Theory of Chain Copolymerization Reactions

Abstract

The kinetics of chain copolymerizations is developed for reactions consisting of three steps: first, an activation of stable monomer; second, a growth of activated polymer radical by means of monomer addition; third, a stabilization of the growing chains by (a) monomer addition, (b) by means of growing polymer [Eq. (1)]. The existence of a steady state in respect to the concentration of growing chains beyond the induction period is assumed. The rate constants of growth and termination will in general depend upon the individual composition and upon the nature of the activated chain end. Equations for the rate of change of mole ratio z of the two monomer species are developed in terms of mean rates of growth and termination obtained by averaging the actual rates over the distribution of growing polymer [(4), (4a), (4′)]. The equilibrium conditions lead to a set of difference equations for this distribution [(5), (5′)]. It is investigated whether the solution and results derived therefrom are of a form which permits a determination of the dependence of the rate constants for growth and termination upon the composition of the polymer molecule (6). In addition, the influence of the type of active chain end involved on over-all rate and size distribution is considered by introducing four constants for propagation and termination, respectively, according to the four possibilities A — A, A — B, B — A, B — B [(6a), (7), (4b), (4b′)], but independent of chain composition. Various special cases according to the relative magnitude of the rates for the two reactants are presented. Experimentally it is difficult to distinguish on the basis of kinetic data between the foregoing mechanism and one in which the rates of growth (and termination) for each of the two kinds of monomer depend solely upon the nature of the monomer molecule added and are independent of the nature of the active chain end [(4c), (4c′), (4c″)]. Relations are derived for the molecular size distribution, the inhomogeneity of the copolymer mixture in regard to composition, the average molecular weight, and the average composition of copolymer as function of the composition of the monomer residue [(8a), (8a′), (9a), (10)]. The importance of these results for soluble and insoluble copolymers and for the theory of gel formation in vinyl-divinyl type polymers is pointed out.

Mass spectrometric investigation of the thermal decomposition of polymers

“…Assuming that the effect of side reactions on the yield of a given monomer remains constant in going from simple polymer to copolymers, and that the C-C bonds in the vinyl chain and sequences are of equal strength for a given monomer, then the pyrolysis yield of monomer from the copolymer formed at low conversion can be calculated if one lmows the yield from the simple polymer, the monomer reactivity ratios (r A and rB) [11,12], and the composition of the monomer charge. The probability of regenerating monomer A, for example, styrene, from the simple polymer can be considered unity.…”

Bulk and Surface Properties of Random Copolymers in View of the Simha–Somcynsky Equation of State

“…This will also lead us to relations between surface and bulk properties. It is worthwhile to mention that Simha contributed to understanding random copolymers not only with the equation of state but also with the pioneering paper on kinetics of copolymerization [Simha and Branson, 1944].…”

Production of Fluoroelastomers

“…Using the assumption that the rate of monomer addition to a radical chain depends only on the nature of the last unit on the chain, Dostal, [1] in 1936, showed that only four propagation reactions and corresponding rates would describe copolymerization of two monomers: In 1944, a useful copolymer composition relationship was derived independently by Alfrey, [2] Mayo, [3] Simha, [4] and Wall, [5] by making the further assumption that steady state applies to each radical type separately. Composition relationships for dipolymers were derived by early workers in the polymer field.…”

“…4 An overall radical generation rate at 100% efficiency ρ is used, and an overall polymerization rate coefficient k p for the particular copolymer composition and reaction temperature.…”