Termination processes, in free radical polymerization—7: The treatment of chain length dependent termination in presence of chain transfer

Abstract

A numeric solution is developed for a kinetic scheme involving chain length dependent termination (by disproportionation) and chain transfer on the basis of the harmonic and the geometric mean approximation for the two radicals involved in the termination process. In addition, solutions in terms of series expansions, which show fair convergence behaviour except for a narrow range when the rate of chain transfer roughly equals the rate of chain termination, are given for the geometric mean approximation in the long chain limit. Due to the fact that the kinetic chain length decreases with increasing chain transfer agent concentration if the rate constant of bimolecular termination k t depends on chain length, conventional Mayo-plots would yield chain transfer constants which are too high. Fortunately, however, the error is comparatively small and probably will not exceed the limits of experimental uncertainty in most cases. Furthermore, it is found that the dependence of k t on the (average) length of the two living radical chains undergoing bimolecular termination is quite similar to the dependence of apparent k t (which might be measured experimentally) on the degree of polymerization of dead polymer formed in the same experiment.