On the Diffusive Step of Free-Radical Entry in Emulsion Polymerization and the Applicability of the Smoluchowski Rate Coefficient

An algebraic equation for estimating the rate coefficient of the diffusive step of free-radical entry kc, is proposed. It is an extension to emulsion polymerization of the approach developed in previous works of the authors for describing the rate coefficient of the termination reaction between (mobile) “short” and (immobile) “long” radicals in bulk free-radical polymerization. It is based on geometrical considerations and on the use of the Einstein diffusion equation. Predictions of the proposed equation are compared against results of Montecarlo simulations (MCS) reported in the literature and against values from the Smoluchowski rate coefficient (SRC). Analysis of this comparison allows to point out explanations for the similarities and differences between the MCS data, the SRC and the proposed equation. In this context, the applicability of the SRC is questioned.