Copolymerization propagation kinetics

There are two cases to consider when predicting flie effect of solvent polarity on copolymerization propagation kinetics (1) the solvent polarity is dominated by an added solvent and polarity is thus independent of the comonomer feed ratio, or (2) the solvent polarity does depend on the comonomer feed ratio, as it would in a bulk copolymerization. In the first case, the effect on copolymerization kinetics is simple. The monomer reactivity ratios (and additional reactivity ratios, depending on which copolymerization model is appropriate for that system) would vary fi om solvent to solvent, but, for a given copolymerization system they would be constant as a function of the monomer feed ratios. Assuming of course that there were no additional types of solvent effect present, fliese copolymerization systems could be described by their appropriate base model (such as the terminal model or the explicit or implicit penultimate models), depending on the chemical structure of the monomers. 

There are two cases to consider when predicting the effect of solvent polarity on copolymerization propagation kinetics ... 

Basis Model. For many years, people believed that the terminal model was the basis of copolymerization propagation kinetics because it could be fitted to the composition data for most systems tested. However, in 1985 Fukuda and coworkers (7) demonstrated that the terminal model failed to predict the propagation rate coefficients for the copolymerization of styrene with methyl methacrylate— a system for which the composition data had been widely fitted by the terminal model (see Fig. 1). These results were later confirmed by several independent groups, both for the styrene-methyl methacrylate system (imder a wide range of different conditions), and also several other copolymerizations—indeed for almost all systems so far tested (37). It now appears likely that the failure of the terminal model to describe simultaneously the composition and propagation rate coefficients of ordinary free-radical copoljrmerization systems is general, with the terminal model being applicable only to those exceptional systems in which the comonomers have very similar reactivities. 

To summarize, we know firstly from simple model-testing studies spanning the last 20 years that for almost all systems tested, the terminal model can be fitted to (kp) or composition data for a copolymerization system, but not both simultaneously. Secondly, more recent experimental and theoretical studies have demonstrated that the assiunption of the implicit penultimate model— that the penultimate imit affects radical reactivity but not selectivity—cannot be justified. Therefore, on the basis of existing evidence, the explicit penultimate model should replace the terminal model as the basis of free-radical copolymerization propagation kinetics, and hence the failure of the terminal model kp) equation must be taken as a failure of the terminal model and hence of the terminal model composition equation. This means that the terminal model composition equation is not physically valid for the majority of systems to which it has been apphed. 

This model provides a better description of the rate of copolymerization for some systems but has been criticized as having too many adjustable paramelers. " Fukuda and coworkers have recently derived a model equivalent to the Russo-Munari model but where the implicit penultimate model is used to describe the propagation kinetics. 

Hutchinson and coworkers investigated [147] effects of solvent on free-radical copolymer composition and propagation kinetics in copolymerizations of styrene with three methacrylates. 

The equilibrium constants for the CTC of cyclopentene, norbornene, and styrene monomers with MA are 0.03, 0.015, and 0.33 liter mole respectively (table in the appendix to this chapter). However, when these three pairs are copolymerized with acrylonitrile only the cyclopentene-MA pairs remain equimolar at all feeds. This shows the CTC does not always have to be the most reactive species in the systems. Even though charge-transfer complexes are present in a ternary mixture of MA-methyl methacrylate-methyl acrylate they have little influence on the propagation kinetics. The equilibrium constants for the MA-methyl methacrylate and methyl acrylate-MA pairs are 0.43 and 0.32 liter mole, respectively. Since these CTC equilibrium constants are comparable to many of the other donor monomer-MA pairs reported to undergo alternating copolymerization, these results are definitely nonsupportive of a CTC mechanism. 

When solvent effects on the propagation step occnr in free-radical copolymerization reactions, they result not only in deviations from the expected overall propagation rate, but also in deviations from the ejqiected copolymer composition and microstracture. This may be trae even in bulk copolymerization, if either of the monomers exerts a direct effect or if strong cosolvency behavior causes preferential solvation. A number of models have been proposed to describe the effect of solvents on the composition, microstmcture and propagation rate of copolymerization. In deriving each of these models, an appropriate base model for copolymerization kinetics is selected (such as the terminal model or the implicit or explicit penultimate models), and a mechanism by which the solvent influences the propagation step is assumed. The main mechanisms by which the solvent (which may be one or both of the comonomers) can affect the propagation kinetics of free-radical copolymerization reactions are as follows ... 

Any understanding of the kinetics of copolymerization and the structure of copolymers requires a knowledge of the dependence of the initiation, propagation and termination reactions on the chain composition, the nature of the monomers and radicals, and the polymerization medium. This section is principally concerned with propagation and the effects of monomer reactivity on composition and monomer sequence distribution. The influence of solvent and complcxing agents on copolymerization is dealt with in more detail in Section 8.3.1. 

The influence of penultimate units on the kinetics of copolymerization and the composition of copolymers was first considered in a formal way by Merz et al and Ham.8 They consider eight propagation reactions (Scheme 7.2). 

The kinetics of many copolymerizations have now been examined with absolute (overall) propagation rate constants being determined by the rotating sector, PLP or FSR methods. A similar situation as pertains for the MMA-S... 

Terpolymerizations or ternary copolymerizations, as the names suggest, are polymerizations involving three monomers. Most industrial copolymerizations involve three or more monomers. The statistics of terpolymerization were worked out by Alfrey and Goldfinger in 1944.111 If we assume terminal model kinetics, ternary copolymerization involves nine distinct propagation reactions (Scheme 7.9). 

In early work, it was assumed that the rate constant for termination was determined by the monomer unit at the reacting chain ends. The kinetics of copolymerization were then dictated by the rate of initiation, the rates of the four propagation reactions (Scheme 7.1) and rales of three termination reactions... 

The ends of polymer chains are often not representative of the overall chain composition. This arises because the initiator and transfer agent-derived radicals can show a high degree of selectivity for reaction with a particular monomer type (Section 3.4). Similarly, there is specificity in chain tennination. Transfer agents show a marked preference for particular propagating species (Section 6.2.2 and 6.2.3). The kinetics of copolymerization are such that the probability for termination of a given chain by radical-radical reaction also has a marked dependence on the nature of the last added units (Section 7.4.3). 

The relative rate of cationic homopolymerization is governed by three factors, ie. the concentration of the propagating species, the ring-opening reactivity of the growing species and the nucleophilic reactivity of the monomer. From kinetic studies196 197 of the polymerization of oxazolines and oxazines it was found that the second factor was the most important. On the other hand, the relative reactivity in the cationic copolymerization is mainly determined by the nucleophilicity of the monomer and for 2-substituted 2-oxazolines this is in the order of benzyl > methyl > > isopropyl > H > phenyl195. ... 

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