This review aims to present as completely as possible the description of the current concepts of quantitative radical copolymerization theory. Its various aspects are discussed on the basis of a critical analysis of numerous original publications dealing with this problem. A number of approaches to the solution of the theoretical problems of practical importance, and their application to the prediction of copolymer properties have been considered. Serious attention is also paid to the discussion of kinetic copolymerization models, their experimental corroboration and discrimination of the above models to the description of concrete systems.

Modern aspects of quantitative theory of free-radical copolymerization

Equations for the degree of polymerization and the cooligomer composition in the styrene (A)–methyl methacrylate (B)–CCl4(S) system were derived from the assumed reaction scheme by the use of some assumptions for simplification, and their appropriateness was examined. The chain transfer constants of the growing radicals of styrene (CSA) and methyl methacrylate (CSB) to CCl4, which were estimated from the apparent chain transfer constants CSAB in the cooligomerization system, agreed with the homooligomerization values. This means that the degree of the polymerization of the cooligomer can be expressed by the equation: 



where Pn is the degree of polymerization of the cooligomer and PnO is that when no chain transfer agent (CCl4) is added; rA and rB are the monomer reactivity ratios of monomers A and B in this system. The cooligomer composition deviated from the statistical steady-state composition on the low molecular weight side, and this deviation was explained by the equation:

Simplified treatment of cooligomerization kinetics

The analysis of the endgroups of the oligomers produced in the styrene (A)–CCl4(S) system (system I), the methyl methacrylate(B)–CCl4 system (system II), and the styrene–methyl methacrylate–CCl4 system (system III) was carried out in order to clarify the mechanism of the initiation, transfer, and termination. In system I, the number of Cl atoms per oligomer molecule NCl increases with the molar ratio of [S]/[A] when the molar ratio of [S]/[A] is below unity and is about four when the molar ratio of [S]/[A] is above unity, and the number of initiator fragments per oligomer molecule NI decreases with the increase in the molar ratio of [S]/[A]. In system II, NCl is about 0.45 over a considerably wide range of the molar ratio of [S]/[B]. In system III, NCl increases and NI decreases with the increase in the molar ratios of [S]/([A] + [B]) and [A]/[B]. From the data of NCl and NI, the fraction ICC14 of the initiation by the tri-chloromethyl radical in the overall initiation reactions and the fraction TCC14 of the chain transfer reaction of the growing radical of styrene in all the reactions which produce the cooligomer in the system III were calculated. ICCl3 and TCC14 both increase with the molar ratios [S]/([A] + [B]) and [A]/[B].

Initiation and termination mechanism in the cooligomerization of the styrene–methyl methacrylate–carbon tetrachloride system

In order to clarify the kinetic features of the styrene (A)–methyl methacrylate (B)–CCl4(S) cooligomerization system, a computer simulation was carried out. The experimental data on the degree of polymerization and the deviation of the cooligomer composition from the statistical steady-state composition were comparatively well explained by calculations based on the kinetic equations derived from the assumed reaction scheme and the values of the velocity coefficients, although the values of the four velocity coefficients in the initiation step and the velocity coefficient of the termination by the coupling of two solvent radicals were estimated. The results of the calculation of the rate of each component reaction show that the following two reactions are the most important in the initiation and in the transfer and termination steps when the [S]/([A] + [B]) ratio is large: 



where, A, A*, and P are styrene, polystyryl radical, and the cooligomer, respectively. Moreover, it was concluded that the deviation of the cooligomer composition from the statistical steady-state composition was caused by these two reactions.

Computer simulation for the cooligomerization system

In the present chapter, the main concepts used in this book are discussed (i.e., models, random numbers and computer Monte-Carlo models), and then a short review of Monte Carlo applications in Chemistry and an up-to date review of Monte Carlo application in Polymer Science are given. It is hoped that the large number of references contained in this chapter provides a useful guideline to the relevant literature.

The Monte Carlo Method and Applications

It was found that the composition of cooligomer produced in the styrene(A)–methyl methacrylate(B)–CCl4(S) system deviates from the statistical steady-state composition predicted from the Mayo-Lewis equation on the low molecular weight side when the molar ratio of [A]/[B] is large. When the molar ratio of [A]/[B] is small, however, it is not obvious whether or not this phenomenon is observed, because the cooligomer of low molecular weight cannot be obtained easily since the chain transfer constant of the poly(methyl methacrylate) radical to CCl4 is very small in comparison, with that of the polystyryl radical. This behavior is shown to be attributable mainly to the preferential consumption of styrene monomer in the initiation step, based on the structure of the cooligomer, as inferred from the mechanism of the initiation, transfer, and termination, and the stochastic approach in which the cooligomerization process is regarded as a Markov process.

Statistical nonstationarity of the composition of styrene with methyl methacrylate in the cooligomer

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Computer simulation for the cooligomerization system

Statistical nonstationarity of the composition of styrene with methyl methacrylate in the cooligomer