A numerical study of one-step models of polymerization: Frontal versus bulk mode

Abstract

In free-radical polymerization, a monomer-initiator mixture is converted into a polymer. Depending on initial and boundary conditions, free-radical polymerization can occur either in a bulk mode (BP) or in a frontal mode (FP) via a propagating self-sustaining reaction front. The main goal of this paper is to study the role that bulk polymerization plays in frontal polymerization processes for various one-step kinetics models. We use numerical simulations to study the influence of reaction kinetics on one-dimensional frontal polymerization. We show that the long-time behavior of systems modeled with discontinuous distributed kinetics (e.g. step-function kinetics) significantly departs from the long-time behavior of systems modeled with Arrhenius kinetics. The difference is due to slow BP in the initial mixture of reagents, which influences both the speed and the long-time stability of the reaction front. Further, we show that for distributed kinetics a “true” FP is only possible for a steadily propagating, traveling-wave reaction front. When a front propagates in a pulsating mode, we demonstrate the existence of pockets of unreacted monomer behind the front. These pockets evolve via a bulk polymerization mechanism. A mathematical model of one-step free-radical frontal polymerization is identical to the model of gasless combustion, so bulk reactions play a role in the latter context, as well. However, fronts propagate much faster in combustion than in polymerization, and slow bulk reactions in regions ahead of the burning front can generally be neglected.