A Simplified Model for Non-Isothermal Crystallization of Polymers

Abstract

Recently, Burger and Capasso [M3AS 11 (2001) 1029–1053] derived a coupled system of partial differential equations to describe non-isothermal 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. 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 like the original model.