Polymers, kinetic modeling synthesis

A simple algorithm [17] makes it possible to find the probability of any fragment of macromolecules of Gordonian polymers. Comparison of these probabilities with the data obtained by NMR spectroscopy provides the possibility to evaluate the adequacy of a chosen kinetic model of a synthesis process of a particular polymer specimen. The above-mentioned probabilities are also involved in the expressions for the glass transition temperature and some structure-additive properties of branched polymers [18,19]. 

The Flory principle is one of two assumptions underlying an ideal kinetic model of any process of the synthesis or chemical modification of polymers. The second assumption is associated with ignoring any reactions between reactive centers belonging to one and the same molecule. Clearly, in the absence of such intramolecular reactions, molecular graphs of all the components of a reaction system will contain no cycles. The last affirmation concerns sol molecules only. As for the gel the cyclization reaction between reactive centers of a polymer network is quite admissible in the framework of an ideal model. 

When there is a need to calculate only the statistical moments of the distribution of molecules for size and composition, rather than to find the very distribution, the task becomes essentially easier. The fact is that for the processes of polymer synthesis which may be described by the ideal kinetic model the set of equations for the statistical moments is always closed. 

This closure property is also inherent to a set of differential equations for arbitrary sequences Uk in macromolecules of linear copolymers as well as for analogous fragments in branched polymers. Hence, in principle, the kinetic method enables the determination of statistical characteristics of the chemical structure of noncyclic polymers, provided the Flory principle holds for all the chemical reactions involved in their synthesis. It is essential here that the Flory principle is meant not in its original version but in the extended one [2]. Hence under mathematical modeling the employment of the kinetic models of macro-molecular reactions where the violation of ideality is connected only with the short-range effects will not create new fundamental problems as compared with ideal models. 

In subsequent sections some results will be reported relevant to the theoretical consideration of several principle processes of the synthesis of polymers described by various kinetic models. This information may be useful in gaining a better understanding of the potentialities of the statistical chemistry of polymers. 

A kinetic model based on the Flory principle is referred to as the ideal model. Up to now this model by virtue of its simplicity, has been widely used to treat experimental data and to carry out engineering calculations when designing advanced polymer materials. However, strong experimental evidence for the violation of the Flory principle is currently available from the study of a number of processes of the synthesis and chemical modification of polymers. Possible reasons for such a violation may be connected with either chemical or physical factors. The first has been scrutinized both theoretically and experimentally, but this is not the case for the second among which are thermodynamic and diffusion factors. In this review we by no means pretend to cover all theoretical works in which these factors have been taken into account at the stage of formulating physicochemical models of the process... 

Along with the isomerism of linear copolymers due to various distributions of different monomeric units in their chains, other kinds of isomerisms are known. They can appear even in homopolymer molecules, provided several fashions exist for a monomer to enter in the polymer chain in the course of the synthesis. So, asymmetric monomeric units can be coupled in macromolecules according to "head-to-tail" or "head-to-head"—"tail-to-tail" type of arrangement. Apart from such a constitutional isomerism, stereoisomerism can be also inherent to some of the polymers. Isomers can sometimes substantially vary in performance properties that should be taken into account when choosing the kinetic model. The principal types of such an account are analogous to those considered in the foregoing. The only distinction consists in more extended definition of possible states of a stochastic process of conventional movement along a polymer chain. 

When the statistical moments of the distribution of macromolecules in size and composition (SC distribution) are supposed to be found rather than the distribution itself, the problem is substantially simplified. The fact is that for the processes of synthesis of polymers describable by the ideal kinetic model, the set of the statistical moments is always closed. The same closure property is peculiar to a set of differential equations for the probability of arbitrary sequences t//j in linear copolymers and analogous fragments in branched polymers. Therefore, the kinetic method permits finding any statistical characteristics of loopless polymers, provided the Flory principle works for all chemical reactions of their synthesis. This assertion rests on the fact that linear and branched polymers being formed under the applicability of the ideal kinetic model are Markovian and Gordonian polymers, respectively. 

In this section, some general results are reported of the theoretical consideration of the main processes of polymer synthesis in the framework of different kinetic models. This information could be of assistance to an engineer-researcher in making a scientifically grounded choice of such a model. 

Flory [34] was one of the pioneers in the development of models to predict the kinetics of polyester formation. Simple equations derived to predict the kinetics of synthesis of linear polyesters, which can be found in excellent polymer textbooks, are briefly overviewed next [35-37]. 

Empirical kinetics are useful if they allow us to develop chemical models of interfacial reactions from which we can design experimental conditions of synthesis to obtain thick films of conducting polymers having properties tailored for specific applications. Even when those properties are electrochemical, the coated electrode has to be extracted from the solution of synthesis, rinsed, and then immersed in a new solution in which the electrochemical properties are studied. So only the polymer attached to the electrode after it is rinsed is useful for applications. Only this polymer has to be considered as the final product of the electrochemical reaction of synthesis from the point of view of polymeric applications. 

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