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 f ormation during isothermal and nonisothermal crystallization in sample s of finite thickness, strips and plates, is based on the assumption o f the momentary randomness of primary nucleation. The time distributio ns of the formation of the spherulite interiors as well as the time de pendence of the conversion degree of a melt into spherulites are deriv ed for time dependent primary nucleation rate and spherulite growth ra te. The spherulitic final pattern is described by means of the distrib utions of distances from spherulite centers to spherulite internal poi nts. The influence of the nucleation of sample boundaries on the kinet ics 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.