Nonisothermal crystallization of polymers in samples of finite dimensions - 1. Background of the mathematical description of spherulitic pattern formation

The mathematical description of the kinetics of spherulitic patterns formation during isothermal and nonisothermal crystallization in samples of finite thickness, strips and plates, is based on the assumption of the momentary randomness of primary nucleation. The time distributions of the formation of the spherulite interiors as well as the time dependence of the conversion degree of a melt into spherulites are derived for time dependent primary nucleation rate and spherulite growth rate. The spherulitic final pattern is described by means of the distributions of distances from spherulite centers to spherulite internal points. The influence of the nucleation of sample boundaries on the kinetics of crystallization and on the final spherulitic structure is also determined. In all dependencies derived the components resulting from both nucleation processes - at sample boundaries and inside a sample - are distinguished.