Reaction, chain, copolymer kinetics, rate equations

For any specific type of initiation (i.e., radical, cationic, or anionic) the copolymer composition equation is independent of many reaction parameters. Since no rate constants appear as such in the copolymer equation, the copolymer composition is independent of differences in the rates of initiation and termination or of the presence or absence of inhibitors or chain transfer agents. Thus the same copolymer composition is obtained irrespective of whether initiation occurs by the thermal homolysis of initiators (such as AIBN or peroxides), photolysis, radiolysis, or redox systems. Under a wide range of conditions the copolymer composition is also independent of the degree of polymerization. The limitation on the above generalization is that the copolymer be of high molecular weight. It may be recalled that the derivation of Eq. (7.11) involved an assumption that the kinetic chains... 

The copolymer composition equation was first applied to co-oxidations in mixtures of aldehydes (25, 39) and later to numerous pairs of hydrocarbons and their derivatives (1, 2, 3, 4, 8, 27, 31, 32, 33). For oxidations of mixtures of A and B, attack by a peroxy radical first gives (by addition or hydrogen abstraction) A and B radicals in the presence of sufficient oxygen all these are then converted to A02 and B02 peroxy radicals. From the relative rates of reaction, A[A]/A[B], of A and B at two or more average feeds [A] / [B], in long kinetic chains, the copolymer composition equation... 

The problem of predicting copolymer composition and sequence in the case of chain copolymerizations is determined by a set of differential equations that describe the rates at which both monomers, Ma and MB, enter the copolymer chain by attack of the growing active center. This requires a kinetic model of the copolymerization process. The simplest one is based on the assumption that the reactivity of a growing chain depends only on its active terminal unit. Therefore when the two monomers MA and MB are copolymerized, there are four possible propagation reactions (Table 2.17). 

Copolymer composition can be predicted for copolymerizations with two or more components, such as those employing acrylonitrile plus a neutral monomer and an ionic dye receptor. These equations are derived by assuming that the component reactions involve only the terminal monomer unit of the chain radical. This leads to a collection of N x N component reactions and x 1) binary reactivity ratios, where N is the number of components used. The equation for copolymer composition for a specific monomer composition was derived by Mayo and Lewis [74], using the set of binary reactions, rate constants, and reactivity ratios described in Equation 12.13 through Equation 12.18. The drift in monomer composition, for bicomponent systems was described by Skeist [75] and Meyer and coworkers [76,77]. The theory of multicomponent polymerization kinetics has been treated by Ham [78] and Valvassori and Sartori [79]. Comprehensive reviews of copolymerization kinetics have been published by Alfrey et al. [80] and Ham [81,82], while the more specific subject of acrylonitrile copolymerization has been reviewed by Peebles [83]. The general subject of the reactivity of polymer radicals has been treated in depth by Jenkins and Ledwith [84]. 

Since the composition of a copolymer chain is critical for determining its properties, understanding how the kinetics of the copolymerization impact the composition is an important consideration. To cut to the chase, the composition of a copolymer formed under a particular set of conditions depends on the relative rates of the four principal reactions. This in turn depends on the rate constants (e.g., those shown in Figure 12) and concentrations of reactive species and monomers. Using either a steady-state approximation or a polymerization statistics derivation, one can determine the following expression for the relative amount of monomer A in copolymer given the amount in the feed through equation [12] where Fa is the mole fraction of A in the copolymer and/a is the mole fraction of A in the feed ... 

It is generally assumed that the stereosequence distributions, or tacticity, obtained in polymerization reactions of vinyl and related monomers is primarily a kinetically-controlled process (1). That is, as in other important aspects of chain-growth polymerization reactions (e.g., molecular weight and copolymer composition), tacticity is determined by the relative rates of competitive reactions, in this case the rates of isotatic, kj, and syndiotactic, ks, additions, as shown in Equation 1. 

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