Numerical study of the relationship between the spherulitic microstructure and isothermal crystallization kinetics. Part I. 2-D

Abstract

In this paper, we proposed a numerical model to study the kinetic properties and the spherulite microstructure of a semi-crystalline polymer under isothermal crystallization, which further exhibits the potential in generating the 2D spherulitic structure according to the observations obtained by experimental techniques. Two characteristic parameters are introduced, namely, characteristic length Lc and characteristic time tc, which are dependent on the growth rate, G and the nucleation rate, I. In addition, two non-dimensional parameters are introduced to model the nucleation saturation: Ld/Lc and t⋆/tc, which is related to the thickness of nucleation exclusion zone Ld, and the effective nucleation time t⋆, respectively. In 2D modeling, the kinetics are confirmed by Avrami fitting, and the effects of the four characteristic parameters on the Avrami parameter n and the crystallization half-time t0.5 are presented. The regularity of how the spherulite density or the mean radius of spherulites R change along with these parameters are also given, respectively. It shows that Lc is the prominent parameter for the size of the spherulite, and tc controls t0.5 as long as there is no nucleation saturation (Ld=0 and t⋆→∞). Besides, the existence of the nucleation saturation increases the mean radius of spherulites, but decreases n from 3 to 2 in 2-D modeling. Finally, a relationship between crystallization kinetics and microstructures is provided, giving a new perspective to estimate the nucleation rate.