic groupings) in oligomers. If this assumption is correct, then the necessary condition for their kinetic method discovery is, at least, the commensurability of the aggregates life time with the time of the elementary act of the metaacrylic bonds chemical 4 reaction. The latter equals the value of > 10- s, which is two orders higher than the kinetic method resolution (see Table 2.4). It seems that the aggregative structures could not have been revealed in the above described kinetic experiments. This contradiction disappears if you take the following ideas into account [146]. The estimations show that the aggregates τ can be registered in the above described experiments if 4 their value is ≥ 10- s, and the value of Е is ≥ 12 kcal/mole. This situation is quite possible. 1
The molecules of oligomers, oligoesteracrylates in particular, usually have several intermolecular interaction centers* with Е1 = 3 - 9 kcal/mole. If we assume that the interactions of separate bonds are not isolated but correlated, and the supramolecular aggregate is kept by the interaction of the “bunch” of the n bonds of intermolecular interaction centers *), then the aggregate can dissociate, or two “bonded” molecules can be separated due to the translation diffusion, provided that all of the n bonds connecting
* A similar postulate has been used by R.Fox [153] in order to prove the possibility of the anti-entropy processes during the formation of the biologically active macromolecules.
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neighboring molecules dissociate simultaneously. This requires an energy fluctuation much higher than12 kcal/mole. -2
-4
Therefore, the value of the aggregates τ > 10 - 10 s is enough for the total n bonding energy of one molecule intermolecular interaction center to be > 12 kcal/mole. For the majority of oligomers this condition ∑ Е1 ≥ 12 kcal/mole can be satisfied. Thus, there are no principal objections against the formation of the long living (commensurable with the experimental methods resolution) aggregates with anisotropic orientation of the molecules within the liquid oligomers.
2.6. EXPERIMENTAL EXAMINATION OF OLIGOMER SUPRAMOLECULAR STRUCTURE 2.6.1. Analysis of Structure Components Distribution Function The radial distribution functions of the fluctuations g(r) are the most frequently used primary characteristics of liquid structures [155,156] and they determine the particle detection probability at a distance r, r+dr from the other chosen point of the plane with a bigger time averaging in comparison with τ (average time of settled life near the equilibrium center). They are obtained by the Fourier transformation of static structure factor S (k), characterizing the average particle configurations in the system volume: 3
-1
g(r) = 1 + (8π ρ) ∫ [S(k) - 1] exp(-ikr) dk,
(2.86)
S(k) is deduced experimentally according to the data [156]: 2
S(k),= I/I0 N f
(2.87)
where I and I0 are the densities of exciting and scattered radiation, N is the number of scattering centers in the volume V, f is the dissipation factor, k is the module of wave scattering vector, ρ = N/V is the average numerical density. It is possible to determine the imperfections by changing the length of the wave and scattering angle, that is, by setting k, its linear dimensions of the emission wavelength. There 2
is a simple dependence between S(k) and average fluctuations 〈(N - N) 〉 / N [157] in the long-wave limits: 2
lim S(k) =1 + ρ∫ [g(r) - 1] dV = 〈(N - N) 〉 / N
(2.88)
k →0
(there is a line over the two last N) (ensemble\assembly average is marked by angle brackets). In order t account not only spatial but also temporary structure particle order correlation, in principle, it is possible to use the dynamic structural factor S (k,ω), determined by the neutron scattering method.
Homogeneous Oligomer Systems S(k,ω) = ρ∫∫ exp [-I (kr - ωt)] G(r, t) dr dt,
101
(2.89)
where the function G(r, t) is the number-average particle number density around point r at the time moment t in the case if the origin of the coordinates is overlapped by one of the particles: if t=0; w is the frequency content. Integration S (k,ω) in all frequencies results in the static structure factor [77]. Unfortunately, such papers, relative to oligomeric systems, have not been published, yet. The radial distribution experimental function, obtained by the primary X-ray scattering curve transformation (I = f (2θ), where θ is the scattering angle), consists of the open-chain interatomic spacing distribution function and the intermolecular interatomic spacing distribution function. Intermolecular part speculation of the electron density radial distribution function is a rather complicated procedure, connected with the introduction of some estimates and assumptions, checked experimentally afterwards. Intermolecular distribution function analysis is usually carried out in the frame of the paracrystalline order, and the average statistical periodicity value of the basal plane and of the nearest environment are determined. Methodical and methodological basis application of radiography for oligomeric system study is stated in the monograph [158]. Figure 2.18 shows the radial distribution normalized curves, obtained in the [158] for solid and liquid states of the three oligoalkyleneglycol – oligo ethyleneglycol (OEG) with the molecular weight of 1000, atacticoligo propyleneglycol (OPG) with the molecular weight of 1000 and oligotetramethylene glycol (OTMG) with the molecular weight of 1350. Molecular chain fragments of the given oligomers are shown in Figure 2.19. Experimental distribution functions in Figure 2.18 characterize the deviation scope of the atomic center numbers, located in the spherical layer with the density g(r) at a distance of r from the central atom, from the number of these centers at the same layer with density p (with a line over p).
Figure 2.18. Experimental curves of the normalized radial distribution function G(r) for oligoalkyleneglycoles. 1 - liquid OEG; 2 - crystalline OEG; 3 - liquid OPG; 4 - liquid OTMG with Smax = 6,4 A°; 5 -crystalline OTMG; 6 - liquid OTMG with Smax = 8,7 A.
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
Figure 2.19. Chain fragments of OEG (a), OPG (b) and OTMG (c).
To obtain the distance distribution function between the atoms of the different molecules it is necessary to subtract theoretical curve of the intermolecular distance distribution from the experimental curve. However, the result of such subtraction will show the real picture only in case, the theoretical curve is calculated only for those molecule chain conformations, which are realized in the oligomer in the reality. Thus, only the right choice of the conformation model made the calculation approximation result in the experiment. The analysis of the theoretically possible oligoalkyleneglycol molecule conformations and their correlation with the potential energy rotation angle-dependence map and the calculation of literary data for high-polymeric analogues [159], complemented in [158], allowed the authors of the work [158] to choose optimum schemes of molecule layout in basal planes for given oligomers (the specific example is presented in Figure 2.20), to plot a distribution bar chart of intermolecular distances in solid and liquid states and compare them with their experimental functions (Figure 2.21).
Homogeneous Oligomer Systems
103
Figure 2.20. Layout chart of molecules in basis planes of a crystalline cell (a) and the model paracrystalline lattice (b) of a liquid OTMG.
Figure 2.21. Experimental curves and calculated histograms of distribution of molecular distances in crystalline (а) and liquid (b) OPG.
It is possible to see, though there are changes both in the basal plane (they naturally increase) and in the periodicity of the nearest environment of the investigated oligomers during the transfer from the solid (crystalline state) to liquid state, nevertheless, that the paracrystalline order models describe well the local atomic order features of the given oligomers in the liquid state. In other words, liquid oligomers preserve the elements of the local atomic order typical of their solid state. According to the estimates given in [158], the interaction zones (the volumes with the relative position correlation of the structural elements inside them) spread for the liquid state of the investigated oligoalkyleneglycol approximately to 30 inter planar spacing and it makes 50-60 А° in the direction of the perpendicular molecular axes. At the same time, the extension of the correlated volume along the molecular axis does not exceed 1,5 А°, that is, the inter open-chain periodicity for such oligomeric liquids is practically missing.
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2.6.2. Radiographic and Electron Microscope Examination Regular structures of bigger size have been found for other oligomers as well. In a number of works [137,160-166] an integrated study of oligomers of the following homologous series have been carried out through radiographic and electron-microscopic examination: α, ω -tetramethyleneglycol (MTG) of the general formula СН2=С(СН3)СОО[(СН2)4О]n СО (CН3) С=СН2, where n = 5-210, and Мn = 500-15300; α, ω -dimethacrylatoligoethyleneglycolformal (MEF) СН2=С (СН3)СОО[(СН2)2ОСН2О]n СО (CН3) С=СН2, where n= 7-98, and Мn = 650-12800; α, ω - dimethacrylatoligodiethyleneglycolformal (MDF) СН2=С(СН3)СОО[(СН2)2О(СН2)2СН2О]n СО (CН3) С=СН2, where n= 4-55, and Мn= 600-10600 and α, ω -bis-(4-methacrylatoxyethylurethanetoluylene ethersoligoethyleneglycol (METG)
2-aminoformic)
[СН2=ССН3СООСН2СН2ОСОNНС6Н6(СН3)NНСО-]2 О(СНСНО)n, where n=1 -140, and Мn = 600 - 10000. According to their molecular weight, these oligomers constitute the viscous or cereous fluids as well as solid crystalline materials in ambient temperature. For example, oligomers METG with Mn <1600 are amorphous, the crystallinity degree of oligomers with Мn =2250 is no more than 10%. With the growth of the oligomeric block length of the METG, however, it increases and after reaching 50% with Мn >3000, the crystallinity goes beyond the limits. The liquid oligomer roentgenogram of the MTG and MEF type with n < 10 is characterized by radiosity, however, when the value n > 17 shows on the roentgenogram (see Figure 2.22) there apeear characteristics specific for ordered liquid-crystalline systems with the “long range ordering” elements [159,165]. During the electron microscope examination, described in [162, 163], all oligomers were transferred into the liquid state by heating to 3-5°С above the melting temperature and then were instantly cooled in the liquid nitrogen. The fixation of the melted oligomer supramolecular structure was supposed to take place in that case. Figure 2.23 shows the platinum carbonic replicas obtained from the oligomer sample chips of the homologous series METG frozen in such a way. It is possible to see that the electron microscope image of the oligomer supramolecular structure is determined by their molecular weight. For all oligomers
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of the series under study with Мn < 1200 this image is presented in the form of the closepacked globules with the size of 160 -500 А°.
Figure 2.22. X-ray pattern of dimetacrylate-oligotetramethyleneglycole (Мn = 5900).
Figure 2.23. Electron microscopic pictures of frozen METG chips with Мn: 1200(a), 1600 (b), 2250 (c) and 3600 (d). (Χ 30000).
For the frozen oligomer melts with Мn = 1600 and 2250 the structure becomes more complex and the electron microscope shows the form of the laminate structures with the plate thickness of about 100-130 and 150-180 А°. The structure of the frozen melt with Mn=3600 is characterized by the presence of the various size and form fibrillar structures with
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sufficiently distinct contours. There are maximums of such oligomer type on the curves. Their position also depends on the oligomer molecular weight. The values of the long period for METG oligomers with Mn=1200 and 2250 are equal to 150 А° and 170 А°. The packing of the molecules both in solid (crystalline) and in liquid (paracrystalline) states in general is determined by the oligomeric block, but not by the end groups when comparing the intensity and interplanar spacing of the special oligomers and corresponding oligotetramethyleneglycols. It was possible to make a conclusion that the local order in the liquid oligomers is provided by the intermolecular interaction of the anisometric part of the molecule, as the result, supramolecular structures are formed with periodicity not along the molecular chain but in the perpendicular direction. In the ordered structures of such kind the molecular motion is hindered due to the strong dipole-dipole interactions.
2.6.3. Thermodynamic Estimations A number of experimental works appeared in the recent years devoted to the examination of the oligomer structure organization dispersed in the polymeric matrix. Extensive studies in this direction have been made by A.E. Chalikh (the summary is given in monograph [166]), where the confusion processes, diffusion and interodilution at the phase equilibrium determination have been studied for a wide range of oligomers (methacrylic, epoxy, urethane\urethan, hydrocarbon and etc.) and polymers (PVC, PMMA, polycarbonate, polyimides and etc.). Thus, papers [140, 167] studied the mixture thermodynamics in the PVC system of oligoetheracrylate by microinterferometric method . The theory of Flory [15,168] allows us to differentiate contributions of combinatorial (Δ к
R
S1 ) and non combinatorial mixing entropies (ΔS1 ) and to divide, in that way, the molecule fraction in the mixture, the structural order of which has changed in comparison with the order degree in the components formed before mixing. According to [15,168] the general mixing entropy is determined as: к
S1 = ΔS1 + ΔS1
R
(2.90)
к
ΔS1 is always positive, as the molecule rearrangement number in the mixture is more R
than that in the individual components, ΔS1 , reflecting the order increase or, on the contrary, disorder in the molecule arrangement of the same components during mixing, in comparison with their individual state, can take either positive or negative values. к
R
Figure 2.24 shows the mixture composition dependences ΔS1, ΔS1 and ΔS1 on the mixture composition of trihydroethylendimethacrylate - PVC [167]. Unusual high absolute values of the mixing redundant entropy draw our attention to such a phenomenon first of all. It should be noted that the concentrated dependences of combinatorial and non combinatorial к
components of the general entropy are completely different. ΔS1 naturally decreases (the number of combinatorial units during mixing has increased) with the increase of ϕ1 in the
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whole interval concentration range, but ΔS1R changes extremely. At first it increases, and then if 0.2<ϕ1<0.6 decreases proportionally to the oligomer concentration in the solution. The changes of the total entropy has an extreme form because the contribution of non combinatorial entropy in ΔS1 is far above the concentration ΔS1. The value ΔН1 (as the function of ϕ1) also passes through the maximum (Figure 2.25).Two opposite situations can be distinguished in the concentrated dependences of thermodynamic parameters. If ≤ 0.2 there R
к
is an increase of ΔН1, ΔS1 and ΔS1 and the decrease of ΔS1 . It proves the fact that in the given range of solution concentrations in PVC there is a structure disorder of the mixture components in comparison with their initial state. If ϕ1 > 0.2 there is a decrease of values Δ Н1, ΔS1 and ΔS1R, which is interpreted in [139,167] as the order system increase and, particularly, as the micro volume formation with a high oligomer concentration. Comparison of the given data with the phase plot of the system [166] shows that the molecule aggregation OEA in the mixture PVC starts at a considerable distance from the binodal and increases as it approaches it (on the binodal). The order degree reaches its maximum if the concentration is R
close to ultimate, and the values ΔН1 and ТΔS1 approach so closely that the value Δμ1 = ΔН1 − ТΔS1 tends to zero (Figure 2.25), this means that the system is ready to form a new order level-phase division.
Figure 2.24. Concentration dependencies ΔS1, ΔS1R, ΔS1K in a system PVC - trioxyethylenedimetacrylate. ϕ1 –is the volume fraction of oligomer [167].
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Figure 2.25. Dependence of F ≡ Δμ1, ΔΗ1, ΤΔS1 on ϕ1 in PVC - trioxyethylene-dimetacrylate at 90 and 150 °С [167]. R
Figure 2.25 shows that the contribution for the enthalpy component in Δμ1 of the given mixture is distinctly less than that for the entropic, i.e. the molecule dispersion driving force, first of all, is the entropic part of the chemical potential for the system PVC-OEA. In other words, most of the solution energy is spent on the order fracture of the initial components, when mixing PVC and n-hydrooxyethylene-dimethacrylates at the first stage (if ϕ1 ≤ 0.2). This is the possible explanation of the initially bigger values of the redundant mixing entropy, mentioned above, and only if ϕ1>0.2, we can see the new processes start, which result in the stable oligomer concentration (aggregate) fluctuation formation with a higher molecule order degree than that in the initial (before the mixing) oligomer state.
2.6.4. Orientation Phenomena The coefficient ε is the effectiveness measure of the polymer chain influence on the “sample” (oligomerоus) additives orientation determined by the ratio [169]
uiu j
g
= ε uiu j
m
(2.91)
where vector u describes the chemical bond orientation, and the vector components are marked by indices i and j; the bonds are marked indices g and m, related to the “sample” molecule and polymer matrix, correspondingly, ε is the coefficient, characterizing the
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measure of their interaction: ε=0 in the lack of interaction, ε=1 if there is a complete correlation. Papers [95,96] studied the orientation relaxation of the ten-link deuterated butadiene oligomer in its “home” polybutadiene matrix by the 2Н NMR method. The orientation of the oligomer turned out to exceed twice the polybutadiene orientation under the infinite matrix dilution [96]. In the range of the oligomer molecular weight from 500 to 4000, the coefficient of the orientation interaction is ε=1 for all degrees of matrix swelling and joining. Paper [97] studied the system consisting of polybutadiene grating with the chain value Мс~4000 swollen in the butadiene oligomer with the molecular weight of about 800 by the same method. It has been found out that if the inclusion volume fraction of the cross-linked polymer is ϕ=0.8, oligomer molecule orientation is the same as the grading chain for all deformation degrees and greatly less if ϕ=0.6. The coefficient of the orientation interaction is ε≈0.2 if ϕ<0.7 and is ε≈0.9 if ϕ≥0.8. The authors explain this effect by the concentration fluctuations. Papers [98, 99] studied the dimethylsiloxane system by the 2Н NMR method. It is shown that the value is ε≈1 regardless of the oligomer chain length (4 samples with the molecular weight from 300 to 1000) and the swelling degree (from 5 to 20%) in the cross-linked polysiloxane matrix. The value of the orientation order parameter decreases abruptly under the low-molecular dilution. The molecule orientation degree depends on the oligomer nature. Paper [100] studied non-cross-linked polystyrene system by the infrared dichroism. The oligostyrene with the chain length less than M was introduced into it. ε=0.26 for all the chains under examination. The authors connect this low coefficient value of the orientation interaction with the side groups of phenyl rings, preventing the “sample” oligomer molecule from the interaction with the chain segments. Paper [101] used the methods of infrared dichroism and double refraction to examine the orientation interaction. The first method allows us to observe the orientation of the “sample” molecules containing heavy hydrogen atoms in their structure. The second method characterized the general orientation polymer order.. Monodisperse butadiene oligomers with the molecular weight from 500 to 22000 and the content of heavy hydrogen ~70% were dissolved either in the netlike or in the linear polybutadiene matrix (the molecular weight 268000). The oligomer concentration in the matrix was ~ 20%. The experiment was run in the wide range of the oligomer molecular weight and temperature and it demonstrated that ε lies in the range of 0.9 – 0.4 . The high value of the orientation interaction coefficient is typical of the oligomers with the molecular weight less than 1000, and the second value is comparatively low for the oligomers with MW ≥ 10000. There is an abrupt transfer from the high value ε to a lower one between these molecular weight values. And at the same time, the orientation relaxation of the “sample” molecule with the MW≥ 10000 and the polymeric matrix practically coincide, whereas oligomers with MW ≤ 1000 relax considerably quicker. Nevertheless, the relaxation time of the last molecules exceeded the theoretically estimated time by more than 6 degrees: the apparent time of oligomer relaxation with MW ≤ 1000 constitutes the order time in the experiment in the range 10-3 sec, whereas according to theory [170] the maximum of the Rouse time for such oligomers must not exceed 10-9sec.
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2.6.5. Computer Simulation Computer experiments are used in physical chemistry of oligomers for solving different problems. Traditional, but very specific problem is “transfer” into the molecules with the little n number of theories, for high molecular weight polymers and application search of such theories for oligomers. [35]. But another problem is much more interesting: there are attempts to obtain information about molecular interaction, the structure of supramolecular features, packing of molecules, equilibrium and dynamic properties of oligomeric systems by setting chemical structure of the oligomeric molecule, taking into account interatomic interaction energy, bond length, bond angles (in general geometry of molecule), by setting the length of the chains and their flexibility (rigidity), or other characteristics. Let’s take a look at examples of oligomer supermolecular structure study. In [171,172] an associated structure was simulated by molecular dynamics, which conformed to the minimum of potential energy for n-alkyl acrylate and n-alkyl metacrylate structure of СН2=CRСОО(СН2)nСH3, where R = H or СН3, and n varied from 0 to 15. “Steric” energy of the molecules, the constituent of the aggregate, was analyzed as the sum of interactions: Е = Еb + Е0 + Еb0 + ЕΨ + Еnb, where Еb is the tensile energy of valence connected atoms, Е0 is the deformation energy of valence bonds, Еb0 is an amendment to the changes of chain length when converting bond angles, ЕΨ is the internal rotation energy, Еnb is the non valence interaction energy. The energy of one isolated molecule ЕS1, the energy of molecule in aggregate ЕSA and the intermolecular interaction energy (IIE) to one molecule in aggregate ЕIIE = (n ЕS1,- ЕSA) / n were analyzed during the minimizing energy process. Then the structures were searched for, which could provide minimal energy. The search was carried out by randomly chosen different initial conformations, which made it possible to determine the most probable stable conformers. Figure 2.26 shows the aggregate structures which were obtained due to simulation and minimization of their energy for dimeric polymers (the number of molecules in the aggregate m is 2), for methyl acrylate (MА, n = 0), for butyl acrylate (BА, n = 3), and for cetyl acrylate (CА, n = 15). Figure 2.27 shows the results for the same compounds, but for the aggregates built up of 16 molecules (m = 16). It is possible to see that the increase of n in the molecule of n-alkyl acrylates results in “straightening” of alkyl fragments and in formation of aggregates with symmetrical and assymetrical molecule arrangement. It is difficult to define regular regions for the lowmolecular weight MA in 16 molecule aggregate of the size bigger than that of the dimers. In case of the chain length increase, however, mutual orientation of alkyl fragments appears (for the BА), which leads to the increase of the whole system ordering. In such a 16-fold aggregated structure (for CА) the molecules are arranged according to the strict orientation of hydrocarbon fragments, ester groups and double bonds. Here, our terminology implies the transfer of “associate into cybotactic group”.
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Figure 2.26. МА (a), BА (b) and CA (c) dimers in a minimum of steric energy. I – asymmetric dimer; II – symmetric dimer.
The same results have been obtained during the simulation of the n methyl acrylate molecule aggregation. This data confirms the aggregative nature of oligomeric systems and it is used in [173] for the explanation of the drying kinetics anomalies of unsaturated oligomers. Monte-Carlo method [39] was used to study the local packing of the chains with the length of 12, 24, 48 and 96 links with two gauche- and one trans-isomers. The indispensable condition of the locally organized aggregate existence (the authors call them domains), as considered in [39], is thought to be the local firmness, which can be determined by transisomer energetic advantage in comparison with gauche-isomers. The probability of transcondition is assumed to be ωt = 1, and the probability of gauche-condition depends on the temperature ω g = exp(−ε g / k B T ) = exp(−1 / T*) , where Т* is the reduced temperature.
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Figure 2.27. МА (a), BА (b) and CA (c) aggregates of 16 molecules in a minimum of steric energy.
The attractive interaction energy of the non-bonded nearest links in the immediate surrounding εа are supposed to be proportional to εg: εа =-Аεg. There are two dimensions, which are the main system criteria. They are the order parameter Р2 and the radial distribution function center of the chain mass g(r). The parameter
r
r
r
r
of cos(θ ij ) = ( h i ⋅ h j ) /( h i ⋅ h j ) determines mutual orientation, where
r r h i и h j are
the
radius-vectors of the corresponding sub-chains (the analogy with the Kun’s segment), belonging to the same chain. The radial distribution function of the sub-chain center mass is
g(r ) = ω(r ) / v r , where ω( r ) is probability of the fact, that the mass centers of the subchains i and j are divided by the distance r, and v r = 4π ( r + Δr / 2) 3 − ( r − Δr / 2) 3 ,
3
(
)
where Δr is the lattice spacing. The following results have been obtained. If 1/Т*=0, the arrangement coefficient is 0.75, and εа=0 is the radial distribution function of the sub-chains with the length of 3, 7, 11 increasing monotonously with the dimension rij, and reaches the unit value of rij ~6. If Т*=0.625 g(r) suddenly increases, starting with r=1,5, if r=2, it reaches the value of 0.7 and then increases slowly. For the first case Р2, beginning with the unit value r~3, equals zero, for the second case Р2- increases up to Р2≈0.3 if r≈2.5 and then descends to zero. Р2=1 if Т*<0.4,
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then suddenly descends and after Т*≈0.65 comes to the plateau with the unit value 0.2 for the sub-chain with the length of 3 and zero for the sub-chain with the length of 11. In all cases сos (θij) falls nearly exponentially with the unit value increase (j-i), depending on the moving off selected sub-chains from each other along the chain. The interpretation of the results has the following form. Local rigidity is the minimum demand for local order development: absolutely flexible chains do not display local orientation correlation. Semi-rigid chains produce “swimmy domains” (quoted in [39]), determined only in the statistical sense (fluctuating structures). With the inter-chain gravitation and system density growth they become “more distinct” (at certain rigidity). The domain formation is proven to be a cooperative process. The chain rigidity is also determined to be very important in the experiment [175]. The chain relaxation process orientation of the 5 to 1000 links with the persistent length from 1.4 to 5 was studied by the method of molecular dynamics. The system density is 0.85. It has been found out, that there are two different parts of relaxation function for all simulated systems. The first part (short periods) is described by the exponential law, and the shorter the chain and the higher its flexibility is the less is the time interval for that part. The second part is the order parameter exponential regression. The first part is expected to be determined by the local dynamics, and the second one is believed to be determined either by the big chain segment relaxation or by the “organized system fragments”, or, for an extreme case, by the whole chain rotational diffusing. The effective relaxation time τ on the second part increases with the chain length and its rigidity. More than two hundred linear oligomeric hydrocarbon chains of the general formula CH3-(CH2)l-(CH=CH-CH2)m-(CH2)n-CH3 with the length up to several dozens of links, different number and double linkage position were investigated by the Monte-Karlo method in [41,174]. Chains were simulated in the unperturbed state (Θ-conditions). The continuous spectrum of the chains was used to generate all their conformations. Property investigation was conducted in the molecular system of coordinates, connected with the mass center and the inertia tenser vectors of each molecule. Form characteristics, molecule geometrical dimensions, radius and radius squares of inertia, temperature coefficients of such criteria, intramolecular link ordering of all oligomers have been investigated. Computer experiments in [41,174] made it possible to find out that: •
• •
the dimensions and forms of the oligomeric chain spatial region (when approximated by the simple solid body, for example by the three axel-ellipsoid), undergo nonisotropic transformations when changing the temperature; the isolated chain lips display the properties of the intramolecular orientation order relating to its main inertial axes; specific characteristics of these properties, theoretically established for oligomeric chain in Θ-conditions, are developed experimentally in real membrane systems, formed by such molecules.
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A more serious problem was approached in the experiment [40] (see Part 2.2.3). The molecular dynamics method was used to carry out various bilayers properties research, which consisted of the hydrocarbonic oligomer molecules of different length and double linkage numbers. Such molecules are a part of natural lipids of biological membranes. Each lipidic molecule contained two oligomeric hydrocarbon chains – one without double linkage, with the length of 18 hydrocarbon atoms (18:0), the next one has the length of 18, 20 or 22 hydrocarbon atoms, which could contain up to 6 double linkages. Bilayer molecules with the chains of 18:0, 18:1, 18:2, 18:3, 20:4 and 22:6 were analysed. The model, with the main molecule group approximated by the effective atom (diacylglycerolipid molecules), was used to describe lipidic molecules and bilayer heads. Bilayers were formed from the pre-relaxing monolayers. Bilayers were obtained by the turnover through a full 180º angle of one monolayer relative to another layer around the surface normal (of the Z-axis), which goes through the center of the cell, with further slippage along the axis to a certain space and turnover through a full 180º angle around the X-axis. A final summary specified cell consisted of 96 diacylglycerolipid molecules. The total number of single molecule energy, intermolecular energy and interaction energy of all molecule atoms off the surface were calculated to determine the bilayer energy. The energy of the single molecule was represented as the total sum of the valence bonds and angle energy, nonvalent interactions, torsion angles, non-planar atom variations with the double bonds and groups C=O. As the result the geometrical means of oligomeric chains in every bilayer and order properties relative to normals were calculated. There are also works on computer modeling which do not prove the conclusions, obtained by other methods. For instance, Part 2.6.4 quotes the tests, where the methods of 2Н NMR, infrared dichroism and double refraction proved long chains together with short chains to be conductive to the increase of the dimensional orientation of the short chains. But this effect was not found out in the test [176] on simulating binary system of one long (5000 links) and short (5, 10 and 25 links) chains. All the systems investigated were characterized by the low orientation interaction coefficient ε, the value of which does not depend on the chain length of the small molecules.
2.7. KINETICS OF EQUILIBRIUM SUPRAMOLECULAR STRUCTURE FORMATION IN HOMOGENEOUS OLIGOMER SYSTEMS The processes which take place after oligomer exposure to energy or after the contact of oligomer system components (sorption, swelling, dispergation, dissolving, etc.) are widely discussed in the literature (see [70, 74, 177,178]). Typically, the discussions deal with reaching the concentration equilibrium. The arrangement of molecules exists in oligomeric systems, which has been shown in works [138,179-181]. This process keeps going after the completion of sorption, equilibrium swelling, and reaching concentration equilibrium in coexisting phases. This relates [182] to the equilibrium process for structure parameters of supramolecular formations. The latter proved to be slow and they limit the whole thermodynamic equilibrium process in oligomeric systems. For the first time the hypothesis about the duration of supramolecular structure formation in oligomeric systems was raised in work [138]. It was related to the absence of alternative
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ideas, which could explain the dependence of initial velocity of oligoester acrylates solidification W0 on the temporary historical data of rubber-oligomer systems. Soon this hypothesis was confirmed by another experimental technique using other objects. Apart from the band of free NH-bonds υNH in the range of 3400-3450 cm-1, a band of associated NH-bonds (υNH)а was determined in the range of 3300-3350 cm-1 after 2-60 days of storage in infrared spectrum [183] of mixture solution of oligoisoprenedihydrazone and diisocyanate with proton acceptors (dioxane, acetone) as additives. The dilution or warm-up of solution results in the reduced band intensity (υNH)а, but after the end of exposure its intensity increases again and reaches the original value in 40-60 days. There is another side of this problem. The authors of paper [101] paid a special attention to the fact that relaxation period of oligobutadienes with ММ ≤ 1000, characterized by a high level of molecular orientation degree, exceeds the values predicted by Don-Edward theory [170] for nonaggregative systems 6 times. Since 1980s there have been many theoretical and experimental works described in literature, devoted to a full-scale (direct) investigation of equilibrium supramolecular structure formation kinetics in oligomeric systems [68,88-92,114-116]. Some of them will be discussed below.
2.7.1. NMR Data on Relaxation to Equilibrium:Experiment and Theory Figure 2.28 shows the dependencies of spin-spin relaxation time Т2, characterizing the movement of relevant system components, and their fractions Р (the total sum of all Т2 is 1) on exposure time τэ (the time period from getting the sample to the beginning of measurement) for tetramethylene -α, ω- dimethacrylate and cis-polyisoprene before mixing and for their mixtures after rubber equilibrium swelling in oligomer. It can been seen that the characteristic relaxation time value of oligomer Т20, rubber (Т2к)’ and (Т2к)″, (the presence of two relaxation time values for rubber reflects the existence of regions with different densities of molecular arrangement), measured in each component before mixing, do not depend on τex (curves 1-3). The situation changes after the process of swelling. In swelled system three time Т2 values were found. One of them (Т20)с is for oligomer, two others (Т2r)′с and (Т2r)″ are for rubber. These values differ from relevant times of individual components in their absolute values. In spite of the fact that there are no visible changes of system in the exposure period, they are dependent on τe. Since the mobility of oligomeric molecules damps in the presence of rubber, it is natural that (Т20)с<Т20. On the contrary, (Т2r)′с>(Т2r)′ , (Т2r)"с>(Т2r)". This can be explained by the increase of molecular mobility of rubber due to its plasticization by oligomer. These phenomena are expected. But there is another unexpected phenomenon. The characteristic times of individual components nuclear relaxation do not depend on τe before mixing, but after swelling the value Т2 of each component in the mixture changes as the function of τe. At first the value (Т20)с increases 3-4 times at τe rise, then (in 5 days) it returns to the initial value. (Т2к)"с also increases and passes through the slight maximum.
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Figure 2.28. The dependence of lg Т2 (а) and Р (b) on τe for tetramethylene-dimetacrylate (1), cispolyisoprene (2, 3) and cis-polyisoprene swelled in tetramethylene-dimetacrylate (1’ - 3’).
After 12 days of exposition it goes over the limit. Within the same period the proton fraction ratio Р, corresponding to each of three characteristic relaxation time values, is constantly changing. All changes of each parameter of nuclear relaxation as the function of exposure time stop only at τe ≥ 12 days [181]. Similar results were obtained during the study of relaxation characteristics of different polimer-oligomer and oligomer-oligomer systems [90,92,184,185]. Let us discuss only two consequences following from the data shown in Figure 2.28. They are very important for this problem. 1) After reaching the swelling limit (equilibrium swelling system [177]) the structure rearrangement occurs, stipulating the dependence of Т2 and Р on τe. As no chemical reaction is possible during this period, the macroscopic concentration in the system does not change; neither do the other parameters of the system. Hence, we can relate the changes of Т2 and Р to the rearrangement of supramolecular system structure, which occurs during the exposition due to the rearrangement of molecules between the system elements.
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2) On the 10th or 12th day of exposition (τecr) all the curves exceed their limits Т2=f(τe) and Р=f(τe), i.e., the rearrangement processes of supramolecular structure in swell samples for these systems stops. This time period 30-50 times exceeds the equilibrium swelling time (τнcr), which is about 6-8 hours for the systems already studied. This critical time τeкр is assumed as the time of thermodynamic equilibrium at the level of supramolecular system structure. The value τэcr ≈ 12 days, determined using the nuclear relaxation test, agrees with the evaluation of equilibrium time for similar systems, carried out in paper [138, 180] using a test which does not depend on exposure time of kinetic characteristic of consolidation. The equilibrium time may be different for other systems. For example, paper [186] shows that during the study of oligoethylene glycol mixtures (Мw = 200, 400 and 600) with polyvinylpyrrolidone (Мw =1000000) the scientists noticed that the shape of diffusion damping curve is changing with the storage time of a sample (2 – 41 days), but initially the normal logarithmic distribution of self-diffusion coefficient turns into a double exponential one. According to the data [90] for some epoxy systems the equilibrium time, also determined by NMR test, can last several months. The equilibrium process depends on the nature of the component.
Figure 2.29. Dependence of −lgТ2 on τe of oligomer components, taken from summarized nuclear magnetization decay curves, measured for single phase systems of cis-polyisoprene otioxyethylene-α, ω-dimetacrylate (1) and tetramethylene-α, ω-dimetacrylate (3), butadiene-nitrile copolymer with tetramethylene-α, ω-dimetacrylate (2) and cis-polybutadiene with α, ω-dimetacrylate-bis(trioxyethylene)-adipinate (4).
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Figure 2.29 shows the logarithmical dependencies of characteristic times of spin-spin component relaxation Т2 on the exposure time of mixtures from the beginning of τэ measure. They were chosen from the total nuclear magnetization decay curves, measured for the samples of single-phase mixture of cis-polyisoprene with trihyethylene-α, ω-dimethacrylate (curve 1) and tetramethylene-α, ω-dimethacrylate (curve 3), butadiene-nitrile copolymer (rubber “SKN-26”) with tetramethylene-α, ω-dimethacrylate (curve 2) and cis-polybutadiene with α, ω- dimethacrylate-bis-(trihydroxyethylene)-adipinat (curve 4). The value τэ is determined as time from the moment of the sample preparation till the beginning of measurements. The samples, as in the case of dimethylurea-4 + cis-polyisoprene, were obtained by rubber swelling in oligomers till it reaches constant weight. Swelling time for these systems is 4-9 hours at 20-22°C. The initial time τэ is the time when equilibrium swelled samples were taken from the liquid and put into a glass bulb for further testing. The temperatures of swelling, exposition and testing differed from each other by no more than 1°C. The values −lgT2 for all oligomeric samples in “free” state (outside the rubber matrix) were measured in the conditions, which were used for mixture samples. The results ranged from 5.9 to 6.2 and did not depend on τэ. Before analyzing these experimental data, let us return to the model of oligomeric supramolecular structure formation (see Part 2.4). According to one of the consequences of relaxation model (Part 2.4.2), the stationary distribution of aggregate concentration unc can be determined by equation ⎛
unc = F0zc ⎜⎜1 − ⎝
F ⎞ 0zc ⎟ N ⎟⎠
n −1
.
(2.92)
(see (2.68) for the indication of symbols) In case the active molecules split-off from aggregate rate constant q→0 (decay process of aggregates is neutralized), the concentration of active molecules outside the aggregate tends to zero (vc→0), and if F ≈ N 2 , then 0zc M
N2 ⎛ N ⎞ u = 1− nc M ⎜⎝ M ⎟⎠
n −1
.
(2.93)
where N − concentration of all aggregates in the system, irrespective of their size, M − active molecules concentration, including the molecules within the aggregates. On the other hand, if we assume that q≡0 in equations (2.66) – (2.67), obtained in the postulates of relaxation model, then:
v(t ) = v exp(−kNt ), 0
(2.94)
Homogeneous Oligomer Systems ⎧ F ( z, t ) = F ( z)exp ⎪⎨ 0 ⎪ ⎩
v
( z −1) N
0⎡ 1− exp ⎣⎢
( −kNt )
⎫ ⎤ ⎪, ⎦⎥ ⎬ ⎪ ⎭
119
(2.95)
where v0=v(t=0) and F0(z)=F(z,t=0). Al large values t (t>>1/kN) according to equations (2.94) and (2.95) v(t)→0 and we obtain the equation: ⎧ F ( z, ∞) = F ( z)exp ⎪⎨ 0 ⎪ ⎩
( z −1)
⎫ 0⎪ ⎬, N⎪ ⎭
v
(2.96)
Equation (2.96) shows that the asymptotic size distribution of aggregates at q≡0 can be written in the form:
⎛ v ⎜ u (∞) = exp ⎜ − 0 n ⎜ N ⎝
⎞ n −1 u (t = 0) ⎛⎜ v ⎟ 0 n−m ⎟ ∑ ⎜ m! ⎜N ⎟ ⎝ ⎠ m=0
⎞m ⎟ ⎟ . ⎟ ⎠
(2.97)
The comparison of (2.93) and (2.97) shows, that these two distributions are totally different. This, in its turn, means that at small values of the constant of molecules split-off from aggregates q, i.e., when this process stops, the formation kinetics of equilibrium size distribution of aggregates has two stages. First, some quasistationary size distribution of aggregates is rapidly formed. It is formed due to the addition of activated molecules to the existing aggregates in the system. This formation is defined by the initial state of the system. Second, slow rearrangement of molecules between the aggregates takes place, and the system relaxation to equilibrium occurs due to the individual molecules split-off from the aggregates. By estimating this relaxation time of the system due to transformation of equation (2.67) for relaxation model (for more details see [116]), we can obtain function F(z,t) at small values of constant q (q<
z ⎛ π qt ⎜⎜1− z ⎜ ⎝
⎤ v0 ⎥ ⎥ ( z −1) ⎡⎣1 − exp ( −kNt ) ⎤⎦ N ⎥ ze ⎥ ⎞⎥ ⎛ N N ⎞ 1− ⎟⎟ ⎥ π qt ⎜⎜1− z 1− ⎟⎟ M ⎟⎠ ⎥ ⎜ M ⎟⎠ ⎝ ⎦⎥
⎞2 ⎟ t ⎟ ⎠
⎡ ⎛ N ⎢ ⎢ −q ⎜⎜ ⎢ ⎝M exp ⎢ ⎞ ⎛ ⎢ N N ⎢ 2⎜ 1− + 1− ⎟⎟ ⎢ ⎜⎜ M ⎟⎠ 2M ⎝ ⎢⎣
⎤⎫ ⎥⎪ ⎥⎪ ⎥ ⎪⎪ ⎥⎬ ⎞ ⎥⎪ N 1− ⎟⎟ ⎥ ⎪ M ⎟⎠ ⎥ ⎪ ⎥⎦ ⎪ ⎭
⎞2 ⎟ t ⎟ ⎠
.
(2.98) +
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
According to equation (2.98) if there is a strong inequality between direct rate constants k (addition of individual activated molecules to aggregates) and inverse rate constants q (molecules split-off from aggregates) q<
τ1 = 1 ,
(2.99)
kN
and it is described by equation (2.95). All the available activated molecules are added to aggregates at this stage. Quasistationary size distribution of aggregates is formed due to the initial system state. The time of the second stage is ⎛
τ 2 = 4 ⎜⎜ M q⎝ N
⎞2 ⎟ , ⎟ ⎠
(2.100)
During this time, the existing distribution relaxes to the stationary distribution (due to the rearrangement of split-off individual molecules between aggregates). This distribution depends neither on the initial nor on the intermediate state of the system. At this stage the dependence F(z,t) is described by correlation (2.98). There is one important feature of the process studied following from equation (2.100). The characteristic relaxation time to equilibrium is significant in such systems. It is related to the factor (M/N)2 in the equation for characteristic relaxation time τ2, but not to a small value of constant q (the numerical value q may increase at large value M). If the processes and sizes of aggregate formation are essential in oligomeric systems, the dependence of squared relationship τ2 on average size of associate, which is the ratio of M/N, results in anomalous increase of characteristic relaxation time to equilibrium of the system. Let us consider the experimental data and compare them with the theoretical information, given above. Figure 2.29 shows that parameter −lgT2 has a complicated dependence on τэ. Each of the curves, presented in the figure, is characterized by four parts. These parts reflect different formation stages of equilibrium supramolecular structure. It is necessary to note that the values T2 of oligomeric components in mixed systems, measured at the moment τэ=0, are considerably lower than the similar time values T2 , measured for the same oligomers in “free” state. It is natural for the oligomeric molecules over the molecules of rubber to have a reduced rotational motion [139,184]. At first the mixed systems show rapid decrease of the values T2 at τex>0 (the increase of the value −lgT2). It corresponds to the aggregate growth owing to the addition of the activated molecules to them (addition intensity is higher than split-off intensity). At this stage the number of possible contacts “rubber – oligomer” decreases but the number of contacts “oligomer – oligomer” increases. This results in the increase of molecular activity of oligomers. The values τ1 (process time) and T2 (absolute value of modification) are determined by the nature of mixture component. For the systems studied the value τ1 is in the range of 1−2 days.
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121
There are two types of dependences according to the nature of mixture components at the maximum value −lgT2 (maximum molecule activity of oligomer, corresponding to quasistationary state of supramolecular structure). In some cases (see curves 1 and 2) the value −lgT2 does not change for 5 days, and then the value −lgT2 decreases to the constant value −lgT2с, which does not change for 90 days. In another cases (see curves 3 and 4) the value −lgT2 starts to decrease at the maximum point. Obviously, the quasi-stationary state period of these systems is little due to their properties. In the model described above the relaxation period from T2 to T2с reflects the stage, where a significant molecules split-off and their rearrangement between the aggregates take place. This process completes after 6-7 days for the system shown in Figure 2.29 and the value T2 stops changing. If the value T2 is constant (as the function of exposure time), the system is in the equilibrium state. In order to estimate the relaxation time τ2 of the T2 value to the stationary T2с value, the functions of −lg(T2 −T2с) on τэ were calculated. Relaxation time to system equilibrium τ2 was determined by the tilt coefficient on the linear parts of the curves shown in Figure 2.29. The result of “straightening” has shown that relaxation time was approximately the same for all mixtures. It was about 2 days (the difference was no more than 1 %). Therefore, the time, during which T2 reaches its stationary value, equals approximately 2 ⋅ ln10≈6,5 days (see. Figure 2.30).
Figure 2.30. Dependence of -lg (Т2 –Т2С) on τэ. Curve pieces on the Figure 2.29, corresponding to relaxation time T2, are rectified. (Relaxation time τ2 ≈ 1,9 day.) Same markings as on Figure 2.29.
The comparison of the experimental results given above with the results of the relaxation model shows that the long relaxation to equilibrium may be caused by the following problems. At the first stage, when the energy stops affecting the system, which has to do with the test preparation of the sample, the number of free activated molecules is large. Therefore, the addition of activated molecules to the aggregates prevails over their split-off (there is a growth of aggregates average size and, therefore, the Т2 value increases). At the same time,
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
some (“quasistationary”) size distribution of aggregates occurs (Т2 at the maximum point), determined by the initial state of the system. But this state significantly differs from the equilibrium. At the second stage of the system evolution to equilibrium, when the amount of free activated molecules decreases due to their addition to aggregates, and the molecules addition and split-off processes become comparable, the existing “quasistationary” distribution starts relaxing to equilibrium (Т2 is decreasing). In contrast to the first stage, where the system evolution is purposeful (activated molecules are added to aggregates), the second stage is characterized by a number of random acts of “split-off” and “addition”. The number of these acts is determined by the average size of aggregates. The equilibrium time (Т2 does not depend on τэ) is defined by the amount of all possible options. The larger the average size of aggregates in the quasistationary state is, the higher is the equilibrium time. As the average aggregate size value M/N is usually large for liquids, inclined to aggregate formation, the presence of quadratic factor proves the abnormally high value of relaxation time to equilibrium in such systems. The average size of aggregates in equilibrium state can be estimated using (2.99) and (2.100). The experiment shows that τ2 /τ1 ∝5 (see Figure 2.29). Since the addition rate of oligomeric molecules to aggregates significantly exceeds the rate of their split-off, which is confirmed by the function nonmonotony of T2 to τэ, the p/kN ∝ 5. Hence, the average size of aggregates for the systems studied in equilibrium equals at least 5 oligomeric molecules. This estimation agrees well with the result of independent calculation [187] based on the electron microscopic research.
2.8. SUPRAMOLECULAR STRUCTURE OF OLIGOMERS AND SOME EXPERIMENTAL “ANOMALIES” OF THEIR MACROSCOPIC PROPERTIES The term “anomaly” is used in inverted commas in the title of this part because it represents the unusual phenomena for the oligomeric systems which occur during the experiment. It can not be explained by the traditional theories for low molecular and high molecular weight compounds. But due to the specific structure formation of oligomeric systems, they, in some cases, find their interpretation, which does not contradict the fundamental laws of chemical physics. Therefore, these observations turn these phenomena from anomalous to natural.
2.8.1. Curing Kinetics of Oligomers in its Initial Stage The curing of reactive oligomers is a very complicated process. After the first interactions due to chemical reactions, the changes of molecular structure as well as the system structure parameters at all levels take place. This affects the kinetic constants of the following formation stages of solid polymeric body (see [72,88,89,139,182,188-191]). The analysis of this process is outside the scope of the monograph.
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123
This part operates with the initial polymerization rate W0, assuming that this kinetic parameter of curing is a structurally sensible test for the system comparison with its initial (liquid) state.
Anisotropy in Local Orders Theoretical investigations in the late XXth – early XXIst centuries (see Part 2.2.1 - 2.2.4), showed that there were no principal bans on the formation of microstructures with regular space arrangement of molecules in oligomeric liquids. Furthermore, this structural organization is more typical of oligomers than of monomers or polymers. These theoretical assumptions appeared much later than the experimental data, which were interpreted on the basis of oligomers complex supramolecular structure with separate “microphases” (a wrong term). Scientists tried to explain these phenomena intuitively by different local microstructures of oligomers. This explains the skepticism in relation to aggregative structure of oligomeric systems and to associate cybotactic groupings model, in particular, although the concept of associates, clusters, cybotactic groupings and other subsystems existence has become canonic in the literature on low molecular weight organic and metal liquids, polymer solutions and melts (see [77,80,82,85,87]). Some experimental facts, which can only be explained by the aggregative model of oligomeric systems, will be given below. Background of Problem The problems of internal structure of oligomeric liquids supramolecular formation and anisotropic molecular arrangement inside the aggregates arose in 1960s because of the anomalies found for initial curing velocity Wо of some oligoester acrylates [154,192]. It proved impossible to explain the whole complex of unsaturated oligomers experimental polymerization kinetics using the theory of ordinary chaotic associates’ presence in the reactive liquid, namely, the presence of local microstructures with the increased functional groups concentration in the system. Thus, some new assumptions appeared. One of them involved the possibility of anisotropic arrangement of reactive molecules inside the fluctuations of the liquid system concentration. The scientists used this theory to explain the abnormally high values of the growth velocity constants for polymer chain Kр during the chain initiated polymerization of α,ωdimethyl acrylate-n-tetramethyl glycol type anisometric oligomers at polymerization depth D → 0. These constants were much higher than the Kр values for monomer methyl meta acrylate. A.A. Berlin and G.V. Korolev [154] supposed that liquid oligomers possessed some supramolecular aggregates (“kinetically preferred products”), the spatial orientation of molecules in which was not chaotic but anisotropic. The arrangement of molecules in these aggregates makes the double bonds of methyl acrylic groups aligned in a kinetically preferred order (see Figure 2.31). If the τр lifetime of these unstable products (in our terminology, cybotactic groupings) is comparable to or exceeds the lifetime of an elementary act of chemical reaction τх (the lifetime of the active center or the transition state), then due to the increase of the pre-exponential multiplier in the expression for Kр, the τр lifetime should provide an increase of the Wо value in comparison with the “normal” (determined by the methyl acrylate bond reactivity in the polymerization process of methyl meta acrylate) polymerization velocity.
124
S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev CH2 X C C
O
O
C
O
X C
C
O
C
X
X C
C
O
C
C
X
CH2
C
X C CH2
O
C C
O
O C
CH2
X
O
O O
X C CH2
CH2
CH2
O
O O
X C CH2
C O
O O
CH2 X C
O
O C
CH2 X C
O
O C
O
O
X C CH2
CH2
Figure 2.31. Schematic presentation of Cybotaxis ↔ associate transition in oligodimetacrylate Х=Н, СН3.
This idea about the important role of supramolecular aggregates, the molecules of which are arranged in one direction, for the liquid systems polymerization, was “in the air”, and different authors described it in their papers (substrate layer, smectic structures [193-198]). In 1957 N.N. Semenov [194] was the first to prove that chain processes were dependent on ordered structure. He tried to explain the abrupt increase of polymerization velocity of crystallizing monomers, which was only observed under temperature decrease in a very narrow range of temperatures close to the phase change. It seemed impossible at that time. Later on, numerous indirect confirmations of the hypothesis about the existence of regions with spatial molecular arrangement in oligomer liquids, were obtained. In addition to the analysis of early works [72, 146, 191], allowing us to formulate and prove the hypothesis about anisotropy of molecules inside the aggregates of liquid oligoester acrylates, we will study only one experimental result, which was not analyzed in the above mentioned papers. Associative cybotactic grouping model was used to explain this result.
Anisotropy of Local Orders as the Factor Defining Initial Cure Velocity of Reactive Oligomeric Systems The initial stage of tetramethylene-α,ω-dimethyl acrylate (MB) monophase solutions polymerization was analyzed in papers [189,199]. The characteristic viscosity of tetramethylene-α,ω-dimethyl acrylate η ≈ 5 centipoise. Polymerization was carried out in nonreactive oligomers with different viscosity: in bis-(di-oxyethylenephthalate)-α,ω-diisobutyrate (IDF), (η ≈ 1000 centipoise); in trioxyethylene-α,ω-di-isobutyrate (TGI) (η ≈ 10 centipoise) and in full saturated analogue of tetramethylene-α,ω-dimethyl acrylate, tetramethylene-α,ω- di-isobutyrate (IB), (η ≈ 5 centipoise). The obtained results were compared with polymerization kinetics of methyl meta acrylate, dissolved in the same nonreactive oligomers. Figure 2.32 shows the dependences of polymerization velocity of MB, extrapolated to zero (initial) time, Wо on the weight fraction of MB in these solutions ϕ1. In this case polymerization velocity is normalized to the concentration of methyl acrylic groups in the solution. The data for methyl meta acrylate (MMA) polymerization in the mixture with IB are shown in the same figure (only ϕ1 is a fraction of MMA) (in the mixture with TGI and IDF we can see a similar dependence). There is a maximum in the region of higher concentration of oligoester acrylate for the solutions of MB in a high-viscous solvent on the curve Wо = f (ϕ1) (curve 1). The maximum of velocity gradually decreases (curve 2) with the viscosity
Homogeneous Oligomer Systems
125
decrease of nonreactive solvent. The maximum for the mixture components with close values of characteristic viscosity Wо decreases as soon as the fraction of nonreactive analogue starts to increase (curve 3). There is no dependence on concentration for the solutions of methyl meta acrylate Wо (curve 4).
Figure 2.32. Dependence of ω0 on ϕ1 for mixtures MB with IDP (1), TGI (2), IB (3) and methylmetacrylate – IB mixture (4).
Why does the addition of an “ideal” dilutant (IB does not differ from MB in chemical structure, the double bond is only substituted for saturated) or a gellatant (the MB and IDF viscosities differ by more than two decimal exponents) to reactive oligomer result in a decrease or an increase of the Wо value, correspondingly? The explanation of this experimental phenomenon in the framework of the classical “gel effect” (viscosity growth results in kinetic chain interruption velocity constant decrease and, therefore, in Wо increase) describes only one part of curve 3 (Figure 2.32), namely, the increase of Wо when a more viscous IDF is added to MB. But it can not explain the further velocity decrease during the gellation of the reactive system. Other widely used physical assumptions [200-204] in chemical kinetics can neither give a reasonable explanation of the whole complex of discovered effects. Some of these physical theories will be discussed below. As the values of Wо, used in works [189,199], are normalized (they refer to the total quantity of reactive groups in the system) and, therefore, in trivial kinetic sense they can not depend on concentration of MB in solution, the behavior of curves 1-3 (Figure 2.32) should be the same as the behavior of monomeric methyl meta acrylate curve 4. Nevertheless (see Figure 2.32), the experiment shows a complex dependence of Wо on ϕ1 for solutions of anisometric telechelate oligomers, which is impossible within the traditional theories. The above described data, however, can be explained by the cybotactic groupings model of oligomeric liquid.
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If we assume that an oligomer system is characterized by several types of distribution, namely, by number, size and lifetime of cybotactic groupings [189,199], and if we assume that Wо increases with the growth of the cybotactic groupings number (“kinetically preferred products”), with the increase of their lifetime and the number of reactive molecules in one cybotactic grouping (i.e., its size) [146,188,199], then the regularities described above can be explained in the following way. The initial growth of Wо in thickened systems in comparison with Wо for “clear” MB, results from the increase of number and lifetime of cybotactic groupings, which occurs when high-viscous components are added. This corresponds to the idea described in works [146,188,200]. The decrease of Wо, which is observed in the systems with components of the same viscosities, is the result of “infusing” a nonreactive component into the structure of the “kinetically preferred order” of reactive oligomer without any thermodynamic limitations (see Figure 2.33). It is obvious that even if the structural parameters of the B type cybotactic groupings in mixed system do not differ from the characteristics of the A type cybotactic groupings, formed only from the molecules of oligoester acrylate, the number of chemical interaction elementary acts at the initial reference time in the B type cybotactic groupings will be less than the same number in the A type and, therefore, the Wо value will decrease.
Figure 2.33. Schematic presentation of cybotaxises consisting of oligoesteracrylate molecules (а) and its saturated analogue (b) of analogue
- the molecule of oligoesteracrylate,
- the molecule
For the mixed systems (Figure 2.33), the Wо velocity decrease cannot be directly proportional to the dilutant concentration. Furthermore, at equimolar ratio of reactive and nonreactive molecules in the solution, the supramolecular structures do not influence the polymerization processes. This fact occurs due to the pair-wise interaction of two methyl acrylate groups and one-methyl acrylate and isobutyrate group inside the cybotactic groupings. Hence, the laws of classical kinetics must operate in this range of concentrations. As we can see from the experiment (Figure 2.32, curve 3), at ϕ1 ≈ 0.5 the velocity does not depend on ϕ1. The fact that the experiment for the system with high viscosity of the nonreactive component shows an extremum on the curve, Wо=f(ϕ1) is explained by competition between the positive influence of the second component (thickener) on polymerization (the number of cybotactic groupings with the lifetime comparable to the elementary acts time increases) and its negative influence (the “addition” of nonactive molecules to the structures with kinetically preferred order results in the decrease of the elementary acts number). It is natural that at small dosages of the thickener the first factor prevails over the second one, while at large dosages of the thickener the second factor is predominant.
Homogeneous Oligomer Systems
127
All these conclusions were confirmed in the latest works [205,206], where a similar experiment was used for different objects. The above described statements are confirmed by theory. The authors of works [207,208] established the concept of constant velocity spectrum of elementary chemical reactions, which is due to the different levels of reciprocal arrangement of reactive molecules. This concept is used for the description of chemical processes in liquid condensed systems within the polychronic kinetics model [209,210]. The level of structural organization is characterized by the orientation order parameter α, similar in its physical sense to orientation interaction coefficient ε, which was used by the authors of works referred to in Part 2.6.4. Parameter α can vary from 0 (isotropic system) to 1 (maximum anisotropy, the molecules are parallel). According to these postulates the kinetics of biomolecular reaction can be described as dC(t)/dt = Keff(α) C2(t)
(2.101)
where C(t) – is the function of the reagent current concentration. In the linear approximation Keff(α)= Keff(0)+dKeff(0)/dα(1-α) = k1α + k2(1-α)
(2.102
where k1 and k2 are the velocity constants of chemical reactions in ordered and disordered subsystems, correspondingly. The evolution of the order parameter can be presented as dα/dt = WTh(α) + WCh(C,α)
(2.103)
The WTh(α) function defines the change of the system order in the absence of chemical reactions, and the WCh (C,α) function defines the change of the system order during conversion. For the problem studied, the WTh(α) function [222] is the most interesting one. It is presented in the form WTh(α) = -(α – αTh) fTh(α) = - k3(α – αTh) ,
(2.104)
where αTh is the value of the order parameter corresponding to the state of thermodynamic equilibrium. The last correlation in (2.104) occurs when fTh(αTh) = const. In general, αTh → 1 or αTh → 0, in other words, on the way to system equilibrium, both self-organization and disordering of molecules occur. Thus, from works [207,208] it follows that scientists use only one essential approximation where kinetic constant spectrum of chemical reaction does not self-average as it does in classical gas kinetics. Due to the long structure relaxation times in condensed matter, it is presented as the distribution function of orientation order parameter of reactant molecules. Hence, the rate of chemical reaction must depend on this distribution function, both in equilibrium state and on the way to equilibrium. In particular, this means that the initial rate of the chemical reaction should depend on the number of reactant molecules which
128
S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev
have formed supramolecular structures with “kinetically preferred orders”, or on the share of associates which have relaxed into cybotactic groupings. It is necessary to point out that the oligomer ability to form aggregates with “kinetically preferred orders” depends not only on the length of molecular chains, nature of its surroundings, and system conditions but also on the molecular structure of the oligomer chain. Even minor changes of molecular structure of oligomer can eliminate (complicate) the formation of cybotactic groupings. The works referred to above [205,206] show that “abnormal” growth of initial polymerization velocity which occurs in methyl acrylic systems, does not take place at the same conditions in acrylic systems.
Initial Curing Velocity as Thermodynamic Equilibration Test in Oligomer Systems Figure 2.34 (here, α is conversion degree or level, unlike the previous paragraph) shows the polymerization kinetic curves for tetramethylene -α,ω-dimethyl acrylate (4-DMM) and cis-polyisoprene mixtures [180]. The kinetic curves of polymerization were obtained by calorimetric method at variations of the τex values. The test samples were prepared by rubber film swelling in oligoester acrylate till it reached its maximum weight; it took no more than 8 hours under ambient temperature [181] (see the Part 2.92). After that the samples were taken out of the liquid and the swollen films were left in contact with air, the τex values being fixed. During the storage no chemical or any other visible modifications occurred: neither weight nor volume changes. The oligomer perspiration onto the film surface was not registered.
Figure 2.34. Kinetic polymerization curves of tetramethylene-dimetacrylate in a matrix of cispolyisoprene at various values of τex (I-IV) and τin: 8 (1), 24 (2), 48 (3) and 240 (5) hour. Blackened markings show samples after secondary swelling. Explanation is provided in the text, see table 2.5.
Figure 2.34 shows the results of the curing kinetics of three sample series (see Table 2.5): A. At τн=Const, the value of τex varied from 0 minute to 90 days; B. The τin swelling time varied from 8 to 240 hours; C. The swollen samples (τincr =8 hours), stored for 240 hours in the air, were put into contact with 4-DMM for the second time. After 8 hours in oligomer, the
Homogeneous Oligomer Systems
129
film weight did not change; the films were taken out of the liquid and the procedure was repeated, as in the A and B series. Table 2.5. Samples of cis-polyisoprene tetramethylene dimethyl acrylate system obtained by the primary and secondary swelling The type of the sample
А
The mark in the figure
1
2 B
3 4
C
5
τin, hour
τex, day
The curve number
τin, hour
τex, day
The curve number
The primary swelling
The secondary swelling
8
0
I
-
-
-
8
1
II
-
-
-
8
5
III
-
-
-
8 8 24
10 90 0
IV IV I
-
-
-
24
10
IV
-
-
-
48
1
II
-
-
-
48
5
III
-
-
-
240 240 8
0 10 10
I IV -
8
0
I
8 8
10 10
-
8 8
1 10
II IV
The analysis of the given data in the figure shows: 1) The increase of τin > 8 hours does not influence the curing kinetics at τex=Const, that is, if the concept of the W0 relation to the structural order in liquid phase [137,179,191] is true, the changes within the swelling period τin > τincr = 8 hours in the supramolecular structure of the system do not happen and even if they do, they happen outside the response limit of the given testing technique. 2) The primary oligomer polymerization velocity increases with the increase of τin within the τin = 0-10 days interval. At a certain critical time of exposure τexcr, which in this case equals 10 days, any further increase of τex does not influence the thickening kinetics. In other words, the supramolecular structure transformation, which the kinetics of chemical transfer is sensitive to at initial time, occurs during the sample storage period and finishes at τex= τexcr. This time is considered to be the system relaxation time to thermodynamic equilibrium at the supramolecular level of structure organization. 3) After the second contact with oligomer (samples of the C series), the swollen films, which were first exposed to oligomer under τex ≥ τexcr, “forget” about their kinetic stability and their behavior is kinetically similar to the behavior of the samples after
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev the primary swelling, that is, once again, they show the polymerization rate constant dependence on τex. In other words, the change in the supramolecular structure, which takes place at τex, is reversible: the supramolecular system structure reverts (to its initial state) after the second contact with oligomer.
Therefore, the spontaneous formation of the equilibrium supramolecular system structure, which provides its kinetic curing stability, and does not depend on the prehistory of the sample, occurs after the completion of swelling, within the exposure period 0<τex≤τexcr and in the absence of the swollen film contact with the liquid phase. During this period, local molecule concentration redistribution and spontaneous supramolecular structure elements formation (cybotactic groupings and associates) occur in the macroscopic sample volume. The characteristics of these elements (lifetime, correlation radius, strength of physical bonds) differ from the similar indices or coefficients in the initial oligomer and in the polymeroligomer film, which is in contact with liquid. What are the driving forces, which activate this drastic system structure transformation within the τex period, without any visible thermodynamic reasons? Indeed, if concentration averaging according to macroscopic volume is diffusive at the swelling stage due to minimization of the internal energy of the mixture [70,177], then in the systems, swollen up to their constant weight, the chemical potential gradient within the range of experimental measurement error tends to zero [211,212]. Since macroscopic state parameters (temperature, concentration, pressure) are permanent during the exposure, the thermodynamic nature of supramolecular structure transformation, and the very fact of transformation itself can be argued. To resolve these doubts, let us consider several versions. The first version (see equations (2.101) – ( 2.104)), shows that the dC(t)/dt value (if t→0 it is identical to W0) depends on the α order parameter in the relative molecule order (reaction centers); distribution function WTh(α) changes in the process of reaching thermodynamic equilibrium. Therefore, W0 should depend on the thermodynamic equilibrium achievement time, that is, on τex. According to the second version [146] it is assumed that anisotropic structures with oligomer molecules arrangement in a strictly defined order are formed (according to our terminology there is a transfer of associates to cybotactic groupings) as the result of chaotic disorder due to the strong bonds formation between molecule interaction centers (MIC) of different oligomer molecules in the local microvolumes of concentration fluctuations. The more interaction centers a molecule has, the more possible is the process. In this case, entropy loss (transfer from disorder into order) is compensated by energy gain (strong intermolecular bonds formation). This consideration is supported by thermodynamic data [140,170] showing that entropy and enthalpy components redistribution in oligomer systems of free energy and cancellation of combinatorial and noncombinatorial fraction of total entropy were proven experimentally, and, on the other hand, the coefficient of molecular packing (CMP) is higher in the liquid oligomers than in the low-molecular liquids. For example, CMP=0.639-0.702 [72] for oligoester acrylate, while for the ordinary liquids the maximum value CMP=0.58 [213]. If we accept that the transfer process from associates to cybotactic groupings runs during a certain time period, the version about strong intermolecular bond formation stimulating the order occurrence turns to be true. Though, it does not explain the duration motives of this transfer. Neither it is clear why strong intermolecular interactions appear only
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after the change of the storage conditions of the caotchouc-oligomer system, i.e. why equilibrium is broken only after caotchouc-oligomer film has been taken out of the liquid. The third version gives explanation of the last fact. In [180] it was assumed that the driving force of the spontaneous supramolecular structure transformation is the disturbance caused by fact that the interaction of molecular forces is not compensated at the surface layer, and as the result, the concentration profile changes. Qualitative interpretation of this idea is as follows. A system, where the swelling limit has been reached, is considered to have two phases. The first phase is a swollen film (oligomer solution in rubber), and the second phase is a very diluted solution of cispolyisoprene in oligomer (during the swelling process up to 0.1-0.3%, cis-polyisoprene molecules are dissolved in oligoester acrylate [139]). This very macroscopic system, where the film contacts with the liquid and the phase boundary is penetrable for non-gradient component migration, should be considered an equilibrium system. After the swollen film is taken out of oligomer and the remains of the liquid are removed from its surface, thermodynamic equilibrium is disturbed, as the “film-liquid” contact is substituted by the “film-gas (air)” contact. The system starts relaxation to a new equilibrium state. It is natural that the surface tensions at the “film-liquid” and “film-gas” boundaries are different. Therefore [86], local concentrations and molecular orientation rates should be different on the surface layers and inside the volume. That is why as soon as the film is taken out of the liquid, the earlier established equilibrium is disturbed, and a new equilibrium has to be formed with its own concentration profile. Note that the concentration profile formation itself, i.e., the occurrence of the differences in the concentration values on the surface layers and in the volume, could not influence the experimentally determined constant values of oligoester acrylate polymerization (in the experiment, W0 is normalized to general oligomer concentration), but it causes a change of anisotropy degree in the newly formed elements of supramolecular structure. Started at the surface layers, supramolecular structure rearrangement spreads into the system volume. The process of associate and cybotactic groupings number and size averaging is comparatively slow due to the high medium viscosity. It is characterized by the τex cr time. If the swollen film which was kept in the open air for τex ≥ τexcr (i.e., when equilibrium supramolecular structure has already been formed), gets into contact with oligomer again, in other words, if the component migration phase boundary is open, then the previous supramolecular organization, “status quo”, will be reconstructed. Apparently, it is reversibility that determines the identity of the sample curing kinetics of the B and C series (Figure 2.34). This scenario is supported in a number of works on phase equilibrium problems near the phase boundary (see reviews [214-218] and references in them). These works, using a large number of different objects (magnets, low molecular weight liquids, solutions and polymer mixtures) as the examples, prove that the structural reconstructions in the volume are related to the processes near the phase boundary in a very complex way. Sometimes this relation results in the formation of anisotropic structures in the volume [217,218]. Out of the whole variety of theoretical and experimental results in this field, let us consider the numerical dependences of dispersion concentration as the function of the distance from the surface, obtained in the scaling approximation by de-Zhen [32]. When studying the behavior of the semidiluted solution in contact with the impenetrable wall, he showed that
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S.M. Mezhikovskii, A.E. Arinstein and R. Ya. Deberdeev F1 ≈ F9/4,
(2.105) m
F (z)= Ff(x ),
(2.106)
where F1 is the concentration in the first layer, F is the volume concentration, F(z) is the concentration at the z distance from the wall, х=z/ξ, if the layer thickness is ξ. If х >1, then m=1. But if х<1, then=3/5. The power function of the profile concentration becomes more complex, when the long distance Van der Waals forces are taken into consideration, different for different components. In general case, according to Edwards [225], the exponent of power for F in equation (2.105) can take the values which are either higher or lower than 1. In supplement to experiments, given in paper [180] and confirmed later in papers [90, 92, 183-186], this means that the supramolecular structure reorganization during the τex period, should result in the increase of the system order degree for some cases, while for the other cases it results in the system disorder. This fact corresponds to the theory [208], which studies anisotropy dynamics of molecules in condensed medium. If this is true, the supramolecular structure disorder (decrease of the cybotactic groupings anisotropy degree, or reduction of the cybotactic groupings number or size, which is equal to the reduction of anisotropic molecules number in a single cybotactic grouping) should result in the decrease of the W0 value, while the supramolecular structure order increase should result in the growth of this value. The experiment has confirmed this result [138]. Generally, the causes which determine the dependence of the curing process kinetic parameters on the exposition time (exposure) τэ, can be related to either structural characteristics of the reactive systems mentioned above (the time period to reach equilibrium during the formation of elements of “kinetically preferred or non-preferred degrees”), or to kinetic effects themselves, i.e., the processes of polymerization initiator redistribution in the system volume or changes during the storage of inhibitor and admixtures concentration samples, which might activate or deactivate polymerization (peroxides, accumulated during the storage [8], oxygen, absorbed by the system [146]) and etc. Paper [219] shows that during the study of high-temperature curing kinetics of trihydroxyethylene-dimethyl acrylate in the presence of 0.5% dicumyl peroxide (DCP) and 0.007% inhibitor residual (hydroquinone) it was found out (Figure 2.35a) that the value of the τind induction time of polymerization is about 20-30 min at τex = 0, while with the increase of the exposure time it decreases and reaches zero at τex ≥ 5 days. This effect was considered in [219] as a slow “eating away” of inhibitor due to its interaction with the initiator decomposition products, which appear during the τex period. The following facts were given to confirm this conclusion. First, the value of W0 naturally increases with the increase of τex, second, both at τex =0, and at τex = 5 days W0 is proportional to the first degree of initiator concentration (Figure 2.35b), third, during thermal initiation in the absence of DCP, τind increases up to 2-3 hours and practically does not depend on τex in the range of 0 < τex < 20 day.
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Figure 2.35. Kinetic curves (а) and the dependence of initial polymerization rate W0 on the concentration of initiator “PDK” (b) during block polymerization of trioxyethylene-dimetacrylate at 110 0С and exposition times τe = 0 (1), 5 (2) and 20 day. (3) and hydroquinone content 0,007%.
The role of kinetic factors is very important, moreover, in certain cases it is prioritized for the explanation of some specific characteristics of oligomer curing. If, however, we take only these positions, many other experimental observations of oligomer systems curing kinetics remain disputable. For example, paper [138] proves that while the value of W0 increases with the increase of τex (Figure 2.36) in some systems, it decreases in other systems (Figure 2.37). If we accept, as they did in paper [219], that for the polyisoprene rubber - oligoester acrylate system under the study the growth of the W0 value with the increase of τex, (2.106) is the consequence of the inhibitor concentration decrease during exposition, or if we accept another “kinetic” version where this effect is the result of gradual peroxide compounds accumulation in these samples during the storage (experiment in [219] did not reject it), then the reasons for the W0 value decrease in similar experiments with butadiene-nitrile rubber - oligoester acrylate mixtures (2.107), would still remain unknown. If, on the contrary, we assume that the decrease of the W0 value as the function of τex for the latter system is related to oxygen accumulation during the storage period (which should have resulted in the decrease of the initial curing velocity [220]), this assumption would contradict the above mentioned increase of the W0 value for another cautchouc - oligomer system where oxygen dilution is also possible. When searching for the differences in oxygen sorption processes by isoprene and nitrile rubbers, and in the oxidation mechanisms of these rubbers, no serious arguments to prove the possibility of inverse dependencies W0 = f(τex) during oligoester acrylate curing in their matrices were found [221,222]. Other hypothetical explanations of the results given in [138] and based on the classical principles of kinetic effects [201-204,223] are also contradictory.
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Figure 2.36. The dependence of W0 on τe for a system formed by cis-polyisoprene – tetramethylenedimetacrylate during curing at 800С, the concentration of initiator “PDK” is 0,5% and oligomer content is 10 (1), 26 (2), 36 (3) and 50% (4).
Figure 2.37. Dependence of W0 on τe for a system formed by polybutadiene-nitrile rubber ("SKN-26”) tetramethylene-dimetacrylate during curing at 800С, the concentration of initiator “PDK” is 0,5% and oligomer content is 70 (1), 60 (2), 50 (3) and 30% (4). Synthesis of samples: 1-3 – from joint solutions, 4 –from solutions (I) and through swelling (II).
Since the methods (mechanical mixing, swelling, common solutions) and the order (into oligomer, into cautchouc, into mixture) of the initiator introduction described in the experiments studied did not influence the kinetic curves of curing in both systems and the
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τexcr values (because both systems were thoroughly purified of inhibitors), and no chemical transformations occurred in the systems during the storage period, it is natural to suppose that the most possible reason for the existence of the dependence of curing kinetics on the time history is the change in the structural organization of the system during the 0 < τex < τexcr period, while the differences in the W0=f(τex) function character for the above described systems are conditioned by the contrary trends in their supramolecular structure parameters changes. According to the theoretical and experimental rules of thermodynamically equilibrium structure formation in oligomeric systems (see Parts 2.4 and 2.7), we can assume that an equilibrium structure is formed stage by stage: the concentration of components gets to be average (at the molecular level), the associates and cybotactic groupings composition gets to be average (at the supramolecular and topological levels), and the morphological parameters become average (at the colloidal level). The last stage will be studied separately. The influence of the oligomer systems time history on the curing kinetics at the molecular transformations level (e.g., concentration dependences of the initial polymerization velocities in monophase systems at different τex values ), can be analyzed using the classical kinetics methodology and terminology [201,202,223]. However, in order to understand a number of uncommon experimental observations it is necessary to have their descriptions, taking into account the influence of the initial system evolution at the supramolecular and phase configuration levels of the structure. Within the relaxation model of the associate and cybotactic grouping structure of oligomer liquids [116,117,224], the velocity of relaxation to equilibrium is determined by correlation of velocity constants for separate (single) oligomer molecules addition to and split-off from supramolecular aggregates, while the equilibrium functions of distribution according to the supramolecular structure elements number and size are determined by the parameters and nature of the medium in which relaxation occurs. In supplement to the experiments presented above this may mean that depending on the polarity of the medium (relationships between the components), the supramolecular structure reorganization during the 0 < τex < τexcr period, which, in the long run, results in the equilibrium distribution function of associates and cybotactic groupings according to their number, size and lifetime, in some cases can be followed by the increase of the system order degree, while for the other cases it results in the system disorder. Naturally, the films of butadiene-nitrile rubber, swollen in tetramethylene-dimethyl acrylate, possess better thermodynamic affinity of components (χ=0.012) than the cis-polyisoprene films, swollen in the same oligomer (χ=0.136); therefore, the initial polymerization velocity of the first group films decreases as the function of τex, whereas the initial polymerization velocity of the second group films increases. This is the consequence of the fact that the random function of the aggregates distribution after the swelling (quasi-equilibrium situation – see Part 2.7.1), can behave differently for different systems during the τex period. In case of the low affinity of the unlike components, the dominant trend during the τex period is considered to be similar molecules segregation (aggregates formation), while in the opposite case, the dominant trend is molecular dispersion (aggregate destruction). In other words, when polar oligoester acrylate is dissolved in polar nitrile cautchouc, molecular dispersion is observed, and, therefore, on the way to equilibrium, supramolecular aggregates are partially destroyed in these solutions, i.e., the level of the structure self-organization decreases in the long run. The disorder of the
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supramolecular structure (decrease in the number of aggregates, decrease of the cybotactic groupings anisotropy level or decrease in the number of cybotactic groupings or their sizes, this equals the decrease of the number of anisotropic molecules in a single cybotactic grouping) should result in the decrease of the W0 value [72,88,191]. That is why the W0 function on τex is decreasing in this system. At the same time, the mixtures of oligoester acrylate with non-polar cis-polyisoprene rubber are characterized by segregation of oligomer molecules (aggregates size increase, anisotropy level increase), and, therefore, an increase of the W0 value during the 0 < τex < τexcr period. According to theories [208] and [225], the values of the α order parameters in the process of reaching the αTh value corresponding to the system thermodynamic equilibrium state (see equation (2.104)), as well as the exponents of power for the concentration gradient (see equations (2.105) and (2.106)) can either increase or decrease. Thus, this study shows that the kinetic curing constant is independent from the preliminary exposure time. This is the consequence of thermodynamic equilibrium in the system at all the structural organization levels. The above given considerations were proven by the direct examination of the relaxation kinetics in different oligomer systems, carried out by the impulse NMR method (Part 2.7.1). Moreover, they were proven during the study of oligomer macroscopic characteristics by different physical methods such as IR spectroscopy [183], viscosity measurements [226-228] and etc. [214,215,229].
2.8.2. Rheological Properties of Oligomeric Systems Oligomers in the single-phase state show the same varieties of behavior as homogeneous high-viscous polymer liquids [177,178]. For example, depending on the test temperature and shear rate, the experiments show both Newtonian and non-Newtonian types of flow in oligomers [230-236]; depending on the ratio of components in oligomer mixtures the curve types can be additive or non-additive, both positive and negative deviations from additivity being possible [144,230]; the same phenomenon of dilatancy was found for oligomers as for polymer solutions [141,178,226,236,238]; the viscous properties of oligomers are dependent on the temperature prehistory of the system [139, 144], and etc. The deviations from typical behavior of oligomers are usually explained at the qualitative level within the kinetic theory of liquids by Ya.I. Frenkel [80]. Here, the models of the “hooking network” [177] or aggregative structure [128,141,230] are used. The application of the scaling hypothesis [32] for the analysis of oligomer solution dynamic properties gave a form of quantitative dependences to the “hooking network” idea [237]. Oligomeric systems in the single-phase state, however, showed a number of viscosity dependences (it is necessary to point out the unusual character of oligomer systems viscosity dependence on time and temperature prehistory of the samples, temperature hysteresis of viscosity, increase of the mixture viscosity when adding low-viscosity oligomers to highviscosity components, and etc. [141,226,231,232,238-241]) which can not be explained within the traditional theories. In most cases the unusual behavior of oligomer rheological properties is related to oligomer supramolecular structure formation.
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Rheological Properties Dependence on Deformative and Time-Temperature Prehistory of Oligomeric Systems Many works (see [69, 71, 188, 260, 261]) touch upon the issue of the system prehistory influence on its rheological constants. The interpretation of these effects is related to different models of the “structured” liquid [69,71,177,144,244] in one way or another. Let us consider a number of specific experiments which can not be explained within the framework of traditional interpretations and require additional references to supramolecular structure formation kinetics of oligomeric liquids. Figure 2.38 shows logarithmic dependences of the η viscosity (registered by rotational viscometer) on the τt test time at 20°С and at shear rate γt=54 sec-1 during the test. These values were obtained for a sample of oligobutadiene urethane acrylate (OBUA) [226], different methods of preliminary treatment were used for this sample. Curve 1 shows the η = f (τt) function of the initial sample; curve 2 shows the initial sample after the γp preliminary shear influence at γp = 2 sec-1 for 90 min.; additional 90 min. influence at γp = 6 sec-1 is shown on curve 3; finally, curve 4 shows the same sample after a 15 hour “relaxation” in the meter cell of the device.
Figure 2.38. Dependence of lgη on τin at 20°C and γ = 54 s-1 of OBUS sample, which was kept at the room temperature before test. Testing sample without preliminary deformation (1), after preliminary deformation at γп = 2 s-1 (2), at γп = 6 s-1 (3) and in τ0 = 15 hour (4).
We can see that: а) even a small (in comparison with the loads at experimental deformation conditions) preliminary shearing influence on oligomeric liquid reduces the time of transition to the stationary flow regime (where η = ηs, ηs is not dependent on τt) irreversibly and significantly (by decimal exponents); b) within the studied range of γp, the ηs absolute value does not depend on γp, however, it increases significantly if the liquid takes a short “relaxation” after preliminary deformation.
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Figure 2.39 shows the ηs = f (γt), functions obtained for a sample of OBUA at different τr “relaxation” time variations. The latter was determined as the time between the moment of preliminary sample deformation (e.g., the end of measurement in the previous experiment) and the beginning of the ηs registration in the current experiment. The sample stayed in the test chamber. The τr variable is formally similar to the τex value in the experiments on curing kinetics of equilibrium swollen rubber films in oligomer, considered in the previous paragraph, however, τr represents a different level of the system approach to thermodynamic equilibrium than τex.
Figure 2.39. Dependence of lgηс on lg γi for OBUA at τо = 0 (1), 15 (2), 30 (3), 60 (4), 90 (5) and 120 min. (6).
This figure shows that the τr value determines not only the ηs value, but the flow regime as well. Actually, if τr ≤ 30 min., OBUA shows a non-Newtonian liquid type flow (η depends on γ), but if τr > 30 min. the system behaves like a Newtonian liquid. For the problem studied it is very important that within the range of 0 < τr ≤ 30 min., the ηs absolute values increase with the increase of τr, while within τr > 30 min. the stationary viscosity does non depend on τr. Relaxation time, where ηs is not dependent on τr, is assumed as critical value τrcrit. It has the same physical meaning as τexcrit, i.e., this is the time to reach equilibrium according to viscosity test. Figure 2.40 shows the curves of two OBUA samples flow with different temperature prehistories. One of them (sample 1, curve 1) was stored at 8-10°С before the test, then it was put into thermostat for 10 minutes at 20°С in the test chamber of the device (the temperature of the liquid sample and the temperature of the test chamber became the same in 5-7 minutes). After these procedures the rheological flow curve was determined. Before the second sample (sample 2, curve 2) was put into the test chamber of rotational viscometer, it
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was heated for 15 minutes at 50°С, then it was cooled to ambient temperature and only after that it was put into thermostat at 20°С for 10 minutes; it was then tested. Shear and temperature regimes of rheological tests were identical for samples 1 and 2.
Figure 2.40. The dependence of lgηс on lg γi at 20°С for OBUA samples with different prehistory: 1 – sample was kept at 8°С before thermostating in a test camera; 2 – sample was heated to 50°С pending 15 min. before thermostating; 3 and 4 – the same samples after exposure to a field of constant force at γ = 90 s-1.
Though both samples show the same character of the ηs viscosity dependence on the γ shear rate (there is a small rise of viscosity on the ηs=f(γt) curves at a certain critical shear rate γcrit), the numerical values of their viscosity are different both at the lower and at the higher levels. Moreover, the samples with different prehistories have different γcrit values. If γ ≥ γcrit, viscosity, despite expectations, does not decrease, it increases. It is important to point out that after a strong shearing influence (γ=90sec-1) the above mentioned differences disappear: the systems “forget” about their temperature prehistories and the absolute values of stationary viscosity start to increase (curves 3 and 4).
Relaxation to Equilibrium According to Rheological Tests Data At least two obvious conclusions can be drawn from the complex of the above given rheological results. The first conclusion. The influence of deformation or heat results in structural transformations of oligomeric liquid, which cause essential modifications of oligomer flow and absolute values of shear viscosity. The limiting values of these effects define the stationary rheological characteristics. We must point out that special tests [227] showed no chemical transformations or phase transitions of OBUA during rheological experiments,
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preliminary deformation or “relaxation” period. Therefore, all the observed transformations of oligomer rheological properties are not related to the rearrangement of molecular of phase structure; they are related to supramolecular structure transformations. The second conclusion. Structural transformations do not occur instantly; they take a certain period of time comparable to the rheological experiment time. The system “relaxation” time τr after heating and mechanical effects is one of the most important characteristics of the process, since the formation of the structure responsible for rheological properties of the liquid occurs during this period, which is. There are certain limiting values τr=τrcrit, when rheological characteristics obtain their standard values. Typical molecular-kinetic models of the “structured liquid” [69,71,80,177,144], e.g., the hooking network of Gressly [244] or the thixotropic systems of Denny-Brodky [245], can neither give a reasonable explanation of all the known ηс=f(τr, τrcr,γt,γp,γcr) functions for oligomer complexes [69,141,144,178,226,227,246], nor can they explain the above given experimental results. For example, the fact that the liquid flow character changes after the intensive mechanical influence at γ=90 sec-1 could be explained by deformation of the hooking network (or some other supramolecular structures), however, these changes do not occur (at least, they do not show on the η=f(γ) experimental curves) as the result of the similar deformations during the rheological experiment itself (Figure 2.39). Another contradiction is the fact that the “unstructured” liquid [177] viscosity is higher than that of the “structured” liquid while the hooking network is destroyed at γcrit (Figure 2.40). The wellknown models do not explain these contradictions. The situation changes if we take into account the possible influence of supramolecular structures formation kinetics on rheological properties within the aggregative model of oligomer liquids structure. We must assume: 1) The formation of liquid oligomers equilibrium supramolecular structure is an activation process, the works of P.A. Rebinder [247] prove this fact. However, in contrast to work [247], the shear energy may be used not only for destruction in this case. After a certain energy barrier is surmounted the evolution of the system structure to genuine equilibrium can start. Further on, the formation of a more complex supramolecular structure is possible. 2) The rate of equilibrium supramolecular structure formation in oligomers is lower than that in low molecular weight liquids, while the time to reach equilibrium is comparable or longer than the time of rheological experiment. 3) Rheological methods are sensitive to supramolecular structure transformations on the way to equilibrium. If the time of transition to equilibrium τeq ≤ τr, the rheological experiment shows equilibrium. If τr ≤ τeq, the experiment registers a superposition of equilibrium and non-equilibrium structures. The postulates on activation nature and oligomers supramolecular structure formation time, first given in works [138,180,226], eliminate many contradictions inherent to traditional models of the “structured” liquid. They allow us to give a logical explanation of the phenomena found during the study of the sample prehistory influence on rheological properties of oligomers at the qualitative level.
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Before comparing the obtained results with the consequences of the quantitative theory of supramolecular oligomeric structure formation activation mechanism (see Part 2.4.1), let us consider some seemingly contradictory results of the above given experiments, where different methods were used. The τr values were obtained during the study of OBUA rheological properties, and the τexcrit values were found during the investigation of rubber-oligomer systems curing kinetics. They differ even in the order of magnitude (minutes – days). This can be related to different reasons. The most possible reason is the fact that the reactivity and transfer properties of oligomers are “limited” by different parameters of supramolecular structure, and it takes different times for them to reach equilibrium. The internal structure of inhomogeneity does not play an important role in the transfer process (rheology), while the other parameters (size and number of aggregates, their bond strength) are very important; apart from these parameters the molecular orientation within the supramolecular structure volume, i.e., their “kinetically preferred order” formation, is most important for kinetic experiments [72,160]. It is natural that equilibrium according to the molecules mutual orientation within the aggregate can be reached only after the averaging of the aggregate structure external parameters. Therefore, although the relaxational rearrangement inside the volume of a supramolecular structure (aggregate) element may be still uncompleted, this fact does not influence the viscosity value. That is why, ceteris paribus, η reaches its stationary value earlier than W0. Data in Part 2.8.1 can serve an indirect confirmation of this fact. They show that the infusion of a non-reactive analogue into oligoester acrylate results in the decrease of polymerization initial velocity W0 [179], but it does not influence the rheological parameters of the mixture [91]. This fact can only appear in the experiment if polymerization constants are sensitive to internal structure of supramolecular formation, i.e., to the transitions associate ↔ cybotaxis, while rheological constants are not sensitive to this structure. Moreover, one of the consequences of oligomer supramolecular formation theoretical model, a kinetic consequence, (see Part 2.4.4) was as follows: the transition to the stationary state can be different for different properties of oligomer systems, e.g., for the properties which depend on the numerical concentration of aggregates, the transition to equilibrium can occur earlier than for the properties which are more dependent on the aggregate structure. The results on equilibrium of oligomeric supramolecular structure, obtained by different experimental methods, may not coincide with each other, since they reflect different levels of system approximation to thermodynamic equilibrium.
Comparison of Rheological Experiment and Theory Within the activation model (see Part 2.4.1), several equations (2.59) – (2.61) were obtained. They are given below under different numbers for the ease of reading. For the w(t) function related to the v(t) concentration of activated particles by correlation dw(t)/dt = v(t):
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w(t ) =
v0 kN ⎟⎞ ⎡ c − Fz 0 ⎧⎪ ⎜⎛ 1− exp(−kNt ) ⎤⎦ − ⎨⎜ p − kN ( p − kN ) ⎪⎩ ⎝ c − Fz 0 ⎟⎠ ⎣ ⎛
−kF ⎜⎜1− ⎝
(2.107
⎫ v0 ⎞⎟ ⎡ ⎤ ⎪, pt − − 1 exp( ) ⎦⎬ c − Fz 0 ⎟⎠ ⎣ ⎪ ⎭
where Fz0 = dF0(z)/dz, N =Σun = const is the total number of aggregates in the system. For the aggregates concentration: n
n−m u m0 ⎡ , kw(t ) ⎤⎥ ⎢⎣ ⎦ m = 1 (n − m)!
un (t ) = exp ⎡⎢ −kw(t ) ⎤⎥ ∑ ⎣ ⎦
(2.108
and also for v(t ) =
v kN ⎞⎟ c − Fz 0 ⎡⎢ ⎛⎜ p− 0 exp(−kNt ) − ⎢ ⎜ ( p − kN ) ⎢⎣ ⎝ c − Fz 0 ⎟⎠ ⎛
− p ⎜⎜1− ⎝
(2.109
⎫⎤ v0 ⎞⎟ ⎪⎥ pt − exp( ) ⎬⎥. c − Fz 0 ⎟⎠ ⎭⎪ ⎥ ⎦
k is the velocity constant of the single molecules addition to the aggregate and q is the velocity constant of the single molecules split-off from the aggregate. These equations allow us to obtain an equation (in Einstein approximation, according to Landau-Lifschitz [248]) describing the time function of viscosity increase Δη(t), which occurs because of the increase of the aggregates size due to the addition of molecules activated by an external influence. Actually, if aggregates are considered rigid impenetrable formations [115], the contribution of one aggregate into the system viscosity is proportional to its volume, which in case of the close-packed arrangement is proportional to the number of molecules in one aggregate. Taking into account formulas (2.107) - (2.109):
{
Δη(t ) ∝ kFz 0 +
c − Fz0
⎡⎛ ⎢⎜ p − p − kN ⎢⎢⎣⎜⎝ ⎛
− kF1 ⎜⎜1 − ⎝
v0 kF1 ⎞ ⎟⎡ 1 − exp − kF1t ⎤⎥ − ⎦ c − Fz 0 ⎟⎠ ⎣⎢
(
v0 c− F
⎞ ⎟ 1 − exp − ⎟ z0 ⎠
[
)
(2.11)
⎫
( pt )]]⎪⎬η. ⎪ ⎭
The analysis of expression (2.110) shows that there are two characteristic time scales:
τ1=1/kF1 is the characteristic time of the activated molecules addition to aggregates, and τ2=1/p is the characteristic time of molecules activation. There are several possible cases, considered below.
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If τ1 > τ2, which is equivalent to inequality к>>р, i.e., if the rate of the molecules addition activated by external action to the aggregate significantly exceeds the activation rate and, therefore, activated molecules do not accumulate in the system, Δη does not depend on time, which means that viscosity does not change during the system “relaxation” period when τr < τrcrit. Thus, the possibility to register any changes of oligomeric liquid viscosity over the τr period is defined not only by the experimental methods, but also by the correlation of the molecule activation constants and their addition to the aggregates. The activation constant is dependent on the nature of the components, on the energy consumed for activation (preliminary deformation shear rate, in particular), on the period of the system preliminary deformation, on the temperature and etc. If τ1 < τ2, i.e., the addition of activated molecules to aggregates occurs slower than their activation, a certain time interval t1, should exist. During this interval the system accumulates activated “disorganized” molecules. Their influence on viscosity increase is to be determined by correlation of the t1 and τ2 times, i.e., time correlation after the external influence stops, and all the “disorganized” activated molecules are accumulated in the system. During the τ2 τr, second, if all activated molecules are added to aggregates by t1 at t1>τ1, the increase of viscosity will not occur. What is more, it follows from the theory that the р constant and, therefore, τ2, are related to the external influence energy, e.g., the γ shear rate or the τt time of external influence. Therefore, it is necessary to use the limiting values γcrit and τtcrit, which provide the highest possible activation of “disorganized” molecules for these compounds (р → max), after this activation η is no longer dependent on γ and τt. The above described experiment (Figure 2.41 and 2.42) proves this conclusion (see also [226-228]).
Figure 2.41. Dependence of τi on γi for OBUM.
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If correlation τ1>τ2 is true for characteristic times τ1 and τ2, found in activation model and τr is comparable to τ2, the basic changes of rheological properties of the system apply to the second exponent of this equation according to (2.110). They describe the process of molecule activation. Curves 1, 2 and 3 (Figure 2.38) refer to this process at τr<5 min. If exposure (“relaxation”) times are comparable to τ1, and τ1>τ2, the increment of viscosity is defined by the first exponent of equation (Figure 2.40), describing the process of activated molecules addition to aggregates. This process is shown by curve 4 (Figure 2.38) when τr>τ1 . In the framework of activation model there is a simple explanation and revealed dependences of τac on γt (Figure 2.41) ang lgηс on τt (Figure 2.42) for OBUM. The molecular activation is a slow process at low shear rates and at low energy influence. Aggregate growth rate and, accordingly, the rate of reaching stationary viscosity are limited by molecular activation time τ2 (τ1<<τ2, this fits the p<>τ2), the limiting stage is the process of activated molecules addition to aggregates. Therefore, τac=τ1 and starting at certain values of γt, τac is no longer dependent on shear rate. System deformation time (in this case τt), as well as γt, determine the concentration of activated molecules ν. Therefore, according to (2.110) at τr>τ2 and τ1, the ηs value increases with the increase of τt. However, after certain limiting values τtcrit and γtcrit, which determine the maximum increase of stationary viscosity, ηs no longer depends on the degree of external influence.
Figure 2.42. Dependence of lgηc on τi at τо ≥ 30 min for OBUM.
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145
properties of the system. The energy barrier is necessary for the activation of “disorganized” molecules share, which can become a part of the organized structures (aggregates) after their activation (the activation is not a chemical one). Under the influence Thus, in order to form an equilibrium structure of oligomeric liquid, including all the thermodynamically allowed states of supramolecular structure, it is necessary to overcome a certain energy barrier of this system. The structure formed will reflect the real rheologicalof certain thermal or mechanical effects, the limiting values of which are determined by the Тcrit, γcrit and τtcrit values for every specific system, this activation occurs at the р constant rate. After the energy effect, if the constant of activated molecules addition rate to aggregates к < р, the oligomeric liquid requires some time (this is the τtcrit time) for relaxation and spontaneous formation of aggregates equilibrium distribution function, determined by the system parameters. If the time to reach equilibrium is less than τr, rheological experiment (or any other test, which is sensitive to modifications of supramolecular structure) will show equilibrium. If the interval between the end of preliminary influence on the liquid and the beginning of measurement is less than the period to reach equilibrium, the experiment will record the structural elements distribution function, which will have been formed by that time. The inevitable consequence of the equilibrium structure formation activation mechanism is the thermal hysteresis of viscosity proven in experiments [121].
Figure 2.43. Viscosity of OBUA during direct (1−2) and reversed (3−4) variation of temperature. Shear 1 deformation rate is γi=54s− . The dashed line represents a supposed hysteresis curve of viscosity during direct (1−2′) and reversed (2′−4) variation of temperature and the standard bistability mechanism.
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Thermal Hysteresis of Viscosity The analysis of data on the influence of τex on the initial rate of rubber-oligomer system curing (see Part 2.8.1) shows that modifications in supramolecular structure in the τex period are reversible. However, oligomers show other examples as well. Figure 2.43 shows the dependences of the ηs stationary viscosity on the testing temperature of an OBUA sample, obtained in [121] in the conditions of gradual heating (curve 1) and cooling (curve 2). The temperature interval is 10°С. Differences in the methods used for curves 1 and 2 are as follows: the measurements were taken at the same temperatures, however, the curve 2 sample was preliminarily heated at a higher temperature and then it was cooled to the test temperature, while the curve 1 sample was not exposed to any temperatures higher than the test temperature. The condition for the test was the fact that the τr value between the tests was > τrcr, i.e., the test was carried out for a system in equilibrium (see above). Figure 2.43 shows that this oligomeric liquid has a typical picture of hysteresis: direct and indirect characteristics of the viscosity dependence on temperature are different. This means that the structures formed in the liquid preliminarily heated at a higher temperature, and then cooled to the test temperature and in the liquid thermostated at the test temperature without preliminary heating were not equivalent. Note that the hysteresis phenomenon disappears during the second cycle: the curves of the viscosity dependence on temperature in the “heating – cooling” regime for the second cycle test of the same OBUA sample are identical, and they coincide with the “cooling” curve of the first cycle (curve 2). The phenomenon described in the experiment is very unusual. This relates not only to hysteresis itself, but to its manifestation as well, that is, theηc viscosity in the case of “cooling” is larger than the ηh viscosity in the case of “heaing”, measured at Т = const, and Δη = ηc − ηh ≠ 0 in the whole Т interval. This makes the phenomenon fundamentally different from the viscosity hysteresis for diluted polymer solutions related to their associative structure [249]. Furthermore, independent experimental methods showed no chemical transformations in oligomer in the selected interval of temperatures and shear rates γ [226,227] during the whole period of preparation and rheological experiments (~1.5 months). Therefore, this hysteresis of oligomer viscosity is not related to chemical transformations at the molecular structure level; it is conditioned by different processes. There are different explanations of this experiment, since the phenomena of hysteresis can appear due to different reasons [250]. For example, it can be caused by the nonequilibrium state of the system, when the system cannot relax to a thermodynamic equilibrium, in case the control parameter changes (temperature, in this case). At certain conditions, hysteresis may occur in a bistable system. Other explanations are also possible. In case of hysteresis due to the non-equilibrium state of the system, we can give the following qualitative explanations. Modifications of the system properties are dependent on the level of its non-equilibrium state, which can be different for direct and reverse temperature changes. However, the properties of the above described rheological experiment, which showed hysteresis, were measured only after a long exposure of the system after each change of the temperature, until all relaxation processes were completed (η did not depend on exposure time: τr > τrcrit), but hysteresis did not disappear. Hence, it is impossible to explain this phenomenon by the “kinetic” non-equilibrium of the system.
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One of the possible explanations is given in works [91,226,227]: the process of structure formation is of activated nature which determines the differences in viscosities of the preliminarily heated and non-heated samples. By analogy with Ptitsin-Gotlib model [251] the temperature activation allows the system to overcome the energy barrier (since heating is gradual, the system can possess several formal barriers*), after that a new structure is formed spontaneously, the equilibrium level of which corresponds to a higher temperature. Another viscosity level corresponds to this structure. According to the relaxation model of oligomer supramolecular structure formation, the higher is the temperature, the higher is the concentration of activated molecules. The increase in the number of activated molecules in the system results in the growth of the aggregates size, which determines the increase of viscosity. Since the velocity constant of the molecules addition to aggregates is much higher than that of the molecules split-off from aggregates (к>>q), the newly formed structure is irreversible, at least during the experiment. Another explanation of the viscosity thermal hysteresis mechanism was presented in work [120], which is based on the assumption that there are several stable and several unstable stationary states in the system (i.e., the system is bistable). When the system control parameter changes slowly, the system evolves, being in equilibrium, which corresponds to one of the stable stationary states. However, when the control parameter reaches a certain critical value, this stationary state becomes unstable, and no longer exists. The system relaxes to another stationary state on another branch of the bifurcation diagram. If the control parameter changes are reverse, the system remains on this branch of the diagram, and its equilibrium state differs from its initial state, which is the reason of hysteresis appearance. Formally, since hysteresis is observed in equilibrium state in this experiment, it is to be conditioned by system bistability. However, this hysteresis mechanism does not completely comply with the experimental data available. The explanation is as follows: in bistable system at a certain value of the control parameter a discontinuous change of the state occurs, that is, a transition from one disappearing branch of stationary states onto a new branch. This could would have appeared on the experimental curve, namely the changes of the last (or several last points) point on line 1−2, corresponding to direct temperature characteristic. These points should have moved to line 3–4, which relates to reverse temperature dependence. But in this case the experimental curve, shown in Figure 2.43, would have looked differently. In particular, point 2 should have gone upward and lie on the continuation of line 3−4, occupying the position of point 2′. The lack of the dashed interval on the experimental curve, corresponding to a discontinuous reconstruction of the equilibrium state, prejudices the possibility to explain hysteresis using the mechanism based on bistability. Nevertheless, a detailed analysis of this situation, carried out in work [116,120], showed that thermal hysteresis of viscosity, observed in the experiment without any discontinuous reconstruction of the equilibrium state, can be also explained by the system bistability. Work [120] assumed (see Figure 2.44), that three stationary states are available in the system: two of them are stable: N_ (branch AB) and N+ (branch CD), corresponding to the smallest and to the largest values of N, and one of them is unstable: N0 (branch CB), *
Each temperature interval (10º С for this experiment) activates only a part of the potentially available system elements, which take part in the formation of a new level of structure organization. The following heating may activate (there is a possible limit) a new “portion”.
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corresponding to the intermediate N value, branch CB has an interval with the same slope as branches AB and CD have.
Figure 2.44. Bifurcation diagram for a system with bistability. Explanations are provided in the text.
If the initial state of the system corresponds to the N state, then with the T increase at any ΔT interval, the system will always be in an intermediate non-equilibrium state below the AB curve (points 2' and 3' ) and it can relax only to the N state. However, with the decrease of T at a comparatively large ΔT interval, the system can find itself in the intermediate nonequilibrium state above the CB curve (point 4'), where it can relax only to the N+ state on the way 4'→ 4 →...→ 6. As the result, hysteresis can be observed in the reverse temperature dependence. AT certain conditions, the supramolecular structure of oligomeric liquids, presented in the form of molecular aggregates of different organization, may correspond to the required bistability property, with the system of stationary elements, shown in Figure 2.44. This follows from the activation-relaxation model of oligomer supramolecular structure (see Part 2.4.3). This model is based on the assumption that activated molecules are not only added to aggregates at the velocity constant k, but they also relax to the initial state at the velocity constant R; starting at some critical Ncrit value of the average aggregate size N, the ability to attract free molecules increases; thermal effect results in the change of the k and Ncrit values. The natural consequences of activation-relaxation model are equations (see 2.73) for stationary values Fst (z) =
(
)
zu1st , cst = R P vst , u1st = ⎡⎢1−( k q )vst ⎤⎥ N , ⎣ ⎦ 1−( k q ) zvst
(2.111)
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149
where k is the velocity constant of the active molecules addition to the aggregate and q is the velocity constant of the single molecules split-off from the aggregate; Р is the activation rate constant of inert oligomer molecules; R is the relaxation rate constant of active oligomer molecules; c is the inert molecule concentration; v is the active molecule concentration; un is the concentration of aggregates consisting of n molecules, and the F1zst value (stationary value ∂F/∂z at z = 1), is defined from equation:
k ( F1zst ) q M − F1zst , 1− N = F1zst 1+ R P
(
)
(2.112)
In particular, it follows that the aggregation rate constant k depends on the average aggregate size, which is proportional to their overall mass F1zst . Expression (2.112) allows us to estimate the aggregate contribution to the viscosity of the system, which is proportional the to overall mass of aggregates according to Einstein approximation: ∞
⎛
Δη η ∝ ∑ nun + M − ( v + c ) =∂ F ( z,t ) ∂ z ⎜⎜ n =1
⎝ z =1
≡ F (t ).
(2.113)
1z
In order to find an explicit solution of algebraic equation (2.112) a graphic approach was used (see Figure 2.45).
Figure 2.45. Graphic solution of equation (2.112) assuming that the ratio (k/q)/(1+R/P) increases with temperature. The curve L corresponds to the left part of equation (2.112), curves R1 and R2 correspond to its right part at T1 and T2 (T1
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The analysis of the obtained solutions showed that with the increase of Т, depending on the constants ratio (k/q or R/P) decrease (decrease of the k/q or R/P constants ratio depends on the Arrhenius mechanism of activation and aggregation processes), i.е. depending on the increase or decrease of the (k/q)/(1+R/P) ratio, the F1zс value, and, therefore, the Δη/η viscosity increment may either increase or decrease. In the first case, when fraction (k/q)/(1+R/P) increases with the temperature growth, and, with the increase of F1zс, the amplitude of the k constant change is high enough, three stationary states are possible in the system: two of them are stable and one is unstable, i.е. the bistability situation is realized. In this case, it is possible that the values of all three stationary states increase with the temperature growth (see Figure 2.45), therefore, there is no internal contradiction in the unusual dependences: ηr, >ηh, and Δη ≠ 0, which take place in the experiment in the whole Т temperature range. Therefore, at certain conditions the bifurcating diagram of the system of kinetic equations, accepted for the activation-relaxation model (2.69) − (2.72), can be written in the form, corresponding to the bifurcating diagram, presented in Figure 2.44. The proposed model can describe thermal hysteresis of viscosity without discontinuous leaps of the state even if one of the stable states disappears. We should also note that the realization of hysteresis according to this mechanism requires very strict limitations applied to bistability parameters of the system, character dependence on its control parameter, and also process conditions. Evidently, it is related to the fact that thermal hysteresis of viscosity is very hard to register during the experiment. There are some other types of unusual behavior of temperature dependencies of viscosity, which, nevertheless, do not require any complicated theoretical explanations. For example, Figure 2.46 shows a rheological kinetic curve, plotted on the basis of viscosity data. These data were obtained in the process of PVC mixing with trioxiethylene dimethyl acrylate in the scanning mode (temperature increase rate is 1°С/min) [252]. First, it can be seen that the system viscosity as the function of temperature changes over its maximum point, although according to all the well-known laws of rheology, the viscosity should decrease with the temperature increase in the absence of chemical transformations (here, these transformations are impossible); second, in case of the reverse temperature characteristic, viscosity does not take its initial value, it retraces only the character of the right curve branch of direct temperature characteristic η = f (Т), i.e. a kind of hysteresis is demonstrated. This experimental dependence is not unusual. It is caused by the non-equilibrium of the system. The authors of work [252] investigated a multi-stage process of emulsified PVC granules solution in liquid oligomer during heating. The data shown in this figure reflect viscosity of the system at different mixing stages. First, polymer granules swell in oligomer, and the disperse system flow values are registered in the rheological experiment. With the growth of the temperature, the rate of oligomer diffusion in polymer increases, the degree of swelling increases, and, therefore, the size of dispersed particles increases as well. In full accordance with the laws of disperse flow [133,178], viscosity grows.
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Figure 2.46. Rheokinetic curves of the blend PVC - trioxyethylenedimetacrylate (the ratio is 60:40) with heating (1) and cooling (2) rate 1 °С/min.
This stage is reflected by the left (rising) branch of curve 1 (Figure 2.46). When dilution and monolith formation of plastisol is completed, i.e., after a single-phase system is formed, viscosity decreases with the temperature growth in full accordance with the laws of highviscous solutions flow [69,178]. This process is reflected by the right branch of the curve. It is natural that viscosity increases during cooling, since the system has only one phase in this temperature range .
Rheology of Polymer-Oligomer Mixtures (Region of Small Oligomer Additions) Sometimes introduction of small quantities (< 3%) of oligomer into linear polymers results in disastrous changes of viscosity properties. First observed in 1960s, viscosity decrease of polypropylene melt in the presence of 0.05 – 0.1 % siloxane oligomer [253] by more than a decimal order, stimulated numerous investigations on elastic and viscous properties of polymers in the presence of microadditives of different liquids (e.g., see [239, 254,255]). At first, this effect of uneven decrease of viscosity was interpreted (it concurred with the works on the research of supramolecular structure in amorphous polymer) as the result of supramolecular structures surface lubrication by a liquid which was not compatible with polymer. Scientists [253] assumed that this lubrication made the transfer of supramolecular structures easier in case of the system deformation. This effect was called structural plasticization [256]. Later, strict qualitative explanations were given for all the phenomena (they are much more numerous [268]) related to structural plasticization. A detailed description of these phenomena is given in monograph [254,257], we do not consider them in this book. Along with the sharp decrease of viscosity, 1970s saw directly opposite experimental dependencies: when small amounts of some low viscous additives were infused into polymer, the viscosity value increased, and in some cases the viscosity of the mixture appeared to be much higher than that of the most high viscous component [239-241].
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As an example, Figure 2.47 shows concentration dependence of effective shear viscosity for the mixture of cis-polyisopren and trioxiethylene dimethyl acrylate at different tension shears [240]. If ω1 < 0.5%, viscosity increases sharply, after that it decreases to additive values, the relative value decreasing with the increase of the τ shear tension. The increase of oligomer concentration [158] up to 1% limits the range of the τ values, where the anomalous effect is observed. At ω1 > 3% these types of anomalies completely disappear and they do not appear in the whole range of τ (∼ 4 orders).
Figure 2.47. Dependence of effective viscosity on the dosage of oligomer for the blends of cispolyisoprene and trioxyethylenedimetacrylate with shear rates varied.
A systematic research of the anomalous growth* of viscosity in different types of rubber oligoester acrylate systems, carried out in [139,240,241,258,259], showed that there are complex dependences of viscosity on the test regimes and on the molecular characteristics of the components. The anomalous growth of viscosity is observed when linear oligoester acrylates are added to rubber, while branched polymers have a plasticizing influence. At small dosages of oligomer additives, the change of the mixture viscosity is observed for polydispersed rubber only, even small changes of rubber molecular weight distribution (MWD) resulted in regeneration of the effect: viscosity increase was substituted by viscosity decrease, and on the contrary. It was also determined that the increase of viscosity in the presence of oligomers is typical of rubber low molecular weight fractions only. Figure 2.48 shows logarithmic dependences Δη = ηm - ηc, on molecular weight of rubber М. Here ηm is the mixture viscosity, ηc is rubber viscosity. It can be seen that with the increase of the M value, the effect of viscosity relative value growth gradually decreases and linear oligoester acrylates have a “normal” plasticizing influence on high molecular weight rubber. The temperature influence is also ambiguous.
*
The matter concerns “anomalous growth of viscosity”, not “anomalous viscosity”. The latter, as it is known [69,242], is the demonstration of viscosity dependence on shear tension, while the effect studied is anomalous because the growth of the mixture viscosity is observed while adding a low viscous component into a high viscous one.
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Figure 2.48. Dependence of Δlgη on the molecular weight of cis-polyisoprene for its blends with 0,1 % trioxyethylenedimetacrylate at 50 °С (1,3,4) and 70°С (2), lgτ = 4,0(Pa) (1,2), 3,6 (3) and 4,2 (4).
Ceteris paribus, with the increase of the temperature, in some cases the samples which differed only in polymer molecular weight or polymer molecular weight distribution, showed the Δη decrease, while in other cases they showed the Δη increase. Sometimes, anomalous effects could not be observed in the experiments because of the increase in the temperature variation interval. There are different explanations of the experiments concerning the above described phenomenon. Viscosity growth [241] is caused by a more dense packing of polymer chains and by a decrease of the system free volume as the result of macromolecules flexibility increase under the influence of oligomeric plasticizers. Papers [144,238] explain this effect by the increase of the fluctuation hooking network density due to the changes of thermodynamic parameters of solutions. Assuming that these effects are typical of crystallizing systems only (although viscosity growth was also seen in amorphous systems), paper [260] considers the possibility of kinetic stimulation of nucleation in the presence of oligomers and, therefore, the increase of polymer crystallinity which leads to the increase of viscosity. “Anti-plasticization” as the consequence of polymer crystallinity level change up to the formation of liquid crystal regions, is discussed in works [104,261]. Neither of these approaches, explaining one or several experimental dependences, can explain the whole complex of mechanisms (or their absence), determined during the investigation of oligomeric mixtures rheological properties. Although the effect of viscosity increase in rubber - oligomer systems in the experiment implying small additions of a low viscous component appears in the regions which are far from spinodal or critical point, the physical clarity of the theory of viscosity in critical and metastable regions, developed for oligomeric systems [237,262,263], was so attractive that it encouraged scientists [141,264267] to consider the possibility of its application for the explanation of this effect, and to analyze the reasons of formal contradictions between theory and practice.
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• •
•
•
•
Authors of work [141] believe that these contradictions are related to molecular polydispersity of polymer, which leads to “blurring” of thermodynamic stability boundaries of polymer - oligomer mixtures, large-scale fluctuations appearing near these boundaries. We give several points to prove this assumption: It is well known that at certain conditions a “microphase” separation of polymer homolog mixtures occurs [133, 269,270]. It is well known that when polymer homolog mixtures are dissolved in organic solvents, an equilibrium between the solutions of fractions with different molecular weights is reached [257]. Two thermodynamically unequal cases are possible: 1) the solvent forms a molecular solution with all the polymer fractions; 2) some polymer fractions are insoluble at the given temperature and composition. Polymer fractionation is based on this theory. It is well known [136] that if we mix polymers with close molecular weight distributions (MWD), the critical temperature does not depend on composition, however, if we mix polymers with different molecular weight distributions, Тcr shifts to the boundary values. Therefore, when polydisperse polymers are mixed, the appearance of the Тcr and Сcr intervals is possible, their width is determined by molecular weight distribution of the components. It is well known [94] that the tendency of oligomer mixtures to form aggregates increases with the increase of their components molecular weight. If M ’w / M ’’w < 2.5 – 3 times, aggregate formation is not preferred thermodynamically. Here M ’w and M ’’w are molecular weights of the mixed components. It is well known [69] that low molecular weight fractions of polydisperse polymers can serve as plasticizers for high molecular weight fractions. The decrease of the low molecular weight fractions share in polydisperse polymer results in the increase of its viscosity.
When applied to rubber - oligomer systems, these facts mean that the structure of mixed systems in equilibrium has local heterogeneities, i.e., solutions with different concentrations of oligomer, defined by oligomer solubility limits in different molecular weight rubber fractions. Therefore, it is possible that molecules “belonging” to different local regions with various phase structures (true solution, metastable region, critical point) can exist in one and the same system at the same time. Naturally, if Т = Const the system has different Сcr values, and if С = Const the system has different Тcr values. Therefore, if a polymer has a wide molecular weight distribution, the shift of thermodynamic equilibrium between rubber fractions should occur in the presence of oligomer. Low molecular weight fractions should dissolve in oligomer (the lower is molecular weight the better is solubility). This fact is also defined by another factor, which can influence rubber viscosity. The molecules of low molecular weight fractions of polymer, which in the absence of oligomer served as plasticizers of high molecular weight fractions, do not have any plasticization effect after oligomer addition, because they are “bound” by oligomer; moreover, they might find themselves in metastable or critical regions and take part in the large-scale fluctuations. Therefore, it is supposed [141,265] that macroscopic viscosity of polydisperse rubber and oligomer mixture can be presented in the following form
Homogeneous Oligomer Systems ηm = ηs + Δηcr ϕcr+ Δηsp ϕsp+ Δηа ϕа – Δηpl ϕpl ,
155 (2.114)
where ηs is the viscosity of the regular solution; Δηcr is the critical correction, which takes into account the viscosity of some molecules ϕcr in the critical region; Δηsp is the spinodal correction, which takes into account the viscosity of some molecules ϕsp in the metastable region; Δηа is the correction for “anti-plasticization”, caused by the fact that some low molecular weight fraction molecules ϕа plasticize the system no longer; Δηpl is the correction for “plasticization”, caused by plasticization effect of some molecules ϕpl. Expression (2.114) does not include the osmotic correction, proposed in [262] for consideration of fluctuation correlation radii changes. This correction [141] is taken into account in the increase of the absolute Δηpl value and the decrease of the Δηcr and Δηsp values. Obviously, Δηcr, Δηsp and Δηа condition the mixture viscosity increase, while Δηpl conditions the decrease of viscosity. The resultant value of viscosity is based on all these corrections. The above described scheme provides explanations of many mechanisms observed in rubber - oligoester acrylate systems. For example, at small concentrations of oligomer the change of viscosity can be observed for polydisperse rubbers only. Actually, the independence of ηm on the dosage of trioxyethylene- α, ω - dimethyl acrylate up to ω1 = 3% wt. (2.1019) is observed for monodisperse fractions of polybutadiene.
Figure 2.49. Monodisperse cis-polyisoprene flow curves (Mw /Mn = 1,02) with (1) 0,1 (2), 0,3 (3), 0,5 (4), 1,0 w. % (5) of trioxyethylenedimetacrylate at 220С.
It follows from theory that if ΔС = (Сcr - С) → 0 and ΔТ = (Тcr - Т) →0, then Δηcr → max. If the current values of С and Т are lower than the critical ones, their increase will approximate the system to its critical state, i.e. to the decrease of ΔС and ΔТ. Therefore, in
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this case, the increase of viscosity will be observed. If the current values of С and Т are larger than Сcr and Тcr, correspondingly, their increase will give opposite results.* Depending on molecular weight and on molecular weight distribution of rubber as well as depending on oligomer dosage, the values of critical state parameters may fluctuate within the same type systems. Therefore, possible increase or decrease of viscosity with the increase of temperature observed in the experiment is to be considered a law rather than a coincidence. The same conclusions can also explain the above mentioned fact of anomalous effects determination dependence on the temperature interval variation: if the interval is large, metastable and critical states can be skipped. On the basis of assumption on competition between the positive and negative corrections contribution into the total ηm value, it is very simple to explain why the viscosity increase precedes its further decrease on the “viscosity-composition” curve. Ceteris paribus, introduction of oligomer encourages the increase of ϕа, which proceeds until certain values of Сcr are reached (viscosity increases), any further increase of oligomer content leads to an increase of the ϕpl value (viscosity decreases). The statement about the “blurred” phase states of separate fractions for the discussion of contradictions between the theoretical and experimental concentration dependences of viscosity in polymer-oligomer mixtures at low oligomer dosage is not sufficient for the above given scheme to be taken for granted. References to the fact that in case of phase diagrams reconstruction in coordinates “temperature - mole fraction” (neither % wt. nor % vol.), the limited values of oligomer solubility in polymer increase by 10 times, which approximates the theoretical and experimental Сcr values, as well as the estimations, testifying to the onescale correlation between the effective radii of fluctuation and the quantity of added oligomer. These estimations are taken by analogy with the calculations of “macroscopic” relations between the size of supramolecular structures and the number of structural plasticizer molecules [254, 257]. All these references, however, do not answer the question about the qualitative sufficiency of oligomer molecules for thermodynamic reconstruction of the system and shift of equilibrium of different fractions. Nevertheless, work [141] gives indirect experiments to prove the above given hypothesis. Figure 2.50 shows that the viscosity growth effect in rubber-oligomer systems on the basis of high molecular weight rubber can be seen only in case the latter is diluted by a low molecular weight fraction of the same rubber. Hence, it is common sense that the increase of the low molecular weight fraction in rubber will result in the increase of the relative value of the viscosity growth effect. The consequences of the above given hypothesis result in new conclusions: the viscosity increase will proceed until Δηcr ϕcr+ Δηsp ϕsp > Δηpl ϕpl or Δηа ϕа > Δηpl ϕpl , and then the increase of the low molecular weight fraction in rubber will lead to the viscosity decrease, since the Δηpl ϕpl value starts to grow very fast. Figure 2.51 shows that in case of the 1:1 ratio of low molecular weight and high molecular weight fractions in the rubber component, the system viscosity increases in the presence of oligomer; with the increase of the share of low molecular weight fraction (2:1 ratio) at the same concentration of oligomer the mixture viscosity decreases, according to this hypothesis.
*
Analogical consequences are true for the spinodal correction.
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Figure 2.50. Flow curves of cis-polyisoprenes with MW=5.104 (1, 1’ ) and 6,2.105 (2, 2’) and their equimolar blends (3, 3’) without oligomer (1-3) and with 0,1% of trioxyethylenedimetacrylate (1’ -3’).
Figure 2.51. Flow curves of blended cis-polyisoprenes with MW=5.104 and 6,2.105 with and without trioxyethylenedimetacrylate with component ratio varied a) 1 and 2 –the ratio of components 1:1; 1’ and 2’ –the ratio of components 2:1; 1 and 1’ – without oligomer; 2 and 2’ - with 0,05% of oligomer. b) 1 - 3 – component ratio is 2:1; oligomer dosage is 0 (1), 0,05 (2) and 0,5 weight % (3).
Although the real mechanism of anomalous effects of viscosity increase and decrease in oligomer systems has not been completely explained yet, the ideas about the dependence of viscous properties on supramolecular structure parameters of oligomer systems, which, in their turn, are the function of thermodynamic characteristics of components and state parameters of the system, give us a certain physical basis for the explanation of these “anomalies”. Modern ideas about adsorption mechanisms and experimental data on adsorption laws in oligomer systems and in polymer solutions are well presented in reviews [74, 271,272], while the theories of phase separation of various liquids in the presence of solid surfaces, which make essential adjustments to the structural organization of the liquid phase are described in papers [32, 214-218,255,273,274]. As far as oligomeric systems are concerned, many of the laws of adsorption can be described within the molecular-aggregative adsorption mechanism,
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proposed by Y.S. Lipatov [275]. This mechanism states that it is not only separate individual molecules but also their aggregates that move onto the adsorbent surface. Adsorptive equilibrium between aggregated (“organized”) and non-aggregated (“disorganized”) molecules is established in the system and runs in the time period. As equilibrium aggregativity (concentration, size, and lifetime of the aggregate) of oligomer liquids depends on the system temperature and on oligomer concentration in it (aggregation degree increases with the approach to binodal; aggregation degree differs significantly for oligomer impregnated and non-impregnated solutions), depends on the phase structure of the mixture (e.g., in metastable and critical states it is much higher), depends on the thermodynamic affinity of oligomer mixture components (the degree of aggregation increases with the decrease of the chemical affinity of components) and etc., therefore, the knowledge of oligomer supramolecular structure allows us to give logical explanations of the complex laws, discovered during the study of oligomer adsorption processes on solid surfaces. [74, 133, 246,271,275]. Let us consider several examples. Figure 2.52 illustrates kinetic laws of adsorption (А) of oligoethylene glycol from its mixture with acetone on aerodynamic force and on carbon black. Extremums on kinetic curves are related to the first priority of aggregate sorption, while the values of adsorption maximums increase with the increase of oligomer concentration in the C solution, this can be explained [133] by the increase of the aggregates size with the increase of C. The further (after the maximum) decrease of the A values to the constant A value, as paper [74] assumes is caused by the formation of adsorption equilibrium among aggregates of different size. It is not excluded that this phenomenon can be related to kinetics of conformational rearrangement of molecules, adsorbed on the surface.
Figure 2.52. Adsorption kinetics of oligoethyleneglycoleadipinate on aerosil (1) and carbon-black (2) from acetone solutions. Oligomer concentration is 3,84 (1) and 0,76 g/100 ml (2).
Figure 2.53 shows adsorption isotherm in the system of oligoethylene-glycol-adipatedichloroethane-aeroforce and the share of aggregated molecules of oligomer in solution P as the concentration function of oligomer in the C solution [275]. First of all, let us stress that
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aggregates are not detected in the solution immediately after adsorption. They appear in the solution after a certain period of time as the result of a new equilibrium formation: aggregate “disorganized” molecule. The dependences in this figure reflect equilibrium situation and, as we can see, curves Р =f (С) and А = f (С) are antibate: the points of minimum aggregate concentration correspond to the maximum adsorption points. This dependence can be explained by the fact that during adsorption, first aggregates and only then isolated molecules move onto the surface and, at the same time, equilibrium values P depend on oligomer concentration. As the number of aggregates is much smaller than the number of disorganized molecules, at certain values of C, when aggregate “scarcity” becomes apparent, the total adsorption value decreases because more and more isolated oligomer molecules start moving onto the surface.
Figure 2.53. Adsorption isoterm (1) and the dependence of the part of aggregated molecules Р (2) on solution concentration С in a system oligoethyleneglycoleadipinate - dichloroethane - aerosil.
Figures 2.54 - 2.56 show that adsorption isotherms on the glass spheres, obtained in [74] for the system of epoxy oligomer ED-5 - toluene at various temperatures and at different oligomer concentrations, are comparable to the aggregates size and aggregation constants Ка of the system. (Ка = К′/К is determined in the equilibrium system n ↔ Kna +K′nf, where n is the total number of molecules in one unit of the volume, na is the number of molecules in aggregates, nf is the number of “free” molecules). The analysis of the given results reveals a precise symbasis of the adsorption value to the character of the supramolecular organization of the oligomer system. It can be seen that the changes of the aggregate size and the degree of inter-aggregative interaction, occurring at temperature and composition variation, determine the form of isotherm and the adsorption value in the whole test temperature interval and in the whole oligomer concentration range.
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Figure 2.54. Adsorption isotherms of epoxide oligomer “ED-5” from toluene solution on glass spheres.
Figure 2.55. Aggregate size dependencies of epoxide oligomer “ED-5” on its concentration and temperature in toluene solution during adsorption on glass spheres.
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Figure 2.56. The dependence of aggregation constant Ка on concentration and temperature in a system formed by epoxide oligomer “ED-5”, toluene and glass spheres.
These were the examples of the “pure” sorption: no further oligomer solution in glass spheres is possible. However, other situations are also possible, when adsorbed oligomer diffuses into the solid matrix volume. An experiment showing irreversibility of equilibrium shift during the adsorption process is described in [276], where the sorption process of tetrahydroxyethylene - α, ω-dimethyl acrylate (TGM-4) by PVC films was investigated. Figure 2.57, taken from the article cited, presents temperature dependences of sorption - desorption for the given system. It can be seen that oligomer concentration limits for the films, obtained during direct and reverse temperature changes, are considerably different though the temperature is the same. In case of direct changes, the higher is the temperature, the higher is the equilibrium sorptive capacity. However, after concentration equilibrium is reached at Т=Const, any further temperature decrease may cause only a slight desorption of oligoester acrylate from PVC - oligomer mixture. For example, after heating to 90°С and further cooling, the amount of oligomer residual in the PVC film at 20°С, is more than 10 times higher than the equilibrium sorption value at 20°С and is about 1.5-2 times higher than the value of TGM-4 concentration limit for its solution in PVC at this temperature (phase diagram for this system is given in [166]). Thus, a certain type of hysteresis demonstrates itself. Chemical transformations in the system after sorption, further cooling and storage of the mixture are impossible according to [276]. Therefore, in order to explain the differences in oligomer concentration limits for polymer - oligomer films, obtained at different preliminary temperature histories we can consider the following options: а) the equilibrium parameters of the structures, formed at high temperatures, are different from those of the structures formed at low temperatures, therefore, in case of reverse changes of the temperature no return to the initial state is thermodynamically allowed; b) the formation of the supramolecular structure in the given system is of activation nature, energy barrier of the reverse process being much higher than that of the direct process; c) the velocity constants of sorption and desorption processes are significantly different, the reverse process is kinetically limited. The last option, though possible in theory, is hardly possible in practice.
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Figure 2.57. The temperature dependence of sorbtion (•) and desorption (ο) in a system PVC tetraoxyethylene - dimetacrylate.
The above cited work gave experimental conditions which almost excluded the possibility of the system non-equilibrium state. However, the kinetics of the equilibrium state achievement can have an essential influence on the final result. Work [233] studied the system of solid oligoimide - liquid oligomer from epoxide and acryl series. Indirect methods showed that when the initial components are put into contact, fast adsorption of liquid onto solid surface (by molecular-aggregative mechanism) is followed by a slow process of dilution. An attempt to accelerate the latter process due to the increase of the temperature did not give any successful results. The increase of the temperature together with the increase of the diffusion coefficient caused the destruction of comparatively weak sorptive bonds and resulted in the aggregates desorption.
2.8.4. Oligomer Diffusion Characteristics The authors of book [277] proposed an original method of analysis of the nuclear magnetization decay curves taking into account their non-exponential form and dependence on diffusion time. This method explained some characteristics of oligomer and polydisperse polymer self-diffusion; earlier, all the experimental results were contradictory [277-281], and they were beyond the existing self-diffusion theories [32,250]. Figure 2.58 taken from [281] shows diffusion attenuation curves in poly-(oligo-) ethylene glycol melt (PEG) at different td time intervals of diffusion. It can be seen that the curves form is non-exponential and it depends on td. As the td value increases, a trend to exponential state appears, at the same time average self-diffusion coefficient D* does not depend on td. That is, this system shows all the diffusion features, commonly observed in the multiphase
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exchange systems. The authors admit, that “the problem of phase representation with different D* values is not a simple one” (indeed, how could phase inclusions appear if the experiment was carried out in the melt at temperatures far exceeding the PEG melting temperature).
Figure 2.58. Diffusion fadings A(g2) in a PEG melt with Mn = 2.104 at td = 5.10-2 (1), 1.10-1 (2), 3.10-1 (3), 8.10-1 (4), 1,5 (5) and 3 sec. (6) and T=3730 K. The inclination of A(g2), corresponding to D2, is shown by dashed line.
Various interpretations of these nontrivial dependences were analyzed in [277] in detail, including the potential role of the PEG molecules polydispersity, the role of the chain conformation fluctuations and etc.; they all were rejected. According to the authors of [277] the most probable hypothesis, explaining the given results, is reduced to the fact that “the translational mobility of molecules turns to be fluctuating in time and in space due to the random character of the so called hooks formation between separate macromolecules. Macromolecules, probably, due to their inter-hooking, can be united into certain fluctuating formations and move during their life time cooperatively as a single kinetic unit”. If we exclude differences in terminology, the above given explanation of the PEG selfdiffusion characteristics observed in the experiment, is reduced, in the long run, to the fact that transportation is carried out due to the transfer of not only single molecules (as classical self-diffusion theories state), but also molecule aggregates; aggregates themselves having a limited life time. This assumption is even more evitable because molecular weight dependence of self-diffusion coefficients* of narrow dispersion (Mw / Mn ≤ 1,1) PEG fractions (Figure 2.59) are characterized, first, by the bend on the curve lgD* = f (lgMn) at a certain critical weight McrD, which is less than the corresponding critical weight Mcrη, determined by viscosity test, second, by different velocities of the Ď2 value decrease as the function of Mn *
Figure II-8.29 shows Ď2a and Ď2b as the average values of self-diffusion coefficient, characterizing the translational mobility of 30% of macromolecules with the biggest and the smallest values, correspondently, of self-diffusion coefficients in the general spectrum Ď2l.
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above and below McrD, in the Mn region corresponding to oligomer state, dD*/dMn < dD*/dMn, corresponding to molecular weight with a coil state of the chain.
Figure 2.59. Molecular weight dependencies of coefficients D2 (1), D2b (2), D2a (3) and the peak Newton viscosity η (4) for PEG melts. Arrows mark critical values of Мn with respect to diffusion (Mkd) and viscosity (Mkη) tests correspondingly.
Finally, the authors [277] showed, that calculation curves of diffusion decay, drawn on the basis of the hypothesis of molecules integration into aggregates, have a tendency to approach the experimental curves at the increase of the number of molecules in the aggregate**. In connection with the above pointed difference in the critical weight values according to diffusion and viscosity tests, found in [277], it is worth mentioning the study [233], showing that diffusion and viscosity methods give different temperature values as well. In [233] the changes of oligoepoxide ED-20 flow character, occurring with the increase of the temperature, were connected to the changes in oligomer supramolecular structure: the temperature increase results in the decay of oligoepoxides hydrocarbon bonds physical network and in the formation of a strong associated structure of a different type. This statement is proven by the data on temperature dependence of the cross relaxation time in ED-20, obtained by NMR relaxation method. A comparison of experimental curves showed that the structural reconstruction in oligomer is registered by rheological methods at the temperatures which are 30-40° lower than the temperatures which can be registered by NMR relaxation. Work [233] assumes that this is related to the fact that, first, shearing deformations in the rheological testing mode activate the structure rearrangement processes, whereas structural changes, traced in the NMR relaxation mode at micro-viscosity level, are limited only by the thermal effect and, therefore, are registered at relatively high temperatures. These changes, however, can be registered at lower temperatures in the rheological testing mode (shear + temperature), due to high sensitivity of macro-viscosity to the changes of the size of kinetic units, via which the transfer proceeds successfully in the system. A number of tests of translational diffusion, observed in epoxide oligomers and their mixtures was conducted by A.E.Chalykh and his students [93,94,282-285]. **
2 or 4 molecules aggregates diffusion calculations are presented in [277].
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For oligomers of this class, in the molecular weight interval MW = 340 – 7150, nuclear magnetization decay curves, unlike the above described PEG melt curves, obey exponential dependence. Self-diffusion coefficients were calculated for them and Figure 2.60 [94] presents their temperature changes. There is a bend of the D* - 1/Т curves, it corresponds to temperature 150 – 1600С of the given oligomers (the author of work [94] “identifies” this critical temperature with the temperature of the l–l transfer). Activation energies of selfdiffusion (temperature coefficients) Е*D in the temperature range above and below Тll and self-diffusion coefficients Dg* appropriate to Тg (see Table 2.6) were calculated in Arrhenius approximation.
Figure 2.60. Temperature dependencies of self-diffusion coefficients (D*) of individual epoxide oligomers. Numbers of curves correspond to numbers of oligomers in the table 2.6.
Table 2.6. Activation Energies of Self-Diffusion of Epoxide Oligomers [94] Oligomer code*
EО-1 EО-2 EО-3 EО-4 EО-5 EО-6 EО-7
Lg Mw
2.53 2.62 2.78 3.43 3.50 3.82 3.85
Е*D, kcal/mole Т≤ Тll
Т > Тll
Lg Dg*, [sm2 /s]
11.6 11.2 17.8 20.4 24.1 17.0 17.5
6.8 4.6 4.7 5.2 5.9 5.7 4.6
-10.90 -10.90 -10.80 -11.20 -11.10 -10.80 -10.95
* Industrial marks indications: Bisphenol A Di-Glycidyl Ether А (EО-1), ED-20 (EО-2), ED-40 (EО-3), ED-44 (EО-4), DER-664 (EО-5), GT-6610 (EО-6), Epfikote- 1009 (EО-7).
The table shows that: а) self-diffusion coefficient Dg* practically does not depend on oligomer Мw and equals 1 ÷ 2 . 10-11 sm2/s at temperatures close to oligomer glassy state; b) activation energy of translational mobility calculated at Т > Тll, depends weakly on Мw and
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varies from 4.6 to 6.8 kcal/mole; c) at Т≤ Тll value Е*D increases 3-3.5 times, and the author of [94] relates this change to the changes of the free volume distribution in the melt. According to molecular-kinetic theory of macromolecule translation [70], ratio D*≈D0Mb must be obtained in the melts, where D0 is the monomer unit diffusion coefficient, and the b parameter depends on molecular weight of macromolecule. If the М value is less than a certain critical Мcr value, which determines the oligomer region boundary, b = 1, and at М > Мcr, b = 2. Test data processing for epoxide systems, done in [283], demonstrated that the diffusion equation exponent depends on the temperature and differs from the theory forecasts: at Т≤ Тll b=2.4, and at Т> Тll b=2.0. Why is it the oligomer region where the changes are so considerable? First of all, let us note that the methods used in the above given experiments, illustrated in [283-285], excluded the possibility of oligomer chemical transformations and all the further reasoning refers to the single-phase systems. The authors [94,283,284] consider several possible interpretations in the framework of the free volume theory. One of interpretations is as follows. “Adjustable” coefficients are introduced in order to adjust contradictory experimental and theoretical results. It is suggested to consider the “temperature change” values of numerical parameter α in equation f = fg + α(T-Tg), where f is the free volume share, to be continuous, and to accept that for a low temperature region α ≈ 2.10-4К-1, while for a high temperature region α ≈ 6-7. 10-4К-1. Another interpretation is much more interesting [285]. Microcavities of the free volume, existing in polymer and oligomer melts, under certain conditions are supposed to segregate into larger formations, called “blinking clusters”, their size far exceeds the size of the diffusing molecules. The structure of these “blinking clusters” is similar to fluctuations in the pre-boiling zones of the liquid, and the polymer diffusion process is interpreted [285] as the “boiling” of its segments. In this case, the diffusion environment does not limit the size of the diffusing units in the skipping procedures. It is not only single molecules but also much bigger formations, for instance, oligomer molecule aggregates that can migrate into these “blinking clusters”, if their size and life time ≥ the size and the life time of diffusing objects. The arguments for the real existence of these “blinking clusters” are given in [285]. Let us note some of them. First of all, electron-microscopic arguments: during the instant freezing of epoxide oligomer melts in liquid nitrogen, at different initial temperatures (100 – 220ºС), “domains” (“blinking clusters”) are registered on replicas, their share is 10-30% vol. The initial temperature rise results in the increase of the distance between these formations, their size decrease, and also the decrease of the density difference between “domains” and their environment. Secondly, the existence of critical thicknesses and temperatures, at which Knudsen gas flow runs through thin solid films (according to electron microscopy data), formed from oligomers. And, thirdly, thermodynamic mixing parameters were calculated [94], according to the data on oligomer mixture inter-diffusion. They indicate that there is a MWD interval and probability of “blinking clusters” formation and diffusing molecule aggregates appearance beyond these limits becomes thermodynamically non-preferable.
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Thus, realization of the above mentioned mechanism of translational macromolecule diffusion is possible only under the strict conditions, especially for the systems consisting of the molecules with limited length and hardness. Interesting results were obtained in [286], where epoxide oligomers transportations into different matrixes were systematically studied. Oligomer systems with unlimited component compatibility are characterized by three various concentration dependence types of the Dv inter-diffusion coefficients. The first type was observed in the systems with different molecular weights of the components. In this case (see Figure 2.61), the Dv value was changing gradually and steadily along the convex curve during the transfer from one component into another, i.e., from one inter-diffusion coefficient limiting value D12 ≡ Dv at φ1 →0 to another D21 ≡ Dv at φ1 →1 (here index “1” refers to oligomer, and index “2” refers to polymer component), showing concentration dependences Dv for polysulfone system (PSF) with Мn= 1.9 . 104 and epoxide oligomer ED-20 with Мn=380). It is obvious that D12 characterizes translational mobility of oligomer molecule in the matrix of high molecular weight component, and D21 reflects the opposite side, polymer molecule mobility in oligomer environment.
Figure 2.61. The dependence of mutual diffusion coefficients on the composition of “ED-20” – PSP blend. Temperatures: 1 – 230; 2 – 250; 3 – 2800С.
The second dependence type is observed in the systems with close values of the components molecular weights. The increase of Dv during the transition of a diffusion pair from one component to another is typical of these systems. In this case D12 < D21. Figure 2.62 gives an illustration of this situation and shows concentration dependences Dv at various temperatures in the melt of two epoxide oligomers with Мn=380 and Мn=1700.
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Figure 2.62. The dependence of mutual diffusion coefficients on the composition of “ED-20” – “ED44” blend. Temperatures: 80 (1), 100 (2), 120 (3), 140 (4), 150 (5), 160 (6), 170 (7), 190 (8), 210 (9), 2200С (10).
And, at last, the third type of dependence, when the increase of oligomer concentration results in the total decrease of translational mobility of the components and D12 > D21, epoxide oligomer was found for the systems, oligo- (poly-) ethylene glycol with Мn= 102 4·104 (see Figure 2.63). The greatest changes occur to inter-diffusion coefficients (Δ Dv / φ1 ≈ 0.6 ) in the solutions concentrated in epoxide. But in the range of diluted solution, these changes are not considerable (Δ Dv / φ1< 0.06).
Figure 2.63. The dependence of mutual diffusion coefficients on the composition of “ED-44” – PEG blend. MW of PEG: 40000 (1), 10000 (2), 6000 (3), 3000 (4), 400 (5).
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As it is assumed in [286], the value of the marginal diffusion coefficient is related to (within rheological approach [70]) the friction coefficient of the diffusing molecule, with its effective radius (r) and diffusion environment viscosity (η) ratio according to Einstein-Stokes: D12 = kТ/6πr1η2RT and D21 = kТ/6πr2η1RT
(2.115)
If this is true, then according to [70], D12 / D21 = η1 r2 / η2 r1 = (η1 / η2 ) (М2/М1)1/3 = =(D22 / D11) (М2/М1)2/3
(2.116)
In other words, the ratio of inter-diffusion marginal coefficients is determined by the ratio of diffusion environment rheological characteristics, which, in its turn, is determined by the ratio of molecule self-diffusion coefficients in these environments.
CONCLUSION The theory demonstrates that areas with local orientation ordering and various degree of anisotropy can spontaneously form in oligomer systems. Formation of these small - scale structures (aggregates) is the effect of a team statistical behavior of oligomer molecules. Such effect is only possible at some length – rigidity ratio of a molecular chain belonging to oligomeric area of lengths. Any oligomer system combines organized (aggregated) and disorganized molecules. Oligomer systems at the macroscopic scale are conglomerates of aggregates with various size, lifetime and either isotropic or anisotropic arrangement of molecules inside, which are “dispersed” in a media of “disorganized” molecules. These facts form the basis for a theoretical interpretation of experimental observations which seem to be in contradiction with classical laws of chemical physics.
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[170] Doi, M., Ehdvards, S. Dinamicheskaja Teorija Polimerov (Dynamic Theory of Polymers). - M.: Mir, 1998 (in Russian). [171] Korolev, G.V., Il'in, A.A., Cheburnin, R.V. I Dr. // Izv.Vuzov., Ser. Khim., 2001, V. 44, Ed. 6, P. 6. [172] Korolev, G.V., Il'in, A.A., Solov'ev, M.E. I Dr. // Vysokomolek. Soed., 2001, V. A 43, № 10, P. 1822. [173] G.V. Korolev, M.M. Mogilevich, A.A. Il'in. Associacija Zhidkikh Organicheskikh Soedinenijj: Vlijanie Na Fizicheskie Svojjstva I Polimerizacionnye Processy (Association of Liquid Organic Compounds: influence on Physical Properties and Polymerization Properties).- M.: Mir, 2002 (in Russian). [174] A.L. Rabinovich, P.O. Ripatti // Sb. Statejj «Struktura I Dinamika Molekuljarnykh Sistem» (Book of Articles. The Structure and Dynamics of Molecular Systems). – M.: IFH RAN, 2000, Vyp.7, S. 38. (in Russian). [175] Faller, R., Muller-Plathe, F., Heuer, A. // Macromol., 2000, V.33, No 17, P.6602. [176] Kremer, K, Grest, G.S. // J.Chem.Phys., 1990, V.92, P. 5057 [177] A.A. Tager. (Physical Chemistry of Polymers). – M.: Khimija, 1978 (in Russian). [178] V.N. Kuleznev. Smesi Polimerov (Polymer Blends) M.: Khimija, 1980. (in Russian). [179] S.M. Mezhikovskii // Vysokomolek. Soed., A, 1987. V. 29, № 8, P. 1571. [180] S.M. Mezhikovskii, A.E. Chalykh, L.A. Zhil'cova.// Vysokomolek. Soed. 1986. V.28. No 1. P.53. [181] S.M. Mezhikovskii, V.M. Lancov, L.A. Abdrakhmanova. // Dokl. AN SSSR. 1988. V.302. No 4. P.878. [182] S. Mezhikovskii // intern. J. Polym. Mater., 2000, V.47, P.207. [183] O.M. Fedorenko, A.V.Barancova, V.K.Grishhenko. // Tez. Dokl. III Vsesojuz. Konf. Po Khimii I Fizikokhimii Oligomerov (Absrtacts of Plenary and Poster Reports of III AllUnion Conference on The Chemistry and Physical Chemistry of Oligomers) Chernogolovka: Oikhf AN SSSR, 1986, P.185 (in Russian). [184] V.M. Lancov. Dis. ... D-Ra Khim. Nauk. M.: Ikhf AN SSSR, 1989. [185] S.M. Mezhikovskii. // Dokl. Mezhdun. Konfer. Po Kauchuku I Rezine (Reports of The international Conference on Caoutchouc and Rubber) “IRC -94”. M., 1994, V.3, P. 83. (in Russian). [186] R. Sh. Vartapetjan, E.V. Khozina, D. Geshke I Dr. // Sb. Statejj «Struktura I Dinamika Molekuljarnykh Sistem» (Book of Articles. The Structure and Dynamics of Molecular Systems).–– M.: IFH RAN, 2000, V. 7. P. 119. (in Russian). [187] Shilov, V.V.. Dis. Dokt. Khim. Nauk, Kiev: Ikhvs AN USSR, 1982. [188] Berlin A.A., Kefeli T.Ja., Korolev G.V. Poliehfirakrilaty (Polyesteracrylates). M.: Nauka, 1967 (in Russian). [189] Mezhikovskii, S.M. Physico-Chemical Principles for Processing of Oligomeric Blends. - N.-Y.: Gordon & Breach, 1998. [190] V.I.Irzhak, B.A.Rozenberg, N.S.Enikolopov. Setchatye Polimery (Network Polymers). - M.: Nauka, 1979. (in Russian). [191] Korolev G.V. // Al'fred Anisimovich Berlin. Izbrannye Trudy. Vospominanija Sovremennikov (Alfred Anisimovich Berlin. Selected Publications. Reminisciences of Contemporaries). – M.: Nauka, 2002, P.241. (in Russian). [192] Al. Al Berlin., B.R. Smirnov. // Zhurn. Teoret. I Ehksperim. Khimija. 1967. V.3. № 1. P.93.
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[219] A.V.Kotova, L.A.Abdrakhmanova, V.M.Lancov, S.M.Mezhikovskii. // Vysokomolek. Soed., 1987, V.29 A, № 8, P.1768. [220] M.M. Mogilevich. Okislitel'naja Polimerizacija V Processakh Plenkoobrazovanija (Oxidative Polymerization in Film-formation Processes). - L.: Khimija, 1977 (in Russian). [221] A.S. Kuz'minskijj, N.N.Lezhnev, Ju.S.Zuev. Okislenie Kauchukov I Rezin (Oxidation of Caoutchoucs Ans Rubbers). - M.: Gntikhl, 1957. (in Russian). [222] N.M. Ehmanuehl', A.L. Buchachenko. Khimicheskaja Fizika Molekuljarnogo Razrushenija I Stabilizacii Polimerov (Chemical Physics of Molecular Destruction and Polymerization Od Polymers). - M.: Nauka, 1988 (in Russian). [223] N.M. Ehmanuehl', D.G. Knorre. Kurs Khimicheskojj Kinetiki (Chemical Kinetics Course). - M.: Vysshaja Shkola, 1962. (in Russian). [224] Eh. Arinshtejjn, S.M. Mezhikovskii. // Sb. Statejj «Struktura I Dinamika Molekuljarnykh Sistem» (Book of Articles. The Structure and Dynamics of Molecular Systems), Jjoshkar-Ola - Kazan' - Moscow: Marijjskijj Gos. Tekhn. Universitet, 1997, Part 2, P. 49. (in Russian). [225] S.F. Edwards. // Fluids Molekulares. By Eds. R.Balian, G.Well.-N.-Y.: Gordon and Brich, 1976. P.254. [226] Mezhikovskii, S.M., Vasil'chenko, E.I. // Dokl. RAN. 1994. V.339. № 5. P.627. [227] Mezhikovskii, S.M., Vasil'chenko, E.I., Repina, T.B. // Vysokomolek. Soed. 1995. V. B 27. №5. P.887. [228] Mezhikovskii, S.M. // Ifzh. 2003. T. 76. № 3. S. 39. [229] Khozin V.G., Karimov A.A., Dement'eva I.A., Frenkel' S.Ja. // Vysokomolek. Soed. B. 1983. V. 25. №11. P.819. [230] E.I. Vasil'chenko, S.M. Mezhikovskii // Vysokomolek. Soed. B.1989, V.31, №2, P.1362. [231] Ju. S. Lipatov, Ju. N. Panov, L.S. Sushko, S. Ja .Frenkel'. // Dokl. AN SSSR, 1967, V. 176, № 6, P. 1341. [232] A.A. Berlin, A.G. Kondrat'eva, N.N. Tvorogov, Eh. S. Pankova, A.Ja.Malkin. // Vysokomolek. Soed. B.,1973, V.15, № 10, P. 740. [233] S. Mezhikovskii, B. Zapadinskii // Polymer, 2002, V. 43, P. 5651. [234] G.K. Romanovskijj. Dis.... Kand. Khim. Nauk. L.: VNIISK, 1977. [235] R. Sh. Frenkel'. // Izv. VUZ. Ser. Khim. I Khim. Tekhn., 1977, V.20, Ed.4, P. 626. [236] Ju. S. Lipatov, A.E. Nesterov, V.F. Shumskijj. // Vysokomolek. Soed. A.,1984, V.26, № 11, P. 2312. [237] L.I .Manevich, Sh.A. Shaginjan, S.M. Mezhikovskii. // Dokl. AN SSSR, 1981, V. 258, № 1, P. 142. [238] A.N. Gorbarenko. Dis.... Kand. Khim. Nauk. Kiev: Ikhvs AN USSR, 1986. [239] M.A. Nattov, E.Khr. Dzhagarova. // Vysokomolek. Soed., 1968, V.8, № 10, P. 1841. [240] A.A. Berlin, S.M. Mezhikovskii, E.I. Vasil'chenko I Dr. // Koll. Zh., 1976, V. 38, № 3, P. 537. [241] S.M. Mezhikovskii, A.A. Berlin, E.I. Vasil'chenko I Dr. // Vysokomolek. Soed. A.,1977, V.19, № 12, P. 2719. [242] Eh. T. Severs. Reologija Polimerov. -M.: Khimija, 1966. [243] Ja. Malkin, S.G. Kulichikhin. Reologija V Processakh Obrazovanija I Prevrashhenija Polimerov (Rheological Aspects of formation and Transformations of Polymers). - M.: Khimija, 1985 (in Russian).
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[271] G.S. Semenovich, Ju. S. Lipatov. // Fizikokhimija Mnogokomponentnykh Polimernykh System (Physical Chemistry of Multicomponent Polymer Systems). -Kiev: Nauk. Dumka, 1986, V. 1, P. 186 (in Russian). [272] R. Flir, Ja. Likema. //. Adsorbcija Iz Rastvorov Na Poverkhnosti Tverdykh Tel (Adsorption From Solution on Solid Surfaces). - M.: Mir, 1986, P. 182. (in Russian). [273] P. De Gennes. // Rev. Modern Phys., 1985, V. 57, P.827. [274] D.E. Sullivan, M. Telo Da Gama. // Feud interfacial Phenomena. By Ed. C.Croxton. N.Y.: Wiley, 1986, P.45. [275] Ju. S. Lipatov. Fiziko-Khimicheskie Osnovy Napolnenija Polimerov (PhysicoChemical Fundamental Aspects on Filling of Polymers). M.: Khimija, 1991. (in Russian). [276] H.E. Bair, M. Matsuo, W.A. Salmon, T.A.Kwei. // Macromolecules, 1972, V.5, P.114. [277] A.I. Maklakov, V.D. Skirda, N.F. Fatkulin. Samodiffuzija V Rastvorakh I Rasplavakh Polimerov (Self-Diffusion in Polymer Solutions and Melts). - Kazin': KGU, 1987. (in Russian). [278] A.I. Maklakov, V.D .Skirda, G.G. Pimenov // Diffuzionnye Javlenija V Polimerakh (Diffusion Phenomena in Polymers). – Riga:Zantie, 1977, P.85. (in Russian). [279] R.I. Callaghan, I.N. Pinder // Macromolecules, 1980, V.13, №5, P.1085. [280] J. Meerwall, D.H.Tomich, N.Hadjichristdis // Macromolecules, 1982, V.15, №5, P.1157. [281] V.D. Skirda, V.A. Sevrjugin, A.I. Maklakov // Dokl. AN SSSR, 1983, V.269, №3, P.638. [282] A.E. Chalykh, V.K. Gerasimov, A.E. Bukhteev I Dr. // Vysokomolek. Soed., 2003, V. A45, №7, P. 1148. [283] A.E. Chalykh, O.V.Shmalijj, A.E. Bukhteev . // Vysokomolek. Soed., 2002, V. A44, №11, P. 1985. [284] A.E. Chalykh, O.V. Shmalijj, V.G. Chertkov. // Vysokomolek. Soed., 2000, V. A42, №10, P. 1736. [285] A.E. Chalykh.// Pjataja Konferencija Po Khimii I Fizikokhimii Oligomerov. Tez. Plen. I Stend. Dokl (Absrtacts of Plenary and Poster Reports of V Conference on The Chemistry and Physical Chemistry of Oligomers). Chernogolovka: Ikhfch RAN, 1994, P. 21 (in Russian). [286] Bukhtev A.E. Dis. ... Kand. Khim. Nauk. M.: IFH RAN, 2003.
Part 3
HETEROGENEOUS OLIGOMER SYSTEMS ABSTRACT Modern theoretical concepts concerning phase decomposition in oligomer systems have been reviewed. Phase equilibria have been experimentally studied and results provided. The analysis of phase diagrams has been carried out. The aspects of macroscopic properties of heterogeneous oligomer systems are discussed including rotational and translational diffusion, relaxation and rheology.
3.1. BASIC PRINCIPLES OF PHASE SEPARATION The present phase transition mechanism interpretations are based on the fluctuation theory [1,2]. The process of phase destruction in a system usually occurs when its stability is lost. Chaotic heat motion of molecules in single-phase solutions or coexisting components of liquid blends leads to a spontaneous change of concentration Δ on ϕΔ = ϕ -ϕav in local domain ϕl, where ϕav is the average volume concentration. These fluctuations of concentration (heterogeneities) can have relatively broad scale distribution (Δl) and rootmean-square amplitude (Δϕ2) depending on system state parameters. A system is stable if spontaneous concentration fluctuations with any scale and amplitude disappear (they may appear in another area of the system) in the course of time. This effect occurs when system is not in binodal. If fluctuations remain when the state parameters change, further evolution of the system to an equilibrium state can lead to phase destruction. System stability is known to be a function of its free energy F(c,t)on temperature or concentration. According to the classical approach to stability problem [3] ∂2F/∂c2 < 0
(3.1)
(the second derivative reverses its sign) system tends to increase fluctuations of its composition and spontaneously decomposes at phases with equilibrium concentrations. There are two possible states of the system. It can be either under spinodal or between binodal and spinodal (the area near the critical point is not discussed here; for detailed information see [4,5]). The first case is characterized by a quite instant loss of solution stability: even the
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slightest (the lowest scale or amplitude) concentration fluctuations tend to increase their amplitude forming particles (fragments) of a new phase (spinodal decomposition). Further stage of equilibration may go through coalescence “Oswald growth of big particles by the contributions of small ones” depending on the mechanism of the second stage of a process. A system in a metastable state (that is between binodal and spinodal) is tolerant to slight fluctuations of concentrations but looses its stability when fluctuations have a relatively large scale or amplitude. Large fluctuations density (future phase nucleus formation) depends on relative position of a configurative point on a binodal – spinodal diagram and specific system properties When concentration of an iih component increases in some local point, it falls in its neighborhood. Therefore concentration gradient emerges and stimulates diffusion transport from this domain to its nearest neighborhood providing nucleation and diffusion – controlled growth of a particle. The second stage includes either coalescence or “Oswald maturation” of particles to form two - phase equilibrium. In contrast to low – molecular compounds, phase formation in macromolecular systems is more complicated because a polymer chain is a large, strongly fluctuating and somewhat spongy formation [6] as not only a temperature but also a value of a wave vector contribute to its mobility and movement. Therefore a function of system reaction with respect to the gradient of chemical potential is much more complicated for polymers. Phase formation processes in solutions and melts of high – molecular compounds are studied theoretically and experimentally and provided in detail in many publications (see for example [6-26]). The analysis of thermodynamics and kinetics of phase disintegration in polymer melts, blends and solutions in low – molecular solvents, block copolymers, swelled nets etc. is mainly based on various modifications of medium field theory using approximations of KanHallard [27], Flori-Huggins-de Jene [6,23], I.M.Lifshic [28,29] et al. It is determined that phase separation mechanisms differ quantitatively on whether a system is either near binodal or spinodal or a critical point [4-7,27,30]. According to Kan-Hillard [27], when spinodal is crossed, diffusion flow signs reverse and phase separation is based by large – fluctuated heterogeneities in an initially equilibrium solution and is initiated by selective growth of sinusoidal composition fluctuations. The most intense growth of composition fluctuations leading to the phase separation in a relatively narrow wavelength range. Theoretical analysis of a spinodal composition made in [31] for a mixture of two linear polymers considering reptation movement of polymer chains in a virtual tube of hookings, has shown that the growth rate of periodical concentration fluctuations can be expressed by the following equation: τq-1 = - Const⋅ D1 Ne χ a2 q4 (2-q2 E2),
(3.2)
where q = 2π/λ is a wave vector, corresponding to a period of fluctuations with a wavelength λ; Ne is a number of monomer units between hookings; D1 is a diffusion coefficient of a monomer link; χ is a thermodynamic Flori – Huggins parameter; Е = 1/3 аχ-1/2 is a theoretical thickness of an interphase transition layer [32]. The optimal spinodal decomposition wavelength has the following form: λopt =√3 πЕ As it mentioned in [33], there are two possible scenarios of a system structural transformation. The first scenario is followed at close – to – binodal concentrations [7,31,34-
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37] and can be well characterized by scaling correlations. When concentrations are far from critical values, self – similiarity of a structure is not observed during its transformation and scaling correlations cannot be implemented [37,38]. L.I. Manevich and co-authors [33, 34] have discovered during theoretical investigation of a spinodal decomposition that a non-linear stage of a process can be described by a sequence of structural rearrangements with unstable but long – living structures formed between periods when they exist. The free energy is “pumped” boundary layers into this area during a lifecycle of each of these structures. It finally destroys the phase boundary and leads to formation pf a system with large characteristic spatial scale. The first stage of transformation is when new boundaries are formed and prevent this unstable structure from decomposing. The process of sequential rearrangements with intermediate “slowing down” intervals in a blend of linear polymers may finalize in formation of thermodynamically equilibrium structure in a two - phase area. Calculations based on this approach [33,34] let us characterize the process of spinodal decomposition for mixtures of two linear polymers. Figures 3.1 - 3.3 show change of concentration profiles u(x) in the range from 0 to L for a row of fixed points of time τ, their temporal function for medium values, so as the change of full and surface Helmholtz energy in time. Time units in this plots correspond to refresh times of reptation hooking tube τ = tNe / (N13 ⋅τ1), and distance is measured in Δх = 0.5 k1-1 , where k1 is a threshold wave number for instability.
Figure 3.1. Dependence of u(x) on x/L at γ = 0 (a-d) and τ = 0 (1), 40 (2), 60 (3), 70 (4), 90 (5), 450 (6), 510 (7), 590 (8), 690 (9), 820 (10) and 900 (11).
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Figure 3.1 shows that initial “single-humped” distribution u(x) at τ =0 (curve 1) quickly (beyond τ =40) transforms into “four-humped” distribution (curve 2). The fastest growth is observed for modes with wave numbers close to kmax [34]. However, these states are shortliving and the “three-humped” profile is formed at τ=90 (curve 5). Further profile rearrangement drastically slows and lasts appr. 450 temporal units. The change rate u(x) grows again in the next period and the two-humped distribution of concentration is formed relatively fast (curve 8). These states are also proved to be long - living until τ ≥ 900 when they gradually degenerate into “single-humped” distribution (curves 10,11). This is the end of a spinodal decomposition
Figure 3.2. Dependence of u(x) on τ at γ = 0 and х = 0 (1), 0,5 (2) и 0,25 (3).
The process of sequential concentration rearrangements of fluctuations so as acceleration and deceleration of profile formation are well illustrated in Figure 3.2, where u(x) is presented as a function on τ for various х. It can be seen that that the values u(L/2, τ) decrease abruptly at τ=40 and stabilize at τ=80 when close to х=1/2 (curve 2). Futher, in the range of 80 <τ<450, the values u(L/2, τ) grow slightly and then rapidly, reach their maximum at τ ≅ 570 where they stay constant. The behavior of curves u(х, τ) obviously varies for other x, but anywhere shows areas of deceleration and areas of thermodynamically unstable structures with relatively long lifetime. Figure 3.3 shows that full free energy F (curve 1) grows at stages of fast structure rearrangements (exponential growth of fluctuations and “humps being overgrown” at τ =30, 525 и 850) and stays practically unchanged at deceleration intervals (90 <τ< 500, 550 <τ <800 and τ > 880). The gradient component of the free energy Fg ≡ F0 (u, grad(u(r,t)) (see equation (3.12) below) decreases at deceleration intervals (curve 2). It means that when this nonequilibrium but relatively kinetically stable structure exists, energy is pumped inside from surface layers. The end of each rearrangement (the beginning of
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deceleration) is characterized by short – time growth of Fg after decrease. These growth periods are thought [34] to be stipulated by the fact that a surface layer with a relatively high energy is formed here. It provides formation of the new concentration profile with more abrupt change of concentration in a metastable state. The energy Fg of such an abrupt profile u(x) exceeds sufficiently the bulk energy and therefore that prevents this fluctuation structure from immediate destruction and provides kinetic stability for a whole period of the abovementioned energy pumping from surface layers of a heterogeneity into its inner area
Figure 3.3. Dependence of full (1) and surface (2) Helmholtz energy τ at γ = 0.
Flori-Huggins-de Gene model [7,31] describes spinodal decomposition of a binary mixture of linear polymers by means of free energy density: F/ kb T = F0/ kb T + [a2 / 36 ϕ (1-ϕ)] (∂ϕ / ∂x),
(3.3)
where F0/ kb T = (ϕlnϕ/N1)+(1-ϕ)(ln(1-ϕ)/N2)+χ ϕ (1-ϕ)
(3.4)
and diffusion ∂ϕ(r,t) /∂t = div [(Λ/kb T) grad (∂F/∂ϕ)],
(3.5)
where Onzager coefficient is calculated by the following equation: Λ(ϕ(r,t)) = [Ne ϕ (1-ϕ) a2] / [N1 τ1 (1-ϕ) + N2τ2ϕ]
(3.6)
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N1 and N2 are degrees of polymerization (polycondensation) А and В correspondingly of components in a binary mixture of linear polymers; ϕ(r,t) is a volume fraction of component А at point r at the t moment; а= а1 = а2 are А and В links sizes, that are identical in this case; Flori-Huggins interaction parameter χ = χ11 + χ22 - 2χ12, where χ11, χ22, χ12 are temperature normalized interaction energies А-А, В-В and А-В correspondingly; kb is the Boltzmann constant; T is the temperature; τ1 and τ2 are microscopic relaxation times for А and В monomers; Ne is an average part of monomer units between hookings along the chain, that is equal for both types of chains; F0 is the free energy density of a spatially homogeneous mixture; ∂F ⁄ ∂ϕ = μ is an exchange chemical potential, that can be calculated using the following equation: μ(r,t) =∂F/∂ϕ=∂F0/∂ϕ - div{[a2/18ϕ(1-ϕ)] grad ϕ}
(3.7)
χ > 0 in case of a mixture of linear polymers. Therefore, aggregation of single type components is energetically preferable here. Entropy component of the system free energy shows a tendency to homogeneous distribution (dispersing) of all components in a mixture that is concurrent to aggregation. The phase state curve (binodal) is characterized by constant chemical potential μ0 = ∂F0 /∂ϕ = Const, phase-layering spinodal curve has the following form: ∂μ0 ⁄∂ϕ = 0. Spatial inhomogeneity of a blend in a mean-field approximation is included into the static structure factor g0(ϕ), that sets correlation radius for fluctuation of concentration. If this factor is used for polymer chains, we should take into account both correlation radius and Gaussian ball inertion. When interaction radius and monomer link size are within one exponent order, g0(ϕ) = а2 /36 ϕ (1-ϕ), so entropy contribution is dominant. The thermodynamical driving force of a phase layering is an exchange chemical potential μ(ϕ, gradϕ) = μ0 (ϕ) + μ0 (ϕ,gradϕ). When it becomes spatially inhomogeneous, the relative dissipative diffusion flow of components is generated. Chemical potential gradient refers to the diffusion flow density in a following form: I(r,t) = - (Λ/ kb T) grad μ,
(3.8)
where I(r,t) is a diffusion flow density, and in the repetition mode* Onzager coefficient Λ = Λ(ϕ(r,t)) = Const >0. System order parameter u(r,t), reflecting change of concentration (generally, symmetry change), has the following form of temporal evolution ∂u(r,t) /∂t = - div I
(3.9)
Transition of a single-phase system with equilibrium concentration ϕ0 into a state that is thermodynamically nonequilibrium, by fast cooling for example, makes ϕ0 nonequilibrium in new conditions and system starts to relaxate to new equilibrium concentrations set by binodal. Spatial inhomogeneity is defined [2] by the free energy functional with density as a sum of spatially homogeneous gradient (surface) energies:
*
The functions of Λ(ϕ) on inhomogeneity scale (fluctuation wave number), degree of polymerization, concentration etc. [7-9, 39] are known.
Heterogeneous Oligomer Systems F(u(r,t)) = F0 (u(r,t)) + F0 (u(r,t)), grad(u(r,t))
189 (3.10)
Free energy density of a spatially inhomogeneous blend is calculated by the following series expansion F0(u(r,t)) = 1/2 ϕ0 u2 + 1/3 f1 u3 + 1/4 f2 u4
(3.11)
The factor f0 is positive for χ<χс and is negative for χ>χс (where χс is a critical value of the Flori-Huggins parameter), f1 reverses its sign when crosses binodal, where it has zero value, and the factor f2 is always positive. It matches requirement of the free energy minimization with one minimum in a solution area and two minimums in a two-phase area. The gradient part of the free energy: F0 (u, grad(u(r,t)) = 1/2 g0 (grad u)2.
(3.12)
3.2. EXPERIMENTAL INVESTIGATION OF PHASE EQUILIBRIUM 3.2.1. Phase Transitions in Single-Component Systems Many authors studied various classes of oligomers with different molecular weight characteristics in a broad temperature range. Various methods have been used to discover reversible phase transitions of different types: liquid – crystal, liquid – glass, liquid – rubberlike structure as well as mixed amorphous-crystalline transitions (see, for example [20,26,40-53] and associated references). These researches contain discussions on phase separation within a framework of nucleation and spinodal separation mechanisms. They also analyze behavior of oligomer systems beyond and below glass temperature (Тст ≡ Тg). Attribution and temperature localization of α-, β-,γ- transitions and in some cases of l l transitions are provided for relaxation spectrums of oligomers. It was noticed that melting and crystallization temperature have (Тm, Тcr) so as Тg in homologous rows depend on molecular weight (М), chain length (n), Van der Waals volume (Vv) end group concentration and branchings, oligomer unit flexibility etc. All these parameters have different sometimes even opposite tendency of variation. For example, it was shown for epoxide oligomers [46] that their Тg is directly proportional to М (due to contribution of end groups) while Тm of oligourethane ethyleneglycole metacrylates [54,55] is in inverse proportion to М (due to crystallizing segments of an oligomer chain). The curves of a function “maximum crystallization rate temperature Тmcr on n” [56] plotted for dimetacryl derivatives of oligotetramethyleneglycole and oligo ethylenemethyleneglycoleformale tend to have two sections. The first one represents Тmcr as a function of n (growth), while second section shows now such dependence (chain conformation folding is limited by n). These dependencies and many other effects discovered for oligomers have been logically explained using theories and by analogy with low- and high molecular compounds. This huge stock of routine but very important and necessary experimental data will obviously take a worthwhile place in reference books later on.
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We will discuss below another nontrivial experimental effect, that has no direct analogies with experiments known for monomers or polymers and deals with two-stage melting mechanism of vitrified oligomers. M.P. Berezin and G.V. Korolev have applied precision thermomechanic method first to oligoesteracrylates [57], then to other types of oligomers [58-60]. They have discovered that close to Тm at some temperature Т’, that is 5-14 оС below Тm (the value ΔТ = Тm – Т’ does not depend on oligomer nature), abrupt thermal occurs (approximately ten times: from 10-4 degrees-1 to 10-3 град-1, that is typical for liquids) and to keep elastic properties on a level, that is typical for a solid state of matter. Transition into liquid flow state is observed only when it is further heated to Тm. This effect is illustrated in Figure 3.4, taken from the research [60] and showing curves “deformation ε temperature Т” for acrylic monomer and oligomer. Let’s note that the structure of experiment excludes contribution of kinetic effects (nonequilibrium state) that are in principal possible when scanning temperature.
Figure 3.4. Thermomechanical curves of acrylates: 1- methylacrylate; 2 – triacrylate-trimethylpropane.
The authors of [57] use physical nets approach for interpretation of these results. A molecular net is assumed to be dense enough in ΔТ interval to provide molecular mobility, that is sufficient for a volume thermal extension and is typical for liquids, but at the same time it restricts translational mobility of molecules, and keeps them “interconnected” making a system to resist mechanical deformation as a solid body. The necessary condition for such a scenario is that the lifetimes of mesh points τ are not less than the observation time tobs. The authors of [59] provide another interpretation of this phenomenon. They assume that a micro-heterogeneous associative structure is formed in oligomer system within ΔТ interval that consists of “weakly connected discrete microareas of strongly associated molecules”. The monograph [60] provides a more detailed research of two-stage “solid body - liquid” transition. To be more specific, they have used “spin-mark” (paramagnetic probe) method [61] to trace temperature evolution of associative structures of oligoesteracrylate. Figure 3.5 shows EPR spectrums obtained for a stable nitroxyl radical of 2,2,6,6,-tetramethylpiperidine1-oxyl, introduced into oligocarbonatemetacrylate (OCM-2) matrix in a temperature range
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from -120 to +20 0С. We can see that within a temperature range Т> Тm the width of spectrum does not exceed 30-40 oersted. The temperature range Т< Т’ shows signal width of 65-70 oersted. The intermediate temperature range (Т’ <Т < Тm) is characterized by superposition of narrow and wide signals. Considering informational potential of the paramagnetic probe method [61], we can obviously conclude that this probe radical is at least in two types of structures, that suppress its rotary mobility on different ways. Therefore no matter what approach is used for interpretation of discussed effects (a situation when both variants take place is also possible) we can apparently conclude that Тm has aggregative nature. Let’s note here that authors of [53] have obtained two-component form of NMR spectrum lines (see Figure 3.6) for oligocarbonatemetacrylate OCM-1 at Т > Тg and therefore suppose that molecules with different mobility can exist in a system: single molecules (or “disorganized” in terms of this book) and associated molecules (or “aggregated” in terms of this book).
Figure 3.5. EPR spectra of 2,2,6,6-tetramethylpiperidine-1-oxyle in “OKM-2” in a temperature range 120 ÷ + 200С. a) Т’ > Т; b) Т’<Т<Тm; c)Т>Тm. Explanation is provided in text.
Figure 3.6. NMR spectra of “OKM-1” at temperatures: 180 (1), 200 (2), 220 (3), 250 (4), 270 (5) и 280К (6).
Are these aggregates (associates) phase nucleuses or they just transit into solid phase unchanged due to loss of mobility decrease of temperature? It's still not clear. Each of these conclusions is confirmed by various arguments [62]. Phase transition mechanism in oligomer systems most probably depends on conditions of an experiment that are pressure, presence of impurities, scanning rate of temperature etc.
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3.2.2. Phase State Diagrams of Binary Systems As it was mentioned above, the major part of oligomer systems* has limited compatibility and therefore phase state diagrams are the source of the most complete information on these systems. Experimental phase diagrams of all practically important systems (and other ones) can be found in the following monographs and reference books [41,51,52], and [42-48]. We’ll take only some examples of this enormous amount of experimental data to reveal some specific properties of oligomer systems. Figures 3.7 - 3.10 show phase diagrams plotted for various classes of oligomer systems. You can see that all of them have upper critical solubility temperature. You can also see that the position of binodales is determined by molecular characteristics of components. It depends on a molecular weight of components, the nature of oligomer block and functional groups, second component polarity etc. Lower olefins will infinitely mix with cis-polyisoprene even at the room temperature. Increase of n in a homologous row of n-alkanes gradually decreases their compatibility with cis-polyisoprene. As Figure 3.7b shows for these components, when n is increased from 31 to 310, concentration range of solubility gets more narrow and upper critical solubility temperature grows. Binodal curves for components with n > 400 almost merge with ycoordinate axis within entire investigated temperature range, therefore these components are almost mutually insoluble. Polar rubbers (butadiene-nitrile) are characterized by a relatively low swelling in low-molecular olefins and almost insoluble at n > 30.
Figure 3.7. Phase state diagrams of cis-polyisoprene blend with n - methylene-dometacrylates (a) and with n -methylenes (b) at n = 2 (1), 4 (2,2’,2”), 5 (3), 8 (4) 10 (5), 31 (6), 62 (7), 125 (8) and 312 (9). Cis – polyisoprene molecular weight: 220 000 (1-9), 38 000 (2’) and 61 000 (2”). ϕ2 is a volume fraction of cis-polyisoprene.
*
We should remind you that oligomer systems in this monograph are defined as systems with at least one oligomer component and a low-molecular-weight, oligomer, or high-molecular-weight compound as a second component.
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Figure 3.8. Phase state diagrams of PVC - n - oxyethylene-dimetacrylate blends. Numbers on curves correspond to n value. φ2 is the volume fraction of.
Figure 3.9. Phase state diagrams of phenol-formaldehyde oligomer blend with butadiene – nitrile rubbers. “SKN-18” (1), “SKN-26” (2), “SKN-40” (3). φ1 is the volume fraction of oligomer.
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Figure 3.10. Phase state diagrams of polycarbonate blends with epoxide oligomers. “ED-20” (1), “ED40” (2) and “ED-44” (3). φ1 is the volume fraction of oligomer.
N-oxyethyleneglycoles with n = 1-13 displayed no spontaneous mixing neither with polar nor with non-polar polymers in a test temperature range 20 - 140°С [49]. At the same time, as the publication [51] shows, n-ethyleneglycole mixtures (molecular weight = 300 - 20000) with polymethylmetacrylate or polystyrene show decrease of the upper critical solubility temperature when the molecular weight oligomer component grows, in other words their compatibility reduces. These data, so as phase diagrams of oligomer mixtures with limited compatibility consisting of three homologous rows of n-oxyethyleneglycole, n-alkanediole and noxyethylene-( phthalate)glycole bimetacrylic esters, and homologous rows of epoxy oligomers with various polymers[41-49], demonstrate the following: a)
assuming other conditions being the same (the same length and chemical nature of oligomer blocks), solubility is determined by the nature of oligomer end groups and matrix polarity. The following row of groups demonstrates reduction of solubility
when oligomers dissolve in non-polar cis-polyisoprene. However, if non-polar butadienenitrile rubber is chosen as a solvent, this row changes into the following:
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b) increase of n reduces solubility in some cases, but can promote it in other cases c) some systems show that their compatibility does nor depend on n.
Figure 3.11. Dependence of UCST (а) and γ (б) on n for blends formed by n-ethylene - dimetacrylates (1,3,5) and n-oxyethylene-dimetacrylates (2,4,6) with cis-polyisoprene (1,2), butadiene-nitrile rubber “SKN-40” (3,4) and PVC (5,6).
Oligomer nature as well as molecular structure of a second component determines whether solubility depends on n or not. A good graphical presentation of this effect for two of above mentioned homologous rows and three polymer matrices is shown in Figure 3.11, where UCST values as well as its relative variation γ = (UCST)n / (UCST)n-1 are analyzed as a function of n. As we can see, increase of n for n-oxyethylene-bimetacrylic oligomers in mixtures with cis-polyisoprene or polybutadienenitrile or polyvynilchloride always reduces compatibility, while increase of n for n-methylene-bimetacrylic oligomers (at least, for ones used in experiments) leads to expected reduction of compatibility only in mixtures with
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polybutadienenitrile. Other examples show different effects: compatibility in a mixture of nmethylene-dimetacrylate with polyvynilchloride does not depend on n within n=1-10. But a polyisoprene mixture (as in examples shown above, with mixtures of n-ethyleneglycole with polymethylmetacrylate and polystyrene [51]), despite all known experimental demonstrations [50,52,63-67] that growing molecular weight of components reduces their compatibility, increase of n of an oligomer improves mutual solubility of components in this case
3.2.3. Mixing of Oligomer Blends: Analysis of Thermodynamic Parameters The analysis of concentration and temperature dependencies of thermodynamic parameters, calculated using phase diagrams, provides not only explanation of some compatibility features but also the way to estimate structural characteristics of oligomer systems. This approach is rather prospective, that will be illustrated below by examples analyzing mixing thermodynamics of various oligomer system types.
Mixing Thermodynamics of Rubber – Oligoester Acrylates Systems The data provided in Part 3.1.2 seem to be contradictory at the first sight. First off all, experimentally confirmed abnormal growth of compatibility of cis-polyisoprene with oligomers n-methylene-dimetacrylic oligomers so as of polymethylmetacrylate and polystyrene with n -ethyleneglycoles occurs when n increases. This effect contradicts to all known models and doesn’t meet scientific experience that the study of oligomer blends compatibility shows [50,52,63-67]. However, these data have no inner contradictions. The fact is, increase of oligomer’s n in cis-polyisoprene and n-methylene-dimetacrylate mixtures causes well-determined change of entropy and enthalpy in opposite directions: the first one promotes mutual solubility of components while other causes its reduction. The final result is evidently determined by concurrent their contributions into minimization of the system free energy. Calculations made in [68,69] provide quantitative expression for this approach based on restrictions of the modified Flori theory. Figure 3.12 represents phase diagrams (of Figure 3.7a) reconstructed using equation [69] χ12=χн+χs=Δμ1R /RTυ22=ΔH1 /RTυ22 – ΔS1R /Rυ22=Δμ1 - T ΔS1K / RTυ22
(3.13)
Here Δμ1R is a residual (redundant) chemical potential, ΔS1K and ΔS1R are redundant combinatorial and non-combinatorial mixing entropies correspondingly, ΔH1 is a redundant mixing entropy, R is the universal gas constant, υ1 and υ2 are volume fractions of components.
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Figure 3.12. The dependence of χ12 (1), χH (2) and χS (3) on n for blends of cis-polyisoprene with n methylene-dimetacrylates at 40 °С.
As this picture demonstrates, initial decrease of χ12, that follows increase of n, is caused by an observed fact, that the mutual solubility of components improves. However, contributions of χн and χs, into variation of a free energy in a system are different. The enthalpy member χн decreases when n grows, therefore showing that the change of enthalpy during mixing promotes compatibility (the level of self-organization is less than the initial one for components), while the entropy factor restricts solubility (χs decreases because of increase of combinatorial units). At first, contribution of χн prevails contribution of χs and solubility of an oligomer in a rubber increases for bigger n. At certain values of n contributions of χн and χs compensate each other, therefore molecular weight of oligomers exerts a small influence on χ12 and so as on compatibility of components. Further increase of quantity of methylene groups in an oligomer molecule leads to prevailing contribution of entropy factors n=13 - 15, thus making the resulting curve χ12=f(n) grow [49]. The analysis of chemical structure of components that determine their molar polarity [70] leads us to the same conclusions on extreme compatibility of cis – polyisoprene with nmethylene-dimethylmetacrylates. Indeed, molecules of these oligomers include two types of fragments – non-polar methylene units (polarization amount of this component is Р = 55.7), with their quantity varied in homologous rows, and fixed number of metacrylic ends, that are connected with oligomeric block by a polar complex –ester bond (Р=319.4). Therefore increase of n will inevitably reduce the molar polarity of an oligomer component, that will in turn promotes its solubility in nonpolar cis-polyisoprene. On the other hand increase of n means increase of MW, that inevitably reduces compatibility. Compatibility is therefore determined by competitive contribution of two opposite factors: polarity of components closing in and solvent’s (oligomer's) MW growth that occur simultaneously when n increases, but exert opposite influence.
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This assumption is confirmed by the effects of the Flori-Huggins solution theory. The publication [68] demonstrates equation based on the classical variant of the theory and shows oligomer molecular weight Х (1), molar polairities of oligomer and polymer molecules (2) as a function of oligomer chain length n, temperature and concentration (ω): 1/X1 ≈ A1(V/RT)×[(B1 + n)/(B2 + n)]2×(ω1’+ω1”)
(3.14)
where А1 determines contribution of molar links, whereas B1 and B2 are parameters that determine contribution of nonpolar links and groups and are calculated using Van-Crevelen method by group contributions [71]. The application of equation (3.14) to a system of cis-polyisoprene - n-methylenedimetacrylate with n < 15 shows that the contribution of polar groups is comparable with contribution of methylene links. When n > 15 we need not take into account the contribution of metacrylic end groups and the phase equilibrium will be determined by a contribution of just a nonpolar part of a molecule into χ1. These values correspond to estimations based on the modified Flori theory (see Figure 3.12). Calculations for UCST and critical concentrations made for various systems provide satisfactory correspondence to experimental values (Table 3.1). Table 3.1. Critical state characteristics for elastomer - oligomer systems [69] Elastomer
cis-polyisoprene
polybutadiene-nit rile
oligomer
DMM
DMM TGM TGM
n 2 4 5 8 10 8 3 13
UCST, calc. 173 106 51 46 35 111 35 142
(
С exper. 108 53 48 35 110 33 144
’ )cr
1
calc. 0,05 0,06 0,07 0,11 0,06 0,06 0,13
exper. 0,06 0,08 0,08 0,12 0,07 0,11 0,14
∗ n-methylene-dimetacrylate; ∗∗ n-oxyethylene-dimetacrylate; ∗∗∗ contains 40% of nitrile groups.
Mixing Thermodynamics of PVC – Oligoester Acrylates Systems Mixing thermodynamics of PVC with oligoesteracrylates has been partially discussed in Part 2.6.3 Further parts of this book provide analysis of thermodynamic functions made in [72] that were used for mixing of PVC with oligomers of two various homologous rows: nmethylenedimetacrylates and n-oxyethylenedimetacrylates. This analysis raised some important aspects of self – organization in coexistent phases of two-phase mixtures. Figure 3.13 shows the way of how the residual chemical potential of mixing Δμ1R depends on temperature is determined by the nature of an oligomer component of a mixture and the relaxation state of a matrix. Mixtures, containing any of investigated n-methylenedimetacrylates and the first two representatives of n-oxymethylene-dimetacrylates, demonstrate that only Δμ1R as a function Т varies at transition from a glass state to a rubber state, therefore it’s just the rate of ordering that varies. However, mixtures of PVC with n-
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oxymethylene-dimetacrylate at n ≥ 3 demonstrate transition from the disordered state (Δμ1R grows at Т ≤ Тg) to a self - organization (Δμ1R decreases when Т grows at Т > Тg) at the transition point Тg. It leads to a paradoxical conclusion [49,70]: if a phase diagram for these systems was limited by only a glass state of a matrix, it would be characterized by only the Lower critical solubility temperature (LCST). However, oligomer introduced into PVC plastificates polymer and reduces Тс. Phase separation temperature range for different С1 includes α-transition temperature. Experimental heating beyond Тg shows that growth of Δμ1R reverses to decrease, therefore these mixtures are characterized UCST* beyond Тg*.
Figure 3.13. Temperature dependence of Δμ1R in blends of PVC with n-methylene-dimetacrylates (DMM is shown by black dots) and n-oxyethylene-dimetacrylates (DMOE is shown by light dots). Numbers on curves correspond to n value.
More information on a self – structure formation in two-phase state of oligomer systems can be obtained analyzing he function of partial values of redundant thermodynamic functions on oligomer block length (Figure 3.14 and 3.15). As we can see, mixing PVC with oligomers based on n-methylene-dimetacrylate, results in no influence of n on values of thermodynamic parameters, and demonstrates, that compatibility does not depend on n (as we mentioned above for these systems) (Figure 3.11).
*
The work [48] provides extensive information on how thermodynamical parameters and Тg of the matrix are interconnected applying to the system PVC – various weight oligoesterepoxydes.
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Figure 3.14. Dependence of Δμ1R, ΔΗ1, ΤΔS1 и ΔS1R on n for blends of PVC with n -ethylenedimetacrylates (o) and n-oxyethylene-dimetacrylates at 40 °С.
N-oxyethylene-dimetacrylate mixtures with PVC is another case. Increase of n for these systems leads to considerable change off all thermodynamic functions, and the form of such changes is different beyond and under Тg.
In the temperature range that is under Тg (Figure 3.14) ΔS1R values show a considerable decrease even negative values for n >2 already. It indicates, that oligomer concentration fluctuations has been formed, they are stable enough and have higher degree of molecular ordering compairing initial state of oligomer (before mixing). The values of ΔН1 decrease simultaneously indicating weakening of contact interactions between different molecules. The contribution of entropy component into Δμ1R is substantially more than that of enthalpy component and this parameter is proportional to n.
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Figure 3.15. Dependence of Δμ1R, ΔΗ1, ΤΔS1 и ΔS1R on n for blends of PVC with n -ethylenedimetacrylates (o) and n-oxyethylene-dimetacrylates (x) at 100 °С.
In the opposite, temperature ranges beyond Тg (Figure 3.15) both ΔН1, and ΔS1R grow together with increase of n, and enthalpy contribution prevails entropy contribution. Some possible reasons of the fact that the relaxation state of the matrix cannot influence on the character of thermodynamic functions change and therefore on the processes of self – organizations of oligomer systems have been discussed below. Qualitative law patterns, explaining differences in thermodynamic behavior of PVC - nmethylene-dimetacrylate and PVC - n-oxiethylenedimetacrylate blends have been obtained through the analysis of how thermodynamic parameters vary as functions of dipole moments ε of these OEA molecules and their relative association coefficients α. (A liquid is considered to be non – associated at α=1 [73]). The work [43] represents the values of ε calculated using group contribution theory by Van-Krevelen [71]. The increase from 2,71 ⋅103 to 4,44 ⋅103 cl.m for the row of studied nosiethylenedimetacrylates, but for n-DMM row these variations have only third –decimal
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point values. In [74] a method tested in [73] was used to calculate α for various OEA in their initial state from temperature patterns of viscosities. At the room temperature α grows from 1 to 10 for n-oxiethylene-dimetacrylates while n is increased from 1 to 4, however α varies in a range of 1 to 1,3 for n-methylene-dimetacrylates (this estimation is independent of [74]). Considering that thermodynamic characteristics depend on α and ε and comparing the curves obtained with similar dependencies on n, we can see that they coincide on a qualitative level. These data are nothing but confirmation of the logic of ordinary “chemical” reasoning: oligomer n-methylene-dimetacrylate blocks are less flexible and much less polar, then oligomer n-oxiethylene-dimetacrylate blocks, that can explain the tendency of the last ones to intermolecular interactions with same-type molecules and therefore – to self - organization. Let’s note, that the works [75-79] have proved that mixing of oligomers with polymers (it has been confirmed for components with various chemical structure), results in not only growth of association coefficients but also increases orientational interaction coefficients, i.e. increase ordering level inside aggregates themselves. For more detailed information see Part 2.6.4. It is also interesting to mention, that for all studied PVC-oligoesteracrylate systems the position of the point of inflection (Т’i) on the curves Δμ1R = f(Т) is linked with a glass transition temperature by the following equation ΔТ1 = Т’i - Тg = Сonst ≅ 120°С
(3.15)
The physical meaning of the parameter ΔТ1 is not clear enough yet. The explanation in [49] tries to use an analogy with the “special” Chaikov point [80]. The work [43] explains it as a possibility of realization at Т> Т’i off all energetically preferred molecular conformations, that can in principal influence the number of pair interactions of the same-type and different molecules. Based on theoretical data, presented in [81], we cannot exclude a possibility, that the Т’i point describes a situation in a system when a cooperative interaction between aggregates becomes possible*. Observation of system evolution in all temperature range allows to interpret Тс in a simple way as the lower boundary of an area, where molecules can potentially form aggregates through self - association. When temperature increases (in other words, when concentration grows) these systems (at least their oligomer component, according to the analysis of thermodynamic data) initially become more inclined to aggregation. Accumulation of aggregates results in their mutual interaction, the more aggregates form the more is their contribution to the free energy of a system in relation to the energy of interaction between aggregates and separate molecules. UCST is the upper boundary where aggregates “collapse” into a single “cluster”. If it is true, it leads to a conclusion that Т’i can be an intermediate point with similar energies of interaction between separate molecules, which determines if it is possible to form an aggregate, between aggregate and a separate molecule and the interaction energy between aggregates, that will inevitably lead to change of variation pattern of thermodynamic functions.
*
The same approach has been used in [59] to explain two-stage pattern of the “solid body - liquid” transition during devitrification of oligomers.
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These versions however require additional argumentation. Let’s emphasize that independent on possible explanations, the fact of existence at Т>>Тс of a fixed correlation between thermodynamic functions of a solution with Тg (see equation (3.15)), so as their strict connection with UCST, found for oligomer – oligomer blends [82-84] are not casual and may be fundamentally reasoned.
Mixing Thermodynamics of Oligobutadiene Urethane(met- ) Acrylate – Oligoester Acrylate Systems Investigations of mixing thermodynamics of oligomer – oligomer system components with the first component from the row of n-oxiethylene-dimetacrylates and the second one was oligobutadieneurethane-dimetacrylate (OBUM) with ММ=3950 or oligobutadieneurethane-diacrylate (OBUA) with ММ=4500 [82-84], have confirmed in a whole the law patterns, considered above for representatives of the rubber – oligoesteracrylate blends (OEA) and PVC-OEA. They allowed to provide the more exact description of variation patterns of thermodynamic functions in oligomer systems with similar molecular structure of components, to understand commonality and differences of supramolecular structure formation processes in semidiluted (on the left branch of a binodal) and diluted (on the right branch of a binodal) solutions of coexisting phases, to obtain the concentration pattern of thermodynamic functions along binodal up to UCST, etc. First of all let’s note that the values of the critical parameters of these systems, calculated using equations of the modified Flori theory, show a satisfactory correspondence to experimental data (see. Table 3.2). Table 3.2. Critical State Characteristics for OBUA and OBUM Mixtures with Oxyethylene-Dimethyl Acrylates [82] Component
n
OBUA OBUM OBUA OBUM OBUA OBUM OBUA OBUM
2 2 3 3 4 4 13 13
UCST, K calc. exper. 330 338 319 318 345 350 340 350 369 367 357 363 645 588 -
(
’ )cr
(
1
calc 0,19 0,20 0,20 0,21 0,21 0,22 0,27 0,28
exper. 0,17 0,18 0,16 0,18 0,19 0,17 0,24* 0,35*
)cr
12
calc 0,76 0,78 0,77 0,81 0,81 0,83 0,93 0,96
exper. 0,74 0,78 0,76 0,78 0,80 0,81 -
∗ Extrapolated.
Temperature Dependencies Temperature dependencies for the parameter χ12 and its components χн and χs are singletype for all systems formed by OBUA (OBUM) and n-oxiethylene-dimetacrylates and n = 2 13. They are represented in Figure 3.16 for solutions of OBUA in n-oxiethylenedimetacrylates. We can see that within a temperature range 20 - 100 °С the variation of χ12 is relatively low. 80°С increase of temperature results in decrease of their absolute values within 0.1 - 0.2. In addition, approach to UCSTs, that are marked with arrows in Figure 3.16 the rate
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of decrease of χ12 slows down, that is opposite to the pattern of variation of χн, which increases considerably with Т, and χs, which falls down. The absolute values of the interaction parameter at temperatures far below UCST are mainly determined by the value of the reduced mixing entropy χн. Temperature growth is accompanied by decrease of χн contribution while χs contribution increases. And at the area near UCST, χ12is virtually fully determined by the residual entropy value.
Figure 3.16. Temperature dependencies of χ12 (2-4), χH (2’-4’) and χS (2”-4”) in OBUA - noxyethylene-dimetacrylate systems. Numbers on curves correspond to n value.
Let’s discuss temperature dependencies of thermodynamic mixing functions for the left and right binodal branches, i.e. analyze the pattern of their variation at approach to UCST when concentration is either increased or reduced. It is necessary to note that system states analyzed below are for binodal only, that is for coexisting phases. One of them is a semidiluted solution (the left branch) while another one (the right branch) is a diluted solution. This fact stipulates, in particular, a situation when the variation of temperature is by force accompanied by the change of concentration of solutions. If increase of Т in semidiluted solutions leads to increase of solvent’s concentration, which is on of n-oxiethylenedimetacrylates in our case, the situation in diluted solutions is opposite: increase of temperature is accompanied by decrease of concentration of this oligomer.
Semidiluted Solutions The temperature dependencies of thermodynamic mixing parameters for semidiluted solution phase are presented in Figures 3.17 - 3.19. Their analysis leads to interesting conclusions.
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Enthalpy The partial mixing entropy ΔН1 is positive for all studied systems (Figure 3.17). The less is system temperature the more is ΔН1. The largest relative changes of the partial mixing entropy can be registered at considerable distance from USCT. They decrease during approach to UCST, and ΔН1 → 0 in the critical point area.
Figure 3.17. Temperature dependencies of ΔΗ1 (2-4) and Δμ1R (2’-4’) in semidiluted OBUA - noxyethylene-dimetacrylate solutions. Numbers on curves correspond to n value.
At Т = Const (ω1 = var), the partial mixing entropy of these oligomer – oligomer systems, so as of above discussed polymer – polymer systems (see Parts 3.2.3), proves to grow with increase of the n parameter of oligomer. But at fixed distances from the critical point, i.e. if ΔТ = ВКТР - Т = Const (ω1 = Const), ΔН1 are approximately equal for all studied systems.
Entropy The pattern of variation of the partial mixing entropy ΔS1 (Figure 3.18) is the same than that of the enthalpy: increase of Т leads to decrease of ΔS1. Decrease of its combinatorial component ΔS1c (Figure 3.18) is well - stipulated: It is determined by a decrease of OBUA concentration at approach to UCST (let’s remind that the analysis is being carried out for binodal where variation of temperature is accompanied by variation of concentration). The pattern of variation of the non-combinatorial entropy component ΔS1R (Figure 3.19) is determined by a temperature and not only indirectly (through concentration as in the previous case with ΔS1c ), but also directly, because ΔS1R characterizes how the number of possible locations of component molecules varies due to ordering or disordering, and it depends both on concentration and on temperature.
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Figure 3.18. Temperature dependencies of ΔS1 (2-4) and ΔS1K (2’-4’) in semidiluted OBUA - noxyethylene-dimetacrylate solutions. Numbers on curves correspond to n value.
Figure 3.19. Temperature dependencies of ΔS1R (2-4) in semidiluted OBUA - n-oxyethylenedimetacrylate solutions. Numbers on curves correspond to n value.
We can determine three temperature areas with different variations of entropy characteristics for systems discussed. At Т = UCST - ΔТ, where ΔТ > 35-40°С, ΔS1R > 0, and ΔS1 > ΔS1к , i.e., at temperatures far from ВКТР more than 35-40 °С, the blend structure is less ordered than that of initial components. At ΔТ =35-40°С ΔS1R = 0 and ΔS1 = ΔS1к , i.e. the partial entropy of a system is determined by its combinatorial component. At last, at ΔТ < 35-40 °С ΔS1R < 0 and its negative value grows with Т. However, approach to UCST leads to slowing down of variation of values so ΔS1R starts to increase slowly near the critical point but always stays negative. ΔS1 < ΔS1к in this area respectively, i.e. the system structure is more aggregated here comparing initial components.
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Chemical Potential The analysis of the temperature dependence of the residual chemical potential Δμ1R (Figure 3.17), which is determined as Δμ1R = ΔН1 - ТΔS1R, allowed to reveal thermodynamic reasons of limited compatibility of n-oxiethylene-dimetacrylates with OBUA и OBUM type oligomers. The main factor preventing dissolution at ΔТ ≥ 35-40 °С is considered to be high interaction energy of one-type component molecules, which is considerably higher than that of different – type molecules (see ΔН1 variation in this figure). The contribution of disordering processes is small (ТΔS1R > 0) and just partially compensates energy contributed by dissolution. At ΔТ < 35-40 °С and approaching UCST, the energy, that prevents solubility, decreases but at the same time aggregation one one-type molecules increases in a much faster rate (ΔS1R < 0). The critical state area is characterized by the prevailing entropy factor. Diluted Solutions Variations of thermodynamic mixing parameters at the right binodal branch with corresponding temperature dependencies shown in Figures 3.20 - 3.22, differ from dependencies for above-discussed semi-diluted solutions. The first difference is the scale of registered changes, the second one is the observed pattern of their behavior. Enthalpy As a function of temperature in the phase of diluted solutions has an extreme pattern of variation (Figure 3.20), in contrast to the left branch of binodal, where it monotonically decrease (Figure 3.16). The growth of Т here, accompanied by the growth of OBUA concentration in a diluted phase, leads first to increase of ΔН1 and then to its decrease at ΔТ ≤ 35-40 °С. In the UCST area ΔН1 → 0.
Figure 3.20 Temperature dependencies of ΔΗ1 (2-4) and Δμ1R (2’-4’) in the phase of diluted OBUA - noxyethylene-dimetacrylate solutions. Numbers on curves correspond to n value.
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Entropy Figure 3.21 shows that the total partial mixing entropy ΔS1 at ΔТ > 35-40 °С is almost fully determined by its combinatorial component ΔS1к. Though the values of the residual non – combinatorial component ΔS1R are positive (Figure 3.22), their absolute value is small and therefore they don’t make any noticeable contribution to ΔS1. The situation is changed at ΔТ < 35-40 °С. ΔS1R values reverse their sign to negative and quickly fall down approaching to UCST. Though the values of the residual combinatorial component grow (Figure 3.20), the rate of growing does not exceed the rate of decrease of ΔS1R. That is why the resulting curve ΔS1 = f(Т) goes through a flat maximum.
Figure 3.21. Temperature dependencies of ΔS1 (2-4) and ΔS1K (2’-4’) in the phase of diluted OBUA - noxyethylene-dimetacrylate solutions. Numbers on curves correspond to n value.
Figure 3.22. Temperature dependencies of ΔS1R in the phase of diluted OBUA - n-oxyethylenedimetacrylate solutions. Numbers on curves correspond to n value.
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Therefore, when temperature increases, the diluted phase structure is formed through concurrent and different influence of various processes. At ΔТ > 35-40 °С, the main component contributing system disordering is ΔS1c due to small positive values of ΔS1R, ΔS1c is proportional to Т. But at ΔТ < 35-40 °С the total entropy ΔS1 is determined by a contribution of both components, with ΔS1R contribution starting to dominate when Т increases. Therefore, ordering of the diluted solution structure grows. At ΔТ → 0, that is the temperature equal to UCST, the structural organization is the most regular, because fluctuations of concentration of one-type molecules become the main structural element of this phase.
Chemical Potential The temperature dependence Δμ1R in the phase of diluted solution (Figure 3.20) is opposite in its tendency to the phase of semidiluted solution (Figure 3.16) - when Т increases, Δμ1R also increase. And at the area far the critical point, Δμ1Ris virtually fully determined by the positive enthalpy member ΔН1. Increase of temperature in a range ΔТ > 35-40 °С up to UCST is accompanied by intensive growth of positive values of Δμ1R, indicating decrease of thermodynamic affinity of components. And at the area near UCST, Δμ1Ris virtually fully determined by the entropy member ТΔS1R. One of possible schematic approaches to explanation of results, that were provided above, can be expressed in the following assumptions: The main factor preventing dissolution below in the area 35-40°С below UCST is high interaction energy of one-type molecules, which is higher than that of different – type molecules (compare values ΔН1, ΔS1 and Δμ1R ). Further increase of temperature allows to overcome a certain energy barrier, that increases the rate of molecular dispersion, but at the same time results in structural reorganization of a system through formation of long – wave molecular concentration fluctuations of one-type molecules, that is indicated by an acute decrease of non – combinatorial entropy. Such an aggregation in a system certainly prevents dissolution (molecular dispersing). Aggregation level is maximal in the critical point. Concentration Dependencies Figure 3.23 generally represents all dependencies obtained for systems n -oxiethylenedimetacrylate - OBUA (OBUM) in a form F = f (ω1), where F ≡ Δμ1R , ΔН1 and ΔS1. Let’s emphasize that it’s just a plot reflecting tendencies in variation of dependencies observed without consideration of scale at which F values in various phases vary and differ sometimes ten times and more. It is necessary to provide a preliminary comment to Figure 3.23. The arrow а stands for concentration ω1cr, corresponding to UCST, arrows б and в represent concentrations ω1’ and ω1” for semidiluted ( ‘ ) and diluted solutions ( “ ) and corresponding to UCST + 40°С , that is temperature 40°С far from UCST or ΔТ = 40°С. Asymmetrical position of ω1’ and ω1” relative to ω1cr is a result of phase diagram asymmetry for these systems. The movement to the left of ω1cr along the axis ω1 describes behavior of semidiluted solutions and to the right of ω1cr –s for diluted solutions correspondingly. Increase of ω1 at ω1 < ω1cr results in growth of Т, while at ω1 > ω1cr T decreases, in other words increase of ω1 up to ω1cr is accompanied by the growth of Т, however its further increase at ω1 beyond critical point will inevitably lead to decrease of temperature (situation at the binodal).
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Figure 3.23. Chart of concentration dependencies Δμ1R (1), ΔΗ1 (2) and ΔS1 (3) for the system OBUA n-oxyethylene-dimetacrylate. Explanation is provided in the text.
Figure 3.23 allows us make a conclusion that increase of n-oxiethylene-dimetacrylate in a system will be accompanied by decrease of Δμ1R, though fall down, they don’t (in both phases) stay positive (curve 1). Let’s note that considerable differences observed at the scale of variation of residual chemical potential in phases: Δμ1R as a function of ω1 decreases on 2 2.5 decimal orders in semidiluted solutions (for various systems), while decrease of Δμ1R in diluted solutions stays within one decimal order for all range of “binodal” concentrations. However, it’s half as little in the second case. The pattern of concentration dependencies ΔН1 (curve 2) and ΔS1 (curve 3) is virtually the same. Both thermodynamic functions decrease while ω1 increases in semidiluted solutions and approach zero at concentrations corresponding to ω1cr. The values of ΔН1 and ΔS1 in diluted solutions increase up to a maximum at concentrations corresponding to ω1” (ΔТ = 40°С) and then decrease again. All the functions for all oligomer–oligomer systems have the form F = f(ω, T), except the residual mixing entropy ΔS1R, presented in Figure 3.23), which are positive. He last one is negative at ΔТ = 40°С (see [84]).
Thermodynamic Parameters as Related to UCST All above mentioned oligomer – oligomer systems can show a universal dependence of all thermodynamic parameters, indicated here as F: at the fixed distance from UCST of about 40°С both temperature and (in other terms) concentration dependencies vary considerably. This temperature is characterized by either reduction of F to zero with subsequent growth or transition from positive values of F to negative ones or considerable change of the rate of change of function. This point is indicated as transition temperature Т”t for all oligomer – oligomer blends studied in [82-84] and can be determined from the following equation: ΔТ2 = UCST - Т”m = Const = 38 ± 3 °С
(3.16)
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Certain reasons of why ΔТ2 can be considered to be strictly dependent on UCST due to concurrent contributions of “aggregate-aggregate” and “associate - molecule” have been discussed in Part III.2.3.2 so let’s come back to them, though other probable explanations are possible. Nevertheless let’s note again that though both ΔТ2 and ΔТ1 (see equations (3.15) and (3.16)) still lack a strict physical interpretation, the drastical change of patterns that thermodynamic functions represent near these points has been shown rather convincingly for various types of oligomer systems. We have reasons to suppose that both near these points and near UCST and the metastable area the processes of considerable transformation of oligomer systems occur, which result in such a considerable change in an oligomer system behavior.
Mixing Thermodynamics of Oligoalkyleneglycoles Oligoethyleneglycoladipinate Systems Thermodynamic properties of oligomer blends formed by oligoalkyleneglycoles and oligoethyleneadipinates have been first investigated by Yu.S. Lipatov and A.E.Nesterov, who used the reverse gas chromatography method for this purpose [85-87]. The systems mentioned above are interested not only due to their practical importance [88], but because despite systems described above they have both upper and lower solubility temperature and can help to reveal some specific characteristics of mixing thermodynamics of oligomer systems. Figure 3.24 represents thermal dependences of the redundant mixing energy ΔGM for the system formed by oligopropyleneglycole with molecular weight 1050 (ОPG-1050) – oligoethyleneglycoleadipinate with molecular weight 2000 (OEGA-2000). As we can see, the plot ΔGM - Т gives us two minimums with points in minimums coinciding for all range of concentrations. The presence of two minimums is a characteristics that distinguishes this system from polymer solutions and low molecular liquids with only one minimum at the curve ΔGM =f (Т) and only for systems with two critical mixing temperatures (UCST and LCST) [89,90].
Figure 3.24. Dependence of ΔGМ on Т in OPG - OEGA at the dosage of OPG: 0,1 (1), 0,22 (2), 0,35 (3), 0,87 w. % (4).
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Extrapolation of ΔGM from the first minimum to the low temperature range and from the second minimum to the high temperature range to ΔGM =0 (ideal solutions) provides [85] phase diagram with two critical temperatures (Figure 3.25). The temperature range between two minimums ΔGM (the shaded area in Figure 3.25), is characterized by the negative redundant enthalpy ΔНM and entropy ΔSM (see Table 3.3).
Figure 3.25. Phase state diagram of the OEGA - OPG system. Explanation is provided in the text.
Table 3.3. Mixing Enthalpy and Entropy of the System OPG – OEGA [85]
OPG/OEGA weight % 0,12/0,88 0,22/0,78 0,35/0,65 0,50/0,50 0,65/0,35 0,87/0,13
In a temperature range 34….46 С (below of the first minimum) S M, НM, kcal/mol cal/(mol·K) -5,20 -17,50 -2,00 -6,43 -0,93 -2,85 -
60….97 С (between two minimums) S M, Н M, kcal/mol cal/(mol·K) 0,27 -1,34 -0,33 -0,95 -0,16 -0,20 -0,22 -0,39 -038 -1,10 -0,27 -0,70
The negative values of ΔSM indicate that contribution of non-combinatorial entropy into total mixing entropy is negative. As the authors of [85,86] consider, experimentally found exothermal effect and the reduction of entropy are not the result of stronger interaction between different components, that cloud be a logical conclusion [64,90-92]. These effects are stipulated by formation of ordered aggregates of one-type molecules and the heat evolution during crystallization of one of components (OEGA can crystallize).
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The system oligoethyleneglycole (OEG) with MW = 15000 – OEGA represents another thermodynamic and concentration dependencies of thermodynamic parameters. The phase state diagram of this system is shown in Figure 3.26. Shaded area corresponds to ΔGM > 0, that is the state with a low thermodynamic stability.
Figure 3.26. Phase state diagram of the OEG - OEGA system. Explanation is provided in the text.
The research [85] describes a very interesting result, that has been obtained through the study of temperature variation of ΔGM for this system. X-ray data show that OEG and OEGA components crystallize separately when such system is cooled. But the experiment of reverse temperature cure demonstrates formation of an ideal solution in a point corresponding to the melting temperature Тm, ΔGM ≤ 0, that is Тm of a blend. Further increase of temperature leads first to the reduction of thermodynamic stability (ΔGM increases) and ΔGM starts to decrease only when a certain critical composition – dependant temperature is achieved. Let's consider another important fact [85-87]. The specific kept volume of oligomer system in a composition range where systems are compatible was beyond additive volume. And the specific kept volume of oligomer system in a composition range where systems are incompatible was below additive volume.. It means that at the good affinity of components the blend is less densely packed than at the low affinity of components when it is more densely packed. The last case can be explained by the redundant association of blend components according to the authors of [85], that is confirmed in [93-95]. At the same time, [51] demonstrates phase diagrams of oligopropyleneglycole (OPG) with MW = 1025 - oligo-(poly-) ethyleneglycole (PEG) with MW = 600 – 20000 blends (they are shown in Figure 3.27), that are characterized only by UCST. The components of this research are of course different from those we discussed above. These results have been obtained with various experimental methods. Nevertheless the initial chemical structures and aggregative states are similar enough that lets us think about the principal difference of phase
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diagrams. Let’s not hesitate that both experimental results are valid and recall previously used comment by А. Chalykh [51]: “the fact of contradictory experimental data is illusive and reflects complexity of the studied systems.”
Figure 3.27. Phase state diagrams of the blends: OPG, MW=1025 and PEG, MW = 600 (1), 1000 (2), 3000 (3), 4000 (4), 6000 (5), 15000 (6), 20000 (7). φ2 is a volume fraction of PEG.
Invariance of Phase Diagrams and Thermodynamic Parameters The systems (oligomer) - solvent, where the solvent is the representative of a homologous row of oligomers are characterized by invariance (superposition) relative to UCST for all phase diagrams and for all calculates thermodynamic parameters correspondingly [82]. Figure 3.28 show phase diagrams plotted for blends formed by oligobutadieneurethanediacrylate (OBUA) - n-oxiethylenediacrylates. They represent phase diagrams both in traditional coordinates T – ω1 (curves 2-4) and in ΔT – ω1 coordinates where ΔT = UCST - Т (curve 1). As we can see, the last variant shows that all binodals of investigated systems merge into one within the experimental error. It means that for these blends have the same boundaries of existence of stable solutions, if binodals are shifted along temperature axis at the value corresponding to the difference between their critical solubility temperatures. As it is shown in [82], when the distance ΔT from UCST is fixed all thermodynamic mixing functions also have similar values. As an example, Figure 3.29 represents temperature dependencies of the interaction parameter χ and its enthalpy χн and entropy χsparts in coordinates χ= f(ΔT), that have been calculated for these systems: all corresponding curves coincide within experimental error of the definition method used in [82] and differentiating error, that is inevitable at calculations of χ. Similar results provides rearranging of phase diagrams in coordinates χ= f(ΔT) so as the reduction to ΔT of thermodynamic mixing parameters for many other systems formed by polymer – homologous rows of oligomers, which are mentioned in literature, this conclusion has also been confirmed for rubber-oligomer and PVC- oligomer systems [49,68,69,72].
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Figure 3.28. Phase state diagrams for the blends: OBUA - n-oxyethylene-dimetacrylates (2-4 – Numbers on curves correspond to n value) and the summarized diagram of these blends in ω1 - ΔТ coordinates (1). ω1 is the volume fraction of OBUA.
Figure 3.29. Dependence of χ12 (1), χH (2) and χS (3) on ΔТ for blends of OBUA with n -oxyethylenedimetacrylates.
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3.3. FORMATION OF EQUILIBRIUM STRUCTURE IN HETEROGENEOUS OLIGOMER BLENDS The structural evolution during the formation of heterogeneous oligomer systems and their equilibration includes phase formation (or phase decomposition), establishing concentration equilibrium in each coexisting phase, interphase diffusive mass transfer, which leads to diffusive coalescence of the dispersion phase particles and, if kinetic bands are not taken into account, phase layering (separation of the system into layers). Of course, it is impossible to reach equilibrium on supramolecular structure parameters in coexisting phases until interphase gradient mass – transfer processes have finished. It may be the reason why thermodynamic equilibration rate in heterogeneous oligomer systems is 2 - 2.5 times more than that of homogeneous ones, if polymerization rates W0 are independent on τe, (Figure 3.30).
Figure 3.30. Dependence of τecr on the dosage of oligomer φ1 for the blends of tetramethylenedimetacrylate with cis-polyisoprene (1) and polybutadiene-nitrile (2) rubbers. Arrows correspond to phase separation concentrations.
Phase separation mechanisms in oligomer systems were usually analyzed in the framework of classical ideas on nucleation and formation of nuclea or spinodal decomposition, considered in Part 3.1, and described in detail for low molecular and high molecular weight compounds in [26,96-98]. The area these systems belonged to were also taken into account being either metastable or critical similar to the character of transition, for example liquid - liquid, liquid - solid, amorphous – crystalline, and etc. No principal differences for phase transition of oligomers have been found yet. Let us mention the series of works of Noim [20] investigating phase separation kinetics in oligostyrene – oligomethylphenilsiloxane system. It has demonstrated that the critical light scattering indexes in phase formation processes of this system correspond well to similar indexes produced in experiments with low molecular weight systems and can be successfully
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described by Binder theory [99]. Mutual diffusion coefficients measured using photon correlation spectroscopy and calculated based on Kahn – Hillard theory [27] are high enough. They proved to be about 10-11 cm2/s. In systematic works of Chalykh et al. [41,44,46,48,51] involving optical spectroscopy and electron microscopy methods, phase formation processes during mixing in various oligomer – oligomer and polymer – polymer systems have been analyzed. In general, if the dosage of components initially corresponds to the “below spinodal” position, it will finally result in the formation of a two-phase emulsion independent of the way of mixing. The first stage of the system evolution to the equilibrium state involves formation of the diffusion-limited concentration equilibrium, which depends on chemical affinity of components and on temperature, if certain components are used. Note that at Т = Const the equilibrium values of ω’ and ω” correspond to points at the left and right binodals of the phase diagram. Morphology of these emulsions (size and distribution of drops in the volume) depends not only on the nature of components, their correlation and parameters of the system state, but also on the method of mixing (swelling with following reduction of the temperature, forced mixing or components dilution in a usual solvent), on the type of the mixing equipment (rolls, blade mixers, ball mills and etc.), on the regimes of mixing (time, speed and temperature of mixing, the velocity of solvent removal and etc.). In other words, the degree of dispersion of two-phase oligomeric systems which was formed by the end of mixing, is determined by the energy, which “was pumped” into the system in the process of mixing. Available experimental data [43,49,63,100-106] testify to the wide range of the values of the phase inclusions particle size - from 0.01-0.05 to 20 - 60 micrometers – for different types of oligomeric mixtures and different methods of their preparation. Ceteris paribus, the morphology of compatible systems as well as the nature of the disperse phase and the disperse medium depends on the ratio of components. Figure 3.31 illustrates this process graphically, where the character of morphological transformation as the function of composition, was shown using the example of polymer-oligomer mixture. Obviously, with the increase of oligomer dosage in the system, the volume share ratio of solutions I and II changes and the average size of the dispersed phase increases. Phase inversion takes place under the registered values Т = Const ,С = Ci: the phase, which was disperse at С < Ci, became continuous at С>Сi.
Figure 3.31. Schematic presentation of morphological changes in two-phase polymer – oligomer systems with increasing dosage of oligomer. Сi is the phase inversion point.
Morphology of these systems can be variable in time. Their stability depends on the laws of colloidal chemistry [104]. It is necessary to note an important feature of oligomers, the possibility of morphology stability dependence on the viscosity of the system. If viscosities of
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the co-existing phases of oligomer systems (accordingly, solutions I and II ) are close, the situation described in Figure 3.31 determines which of the phases is continuous and which of them is disperse. If viscosities of the co-existing phases are different, for example, they differ by several decimal degrees [49,102] for polymer-oligomer systems, and the low viscous phase serves as dispersion medium, the morphology of these systems is unstable (see Figure 3.32) and confluence (coalescence) of the dispersed phase particles goes comparatively quickly. According to some facts [49,107], the full layering time for different systems is from 2-10 minutes to 24-48 hours. The range of these values is of particular significance. It is essential that the time of layering is comparable to the time of the experiment or other technological operations and that is why, in this case, we can not neglect the kinetics of morphology change. It is important to take kinetics into account for reactive oligomer systems, as chemical curing can register different morphologies [62].
Figure 3.32. Schematic presentation of the phase layering in polymer – oligomer systems with η1 >> η2.
If the high viscosity phase becomes a continuous medium (for example, the solution of oligomer in polymer), the morphology of the mixture can remain the same after the end of mixing. There are certain well-known experiments [43,49,102], showing that some rubber oligoester acrylate systems did not change their colloidal-disperse structure parameters for 5 years at ambient temperature, while PVC- oligoester acrylate mixtures kept their morphological stability for a year. However, this quasi-equilibrium is broken as soon as kinetic bans on layering disappear. For example, viscosity of dispersed medium decreases and the velocity of inter-phase diffusion increases with the rise of the temperature. At certain values of the temperature, the system loses its stability, and the emulsion drops start to coalescence; this situation is described in Figure 3.32. The inter-phase diffusion of oligomeric systems was not investigated, although it is this very diffusion that determines the velocity of emulsion drops coalescence. We can suppose that the mechanisms of interphase transport of polymer and low molecular weight diffusants, described in [108,109], can be evidently applied to oligomer systems. It is generally known [108], that coefficients of diffusion in heterogeneous systems depend on not only on the temperature and structure, but also on the phase interface surface area. Therefore, equilibration time in these systems depends on degree of the mixture dispersion. The morphology of these systems depends on their prehistory and can be changed with time. Obviously, these are reasons of some specific effects of behavior of heterogeneous oligomer blends in the experiment: in contrast to single-phase oligomer systems, dependence from the method of preparation of samples took experimental W0 and also τэcr and τоcr , [110-111]. Interesting opportunities of morphology regulation of oligomeric systems offers usage of surfactants as emulsifiers. The experience, accumulated at investigation of latex and other
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dispersed systems [88, 112,113] is very valuable here, however there is some specific properties, belonging to reactive oligomer blends only. It was offered to use monometacrylate ethers of saturated alcohols in a row СН2=С(СН3)-С(О)-О-(СН2)n-СН3 with n=7-18 as nonionogenic surfactants in [114-117] for modification of rubber-oligoesteracrylate systems. These surfactants can not only emulsify a system, but also have a range of other useful functions. For example, they can take part in processes of chemical curing of oligomeric system due to double bonding in their molecules. In particular, they can be polymerized with oligo-ether-acrylates, reacting with unlimited bonds of molecules of reactive components. Therefore, undesirable side effects can be excluded in curing oligomer systems [118,119], especially colloidal mixtures with traditional surfactants [120]. In the aspect of morphology’s regulation of initial heterogeneous oligomer blends (before curing), the function of above mentioned surfactants is to change the size of emulsion’s drops through change of surface tension. This results in improving of “compatibility” of oligomer blends in the observation experiment. Concentration curves of optic density D for mixtures of cis-polyisoprene with αtrimetacryl-ω-metacryl-pentaerythrit-(dimetacryl pentaerythritedipinat) without or in the presence of 2 % of above – mentioned surfactant are shown in Figure 3.33.
Figure 3.33. Dependence of the optical density D of cis-polyisoprene and α-trimetacryl-ω-metacrylpentaerythrite (dimetacryl-pentaerythrite-adipinate) on the concentration of oligoesteracrylate with (1) and without surfactants (2). The dosage of surfactant is 2% of oligomer concentration. Arrows mark the values of Сcr.
It is evident, that dependence of D from C reveals in the presence of critical dosage (Сcr) of oligomer. According to [63, 121] accompanies transition of system from single-phase state to two-phase and critical dosage (Сcr) of oligomer increases about three times in the presence of a surfactant. It is obvious, that small concentration of the third component (2% of surfactant) can not exert an influence on thermodynamic compatibility of a blend. The experiment has proven, that increasing value of limit swelling of cis-polyisoprene in the mixture of oligoestereracrylate + surfactant grows only under dosages of surfactant exceeding
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10% [114]. Increase of transparency of polymer-oligomer films was observed in the presence of surfactant at С < Сcr. And the increase of absolute value Сcr in this case was caused not by improvement of thermodynamic affinity of mixture’s components, but by the decrease size of emulsion drops, which took place in the presence of surfactant. This experiment was carried out by the nephelometric method, which was able to register particles in a size above 1000 А° only [121]. All the heterogeneities and phase formations of smaller size, existing in this system, cannot be captured by this method.
3.4. EXPERIMENTAL EXAMINATION OF MACROSCOPIC PROPERTIES 3.4.1. Features of Rotational Diffusion The results of the experimental investigation of intramolecular mobility and rotational diffusion in oligomeric systems were obtained by methods of electrical and mechanical spectroscopy and also by NMR method in its different variants (e.g., see [43, 49, 54, 122128]). These experiments revealed only some correlations, between the character of changing of parameters of large scale (molecules, segments) forms of movement and phase organization of these systems. Concentration dependences of relaxation time of dipole polarization τ, of activation energies of this process ΔU, temperatures of the maximum of dielectric losses Тm and values of tangent of dielectric losses at this temperature tgδm have been obtained in the research [123] for the system cis-polyisoprene-trioxyethylenedimetacrylate and are presented in Figure 3.34. The value of critical concentration of oligomer ω1cr (weight fractions), corresponding to phase division into this system under the temperature of preparation of samples (20 °С) is shown in figure by the arrow.
Figure 3.34. Dependence of lg τ (1), ΔU (2), Тм (3) and tg δм (4) on the dosage of oligomer ω1 in cispolyisoprene blended with trioxyethylene-dimetacrylate at the testing frequency 1 kHz. The vertical arrow corresponds to the phase transition concentration at the preparation temperature of tested samples.
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As we can see, all parameters of molecular mobility, which this figure demonstrates, start to change considerably, but abruptly close to ωcr , if their valued dependence on ω1 is small and in limits of single-phase state of a blend. Of course, it is stipulated structural transformations in a system. However, factors of such character of concentration dependences are various for different parameters. The increase tgδm and the decrease lgτ under ω1 > ωcr are stipulated by the increase of microvolumes in the phase, which is enriched by oligomer and where constants of rotational mobility of molecules are noticeably higher, than in a phase, enriched by polymer. Though, mobility of oligomeric molecules are always less, than in initial oligomer in this phase and another one. It is supposed in [49], that besides direct inhibition of mobility of oligomer molecules in the presence of macromolecules, which is natural for the phase, enriched by polymer, it is also stipulated by the different degree of aggregation of molecules in each phase and in “pure” oligomer. It is rather well-defined. In fact, data, which have been already presented in works [54,129], testifies that NMR spectrums of trioxyethylenedimetacrylate and some other oligoesteracrylates are characterized by two-component form of wide lines (см. Figure 3.6). The authors explain it by the presence of molecules with different mobility in the liquid system: single (“disorganized”) molecules and structural “organized” molecules (entering into aggregates). Degrees of freedoms of oscillatory and rotary motions of these molecules are, evidently, limited. Changes, revealed in [129] in wide lines of MMR spectrum at variation of temperature (with bicomponent function of lines and constant total area under curves), give grounds to suppose, that redistribution of ratio of aggregated and unaggregated molecules takes place at Т=var in oligomers. It is necessary to emphasize, that the values of parameters of rotational diffusion, obtained by methods of relaxation of electric polarization and NMR of wide lines, are integral characteristics (averaged to the total of all molecules in both phases). That is why the law patterns, discovered by this method, don’t differentiate variation character of mobility of individual molecules in different phases. NMR impulse method provides other opportunities for the information analysis. Concentration dependence of time of spin-spin relaxation Т2 in the system PVH trioxyethylenedimetacrylate [49] is shown in the Figure 3.35. When the content of oligomer is less 5 %, the NMR impulse method registers only one value Т2 ≈ 25 - 30 m/sec. for the polymer-oligomer system analyzed. This value is in 1.5-2 times more than Т2, measured in “pure” PVC (before mixing) and this value is 5 decimal orders less in “pure” oligoestereracrilate. Only one time of transversal relaxation is fixed in the experiment if the concentration of oligomer in the mixture is below 5%, and in the presence of two kinds of molecules in the system with different times of nuclear relaxation. There is the restriction in the present method, which doesn’t let the component be distinguished correctly from the magnetization decrease curve with small dosages of oligomer. This curve characterizes relaxation of oligomer molecules [122]. Nevertheless, plasticizing effect of small additions of oligomer for PVC is noticeable. If the increase of concentration of oligomer is more than 5 % and to ω1 ≤ ωcr (the last one is marked by the arrow on the picture), that is, in the area of the single-phase state, the decrease of magnetization is already described by two temporal parameters Т2: by “long” Т2а, which characterizes rotational modes of molecular movement of oligomer, and by “short”* -Т2b , which characterizes the mobility of PVC macromolecules. *
“long ” and “short ” times are “professional slang” terms, traditionally used in the NMR analysis [122].
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The fact that at Т2а is much less (∼ three decimal orders) than Т2, of “pure” oligomer, can be stipulated by hindered movement of its molecules, dissolved in polymer. The reason for that can be formation of “oligomer-polymer” contacts, as the additional aggregation of oligomer molecules. The pattern of concentration dependences of thermodynamic parameters in this system confirms this fact. (see Part 2.6.3 and 3.2.3).
Figure 3.35. Dependence of lg Т2 on the dosage of oligomer of PVC - trioxyethylene-dimetacrylate at 40 °С. Explanation is provided in the text.
Four Т2 times have been already chosen in the area of the two-phase state of a system (at ω1 > ωcr) from curves of decrease of transversal magnetization: two are “short”- Т’2b and Т″2b and two are “long”- Т’2а and Т″2а, which characterize the mobility of molecules of oligomer and polymer (indexes a and b correspondingly) in the phase, enriched by polymer (′) and in the phase, enriched by oligomer (″). In the phase, enriched by oligomer Т″2b is in 10 times higher than Т’2b, in the phase, enriched by polymer. It can be explained by small concentration of polymer molecules in this phase (see the phase diagram of this system in Figure 3.8). Probability of “polymer” ”polymer” contacts is less of probability of “polymer-oligomer” contacts than in the phase, enriched by polymer. The opposite opinion is also right. The decrease of number of “polymer- oligomer” contacts induces mobility of oligomeric molecules in the phase, enriched by oligomer, though this mobility is greatly higher (∼ on a decimal order), than in the phase, enriched by polymer. The important result, obtained in above experiment, is the constant character values Т’2а, Т″2а ,Т’2b and Т″2b within one phase. That is the unique indication of the fact, that the concentration of components in co-existing phases is independent on the dosage of oligomer at ω1 > ωcr, and it is therefore confirms thermodynamic equilibrium in a system by NMR method.
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3.4.2. Features of Translational Diffusion Taking lot’s of law patterns, which oligomer-oligomeric and polymer-oligomeric systems have (see for example [43,49,108,109,130-138]): into account, let’s stop on the following ones: a) leap-like change of coefficients of mutual diffusion in the area of phase transitions; b) the change of diffusion rate during devitrification and plasticization of diffusion environment, taking place in the process of diffusion; c) the dependence of the speed of diffusion process from molecular and pre-molecular construction of diffusant. Values of coefficients of mutual diffusion Dv are shown on the Figure 3.36. These values were measured at different temperatures and in the different ratio of components for the PVC mixture with oxiethylenedimetacrylate and compared to the phase diagram of this system [132]. Figure 3.37. shows Dv values, which were measured at the fixed temperature Т = 65°С, for systems cis-polyisoprene –n – methylene-dimetacrylate and compared with corresponding phase diagrams [49,51]. Two facts attract attention to them. At first, the different character of concentration dependencies Dv above and below UCST. Secondly, there are differences in these dependences at diffusion of oligomers in PVC and rubber matrices. For PVC- oligomer systems at Т > UCST, Dv values grow first (5-10 times) at the increase of ϕ1 (volume part of oligomer), and then become virtually independent on concentration. The coefficient of mutual diffusion for rubber-oligomeric solutions in the area above UCST decreases with growth of ϕ1, or little depends on concentration. If Т < UCST, the decrease of Dv is observed in both cases at approach to “binodal.”
Figure 3.36. Phase diagram (dotted line) and the dependence of Dv, measured at different temperatures (numbers on curves) on the composition (solid lines) for PVC - oxyethylene-dimetacrylate system.
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Figure 3.37. Phase diagrams (dotted line) and the dependence of Dv on the composition (solid lines) for cis-polyisoprene - n-methylene-dimetacrylate at n = 2 (1), 4 (2), 5 (3), 8 (4) and 10 (5). The temperature is 650С.
The discontinuity on concentration curves Dv is principally important for these dependences at values ϕ1, close to solubility limit ϕcr at the temperature of experiment. This leap-like change of diffusion pattern is determined by a boundary. This boundary separates the area of oligomer’s solution in polymer from the area of polymer’s solution in oligomer. The discontinuity on curves Dv =f (ϕ1) doesn’t mean that the exchange of diffusant molecules between phases is stopped. This is the indication of change of mass transfer gradient in the diffusion due to change of thermodynamic properties of a system. This effect can be explained within the framework of phenomenological theory of diffusion [108]: mass transfer is the function of chemical potential (μ1) and is determined in binary systems as: Dv = Ds (ϕ1 /RT) ∂μ1/∂ϕ1,
(3.17)
where Ds is the coefficient of self-diffusion. As Δμ1 is decreased when ideality of solutions drops and at approaching to binodal, where the maximum degree of aggregation is reached, that ∂μ1/∂ϕ1 → 0, and, correspondingly, thermodynamic multiplier of the equation (3.17) is turned into zero in the boundary of phase transition. The presence of solutions (ϕ1 < ϕcr ) in the area of flat maximum on the curve of dependence Dv on ϕ1 is determined by the competition of two factors: on the one hand, it is the increase of “amenability” of matrix during dissolution of oligomer in it (as the consequence of plasticization). It results in decrease of “resistibility” of diffusion environment and in the growth of the diffusion rate correspondingly. On the other hand, thermodynamic non-ideality of solutions, caused by aggregation of diffusant molecules, becomes stronger at spontaneous mixture of components. This evidently reduces the speed of translational diffusion. Therefore, the character of concentration dependence Dv for every
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specific oligomer system will be determined by the contribution of above - mentioned factors. The comparison of the character of change of thermodynamic and relaxation parameters, as a function of composition with concentration dependences Dv, has been carried out in [48, 49] and confirms this assumption for some polymer-oligomer blends. It is necessary to note another peculiarity of diffusion process in oligomeric systems. Leap-like change of temperature coefficient of diffusion Еа (effective activation energy) was observed at transition of the system from glassy state in rubber state in [132], Еа, calculated for ϕ1 → 0 at temperatures < Тg , was found to be twice higher, than at temperatures above Тg. The dependence of diffusion rate from the molecular weight M of oligomer in the area of temperatures far from binodal, is described satisfactorily by the following equation: Dv = КМ-b
(3.18)
where index b characterizes geometric sizes and the form of diffusant, and the coefficient K is inversely proportional to local microviscosity of environment (deceleration feature). As shown in [43,132], the dependence of Dv on M within error limits of measurement for PVC - n-methylene and n- oxyethylene blends and also cis-polyisoprene - n-methylenes and n-methylene- dimetacrylate blends, is straightened satisfactorily in logarithmic coordinates of the equation (3.18). At the same time (see Table 3.4), the parameter b for a system PVC oxiethylenedimetacrylate depends neither on temperature nor on composition, while K grows with the increase of Т and ϕ1. Analogous dependence has been obtained for mixtures of oligobutadiene - urethandimetacrylate (OBUA) with n-methylene-dimetacrylates [133]. It means, that transversal section of diffusants remains constant at the variation of the temperature and composition and, accordingly frontal “resistance”, experienced by diffusant, remains constant, so only “side” resistance is changed. Table 3.4. The Dependence of and b Parameters on the Temperature and the Composition for the PVC – Oxyethylene Dimethyl Acrylate System in Equation III -4.2 Parameter K
b
ϕ1
Т,°С 150 130 110 90 90-150
0 4,0·10-3 1,6·10-3 7,9·10-4 3,2·10-4 2,1±0,4
0,1 5,0·10-3 3,3·10-3 1,6·10-3 6,3·10-4 1,9±0,2
0,2 9,5·10-3 5,2·10-3 2,5·10-3 1,2·10-3 2,1±0,1
0,3 1,8·10-2 1,1·10-2 4,2·10-3 1,3·10-3 2,2±0,2
Another situation was observed in [133] for mixtures of OBUA with n-oxyethelenedimetacrylates. The value b for these systems doesn’t depend on temperature in the area of single-phase state too, but the noticeable tendency to the growth of b is appeared at the increase of diffusant concentration. It is supposed, that the rise of the value b at the increase ϕ1, which leads to plasticization of matrix, is stipulated by the possibility of realization of additional molecular flexibility for oxyethylenedimetacrylates. This flexibility is determined
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by the presence of “articulate” oxygen atoms in their oligomeric blocks, which are absent in methylenedimetacrylates. Rotational modes of molecular movement of oxyethylenedimetacrylates are relieved with decrease of microviscosity of environment (growth of K as a function of ϕ1), that results in the corresponding increase of transverse section of diffusant molecule. Besides, the appearance of additional flexibility can promote aggregation of molecules, that can also it can have an effect on geometric sizes of diffusant. Well-known equations [108] have been used in [133] for estimation of the character of diffusion processes, as the function various parameters (molecular weight M, the length of oligomeric block n, the molar volume Vm) of molecules of oxyestereracrylates. They connect coefficients of mutual diffusion with changing of geometric sizes of molecules in homologous series: Dv = (Dv )n=1 / {σα [ 1+ Mn / Mn=1 ]α+1 }
(3.19)
Dv = КvVm -bv
(3.20)
and
Here (Dv)n=1 and Mn=1 –the coefficient of diffusion in systems with the first term of the homologous series and its molecular weight; Mn - molecular weight with a number of repeated links n; σ - fractional increase of cross sectional area of a molecule at transition from one member of homologous series to another; α - a constant for the present homologous series, which depends on composition; Кv and bv – constants for asymmetric molecules bv > 1. The experimental data [133] indicate, at first, on correctness of using of mentioned equations for estimations of changing of diffusion coefficients in homologous series of oligomeric systems. Secondly, these data confirm that oligomeric molecules in the process of mass transfer are oriented in the direction of a diffusion flow by their smallest cross-section. Nevertheless, it is emphasized [133], that constants α and bv, which characterize geometry of diffusant, are the function of composition. They are increased in accordance with the growth ϕ1 and approaching to binodal, and they reach values, which are equal to those, that have been determined for individual diffusants. This one confirms the dependence of diffusion coefficients not only of molecular, but of supramolecular structure of oligomers. In such way, the character of translational diffusion of components in heterogeneous oligomer systems is determined by the following features: Firstly, by the phase state of a system. Experimental dependence of diffusion speed from the structure in single-phase oligomer system is the result of competition of thermodynamic and relaxation factors, acting in the opposite directions. The rate of mutual diffusions of components is decreased abruptly in the area of transition from homogenous to heterogeneous state of a system due to symbate decrease of chemical potential closed to binodal; Secondly, by the physical state of a system. The diffusion rate is 1-2 decimal orders higher and effective energy of activation of diffusion is in 1.5-2 lower in elastic matrixes in comparison of glassy. Process of mass transfer of oligomers into glassy polymers can be lead
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to elastification of the last component, which is accompanied by the abrupt increase of diffusion speed in the running process ; Thirdly, by the molecular construction of diffusant. The dependence of diffusion rate from the molecular weight of oligomer is described by exponential function. Numerical values of coefficients, required for calculation of Dv, have been determined for typical oligomeric systems [43-49,108,109,133-139].
3.4.3. Specific Aspects of Viscous Flow Rheology of many types of oligomeric systems is described in details in the scientific literature. [49, 86, 140-164]. We can take for sure, that peculiarities of shear viscosity of oligomers are mainly stipulated by the phase organization of a system. It is naturally, that flow laws of single - phase and heterogeneous systems are differed in principle. Some unusual demonstrations of viscosity in homogenous oligomeric systems, connected to their supramolecular organization, were described in Section 2.8.2. Reological properties of heterogeneous oligomeric systems will be discussed below.
Phase Transition Area Extreme (with a sign + or -) temperature and concentration dependences of viscosity have been revealed for the whole series of oligomeric system [49,63,104,141,142]. The dependence of effective viscosity of the mixture of cis-polyisoprene with oligoisoprene with final hydrozide’s groups (commercial mark "SKI-GD”) from the dosage, measured in different shear stresses [152] is shown in Figure 3.38.
Figure 3.38. Dependence of viscosity on the composition of cis-polyisoprene blended with “SKI-GD” oligomer at 60 °С and shear stresses τ (10-4) = 0 (1), 0,2 (2), 1,15 (3) and 2,3 Pa (4).
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The extreme growth of viscosity of mixture and its sharply decrease here, so as deviations from additivity with different signs obviously take place. These and other experimental viscosity anomalies [63,141,142,151,158,165] are explained by different reasons, such as structural plasticization and anti-plasticization, change of an independent volume of a system, change of energy of intermolecular interaction etc. [63,104,141,166169]. But they are usually considered to arise from specific structural transformations, which take place at the phase separation. As experimental curves η=f(ϕ) were compared to phase diagrams, Y. Lipatov [104] supposed rightly, that the system must have different flow rules, in different areas of the phase diagram. Describing viscosity of mixture’s systems with different phase organization, he suggested the phase scheme of transition, where three different equations “work” for any of them. The modified Muni equation is used for the area of homogenous state (before spinodal): ηс = η0 К(1 - ϕ1)α М3,4
(3.21)
where, ηс – viscosity of mixture, η0 – viscosity of oligomer (or polymer), К and α -empirical constants, and ϕ1 – concentration of dissolvent. The equation was suggested for the calculation of viscosity of the system in metastable state (between spinodal and binodal). ηс = η0 К(1 - ϕ′1)α М3,4 (1+2.5ϕ1”)
(3.22)
where ϕ′1 + ϕ1” = ϕ′ - concentrations of dissolvent in uninterrupted and dispersed phases and its general contents in the system. According to Lipatov’s supposition, viscosity must be described by the classical equation of Einstein in the area of the two-phase state (under binodal): ηс = η0(1+2.5ϕ1”)
(3.23)
where η0 – viscosity of dispersive medium. The proposed scheme explains the opportunity of display of viscosity’s fall on curves η= f(ϕ) at the beginning and then its growth. But it can not explain plurality of extremums, observing on this curve. It can not be explained in a number of cases, it isn’t why viscosity of mixture is sometimes higher of viscosity of the most high-viscous component of mixture and etc. Besides, this scheme doesn’t give quantitative coincidence with the experiment even in the simplest cases. However, it is naturally, because wasn’t taken account of an opportunity a) of misbalance state of the system, b) of changing of the supramolecular and phase structure in the process of the right rheological experiment, c) of influence of peculiarities of aggregative structure of oligomeric systems on rheological properties and etc. Besides, the equation of Einstein, derived for the flow of dispersions with small concentration of rigid sphere, is used in it. This equation without essential modification is not applied for the description of flow of oligomeric and polymeric colloids with deforming phases and with high contents of impurities. Some peculiarities of flow of oligomeric systems in the area of possible transitions were considered in the work [155]. Mixtures of hard oligoimide with liquid epoxy and acrylic oligomers were studied in it. The consistency of initial compositions in these systems at a
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room temperature depends on the dosage of a liquid oligomer. When content of this component doesn’t exceed 30% the blend is composed of oligoimide powder with particles swelled in epoxide. Compositions containing 35-45% of a liquid oligomer are pastes formed by oligoimide particles swelled in oligomer, which are dispersed in a liquid oligoimide solution in oligomer. When the content of liquid oligomers in a blend is high (≥50%) this is a typical colloid in a viscous flow state. Figure 3.39 represents plots of viscosities of oligoimide compositions with ED-20 oligoepoxide as functions of the ratio of components in the 20-80°С temperature range. As we can see, the increase of viscosity with the dosage of a highly viscous component is well determined, but its rate η depends on experimental temperature considerably, that is reflected
( )
in a form of curves η = f cои , coi is the dosage of oligoimide here. If temperatures are below 50°С can be characterized by a substantial viscosity growth in the range of coi ≈ 3040%, further increase beyond 50°С in the same oligoimide concentration range demonstrates reduced growth of viscosity, that in some cases inverses curves (3.22, curves 5-8). As a result, a paradoxical situation can be observed: the viscosity of oligoimide – oligoepoxide blend (1:1), measured at 70 and 80°C roves to exceed the viscosity of this blend at 60°C. This experimental result is at the first sight in contradiction with both all known temperature dependencies of viscosity for polymers, colloids and other physically structures liquids and traditional interpretations of these dependencies such as [67,140-143].
Figure 3.39. Dependence of viscosity of oligoepoxide “ED-20 ” – oligoimide (OI) blend on the dosage of OI at temperatures 20 (1), 30 (2), 40 (3), 50 (4), 60 (5), 70 (6) and 800С (7). γ=100с-1.
The analysis of the package of results provided in [155] is carried out based on the following concepts:
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•
•
•
the blends studied in their equilibrium state can be either single-phase or two-phase depending on state parameters. Two-phase blends are dispersions formed by oligoimide particles swelled in a liquid oligomer, which are dispersed in a liquid oligoimide solution in a liquid oligomer. Each of coexisting phases in a two-phase system are as heterogeneous as single-phase solutions and are characterized by the complex supramolecular structure. specified preparation conditions of samples cannot guarantee in some cases that the initial blends will reach their thermodynamically equilibrium state by the start of reological experiments, so these systems continue their evolution to the equilibrium state, which can be started (stimulated) during experiments itself; all the changes in reological behavior of the studied systems observed during experiments are stipulated by transformations occurred due to thermal (temperature) and mechanical (deformation) effects. All such transformations have thermodynamic origin, comply with kinetic mechanisms and can be actualized simultaneously and/or successively on a supramolecular and phase structural levels depending on external conditions. Structural transformations can exert unidirectional (i.e. either increase or reduce viscosity) or multidirectional (one of them increase viscosity while other ones reduce) influence on the reological behavior of a system.
This is a framework for explanations of nontrivial temperature – concentration dependencies of viscosity of oligoimide – oligoepoxide blends provided in Figure 3.39. When content of a highly viscous component, that is oligoimide, increases, the viscosity of a whole composition increases. It can be stipulated by at least two factors On the one hand, the increase of oligoimide dosage at Т = const leads to increase of dispersion media viscosity, because of growth of a highly viscous component concentration in oligoimide dissolved in epoxide. On the other hand, it increases the number of dispersed phase particles. Both these factors stipulate that the viscosity of a system increases, but their contributions vary and therefore it’s their ratio, that determines reological behavior of blends. The value of viscosity at the room temperature and oligomer dosage below 30% is determined only by oligoimide concentration in solution (the limit oligoimide concentration in ED-20 is 25-28% at 20°), i.e. the first factor contributed here. If coi is above 30% phase separation occurs and the flow pattern of such compositions up to coalescence threshold and further inversion of phases [67,104] must conform with dispersion flow laws. That is why if coi is above 30% and Т = const increase of oligoimide dosage, which entails increase of the number of dispersive phase particles in unit volume at constant component concentrations in a dispersion media, provides increase of viscosities of compositions only through contribution of the second factor. Increase of temperature will obviously improve mobility of kinetic units, which stipulate viscous properties in each of coexisting phases and assuming other conditions being the same, total system viscosity in a whole reduces, that is shown experimentally: the drop of viscosities of single – phase systems is subject to the Arrenius law (see Figure 3.39). The effect of temperature in two-phase systems is more complex. Temperature – stimulated increase of mobility leads not only to reduction of viscosity. At the same time, it promotes the rate of interphase diffusion and to inevitable increase of the rate of mutual dissolution of components. Firstly, this process results in increase of oligoimide concentration in dispersion
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media (the limit solubility of oligoimide in oligoepoxide reaches 43-45% at 60°C and approaches to 50% at 80°C). It increases viscosity of a dispersion media, which mainly the viscosity of a whole system. Secondly, increase of temperature at coi = const reduces oligoimide concentration in dispersive phase and, therefore, reduces its volume fraction in the system, that must reduce viscosity: The viscosity of two-phase systems in a temperature range 20-80°C is thereby changed due to temperature growth and must be stipulated by the simultaneous competitive influence of three factors. Firstly, Arrenius drop of viscosity due to more mobile units of kinetic flow, secondly, growth of viscosity due to thickening of a dispersion media, and thirdly, reduction of viscosity due to reduction of the volume fraction of dispersive phase. Their competitive contribution specifies the resulting viscosity. If statements provided above are justified, than according to [155], there must always be some threshold concentration and temperature values where the flow mechanism of blended systems changes. This conclusion has been confirmed experimentally: the curves of functions η - T for the studied compositions have well-shown bend, where viscosity drop rate changes. The processing of these data involving peak Newtonian viscosity (ηn), obtained by extrapolation to zero shear rate, demonstrates (Figure 3.40), that dependencies lgηn on 1/Т can be approximated by two linear sections – 20-40°С and 50-80°С, that can be the effect of the blend flow mechanism varied near 45°C.
Figure 3.40. Dependence of the peak Newton viscosity of OI – “ED-20” blends on the inversed temperature, the concentration of OI: 10 (1), 30 (2), 40 (3) and 50 w.% (4).
Effective activation energy values (Еef) of blends, that is temperature factor of viscous flow, have been determined by equation [67]:
Eef = 2,3RΔ lg ηn / Δ (1/ T )
(3.24)
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where R is universal gas constant, and Δlgηn is the change of viscosity in the temperature range ΔТ. As a function of composition, Еef (see Figure 3.41) has different tendencies in above temperature ranges. The section 20-40°C demonstrates, that Еef increases with content of oligoimide concentration up to ∼30%, that approximately corresponds to the position of binodal for these conditions, and then it virtually doesn’t depend on composition of a blend. At the same time, Еef in a temperature range 50-80° monotonically decreases with oligoimide concentration increases up to ∼50%, that also approximately corresponds to the position of binodal for these conditions. Such an nontrivial pattern of variation of Еef as a function of coi (in one case Еef increases up to “exorbitance”, in other case it decreases) is the confirmation of the above suppositions according to [155]. Indeed, single phase systems at low temperatures require additional energy to destroy supramolecular structure. The strength of such structure grows with oligoimide concentration and therefore Еef increases. At high temperatures however, thermal energy is sufficient, so the reduction of Еef is well determined. These two factors (thermal and mechanical impacts) compensate each other in two-phase systems, it particularly results in independence of Еef on coi, which is experimentally observed at coi concentrations beyond threshold.
Figure 3.41. Influence of OI dosage in a blend with “ED-20” on the effective activation energy of viscous flow in temperature ranges 20 – 40 (1) and 50 -800С (2).
Viscosity in Critical Point and in Metastable Area Many low-molecular liquids have been known to have abnormal viscous properties and other transition coefficients near the critical point since the beginning of the previous century. Along with “colloid” models of Smoluhovskii [170] and Oswald [171], the concept of large – scale fluctuations near the critical point has been applied to explained such an abnormal behavior [172-176]. It acquired qualitative interpretation since 60-s, first in M. Fixman works [177,178] providing thermodynamic description of macroscopic properties of liquid within the framework of corresponding modes approximation, then in [179-181] with the concept of large-scale fluctuations considered within the framework of unhooked modes and dynamic renorm-group.
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The physical meaning of all these theories is the following: if a system is in critical composition and concentration range (Сcr and Тcr), the part of mechanical energy brought into a system to deform it (i.e. to induce a flow act), is dissipated on long-wave fluctuations, so the hydrodynamic flow energy partly disperses on these fluctuations resulting in viscosity growth. Experimental viscosity ηс includes regular (“non-critical”) component ηr, which is identified as the viscosity of homogeneous solution where viscosity is, in nature, is the resistance of medium to deformation, and redundant (“critical”) correction Δηcr, where viscosity is defined as a deformation energy dissipation on structural heterogeneities. The value of the critical correction depends on the number and size of long – wave fluctuations, i.e. on the proximity of temperature and concentration modes of experiment to critical conditions, that such system is characterized by: ηс = ηр + Δηcr,
(3.25)
where Δηcr = f(rF), r = (Т – Тcr) / Т, а F is the numeric exponential quantity. The concept of diffusive dissipation of the shear energy on large-scale fluctuations, tested on low – molecular liquids by L.I. Manevich and his colleagues, [182-184] has been further developed in a viscous flow theory in critical and metastable areas for oligomer and polymer systems. Taking non-Newtonian type of flow and phase diagrams of polymer – oligomer systems into account, the following equation for the critical correlation of viscosity has been derived Δηcr = асВ2 1/q M3 (1 + b/q4),
(3.26)
where q ∼ [(Т – Тcr) / Тcr]1/2, сВ is the concentration of the component В, М is its molecular weight, a and b are numeric coefficients. The parameter q is, in turn, relates to the chemical potential μ1 of a system through the following equation: 4πa/ q2 = VА / cВ [RT / (∂μ1 /∂cВ)PT + m],
(3.27)
where m = VВ is the ration of molar volumes of components. An opportunity of energy dissipation on large – scale fluctuations appearing in the metastable area is included into Manevich theory in a form of so called spinodal correction Δηsp =аπ2 {ρf2KTNA (1-c)τA +NBcτB(NANB)1/2}/ / {Ne [NA c + NB (1-c) - 2χc (1-c)NA NB]1/2}
(3.28)
Here c is the concentration of component А in terms of a number of monomer units; ρ is the density of a blend; NA and NB are oligomerization (polymerization) degrees of components; Ne is the number of monomer units between hookings; τA and τB are relaxation times of components; а is the numeric coefficient; f is Onzager coefficient; K is Boltzmann constant; χ is Huggins constant.
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Therefore, the viscosity of a system near the boundary of thermodynamic stability is determined by the expression ηс = ηр + Δηsp
(3.29)
Further development of this theory was directed to consideration of molecular polydispersity of components and the influence of osmotic pressure. The analysis of equations (3.25) – (3.28) in integral form considering distribution function on degree of oligomerization (polymerization) has shown that at the specified mixture composition and the total number of molecules in a system equal to NAc + NB(1-c) only molecules with NA and NB at specified μ1 and χ provide these molecules “falling into” the critical or metastable area, contribute to Δηcr and Δηsp. Other molecules “do not belong” to long – wave fluctuations at the specified time, and perform flow acts that don’t correspond to laws of (3.26) and (3.28) and have just a masking function. Consideration of the osmotic pressure values for components А and В adds one more correction Δηos to the reological equation , which in contrast to Δηcr and Δηsp, is negative. It roots in a fact of better “dispersal” of fluctuations themselves due to osmotic pressure. The reduction of fluctuation correlation radiuses due to osmotic effect results in reduction of critical and spinodal corrections and therefore in reduction of the total system viscosity: ηс =ηр + Δηcr + Δηsp - Δηres
(3.30)
Depending on the ratio of contributions of negative and positive correlations into the regular solution viscosity, ηс can be either below ηр or exceed it. It has been shown that the more Δηos, the more different are NA and NB, the more it contributes to the total value of correlations Δη, i.e. the more different are molecular weights of components, the more probable is the reduction (not growth) of viscosity of their mixture.
Viscosity of Heterogeneous Systems There are two approaches mainly used for interpretation of viscous properties of oligomer systems. The first one considers viscosity within the framework of colloid dispersions flow. The growth of viscosity in such systems is logically determined by the increase of dispersive phase content. Therefore it’s not maximums but minimums of curves ηс=f (ϕ) [63, 149, 151, 156] that are surprising. The second approach is based on interpretation of dependence of viscosity on transformations of macroscopic structural elements, that is caused by the viscous flow itself. For example, it is caused by “fibrous structure” formation in a flow due to elongation of one of the phases in the direction of deformation or formation of interlaced ring layers during capillary flow or other structural (not chemical) transformations arising such effects as calander effect [63, 185-189]. As it was noted above, the Einstein equation cannot be ideally applied heterogeneous polymer systems, which are considered as dispersions with dispersive phase particles deformed under stress applied to a system (the shape of particles is therefore a function of τ and γ). It is thereby relevant to quote A.Ya. Malkin [190] who has carried out an analysis of some researches where non-linear pattern of concentration dependencies is explained by
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specific “polymer effects”. He noted that there was no point to discuss if these or those experimental data correspond to Einstein formula if initial basis of the theory, which has classically clear core statements, is not correct: no interaction between phases, Newton and laminar flow and spherical particles of dispersive phase. The viscosity and shape of particles in heterogeneous oligomer systems so as morphology formed during flow of extrudate will depend on deformation modes, the construction of capillary (diameter/length ration D/L) etc. Such a dependence may show up both in growth and fall of viscosity, that has been observed in experiments. A universal theory describing the flow of polymer dispersions has not been worked out yet. Interpretation of experimental observations (depending on the size of dispersive phase particles, concentration range, the ratio of viscosities of dispersion and dispersive phases.) is based on the empirical equations by Gut, Vand, de Gusman, Muni, Showalter - Teilor etc.[63,140,149], but no one provides satisfactory explanation for abnormally high experimental values Δη. Let’s note that all effects that oligomer systems demonstrate in variation of system morphology during viscous flow are essential not only because they mainly determine technological properties of “raw” systems. The are also of key importance at formation of structure of cured composites.
3.4.4. Effect of Phase Structure on Initial Curing Rate Table 3.5 contains values of the initial curing rate W0 of tetramethylene-dimetacrylate (MB) and trioxyethylene-dimetacrylate (TGM-3) in the matrix of polyisoprene rubber (SKI3) at temperatures and 107°С and with various concentrations of oligoesteracrylates ϕ1 corresponding to a single-phase state of these systems. Figure 3.42 shows concentration dependence for tetramethylene dimetacrylate - polyisoprene blend within a broad concentration range together with the phase diagram of this system. As we can see: a) W0 plot leaps in the area of phase transitions; b) W0 is almost independent on ϕ1 in single – phase systems; c) the curing rate at the phase enriched with oligomer (phase II) is 5 - 10 times more than in the polymer – enriched phase (phase I); d) block polymerization rate (homopolymerization of oligoesteracrylate without second component) is higher than that in phase I and lower than that in phase II. Table 3.5. W0 values at different concentrations of oligomer in single – phase systems of cis-polyisoprene - oligoesteracrylate System (commercial rubbers) SK1.3 – MB*) SK1.3 – MB **) SK1.3 – TGM-3**)
W0 (min-1) at oligomer concentration, vol. parts 0.05 0.09 -
0.10 0.12 0.16 0.10
0.15 0.13
0.20 0.14 0.18 -
0.30 0.16 0.16 -
*) The curing temperature is 100ºС; **) The curing temperature is 107ºС.
0.99 0.97 1.74 -
0.995 1.05 1.58
1.0 0.32 0.64 0.88
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Figure 3.42. Phase diagram (2) and the dependence of W0 on ϕ1 for the system cis-polyisoprene tetramethylene-dimetacrylate at the curing temperature 107 °С and initiator concentration (azo-bisisobutironitrile) 0,5% (1). Light dots are experimental values dark dots represent calculation results using equation (3.31).
It is necessary to make an additional note before discussing these results that concerns experimental methodology. All the data provided in Figure 3.42 and table II1.5, are related to the equilibrium state of initial systems because they have been obtained on the assumption of τe ≥ τecr. Though the exposition of samples in this experimental series has been carried out at the room temperature (it is the temperature that equilibrium structural parameters relate to), and polymerization temperature was 100 and 107°С, the temperature leap in this case is not so fast to make any considerable “perturbances” in the phase and associative – morphological organization of a system at the period between completion of exposition and the start of polymerization, that has been shown experimentally in [192]. The above – noted dependence of W0 on ϕ1, taking place in single-phase solutions of the rubber-oligomer systems is evidently based on well-known laws of chemical kinetics [193,194] and particularly from kinetic law – patterns of the block – polymerization of acrylic oligomers [195]. As W0 is not a value reduced to the initial oligoesteracrylate concentration (it is normalized to the total number of metacrylic groups in a system), it cannot depend on ϕ1 in this case. The reasons that stipulate various phase I and II polymerization rates and that they are different from W0 at block polymerization, are not so trivial and are based on the influence of the media viscosity on supramolecular structure parameters of each phase. Part 2.8.1 shows that in two – component oligomer systems the function of distribution of supramolecular elements is determined by the viscosity of a system and the concentration of a reactive compound. Introduction of relatively low dosages of thickener may increase the number, size, and lifetimes of supramolecular aggregates with “kinetically preferred orders”, that in turn can increase W0. That is why the phase II is characterized by both 8-15 times increase of viscosity due to dissolution of ∼ 1% of polymer [49] and W0 growth. When the
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dosage of thickener is above 50% , the structural organization of a system is disordered, the number of aggregates with “kinetically preferred orders” decrease, and the curing rate becomes lower that that of block polymerization. In systems, which are initially heterogeneous, the change of component ration doesn’t lead to the change of concentration in coexisting phases. It only results in change of the volume ratio of phases I and II (see Part 1.4.5). Transition from homogeneous state to heterogeneous occurred, for example, when oligomer dosage ϕ1 in initial system increases above (ϕ1)Б leads to formation and accumulation (when ϕ1 increases) of polymer solution phase in oligomer (phase II) in the phase of oligomer solution in polymer (phase I). Phase II has higher initial rate pf polymerization. The curing of heterogeneous polymerization systems in each phase has its own principles and the brutto – function W0( ϕ1) obtained in experiment describes change in the volume ratio of phases. In the additive approximation [49] W0=W01(V1ϕ1’/V0 ϕ1) + W02 (1 - V1 / V0) ϕ1”/ ϕ1
(3.31)
where W0 is the initial polymerization rate of oligomer in a heterogeneous system with oligomer content ϕ1; W01 and W02 are initial polymerization rates in phases I and II with oligomer concentration ϕ1’ and ϕ1” correspondingly; V1 is phase I volume. V1 = ϕ1” - ϕ1 + ϕ1 (ϕ1’ / 1- ϕ1’ ). Comparison of W0 values calculated using equation (3.31) with experimental values of initial polymerization rates in heterogeneous systems formed by cis-polyisoprene tetramethylene-dimetacrylate demonstrates satisfactory coincidence (Figure 3.32). Nevertheless it’s necessary to note that the phase diagram contains parts where concentration dependencies are not additive, because these parts are areas where the structure of systems formed has much more complex relations between system properties and its phase organization. It is generally known [1,4,5], that correlation radiuses of concentration fluctuations grow abruptly if a liquid system falls into metastable state or the area near the critical point (upper or lower one). Discussing mixing thermodynamics of PVC - oligoesteracrylates mixing in Part 2.2.3, we noted, that though the aggregation of oligomer molecules in these systems begins far from the phase transition boundary, it is a metastable state, so as the area near the critical point where drastic change of thermodynamic parameters can be observed due to formation of stable supramolecular structures. Figure 3.43, taken from the research [43] represents concentration dependencies of the initial initiated curing rate W0 at 110 °С for PVC - trioxyethylenedimetacrylate with the phase diagram including binodal and spinodal. We shall not discuss all the data this figure contains (more information will be provided below). Let’s just note some aspects relating to the problem that was taken for the title of this paragraph. As we can see, the curve 3 in this figure, which plots the function W0 = f (ω1) within τэ= 40 days, has at least two peaks in the points of maximum where polymerization rate becomes so high, that its values go beyond detection limits of the measurement method used in [43]. We can safely say in this case, that in experiments where W0 is measured accurately, the rate increases at least 10 - 20 times. We should note, that the first abrupt change of rate coincides with transition to the metastable state (the temperature-concentration mode corresponds to position between binodal and spinodal) and second change corresponds to approach of a system to the critical state
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(coincides with UCST). The question of whether such a coincidence is occasional or welldetermined and stipulated by higher level of self – organization in these areas (with increased number of associative structures, their sizes and lifetimes of supramolecular aggregates, that should result in W0 growth by the concept of associative-cybotaxic structure of oligomer liquids) has no definite answer at the present time.
Figure 3.43. Phase diagram (binodal – 4 and spinodal - 5) and the dependence of W0 on ω1 for the system PVC - trioxyethylene-dimetacrylate at the curing temperature 110 °С and initiator “PDK” concentration. Exposition times are τe = 1 (1), 5 (2) and 40 days (3).
A great number of experimental facts (see, for example, [4,5]) show that lots of absolutely different low-molecular liquid systems with different microscopic basis of interaction demonstrate, as M. Anisimov told [4], “a firework of effects demonstrating changes of singular physical properties, where the main role is played by the interaction (correlation) of abnormally growing fluctuations”, in their critical and metastable states. Let’s note here that on the one hand task – oriented experiments to study critical phenomena have necessary precision (see, for example, Debai work [196]). On the other hand, the above -
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considered experiment has not been carried out to study effects exactly in critical and metastable areas of oligomer systems. The fact that these areas have been analyzed is, in this regard, occasional. In addition, the law patterns presented in Figure 3.43, are to a large extent unclear. In particular, there is no definite interpretation of a slight but steady drop of W0 when ω1 increases, that can observed in single – phase solutions with excess of PVC, whereas in other systems such as rubber - oligomer solutions, the normalized initial rate value is not a function of concentration. There is no reasonable explanation of a catastrophic drop of curing rate at ω1 ≈ 0.85 - 0.90. All hypothetical explanations of this fact provided in [43] require additional proof. Nevertheless, a hypothesis of an abnormal growth of rate as a result of transformation of a supramolecular structure based on the principles of metastable and critical liquids looks reasonable enough and, that is main for us, perspective because it gives an opportunity to provide a clear definition of experimental ideology to search anomalies in other unusual points on phase diagrams of oligomer systems.
3.4.5. The Relative Effect of Thermodynamic and Kinetic Factors on Bulk Properties and Formation of an Equilibrium Oligomer Structure The analysis of possible correlations between thermodynamic and kinetic patterns of structure formation in initial and cured oligomer system is presently not sufficient. This complex problem has taken attention of scientists not so long time ago[122,197-200]. Let’s take just one of its aspects to consider. Comparing experimental results on contribution of various thermodynamic and kinetic factors defining system approach to the equilibrium state in variation of such parameters as for example initial curing rates W0 or dielectric parameters (relaxation times dipole polarization τ, process activation energy ΔU, dielectric loss pike maximum temperature Тm and dielectric loss tangent tgδm for this temperature) shows a seeming dominance of thermodynamic factors. For example, the variation of such a kinetic factor as a temporal prehistory τe, within a framework of a single – phase state of specific systems at fixed values of thermodynamic variables (ω1 and Т = Const) can result in no more than 2 - 2.5 times variation of W0, τ, ΔU, Тm and tgδm, (e.g., see Figure 2.36, 2.37, 3.34). At the same time, the variation of thermodynamic state parameters ω1 or Т, which determine if a system “fits” this or that area of a phase diagram, can lead to change of W0 in a range of exponential orders (see Figure 3.34 and 3.42). It is obviously well - determined: a phase transition is usually accompanied by the jump-like change of properties. However… Let’s return to Figure 3.43 which has already been discussed in the previous Part. It really demonstrates that at transition to the metastable state and near the critical point W0, the rate increases at least 10 - 20 times. But the fact is that the resulting value of W0 is also a function of time of structural reorganization to thermodynamically permitted level. Is there enough time for structural reorganization by the experimental registration moment W0 that will therefore provide corresponding equilibrium value of a target property? Unfortunately, it’s not a frequent question in experimental practice. But taking relaxation kinetics to equilibrium into account (or, to be more specific, disregarding) can change quantitative values of a registered property as well as the qualitative character of partial dependencies. It is this statement, which is illustrated by the data in Figure 3.43. Polymerization rate bursts, that have
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been described above, are maximums on the curve W0 = f (ω1) and can be obtained only if τe ≥ τecr, that is taking into consideration the advance to thermodynamic equilibrium. Indeed, as Figure 3.43 demonstrates, at τe = 1 day (curve 1) no extremums show up on the experimental curve, and they are insignificant at τe = 5 days. It is only τe = 40 days, that is ≥ τecr, that provides correspondence to the picture described above. Indeed, as V. Irzhak noted on another case, “thermodynamics supposes and kinetics proposes.”
CONCLUSION Aggregates with a local orientation ordering in oligomer systems make phase transitions more complicated. The analysis of thermodynamic parameters of mixing allowed to explain the effect of a better compatibility in oligomer – polymer systems with a higher molecular weight of oligomer and set the boundaries for the area where this unconventional effect can occur. Phase diagrams prove to be invariant relating to the critical solubility temperature. Quantitative correlations between diffusion constants, rheological and relaxation properties and the phase organization of oligomer systems have been revealed.
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[193] Kh. S. Bagdasar'jan. Teorija Radikal'nojj Polimerizacii (The Theory of Radical Polymerization). - M.: Nauka, 1966 (in Russian). [194] N.M. Ehmanuehl', D.G. Knorre. Kurs Khimicheskojj Kinetiki. (Chemical Kinetics Course). - M.: Vysshaja Shkola, 1962. (in Russian). [195] A.A. Berlin, G.V. Korolev, T. Ja. Kefeli, Ju. M. Sivergin. Akrilovye Oligomery I Materialy Na Ikh Osnove. (Acrylic Oligomers and Related Materials). - M.: Khimija, 1983. (in Russian). [196] P.J. Debye // Chem. Phys., 1959, V.31, № 3, P. 680. [197] B.A. Rozenberg. Problemy Fazoobrazovanija V Oligomer-Oligomernykh Sistemakh (Phase Formation Aspects in Oligomer – Oligomer Systems). - Chernogolovka: Oikhf AN SSSR, 1986 (in Russian). [198] S.M. Mezhikovskijj. Kinetika I Termodinamika Processov Samoorganizacii V Oligomernykh Smesevykh Sistemakh (Kinetics and Thermodynamics of SelfOrganization Processes in Oligomer Blends). - M.: Ikhf RAN, 1994. (in Russian). [199] V.I. Irzhak, B.A.Rozenberg. // Vysokomolek. Soed., 1985, V.27 A, №9, P.1795. [200] Ju. S. Lipatov. Fiziko-Khimicheskie Osnovy Napolnenija Polimerov (PhysicoChemical Fundamental Aspects on Filling of Polymers). M.: Khimija, 1991. (in Russian).
CONCLUSION Unfortunately, the present state of chemical physics of oligomer systems is far from providing us with reliable quantitative calculations of all correlations between molecular, supramolecular, topological and phase structures of oligomer compounds, their dynamical and statistical properties. New approaches to analysis of regular physico-chemical mechanisms give us correct explanations for some cases of experimental “anomalies” of macroscopic properties which used to look contradictory. We have now a definite interpretation of high reactivity of unsaturated telechelate oligomers at the initial stages of curing; “equilibrium” mechanisms of temperature viscosity hysteresis; peculiarities of diffusion transport in olygomeric systems and the factors influencing their relaxation time; the criteria, which define the boundaries of “oligomeric regions” in homologous rows, where experimental “anomalies” can appear, and etc. It is necessary and very important to add that the interpretation of all these properties and processes, different in their physico-chemical nature, is based on the assumptions reflecting specifics of oligomeric systems. In our opinion, however, another aspect is much more important. The approach to oligomers as a specific condensed state of substance, which dominates in this book, gives us a vague outline of informational area, which Yu. Lipatov called “problems unsolved and not yet being solved” is prospective. We shall not concentrate on the core problems discussed in [1], and identify (only identify) two related problems in the field of molecular and supramolecular structures of liquid oligomers and their transformations during irreversible “liquid – solid body” phase transition. These problems have both fundamental aspects and practical applications in material science. We have not fully implemented yet the initially attractive ideas proposed by Alfred Berlin [2] on using oligomeric molecules as blocks for regular polymer networks formation and on the transfer of the regular liquid oligomer supramolecular structure into solid (or elastic) polymeric material. It was difficult to introduce the first idea due to molecular polydispersity of synthetic oligomers (MWD, FTD); as for the second idea, local defects inevitably appear in the process of microheterogeneous polymerization (or polycondensation), thus affecting the regular polymeric structure. These defects limit physico-chemical and physico-mechanical properties of polymer material. For example, polymer networks produced in the real-life environment possess 0.1 % of their theoretical strength [3]. Is there any opportunity to exclude (restrict, localize) the negative influence of these factors on formation of a polymer structure? We think it is possible to achieve.
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Nevertheless, let us note that all the below mentioned facts fall into the category of “acoustic approximation”*, as one of the authors likes to say. The strength properties of cured oligomers can be drastically improved [8] by formation of an absolutely regular structure according to modern theories describing fracture of solids [4-7] (e.g., by single crystal growth). The opposite method proposes the formation of a polydisperse heterogeneous system with a regular spatial distribution of phase inclusions, but this distribution should be wide according to the size and number of particles, though the upper limit for the first parameter is introduced. The synthesis of polymer single crystals is the problem “which cannot be solved yet”. But the formation of a polydisperse structure with the aforementioned limitations is principally possible. This opportunity is embedded in associate and cybotactic group properties of oligomer liquids. The formation of these predicted structures is possible. We need to learn how to control the structural parameters of aggregated liquids (e.g., by establishing exact temperature conditions, of course, taking into account the time of relaxation or by inserting special “matrix” additives or in any other way (we are often asked “how?”, but this is important) and how to register these regular heterogeneities very fast (before volume compression and syneresis occur), e.g., by carrying out polyreactions in conditions which are very close to critical. Moreover, the spatial orientation of oligomer molecules can differ in various cybotactic groups. That is why control of their arrangement and relative distribution is a possible solution for the synthesis of materials with sophisticated spatial organization referred to as supramolecular structure. This possibility even increases if we take into account some previous attempts. For example, the authors of [9] use polyrotaxane technology for the synthesis of oligosaccharide nanotubes with molecules containing 6-8 glucoside residues. Now, several words about the synthesis of oligomers with molecular homogeneity. The molecular polydispersity of synthetic oligomers is stipulated by the statistic nature of their production processes and side reactions during synthesis, leading to formation of defective molecules. But molecular heterogeneity of bioactive oligomers is still the subject of scientific speculation. The fact is: they are created in nature. How are they created, however? A possible way to the synthesis of molecularly homogeneous products is the structural tendency to self-organization which oligomeric molecules have. There are many definitions for the term “self-organization” [10-13], which sometimes vary in meaning*. Following the opinion of Yu. Neimark and P. Landa [13] we consider the phenomena of self-organization as not reduced just to spatial and temporal order. According to [13], “selforganization is the system ability to form structures which are stable to fluctuations of external conditions varying in intensity and in nature, and which are capable of growth and dissemination. Self-organization is a combination of control and feedback functions which can be analyzed using the theory of information”. Apart from “spatial order” the above given definition contains such keywords as “structure capable of growth”, “stable to fluctuations of external conditions” and “feedback”.
* Acoustic approximation” is the situation when you have “something to discuss” but the topic is vague and abstract and is not supported by models, formulas, strong definitions, experimentally confirmed propositions, and etc. * U. Aschby, one of the fathers of cybernetics, wrote [14]: “the term “self-organization” gives us a rather complicated and contradictory perception of this phenomenon and should not be used at all”.
Conclusion
251
The spatial order of oligomer systems at cybotactic scale can be considered well-proven (see Parts 2.2 and 2.6). The growth of cybotactic group size on the way to thermodynamic equilibrium is considered possible (see Parts 2.4.3 - 2.4.5). The duration of the process leading to structural equilibrium (day and more) of regular supramolecular aggregates has been established (see Parts 2.7 and 2.8.1). And if we change the external conditions of the system in equilibrium (e.g., temperature, pressure or initiation of chemical reactions), we can consider it stable for some time, because the duration of relaxation to a new equilibrium and the duration of elementary acts of chemical reactions are incomparable (days and seconds, correspondingly). At last, Part 3.2.3 shows that associate - cybotactic oligomer system in conditions different by 120 and 40ºС has an external memory about conditions at the Тg points and the upper critical solubility temperature, thus indicating the presence of feedback in the system. According to the above given information let’s make a vague hypothetic scheme of the chemical synthesis of structurally regular oligomers. After the chemical reaction (e.g., telogenic oligocondensation) has started and some target aggregative molecules have been formed, membrane- or sorption-type separation channel appears to accumulate the end product. Though this process is slow, it is supposed to move the area of chemical reaction into a non-eqiulibrium state. It is possible to find conditions for decomposition of by-product molecules to their initial state (e.g., polyester acrylates are known to decompose according to depolymerization mechanism) so that they can react again and form target molecules. It is obvious that such multi-stage processes can not have any technological applications today (or even in the future). But the point is in the principal possibility to produce molecularly homogeneous synthetic oligomers. If these substances are created by nature, they are necessary and they can be synthesized. Some theories [15,16] describe extremely complicated and multi-stage evolution from single carbon atoms to high molecular weight compounds, and, further on, to chiral-homogeneous and self-replicating biosystems. The oligomeric state of molecules is considered to be an inevitable (and necessary) stage of evolution. Why? Maybe the reason is in the structural tendency to self-organization which oligomer molecules have.
REFERENCES [1]
[2] [3]
[4] [5] [6] [7]
[8] [9]
[10] [11]
[12] [13]
Lipatov, Yu. S., Oligomeri – nereshennie problemi i eshe ne reshaemie.- Materiali VIII mezdunarodnoi conferencii po chimii i fizikohimii oligomerov (Oligomers: problems unsolved and not yet being solved. – Publications of VIII International conference on chemistry and physical chemistry of oligomers), Preprint, Chernogolovka: IPHF RAN, 2002 (In Russian). A.A. Berlin, Himicheskaya promishlennost’ (Chemical industry), 1960. № 2. p.14. Berlin, A.A., Korolev, G.V., Kefeli, T. Ya., Sivergin, Yu. M., Akrilovie monomeri i materiali na ih osnove (Acryl monomers and related materials), Moscow: Chimiya, 1983 (In Russian). Ogibalov, P.M., Lomakin, V.A., Kishkin, B.P., Mehanika polimerov (Mechanics of polymers). Moscow: MSU, 1975. Backnell, K. Udaroprochnie plastiki (Shock-resistant plastics). Leningrad: Chimiya, 1981 (In Russian). Kaush, G., Razrushenie polimerov (Destruction of polymers), Moscow: Mir, 1981 (In Russian). Berlin, A.A, Volfson, S.A, Oshmyan, V.G., Enicolov, N.S., Principi sozdaniya compozicionnih polimernih materialov (Principles for creation of composite polymer materials), Moscow: Chimiya, 1990 (In Russian). Mezhikovskii, S.M., D.E. degree thesis, Moscow: IHF AN SSSR, 1983. Topchieva, I.N., Kalashnikiv, F.A., Spiridonov, V.V., et. al. Tesisi plenarnih I stendovih dokladov VIII konferencii po chimii i fizikohimii oligomerov (Thesises of plenary sessions and posters of VIIIth conference on chemistry and physical chemistry of oligomers), Chernogolovka: IPHF RAN, 2002, p. 108 (In Russian). Viner, N., Kibernetica ili upravlenie I svyaz’ v zhivotnom I mashine (Kibernetics or control and communication in animal and machine), Moscow: Mir, 1968 (In Russian). Ivachnenko, A.G., Zaichenko, Yu. P., Dmitriev, V.D., Prinyatie reshenii na osnove samoorganizacii (Self-organization for decision-making) Moscow: Nauka,1976 (In Russian). Frenkel, S. Ya., Cigelskiy, I.M., Colupaev, B.S., Molekulyarnaya Kibernetica (Molecular cibernetics) Svit, 1990 (In Russian). Niemark, Yu. I. and Landa, P.S. Stochasticheskie I chaoticheskie kolebaniya (Stochastic and chaotic oscillations). Moscow: Nauka,1987 (In Russian).
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[14] U.Ashbi. Konstrukcia mozga (Construction of brain). Moscow: Mir, 1962 (In Russian). [15] Goldanskii, V.G., et. al., Fizicheskaya himiya: Sovrem. problemi (Physical chemistry: present day problems), Moscow: Himiya, 1988, p. 198 (In Russian). [16] Foks, R. Energiya i evolucia gizni na zemle (Energy and evolution of life on Earth), Moscow: Mir, 1992 (In Russian).
INDEX A Aβ, 101, 163 acceptor, 17 acceptors, 115 accessibility, 73 accuracy, 4 acetate, 33 acetone, 115, 158 achievement, 89, 130, 162 acid, 1, 21 acoustic, 250 acrylate, 20, 21, 110, 111, 123, 124, 125, 126, 128, 129, 131, 132, 133, 135, 137, 141, 150, 152, 155, 161, 218 ACS, 42 activation, 15, 33, 66, 71, 84, 85, 86, 87, 88, 95, 98, 140, 141, 142, 143, 144, 145, 147, 148, 149, 150, 161, 165, 220, 225, 226, 231, 232, 239 activation energy, 71, 95, 165, 225, 231, 232, 239 activators, 19 active additives, 20 acute, 209 additives, ix, 15, 20, 108, 115, 151, 152, 250 adipate, 159 adsorption, 54, 157, 158, 159, 160, 161, 162 adsorption isotherms, 159 aerosil, 158, 159 agent, 16, 18 agents, 15, 18, 20 aggregates, xv, 2, 12, 13, 23, 24, 35, 77, 80, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 96, 97, 99, 100, 110, 112, 118, 119, 120, 121, 122, 123, 124, 128, 135, 141, 142, 143, 144, 145, 147, 148, 149, 154, 158, 159, 162, 163, 164, 166, 169, 191, 202, 212, 221, 236, 238, 251
aggregation, 2, 13, 23, 26, 31, 76, 79, 84, 88, 95, 98, 107, 111, 149, 150, 158, 159, 161, 188, 202, 207, 209, 221, 222, 224, 226, 237 aggregation process, 84, 150 agriculture, ix air, 9, 124, 128, 129, 131, 167 alcohols, 7, 219 aldehydes, 7 alkanes, 192 alphabets, xii alternative, 12, 90, 114 ambiguity, 2 amendments, 29, 34 amide, 14 amine, 35 amines, 7, 19, 20 amino, 1, 19 amino acid, 1 amorphous, 24, 36, 104, 151, 153, 189, 216 amplitude, 88, 150, 183, 184 AN, 40, 41, 42, 43, 46, 47, 170, 172, 173, 175, 176, 177, 178, 179, 180, 181, 241, 243, 244, 245, 246, 247, 248, 253 anisotropy, 24, 25, 55, 59, 68, 73, 79, 80, 81, 82, 83, 124, 127, 131, 132, 136, 169 Anisotropy, 123, 124 anomalous, 120, 122, 152, 153, 156, 157 antibiotics, xv application, ix, xv, 18, 54, 101, 110, 136, 153, 198 argument, xiii, 203 Arrhenius law, 70, 97 assumptions, 101, 123, 125, 209, 249 asymmetric molecules, 226 asymmetry, 7, 209 asymptotic, 55, 64, 119 asymptotically, 62, 63 atoms, 3, 102, 109, 110, 114, 176, 226, 251 attractiveness, 21 averaging, 11, 52, 59, 62, 100, 130, 131, 141
256
Index
Avogadro number, 6
B barrier, 65, 84, 140, 145, 147, 161, 209 barriers, 66, 147 behavior, vii, xi, 6, 12, 13, 14, 28, 54, 60, 68, 95, 125, 130, 132, 136, 150, 169, 186, 189, 201, 207, 209, 211, 218, 230, 232 bending, 9, 10, 49, 63, 64, 65, 66, 73, 74, 87 bifurcation, 147 binding, 97 binding energy, 97 biological macromolecules, 49 biomolecular, 127 bivariate function, 54 blends, 19, 20, 21, 22, 23, 24, 26, 27, 28, 29, 30, 33, 34, 35, 37, 152, 153, 157, 183, 184, 193, 194, 195, 196, 197, 199, 200, 201, 203, 210, 211, 213, 214, 215, 216, 218, 219, 225, 230, 231 blocks, ix, 4, 14, 15, 18, 21, 194, 202, 226, 249 blurring, 154 boiling, 4, 6, 8, 166 Boltzmann constant, 26, 188, 234 bonding, 95, 96, 100, 219 bonds, 6, 12, 15, 23, 79, 95, 96, 97, 98, 99, 108, 110, 114, 115, 130, 162, 164, 219 boundary conditions, 69 brain, 254 branched polymers, 152 branching, 5, 21, 23, 24 butadiene, 35, 109, 117, 118, 133, 135, 192, 193, 194, 195 butadiene-nitrile, 35, 117, 118, 133, 135, 192, 194, 195 butadiene-nitrile rubber, 35, 133, 135, 194, 195 by-products, 2, 14, 15
C calorimetric method, 128 capillary, 234, 235 carbamide, 15, 18 carbohydrates, 1 carbon, 14, 158, 251 carbon atoms, 251 carboxyl, 19 carrier, 13 castor oil, 35 catalyst, 14 cell, xv, 103, 114, 137 cellulose, 33
Ceteris paribus, 153, 156, 217 chain molecules, 54 chain rigidity, 10, 61, 62, 63, 90, 94, 113 characteristic viscosity, 27, 124, 125 chemical composition, 23 chemical industry, ix chemical interaction, 13, 126 chemical kinetics, 125, 236 chemical properties, vii, 35, 67 chemical reactions, 2, 19, 21, 96, 122, 127, 251 chemical structures, 2, 4, 18, 213 chiral, 251 chloroform, 33 chromatography, 49, 54, 211 cis, 23, 115, 116, 117, 118, 128, 129, 131, 134, 135, 152, 153, 155, 157, 192, 194, 195, 196, 197, 198, 216, 219, 220, 223, 224, 225, 227, 235, 236, 237 classes, 13, 14, 15, 18, 54, 189, 192 classical, xv, 2, 5, 14, 26, 31, 35, 59, 60, 80, 99, 125, 126, 128, 133, 135, 163, 169, 183, 198, 216, 228 classification, 1, 2, 10, 13, 14, 15, 18, 19, 20, 22, 24, 36, 54 clusters, 80, 83, 123, 166 cohesion, 91 coil, 10, 38, 56, 59, 63, 66, 67, 74, 76, 164 collectivism, 12, 60 colloids, 228, 229 communication, 253 community, xiii compaction, xv compatibility, 20, 26, 28, 30, 31, 32, 33, 34, 35, 167, 192, 194, 195, 196, 197, 199, 207, 219, 240 compensation, 12 competition, 126, 156, 224, 226 compilation, 27 complexity, 32, 49, 214 compliance, 52 components, xv, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 34, 35, 37, 84, 95, 106, 107, 108, 114, 115, 117, 120, 121, 125, 126, 130, 132, 135, 136, 143, 152, 154, 157, 158, 162, 167, 168, 183, 188, 192, 196, 197, 202, 203, 206, 209, 212, 213, 217, 219, 222, 223, 224, 226, 229, 230, 233, 234 composites, ix, 20, 235 composition, 23, 31, 35, 49, 52, 54, 80, 106, 135, 154, 156, 159, 167, 168, 183, 184, 213, 217, 223, 224, 225, 226, 227, 230, 232, 233, 234 compounds, 1, 2, 3, 7, 8, 13, 15, 19, 21, 27, 28, 49, 59, 60, 64, 74, 110, 122, 133, 143, 184, 189, 216, 249, 251 conception, 2 condensation, xv, 14, 90 condensed matter, xv, 128
Index conductive, 114 configuration, 23, 135 conformational states, 54, 61, 66 confusion, xii, 2, 106 conservation, 86, 88 consolidation, 117 constant rate, 145 construction, 223, 227, 235 control, 21, 71, 146, 147, 150, 250, 253 conversion, 19, 127, 128 convex, 167 cooling, 146, 151, 161, 188 copolymer, 117, 118 copolymers, 16, 184 correlation, 10, 12, 26, 30, 36, 51, 57, 58, 59, 63, 67, 73, 78, 101, 102, 103, 109, 113, 120, 127, 130, 135, 141, 143, 144, 155, 156, 188, 203, 217, 233, 234, 237, 238 correlation function, 58, 59, 67 correlations, 12, 185, 220, 234, 239, 240, 249 covalent, xv, 96 covalent bond, xv, 96 Cp, 58 CP, 132 CRC, 38 critical density, 57 critical points, 27 critical state, 155, 156, 158, 207, 237 critical temperature, 37, 154, 165, 212 critical value, 3, 77, 87, 138, 147, 164, 185, 189 cross-linking, 16, 18 crystal growth, 250 crystalline, 24, 37, 101, 103, 104, 106, 189, 216 crystallinity, 104, 153 crystallites, 7, 25 crystallization, 8, 34, 189, 212 crystals, 25 curing, 14, 15, 18, 19, 20, 21, 22, 24, 33, 95, 122, 123, 129, 130, 131, 132, 133, 134, 135, 136, 138, 141, 146, 218, 219, 235, 236, 237, 238, 239, 249 curing process, 15, 20, 21, 132 curiosity, xi cycles, 16, 23
D damping, 117 data processing, 166 data transfer, 18 decay, 95, 117, 118, 162, 164, 165 decomposition, 132, 183, 184, 185, 187, 216, 251 defects, 26, 249
257
definition, 2, 3, 4, 5, 8, 15, 32, 35, 63, 68, 69, 79, 214, 239, 250 deformation, 10, 84, 109, 110, 137, 138, 139, 140, 143, 144, 145, 151, 190, 230, 233, 234, 235 degenerate, 186 degrees of freedom, 8, 9, 11, 28, 59, 73, 74, 76 density, 4, 6, 9, 12, 31, 35, 56, 57, 58, 100, 101, 113, 166, 184, 187, 188, 219, 233 density fluctuations, 31 depolarization, 27 depolymerization, 54, 251 derivatives, 189 desorption, 161, 162 destruction, 24, 54, 68, 86, 91, 135, 140, 162, 183, 187 detection, 100, 237 deviation, 9, 35, 101 dichloroethane, 159 differential equations, 89 differentiation, 13, 34 diffusion, 28, 29, 83, 95, 99, 106, 117, 150, 162, 163, 164, 165, 166, 167, 168, 169, 183, 184, 187, 188, 217, 218, 220, 221, 223, 224, 225, 226, 227, 230, 240, 249 diffusion process, 166, 223, 225, 226 diffusion time, 162 dimer, 91, 111 dimeric, 110 dimethacrylate, 20, 115, 118 dipole, 12, 79, 95, 106, 201, 220, 239 dipole moment, 201 dipole moments, 201 Dirac equation, 62 discontinuity, 224 disorder, 106, 107, 130, 132, 135 dispersion, xv, 21, 22, 30, 31, 33, 37, 49, 79, 94, 108, 132, 135, 163, 209, 216, 217, 218, 230, 231, 235 dispersity, 23, 34 dissociation, 86, 91, 96, 97 distribution, 19, 23, 29, 33, 49, 50, 51, 52, 53, 54, 57, 61, 62, 67, 78, 83, 84, 86, 90, 92, 93, 94, 95, 100, 101, 102, 103, 112, 117, 118, 119, 120, 122, 126, 128, 130, 135, 145, 152, 153, 154, 156, 166, 183, 186, 188, 217, 234, 236, 250 distribution function, 23, 29, 33, 50, 53, 61, 62, 90, 94, 101, 102, 112, 128, 130, 135, 145, 234 division, 107, 220 dominance, 239 donor, 17 doped, 19 dosage, 20, 34, 35, 36, 37, 152, 155, 156, 157, 211, 216, 217, 219, 220, 222, 227, 229, 230, 232, 237 double bonds, 110, 114, 123
258
Index
drying, 29, 111 dualism, 28 duration, 28, 114, 131, 251
E eating, 132 ecological, 21 elasticity, xv, 32 elasticity modulus, 32 electrolytes, 80 electron, 101, 104, 106, 122, 166, 217 electron density, 101 electron microscopy, 166, 217 electrostatic force, xv elementary particle, 91 elongation, 21, 234 emission, 100 emulsions, 34, 217 energy, 8, 9, 11, 12, 13, 15, 29, 30, 34, 65, 66, 74, 75, 76, 80, 81, 84, 91, 94, 95, 96, 97, 99, 100, 102, 108, 110, 111, 112, 114, 121, 130, 140, 143, 144, 145, 147, 161, 185, 186, 187, 189, 202, 207, 209, 211, 217, 226, 228, 232, 233 energy density, 8, 9, 187, 188, 189 energy efficiency, 12 Enthalpy, 205, 207, 212 entropy, 12, 26, 74, 75, 99, 106, 108, 130, 188, 196, 197, 200, 201, 204, 205, 206, 207, 208, 209, 210, 212, 214 environment, 12, 29, 52, 60, 68, 69, 70, 71, 78, 79, 81, 101, 103, 166, 167, 169, 223, 224, 225, 226, 249 enzymes, xv epoxides, 20 epoxy, 14, 106, 117, 159, 194, 228 EPR, 190, 191 equilibrium, 15, 23, 24, 25, 28, 29, 30, 31, 32, 34, 36, 37, 65, 75, 76, 78, 80, 86, 89, 91, 92, 93, 94, 95, 96, 97, 98, 100, 106, 110, 114, 115, 116, 117, 118, 119, 120, 121, 122, 127, 128, 130, 131, 132, 135, 138, 140, 141, 145, 146, 147, 148, 150, 154, 156, 158, 159, 161, 162, 183, 184, 185, 188, 190, 198, 216, 217, 230, 236, 239, 249, 251 equilibrium sorption, 161 equilibrium state, 28, 29, 30, 75, 76, 86, 95, 121, 122, 128, 131, 136, 146, 147, 148, 162, 183, 190, 217, 230, 236, 239 ESR, 99 ester, 35, 110, 197 esters, 7, 194 estimating, 119 Ether, 165
ethers, 219 ethylene, 51, 162, 168, 195, 200, 201 ethylene glycol, 162, 168 ethylene oxide, 51 ethyleneglycol, 101 evolution, xv, xvi, 1, 33, 87, 89, 122, 127, 135, 140, 183, 188, 190, 202, 212, 216, 217, 230, 251, 254 experimental condition, 3, 7, 162 expertise, 18 exposure, 30, 114, 115, 116, 117, 118, 121, 129, 130, 132, 136, 139, 144, 146 extrapolation, 231 extrusion, 21
F feedback, 250, 251 fibrillar, 106 field theory, 184 film, 29, 128, 129, 130, 131, 161 films, 29, 128, 129, 130, 135, 138, 161, 166, 220 fish, 2 fixation, 19, 104 flexibility, 3, 8, 10, 11, 12, 27, 28, 60, 65, 79, 110, 113, 153, 189, 225, 226 flow, 21, 136, 137, 138, 139, 140, 150, 155, 164, 166, 184, 188, 190, 226, 227, 228, 230, 231, 232, 233, 234, 235 flow curves, 155 flow value, 150 fluctuations, 23, 29, 30, 79, 80, 81, 95, 97, 100, 109, 123, 130, 154, 163, 166, 183, 184, 186, 200, 209, 232, 233, 234, 237, 238, 250 folded conformations, 69 folding, 189 formaldehyde, 15, 18, 193 Fourier, 62, 100 Fourier transformation, 100 Fox, 97, 99 fractionation, 154 fracture, 108, 250 free energy, 12, 25, 26, 27, 75, 76, 77, 78, 94, 130, 183, 185, 186, 187, 188, 189, 196, 197, 202 free volume, 74, 153, 166 freedom, 8, 9, 11, 28, 59, 73, 74, 76 freedoms, 221 freezing, 32, 166 friction, 169 FTD, 14, 249
Index
G gas, 2, 9, 26, 79, 128, 131, 166, 196, 211, 232 gas chromatograph, 211 Gaussian, 11, 27, 28, 55, 56, 62, 63, 64, 65, 66, 67, 68, 188 gel, 125 gene, 25, 27 generalization, 35 generalizations, 25, 27 genes, xv Gibbs, 25, 29, 32, 35, 47, 240 glass, 32, 34, 118, 159, 160, 161, 189, 198, 202 glass transition, 202 glass transition temperature, 202 glassy polymers, 226 glassy state, 165, 225 glucoside, 250 glycerin, 54 glycol, 20, 21, 101, 117, 123, 158, 159 grading, 109 graduate students, xii grains, xiii granules, 150 gravitation, 113 group size, 251 grouping, 80, 82, 124, 126, 132, 135, 136 groups, 3, 4, 5, 6, 7, 11, 14, 15, 18, 19, 20, 21, 23, 24, 31, 32, 35, 50, 52, 53, 54, 55, 61, 95, 96, 97, 98, 106, 109, 110, 114, 123, 124, 125, 126, 189, 192, 194, 197, 198, 227, 236, 250 growth, 3, 8, 15, 19, 37, 51, 66, 77, 86, 88, 94, 95, 104, 113, 120, 121, 123, 125, 126, 128, 132, 133, 144, 147, 150, 152, 153, 156, 184, 186, 189, 196, 197, 199, 202, 204, 207, 209, 210, 223, 224, 225, 226, 228, 229, 230, 231, 233, 234, 235, 236, 238, 239, 250, 251 growth mechanism, 15 growth rate, 144, 184
H H1, 196 hands, xii hardness, 167 heat, 4, 6, 15, 139, 183, 212 heat capacity, 4, 6 heating, 104, 140, 146, 147, 150, 151, 161, 199 height, 65 heterogeneity, 22, 31, 49, 54, 57, 187, 250
259
heterogeneous, 14, 22, 31, 33, 34, 35, 49, 79, 183, 190, 216, 218, 219, 226, 227, 230, 234, 235, 237, 250 heterogeneous systems, 31, 34, 218, 227, 237 Higgs, 174 high resolution, 99 high temperature, 66, 73, 161, 164, 166, 212, 232 hips, 104 histogram, 103 homogeneity, 250 homogenous, 226, 227, 228 homolog, 154 homopolymerization, 235 hormones, xv hydrocarbon, 15, 106, 110, 113, 114, 164 hydrodynamic, 28, 233 hydrogen, 12, 13, 23, 79, 95, 109 hydrogen atoms, 109 hydrogen bonds, 13, 23 hydroquinone, 132, 133 hydroxyl, 14, 20 hypothesis, 114, 115, 124, 136, 156, 163, 164, 239 hysteresis, 88, 136, 145, 146, 147, 148, 150, 161, 249
I IB, 124, 125 id, 162 identification, 19 identity, 131 ideology, 61, 79, 95, 239 IDP, 125 impurities, 192, 228 inclusion, 109 incompatibility, 20, 28, 29 independence, 155, 232 indication, 118, 222, 224 indices, 108, 130 induction, 132 induction time, 132 industrial, 19, 20, 41 industry, ix, xi, 42, 244, 253 inequality, 59, 66, 69, 120, 143, 144 inert, 14, 85, 87, 88, 149 inertia, 113 infinite, 11, 109 infrared, 109, 114, 115 inhibition, 221 inhibitor, 132, 133 inhibitors, 19, 135 inhomogeneities, 79, 80 inhomogeneity, 49, 79, 80, 141, 188
260
Index
initial polymerization rates, 237 initial state, 22, 34, 87, 107, 119, 122, 130, 147, 148, 161, 200, 202, 251 initiation, 15, 19, 33, 51, 99, 132, 251 injection, 42, 84 insertion, 19 instability, 22, 25, 185 integration, 164 interaction, 6, 7, 8, 9, 12, 23, 26, 28, 38, 60, 67, 73, 79, 90, 91, 94, 95, 96, 97, 98, 99, 100, 103, 106, 109, 110, 112, 114, 126, 127, 130, 131, 132, 159, 188, 202, 204, 207, 209, 212, 214, 228, 235, 238 interaction effect, 9 interactions, 7, 9, 10, 13, 23, 32, 39, 59, 60, 73, 76, 79, 80, 99, 106, 110, 114, 122, 131, 172, 200, 202 interface, 35, 45, 79, 175, 218 intermolecular, 6, 7, 8, 12, 23, 32, 39, 80, 90, 94, 95, 96, 97, 98, 99, 100, 101, 102, 106, 110, 114, 130, 172, 202, 228 intermolecular interactions, 7, 32, 39, 80, 131, 172, 202 interphase, 28, 184, 216, 218, 230 interval, 8, 64, 69, 70, 107, 113, 129, 143, 145, 146, 147, 148, 153, 156, 159, 165, 166, 190 intrinsic, 28 inversion, 37, 217, 230 Investigations, 203 ionic, 15, 16 ionic polymerization, 15, 16 IR, 136 IR spectroscopy, 136 IRC, 46, 174, 177, 244 irritation, xi isomers, 111 isoprene, 18, 133 isotherms, 159, 160 isotropic, 12, 22, 29, 68, 70, 72, 73, 79, 80, 113, 127, 169 Israel, xiii
J Japan, 39 Japanese, 2 judgment, xiii justification, 66
K ketones, 7 kinetic constants, 91, 122 kinetic curves, 90, 128, 135, 158
kinetic effects, 132, 133, 190 kinetic equations, 87, 150 kinetic model, 140 kinetic parameters, 132 kinetics, xi, 13, 15, 24, 29, 30, 31, 32, 52, 78, 83, 84, 86, 91, 111, 115, 119, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 135, 136, 137, 138, 140, 141, 158, 162, 184, 216, 218, 236, 239
L L1, 56 L2, 56 lamina, 235 laminar, 235 language, xi large-scale, 95, 154, 233 latex, 218 lattice, 25, 26, 61, 62, 69, 71, 74, 103, 112 law, 25, 29, 70, 88, 92, 97, 113, 119, 156, 201, 203, 221, 223, 230, 236, 239 laws, 5, 8, 18, 25, 27, 31, 38, 86, 122, 126, 150, 157, 158, 169, 217, 227, 230, 234, 236 layering, 31, 33, 37, 188, 216, 218 lens, 31 life cycle, 78 lifecycle, 185 lifetime, 24, 29, 30, 79, 80, 97, 98, 123, 126, 127, 130, 135, 158, 169, 186 light scattering, 27, 31, 216 limitations, 18, 26, 28, 126, 150, 250 linear, 2, 5, 6, 7, 8, 9, 15, 19, 21, 22, 23, 30, 53, 54, 61, 63, 64, 66, 67, 100, 109, 113, 121, 127, 151, 152, 184, 185, 187, 188, 231, 235 linear dependence, 8, 53 linear function, 5, 6, 7, 8, 9 linear molecules, 54, 61 linear polymers, 22, 23, 151, 184, 185, 187, 188 linguistically, xi linkage, 113, 114 links, 2, 3, 6, 8, 9, 11, 15, 54, 56, 58, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 74, 76, 94, 111, 112, 113, 114, 188, 198, 226 lipid, 114 lipids, 114 liquid crystal phase, 29 liquid nitrogen, 104, 166 liquid phase, 129, 130, 158 liquids, 22, 29, 32, 35, 78, 80, 82, 83, 95, 103, 122, 123, 124, 131, 135, 136, 137, 140, 148, 151, 158, 190, 229, 238, 239, 250 local order, 12, 59, 60, 79, 106, 113 localization, 189
Index logarithmic coordinates, 225 logical representation, 35 London, 172 long distance, 132 long period, 7, 106 losses, 74, 220 low molecular weight, 1, 2, 4, 5, 7, 8, 9, 11, 12, 13, 14, 19, 21, 30, 31, 32, 59, 60, 64, 68, 80, 83, 123, 131, 140, 152, 154, 155, 156, 216, 218 low temperatures, 66, 161, 232 lubrication, 151
M macromolecular order, 12 macromolecular systems, 54, 60, 66, 74, 184 macromolecules, xv, 6, 9, 10, 11, 12, 28, 31, 49, 54, 55, 56, 59, 61, 62, 65, 72, 73, 99, 153, 163, 221 magnetization, 117, 118, 162, 165, 221, 222 magnets, 131 main line, xii market, xv, 18 masking, 234 mass transfer, 216, 224, 226 Mathematical Methods, 171 matrix, 22, 106, 108, 109, 118, 128, 161, 167, 190, 194, 198, 199, 201, 224, 225, 235, 250 maturation, 184 MB, 124, 125, 126, 235 measurement, 5, 8, 31, 115, 130, 138, 145, 225, 237 measures, 29 mechanical energy, 233 mechanical properties, 249 media, 8, 9, 22, 30, 31, 33, 169, 230, 231, 236 medicine, ix MEF, 104 melt, 15, 56, 106, 151, 162, 163, 165, 166, 167 melting, 4, 6, 8, 68, 104, 163, 189, 190, 213 melting temperature, 104, 163, 213 melts, 9, 13, 106, 123, 164, 166, 184 membranes, 114 memory, 61, 251 methacrylic acid, 21 methylene, 35, 192, 195, 196, 197, 198, 199, 201, 202, 223, 224, 225 methylene group, 197 micelles, 80 microscope, 31, 104, 106 microscopy, 31, 166, 217 microstructure, 59 microstructures, 123 microviscosity, 225, 226 migration, 10, 15, 131
261
misinterpretation, 19 mixing, 21, 25, 26, 34, 106, 108, 115, 134, 150, 166, 194, 196, 197, 198, 199, 200, 202, 203, 204, 205, 207, 208, 210, 211, 212, 214, 217, 218, 221, 237, 240 MMA, 124 mobility, 115, 163, 165, 167, 168, 184, 190, 191, 220, 221, 222, 230 modeling, 26, 114 models, vii, 6, 49, 81, 83, 89, 103, 136, 137, 140, 196, 232, 250 modulus, 32 molar volume, 226, 233 mole, 50, 96, 99, 100, 156, 165, 166 molecular dynamics, 110, 113, 114 molecular forces, 131 molecular liquids, 26, 30, 130, 211, 232, 233 molecular mobility, 115, 190, 221 molecular orientation, 115, 131, 141 molecular structure, vii, xi, 7, 12, 18, 26, 30, 49, 122, 128, 146, 195, 203 molecular weight, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 19, 21, 26, 27, 28, 30, 31, 32, 35, 49, 50, 51, 52, 53, 54, 59, 60, 61, 64, 67, 68, 80, 83, 101, 104, 106, 109, 110, 122, 123, 131, 140, 152, 153, 154, 155, 156, 163, 165, 166, 167, 189, 192, 194, 196, 197, 198, 211, 216, 218, 225, 226, 227, 233, 234, 240, 251 molecular weight distribution, 19, 49, 50, 51, 52, 53, 54, 67, 152, 153, 154, 156 monolayer, 114 monolayers, 114 monomer, xv, 2, 3, 4, 8, 9, 10, 11, 14, 20, 21, 27, 35, 37, 38, 65, 68, 73, 123, 166, 184, 188, 190, 233 monomer links, 11, 68 monomeric, 2, 4, 8, 20, 125 monomers, vii, ix, xi, 1, 3, 4, 5, 10, 20, 27, 28, 54, 71, 123, 124, 188, 190, 253 Monte-Carlo, 111 morphological, 21, 23, 25, 135, 217, 218, 236 morphology, 22, 24, 31, 33, 217, 218, 235 Moscow, ix, xiii, xvi, 179, 253, 254 motion, 106, 120, 183 motives, 131 movement, 78, 79, 89, 115, 184, 209, 220, 221, 226 multiplication, 9 multiplicity, 20 multiplier, 123, 224 MWD, 8, 14, 20, 23, 152, 154, 166, 249
N NA, 233, 234
262
Index
NAc, 234 nanocomposites, ix nanotubes, 250 natural, xv, 9, 13, 49, 66, 70, 78, 89, 95, 114, 115, 120, 122, 127, 131, 135, 141, 148, 151, 221 neglect, 64, 67, 218 nematic, 72, 73, 80 network, 18, 21, 22, 23, 136, 140, 153, 164 network density, 153 Newton, 164, 231, 235 Newtonian, 136, 138, 231 Ni, 45, 68, 71, 240 nitrile rubber, 133, 134, 193 nitrogen, 104, 166 NMR, 99, 109, 114, 115, 117, 136, 164, 191, 220, 221, 222, 245 nonequilibrium, 30, 186, 188 non-Newtonian, 136, 138, 233 normal, 114, 117, 123, 152 normalization, 71 nuclear, 115, 117, 118, 162, 165, 221 nucleation, 153, 184, 189, 216 nucleus, 184
O OB, 4, 16, 19, 20 observations, 122, 133, 135, 169, 235 oil, 35 OKM-2, 191 olefins, 192 oligomer molecules, xv, 12, 13, 21, 27, 28, 31, 55, 60, 61, 89, 94, 98, 114, 130, 135, 136, 149, 156, 159, 169, 221, 237, 250, 251 oligomeric, vii, xi, xii, 2, 3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 18, 19, 20, 38, 54, 101, 103, 104, 106, 110, 111, 113, 114, 115, 118, 120, 122, 123, 126, 135, 137, 139, 141, 143, 145, 146, 148, 153, 158, 169, 197, 217, 218, 220, 221, 222, 223, 225, 226, 227, 228, 249, 250, 251 oligomeric products, 2, 19 oligomerization, 51, 52, 233, 234 oligopeptide, 1 oligosaccharide, 250 oligosaccharides, 1 omission, 2 optical, 29, 31, 32, 83, 217, 219 optical density, 31, 219 optical microscopy, 31 optics, 31 organic, ix, 4, 6, 7, 8, 9, 18, 38, 80, 123, 154 organic compounds, ix, 4, 6, 7, 8 organic solvent, 154
organic solvents, 154 orientation, 6, 10, 12, 30, 58, 61, 65, 68, 69, 71, 72, 74, 75, 76, 79, 80, 81, 100, 108, 109, 110, 112, 113, 114, 123, 127, 128, 141, 169, 240, 250 oscillations, 253 osmotic, 155, 234 osmotic pressure, 234 oxidants, 20 oxidation, 133 oxide, 16, 51, 54, 55 oxides, 7, 51 oxygen, 3, 132, 133, 226
P paradox, 79 paradoxical, 199, 229 parallelism, 70 paramagnetic, 190 parameter, 3, 5, 8, 9, 10, 12, 22, 26, 30, 31, 35, 62, 63, 64, 65, 66, 68, 69, 70, 71, 75, 77, 91, 93, 94, 109, 112, 113, 116, 120, 123, 127, 128, 130, 146, 147, 150, 166, 184, 188, 189, 200, 202, 203, 205, 214, 225, 233, 250 particles, 22, 23, 31, 33, 54, 78, 79, 80, 85, 86, 91, 101, 141, 143, 150, 184, 216, 218, 220, 229, 230, 234, 235, 250 PDK, 133, 134, 238 peptide, xv peptides, 1 perception, 250 periodicity, 3, 101, 103, 106 permit, 8 peroxide, 14, 15, 18, 132, 133 PG, 214 phase decomposition, 183, 216 phase diagram, 35, 36, 37, 95, 156, 161, 183, 192, 194, 196, 199, 209, 212, 213, 214, 217, 222, 223, 228, 233, 235, 237, 239 phase inversion, 23, 33, 36, 37, 217 phase transitions, vii, 2, 36, 89, 139, 189, 223, 235, 240 phenol, 15, 18, 193 photon, 217 photonic, 15 physical chemistry, xii, 5, 22, 25, 49, 80, 110, 253 physical properties, 3, 4, 8, 23, 35, 238 physico-chemical characteristics, 21 physics, vii, xi, xii, 10, 27, 43, 122, 169, 249 planar, 103, 114 plasma, xi plasticization, 21, 115, 151, 153, 154, 155, 223, 224, 225, 228
Index plasticizer, 21, 156 plastics, 253 plastisol, 151 platinum, 104 play, 141 plurality, 228 PMMA, 106 Poisson, 50, 51 Poisson distribution, 50, 51 polar groups, 198 polarity, 135, 192, 194, 197 polarization, 197, 220, 221, 239 polybutadiene, 109, 117, 118, 134, 155, 198, 216 polycarbonate, 106, 194 polycondensation, xv, 8, 14, 15, 96, 188, 249 polycondensation process, 15 polydispersity, 49, 52, 53, 154, 163, 234, 249, 250 polyester, 20, 251 polyimides, 106 polyisoprene, 115, 116, 117, 118, 128, 129, 131, 133, 134, 135, 152, 153, 155, 192, 194, 195, 196, 197, 198, 216, 219, 220, 223, 224, 225, 227, 235, 236, 237 polymer, ix, xi, xiii, xv, 2, 3, 4, 8, 10, 11, 12, 13, 14, 15, 19, 20, 21, 23, 24, 25, 26, 27, 28, 30, 33, 34, 35, 36, 37, 55, 56, 57, 58, 59, 60, 61, 63, 65, 67, 68, 73, 74, 83, 108, 109, 123, 130, 131, 136, 146, 150, 151, 153, 154, 156, 157, 161, 162, 166, 167, 184, 188, 195, 198, 199, 205, 211, 214, 217, 218, 220, 221, 222, 223, 224, 225, 228, 233, 234, 235, 236, 237, 240, 249, 250, 253 polymer blends, 20, 21, 28, 33, 34 polymer chains, 61, 68, 153, 184, 188 polymer industry, xi polymer materials, 19, 253 polymer matrix, 108 polymer melts, 184 polymer molecule, 11, 26, 27, 28, 36, 55, 57, 67, 74, 167, 198, 222 polymer networks, 19, 249 polymer solutions, 13, 25, 26, 123, 136, 146, 157, 211 polymer structure, 24, 25, 249 polymer systems, 8, 13, 27, 33, 55, 59, 205, 217, 233, 234, 240 polymerization, xv, 2, 6, 8, 9, 14, 15, 16, 17, 19, 22, 26, 50, 51, 54, 78, 99, 123, 124, 126, 127, 128, 129, 130, 131, 132, 133, 135, 141, 188, 216, 233, 234, 235, 236, 237, 249 polymerization kinetics, 123, 124 polymerization process, 54, 123, 126 polymerization processes, 126 polymerization temperature, 236
263
polymers, vii, ix, xi, xii, xiii, 1, 2, 3, 4, 5, 10, 11, 13, 15, 18, 19, 22, 23, 24, 25, 26, 27, 28, 30, 33, 34, 43, 49, 50, 54, 55, 60, 64, 65, 73, 80, 106, 110, 123, 151, 152, 154, 184, 185, 187, 188, 190, 194, 202, 226, 229, 253 polynomial, 70 polypropylene, 151 polystyrene, 28, 29, 109, 194, 196 polyvinylpyrrolidone, 117 positive correlation, 234 potential energy, 74, 102, 110 powder, 229 power, 64, 97, 132, 136 pragmatism, xii prediction, 18 pressure, 8, 22, 34, 35, 130, 192, 234, 251 probability, 9, 61, 68, 69, 78, 80, 95, 100, 111, 112, 166, 222 probe, 190 processing stages, 21 production, vii, xii, 18, 21, 250 property, 3, 10, 12, 30, 32, 148, 239 propylene, 51 proteins, xvi Proteins, 39 PSP, 167 PT, 233 pumping, 187 pupils, ix PVC, 106, 107, 108, 150, 151, 161, 162, 193, 195, 198, 199, 200, 201, 202, 203, 214, 218, 221, 222, 223, 225, 237, 238, 239
Q quantum, 62 quasi-equilibrium, 135, 218
R radial distribution, 100, 101, 112 radiation, 100 radical polymerization, 15, 84, 99 radiography, 101 radius, 10, 36, 58, 73, 112, 113, 130, 169, 188 random, 49, 79, 122, 135, 163 range, 2, 6, 11, 13, 14, 22, 23, 25, 28, 29, 30, 32, 34, 35, 38, 51, 68, 71, 79, 92, 93, 95, 99, 104, 106, 107, 109, 115, 120, 124, 126, 130, 133, 137, 138, 150, 151, 152, 159, 165, 168, 184, 185, 186, 189, 190, 191, 192, 194, 199, 200, 202, 203, 209, 210,
264 211, 212, 213, 217, 218, 219, 229, 231, 232, 233, 235, 239 ras, ix RAS, 172, 173, 246 raw material, xi raw materials, xi RC, 16 reactant, 128 reaction center, 130 reaction mechanism, 52 reactive groups, 19, 52, 125 reactivity, 13, 21, 123, 141, 249 reading, xiii, 141 reagent, 127 reality, 53, 102 reasoning, 166, 202 Rebinder effect, 21 recall, 214 reconstruction, 59, 70, 147, 156, 164 redistribution, 89, 130, 132, 221 regeneration, 96, 152 regression, 113 regular, 6, 14, 18, 53, 69, 71, 74, 110, 123, 155, 209, 233, 234, 249, 250, 251 regulation, 59, 218 rejection, xii relationship, 120 relationships, 135 relaxation, 15, 28, 29, 30, 31, 32, 78, 83, 86, 87, 88, 109, 113, 115, 117, 118, 119, 120, 121, 122, 128, 130, 131, 135, 136, 137, 138, 140, 143, 144, 145, 146, 147, 148, 149, 150, 164, 183, 188, 189, 198, 201, 220, 221, 225, 226, 233, 239, 240, 249, 250, 251 relaxation model, 118, 119, 121, 135, 147, 148, 150 relaxation process, 30, 87, 113, 146 relaxation processes, 87, 146 relaxation properties, 240 relaxation rate, 30, 32, 149 relaxation time, 30, 109, 113, 115, 116, 119, 120, 121, 122, 128, 130, 164, 188, 220, 234, 239, 249 relaxation times, 30, 128, 188, 234, 239 reliability, 25 repetitions, xii replication, xiii residues, 1, 250 resins, 1, 20 resistance, 225, 233 resolution, 25, 30, 31, 32, 67, 80, 98, 99, 100 restructuring, 89 returns, 115 reverse reactions, 91
Index rheological properties, 136, 140, 141, 144, 145, 153, 228 rheology, 78, 83, 141, 150, 183 rigidity, xv, 10, 12, 21, 49, 54, 56, 60, 61, 62, 63, 64, 65, 66, 67, 70, 73, 74, 75, 76, 77, 87, 90, 94, 110, 113, 169 rings, 109 rods, 12, 56, 57, 58, 61, 76 rolling, 21 room temperature, 137, 192, 202, 229, 230, 236 root-mean-square, 27, 63, 183 rotational mobility, 221 rubber, 15, 95, 115, 118, 120, 128, 131, 133, 136, 138, 141, 146, 152, 153, 154, 155, 156, 197, 198, 203, 214, 218, 219, 223, 225, 235, 236, 239 Rubber, 43, 46, 174, 177, 196, 244 rubbers, 18, 21, 133, 155, 192, 216, 235 Russia, xiii Russian, ix, xi, xii, xiii, xvi, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 240, 241, 242, 243, 244, 245, 246, 247, 248, 253, 254 Russian Academy of Sciences, ix, xii
S sample, 8, 28, 29, 30, 32, 33, 58, 68, 71, 104, 108, 109, 115, 117, 118, 121, 129, 130, 131, 137, 138, 139, 140, 146 sampling, 69 saturation, 95, 99 scalar, 71 scaling, 12, 25, 27, 49, 56, 60, 68, 132, 136, 185 scarcity, 159 scattered light, 27 scattering, 7, 27, 31, 100, 101, 216 school, 49 scientific community, xiii search, 19, 110, 239 searching, 133 segregation, 29, 135 selecting, 19 Self, 46, 165, 173, 181, 244, 248, 250, 253 self-ordering, 68 self-organization, xv, 12, 74, 127, 136, 197, 250, 251 sensing, 67, 99 sensitivity, 5, 164 separation, 26, 28, 29, 31, 33, 34, 35, 37, 82, 95, 154, 158, 184, 189, 199, 216, 228, 230, 251 shape, 24, 27, 28, 117, 234, 235 shares, 71 shear, 136, 137, 139, 140, 143, 144, 146, 152, 164, 227, 231, 233
Index shear rates, 144, 146, 152 short period, 113 shortage, 34, 36 side effects, 219 sign, 77, 183, 189, 208, 227 signals, 191 signs, 184, 228 siloxane, 151 simulation, 110, 111 single crystals, 250 singular, 238 SKN, 118, 134, 193, 195 smectic, 124 solid matrix, 161 solid phase, 191 solid state, 103, 190 solid surfaces, 158 solidification, 115 solubility, 25, 26, 28, 31, 34, 35, 37, 154, 156, 192, 194, 195, 196, 197, 199, 207, 211, 214, 224, 231, 240, 251 solvent, 26, 27, 28, 29, 124, 154, 194, 197, 204, 214, 217 solvent molecules, 26 solvents, 28, 33, 184 sorption, 31, 78, 83, 114, 133, 158, 161, 251 sorption process, 133, 161 Soviet Union, ix spatial, xv, 23, 29, 61, 67, 68, 80, 81, 101, 113, 123, 124, 185, 250, 251 spatial location, 80 spectroscopy, 32, 217, 220 spectrum, 113, 115, 127, 163, 191, 221 speculation, xii, 101, 250 speed, 8, 217, 223, 224, 226, 227 spheres, 79, 159, 160, 161 spin, 73, 99, 115, 118, 190, 221 stability, 22, 23, 25, 70, 78, 130, 154, 183, 187, 213, 217, 218, 234 stabilize, 186 stable states, 150 stages, 21, 29, 54, 72, 87, 119, 120, 122, 150, 186, 249 statistical analysis, 11 statistics, xi, 38, 54, 55, 61, 62, 64, 65, 66, 68 steady state, 119 steric, 60, 73, 76, 111, 112 stiffness, 27 stochastic, 29 Stochastic, 253 stock, 189 storage, 14, 18, 19, 28, 29, 34, 37, 115, 117, 128, 129, 131, 132, 133, 135, 161
265
strength, 23, 130, 141, 232, 249, 250 stress, 34, 159, 234 strong force, 95 structural changes, 164 structural characteristics, 22, 79, 132, 196 structural transformations, 139, 221, 228 structure formation, vii, xv, 28, 29, 33, 83, 97, 114, 115, 118, 122, 135, 136, 137, 140, 141, 145, 147, 199, 203, 239 students, vii, ix, xii, 164 styrene, 6, 20, 35, 51 subjective, 2 substances, vii, xi, xiii, xv, 1, 2, 6, 38, 68, 90, 251 subtraction, 102 summaries, 80 superposition, 140, 191, 214 supramolecular, vii, 13, 20, 22, 23, 24, 25, 26, 29, 31, 34, 35, 49, 78, 79, 80, 81, 83, 95, 97, 99, 104, 106, 110, 114, 115, 116, 117, 118, 120, 121, 123, 124, 126, 128, 129, 130, 131, 132, 135, 136, 137, 140, 141, 145, 146, 147, 148, 151, 156, 157, 158, 159, 161, 164, 203, 216, 226, 227, 228, 230, 232, 236, 237, 238, 239, 249, 250, 251 surface area, 218 surface layer, 131, 186 surface tension, 33, 131, 219 surfactant, 219 surfactants, 33, 218, 219 suspensions, 34 swarm, 80 swelling, 109, 114, 115, 116, 117, 118, 128, 129, 130, 131, 134, 135, 150, 192, 217, 219 swelling process, 131 symbols, xii, 18, 74, 75, 118 symmetry, 6, 79, 188 synthesis, ix, 2, 19, 21, 49, 51, 52, 53, 250, 251
T taxonomy, 13, 18, 19, 22 temperature dependence, 66, 147, 148, 161, 162, 164, 207, 209 temporal, 24, 29, 30, 185, 186, 188, 221, 239, 250 tensile, 110 tension, 21, 152 theoretical assumptions, 123 thermal energy, 232 thermodynamic, 1, 13, 20, 23, 24, 25, 29, 31, 34, 35, 54, 74, 77, 78, 87, 107, 114, 117, 126, 127, 130, 131, 135, 136, 138, 141, 146, 153, 154, 156, 157, 158, 166, 184, 196, 198, 199, 200, 201, 202, 203, 204, 207, 209, 210, 211, 213, 214, 216, 219, 222, 224, 226, 230, 232, 234, 237, 239, 240, 251
266 thermodynamic equilibrium, 13, 31, 77, 87, 114, 117, 127, 130, 131, 136, 138, 141, 146, 154, 222, 240, 251 thermodynamic function, 198, 199, 200, 201, 202, 203, 210, 211 thermodynamic parameters, 23, 24, 107, 153, 196, 199, 201, 210, 213, 214, 222, 237, 240 thermodynamic properties, 13, 224 thermodynamic stability, 154, 213, 234 thermodynamical parameters, 199 thermodynamics, xi, 25, 27, 28, 30, 32, 106, 184, 196, 198, 203, 211, 237, 240 thesaurus, xi three-dimensional, 71, 72, 73 three-dimensional space, 71 threshold, 38, 185, 230, 231, 232 title, xi, xii, xv, 122, 237 Tokyo, 175, 245 tolerance, 60 toluene, 159, 160, 161 topological, 18, 20, 23, 25, 29, 31, 135, 249 topology, 15 traditional model, 140 trans, 23, 111 transfer, 18, 51, 80, 95, 99, 103, 109, 110, 129, 130, 141, 151, 163, 164, 165, 167, 216, 249 transference, 89 transformation, 18, 28, 63, 65, 98, 100, 101, 119, 129, 130, 131, 184, 185, 211, 217, 239 transformations, xv, 2, 22, 24, 34, 68, 75, 113, 135, 139, 140, 146, 150, 161, 166, 230, 234, 249 transition, xv, 2, 4, 9, 10, 11, 12, 13, 24, 25, 27, 28, 29, 33, 34, 35, 36, 38, 54, 62, 68, 70, 71, 72, 73, 79, 81, 123, 124, 137, 140, 141, 147, 167, 183, 184, 190, 191, 198, 202, 210, 216, 219, 220, 224, 225, 226, 228, 232, 237, 239, 249 transition temperature, 73, 199, 202, 210 transitions, xv, 32, 68, 72, 73, 82, 141, 189, 228 translation, xiii, 95, 99, 166 translational, 163, 164, 165, 167, 168, 183, 190, 224, 226 transmission, 31 transparency, 28, 220 transparent, 29, 31, 33 transport, 184, 218, 249 transportation, 163 transverse section, 226 turnover, 61, 114 two-dimensional, 68, 72 two-dimensional space, 68
Index
U uncertainty, 2, 4 universal gas constant, 26, 196, 232 universities, vii, xii urea, 15 urethane, 15, 18, 20, 106, 137 USSR, ix, 42, 173, 177, 179, 246
V vacuum, 29 valence, 15, 65, 110, 114 Van der Waals, xv, 6, 79, 132, 189 vapor, 21 variables, 30, 35, 85, 239 variation, 24, 54, 145, 153, 156, 159, 189, 195, 197, 202, 203, 204, 205, 206, 207, 209, 210, 213, 221, 225, 232, 235, 239 VC, 108 vector, 61, 62, 68, 74, 100, 108, 112, 184 velocity, 84, 85, 86, 87, 88, 89, 96, 99, 115, 123, 124, 125, 126, 127, 128, 129, 133, 135, 141, 142, 147, 148, 149, 161, 217, 218 vinyl monomers, 20 viscosity, 4, 21, 27, 30, 33, 88, 95, 124, 125, 126, 131, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 149, 150, 151, 152, 153, 154, 155, 156, 157, 163, 164, 169, 217, 218, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 249 visible, 115, 128, 130 vocabulary, 80 volatility, 4, 21
W water, 8, 18 wave number, 185, 186, 188 wave vector, 184 woods, 2 writing, xii
X X-axis, 114
