A simplified model for nonisothermal crystallization of polymers

Recently, Burger and Capasso [1]derived a coupled system of partial differential equations to describe nonisothermal crystallization of polymers. The system is based on a spatial averaging of the underlying stochastic birth-and-growth process describing the nucleation and growth of single crystals. In the present work, we reconsider the scaling properties of the dimensional system as well as some special one-dimensional models. Moreover, using an appropriate scaling of the original system, we derive a simplified model which only consists of a reaction-diffusion equation with memory for the underlying temperature, such that the degree of crystallization can be explicitly given by a time integration of the temperature-dependent growth and nucleation rate. Numerical simulations indicate that the reduced model shows at least qualitatively the same behavior as the original model.