Polymers, kinetic modeling copolymerization

Gel Permeation Chromatography (CPC) is often the source of molecular wei t averages used in polymerization kinetic modelling Q.,2). Kinetic models also r uire measurement of molecular weight distribution, conversion to polymer, composition of monomers in a copolymerization rea tion mixture, copolymer composition distribution, and sequence length distribution. The GPC chromatogram often reflects these properties (3,. ... 

This assumption is implicitly present not only in the traditional theory of the free-radical copolymerization [41,43,44], but in its subsequent extensions based on more complicated models than the ideal one. The best known are two types of such models. To the first of them the models belong wherein the reactivity of the active center of a macroradical is controlled not only by the type of its ultimate unit but also by the types of penultimate [45] and even penpenultimate [46] monomeric units. The kinetic models of the second type describe systems in which the formation of complexes occurs between the components of a reaction system that results in the alteration of their reactivity [47-50]. Essentially, all the refinements of the theory of radical copolymerization connected with the models mentioned above are used to reduce exclusively to a more sophisticated account of the kinetics and mechanism of a macroradical propagation, leaving out of consideration accompanying physical factors. The most important among them is the phenomenon of preferential sorption of monomers to the active center of a growing polymer chain. A quantitative theory taking into consideration this physical factor was advanced in paper [51]. 

For example, under kinetic modeling of "living" anionic copolymerization in the framework of the terminal model, a macromolecule is associated with the realization of a certain stochastic process. Its states (a,r) are monomeric units, each being characterized along with chemical type a and also by some label r. This random quantity equals the moment when this monomeric unit entered in a polymer chain as a result of the addition of o-type monomer to the terminal active center. It has been... 

Three factors are important in the development and implementation of successful control strategies for copolymerization reactors the availability of kinetic models which adequately describe the rate of polymerization and the properties of the resulting polymer as functions of the process variables, the availability of on-line instrumentation which enables rapid characterization of the copolymer throughout the reaction, and the availability of process data which allow for the constraints of the process to be built into the control strategy. This paper discusses the limitations of reported control strategies for copolymerization reactors from the viewpoint of the state-of-the-art of kinetic modeling and copolymer characterization. The critical stages in this process where considerable research effort is required are emphasized. 

To address polymer network formation from nonlinear chain-growth polymerization (or copolymerization), kinetic methods are more appropriate [23, 75-83], Some of the most successful kinetic models to address this type of system are based on the method of moments [23, 75-77, 79, 80, 82, 84], Some divergence problems at the vicinity of the gelation point are common with the method of moments, although there are practical ways to avoid this situation [80], A more refined kinetic method to address the issue of modeling the dynamics of gelation in... 

The modeling of homopolymerization as well as linear and nonlinear (chain transfer to polymer and crosslinking) copolymerizations can be represented with the same polymerization scheme shown in Figure 12.1. The kinetic... 

Under Flory s simplification conditions, it can be proven that (the probability of) the crosslink density of all the primary polymers is equal by using the kinetic model shown here [47]. That is, under Flory s simplified conditions, the kinetic model that considers the change of the crosslink structure and the model based on random crosslinking become identical. Even for the system under kinetic control, the model that is based on random crosslinking will be strictly applicable. Of course in real systems an inhomogeneous crosslink structure will be formed because of (1) the difference in reactivity as expressed in copolymerization reactivity ratio between the double bonds of the monomers (2) the reactivity of the pendant double bonds with the double bonds in the monomers and the... 

Unzueta and Forcada [31] studied the emulsion copolymerization of methyl methacrylate and n-butyl acrylate. It was assumed that both micellar nucle-ation and homogeneous nucleation are operative in this emulsion polymerization system. Based on the experimental data and computer simulation results, the values of the free radical capture efficiency factors for monomer-swollen micelles (f ) and polymer particles (Fj) that serve as adjustable parameters in the kinetic modeling work are approximately 1(T and 10, respectively. The reason for such a difference in the free radical capture efficiency factors is not available yet. Table 4.2 summarizes some representative data regarding the absorption of free radicals by the monomer-swollen micelles and polymer particles obtained from the literature. 

In addition, kinetic models allow to change the ratio between the rate constant of polymer chain growth and decay both at homopolymerization and copolymerization and to observe the effect of this ratio on general kinetics of the process what is impossible during the experiment. All that allows anticipating and managing the process of copolymerization. 

Multi-State Models. In studies of copolymerization kinetics and polymer microstructure, the use of reaction probability models can provide a convenient framework whereby the experimental data can be organized and interpreted, and can also give insight on reaction mechanisms. (1.,2) The models, however, only apply to polymers containing one polymer component. For polymers with mixtures of different components, the one-state simple models cannot be used directly. Generally multi-state models(11) are needed, viz. 

This is the simplest of the models where violation of the Flory principle is permitted. The assumption behind this model stipulates that the reactivity of a polymer radical is predetermined by the type of bothjts ultimate and penultimate units [23]. Here, the pairs of terminal units MaM act, along with monomers M, as kinetically independent elements, so that there are m3 constants of the rate of elementary reactions of chain propagation ka ]r The stochastic process of conventional movement along macromolecules formed at fixed x will be Markovian, provided that monomeric units are differentiated by the type of preceding unit. In this case the number of transient states Sa of the extended Markov chain is m2 in accordance with the number of pairs of monomeric units. No special problems presents writing down the elements of the matrix of the transitions Q of such a chain [ 1,10,34,39] and deriving by means of the mathematical apparatus of the Markov chains the expressions for the instantaneous statistical characteristics of copolymers. By way of illustration this matrix will be presented for the case of binary copolymerization ... 

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