Propagation and interaction of moving fronts in polymer crystallization

摘要

A deterministic model of crystallization in quiescent, two-dimensional polymer samples is proposed. The model includes the nucleation and crystal growth processes and their dependence on the temperature field by means of linearized Arrhenius expressions for the kinetics of these processes, and temperature thresholds that result in partial differential equations for the temperature field and local degree of crystallinity. It is shown that there are three crystallization regimes depending on the temperatures of the boundaries, and that the focusing regime results in the fastest crystallization. It is also shown that, in rectangular polymer samples, complete crystallization first occurs along the shortest dimension of the domain, and then proceeds in an almost one-dimensional fashion along the longest direction with temperature fields which are smooth and a local degree of crystallinity that it is continuous but not smooth. However, inclusion of the random motion of nuclei through a diffusion process indicates that the local degree of crystallinity is smooth, and complete crystallization is only observed for sufficiently small diffusion coefficients; larger diffusion coefficients result in partial crystallization of the polymer sample. It is also shown that cross-diffusion terms have a very small influence on the total mass of crystals, at least, for the conditions considered here, and that non-crystallized material may be trapped in the middle of the polymer sample.