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.
