Compartmentalized polymerization initiated by oil-soluble initiators. Calculation of average number of radicals per particle

Expressions for calculating the stationary state distribution of radicals in compartmentalized systems with a constant number of reaction loci containing an oil-soluble initiator are given. Besides pairwise formation of radicals in the particles, desorption and reabsorption, water phase termination, solubility of the initiator in the aqueous phase, and the possibility of formation of a single radical species are taken into consideration. The calculation is based on a probabilistic analysis leading to a third-order recurrence relation solved using confluent, hypergeometric Kummer functions. Some calculated curves illustrating the de-pendence of the average number of radicals per particle on various relevant parameters are included. © 1995 John Wiley & Sons, Inc.