Polymer growth through radical polymerization and termination

We propose a polymer growth model, in which propagating radicals can grow through propagation processes or annihilate through termination (disproportionation or combination) processes. Considering a simple case in which the propagation and termination rates of each polymer chain are both independent of its length, we then investigate analytically the kinetics of the model by means of the rate-equation approach. The propagating radicals will be exhausted eventually and only the inert polymers (the termination products of propagating radicals) can survive in the end. Moreover, the size distribution of propagating radicals can always take the form of the Poisson distribution at a given time, while that of inert polymers is dependent strongly on the details of the reaction-rate kernels. For the case in which the propagation rate constant J 1 is less than the termination rate constant J 2 , the size distribution of inert polymers can always take a power-law form c k (t) ∼k ―2―J1/(J2―J1) , in the region of t»1 and k»1. For the J 1 > J 2 case, the kinetic evolution of inert polymers is very complex and c k (t) can take one of the three forms: monotone decreasing, single peak (Poisson-like distribution), and double peak. For the special J 1 =J 2 case, c k (t) exhibits an exponential decay in size.