Statistical Theory of the Stable and Metastable Transitions for Crystallization and Fusion of Homopolymers

Based on the structural model of multiple crystal networks and the mechanisms of crystallization by molecular segregation of stems, the process of crystallization for homopolymers was divided into three kinds of correlative and separatory steps, namely, the process of precrystallization under the equilibrium state, the evalution process of dynamics for nucleation in the unsteady state and the evalution process of dynamics for growth in the dynamic state. The kinetic equation of precrystallization under the equilibrium state, the evalution equation of dynamics for the nucleation of micro-nucleus-constituent chain and the growth of micro-crystal-constituent chains under the unequilibrium state were established. The probability distribution functions for the micro-nucleus-constituent chains and the micro-crystal-constituent chains by extending and folding chains with different sizes and the end-to-end vectors at different times(t) were obtained, respectively, from the solutions of the evalution equations of dynamics for nucleation and growth. A new method of establishing the criterion for the stability and metastability of micro-nucleus and micro-crystal-constituent chains was proposed. It is based on the dependence of change in the free energy for the formation of micro-nucleus and micro-crystal-constituent chains(△Gnf and △Gcv) and in the rate of (△Gnf/f) and (△Gcv/v) on their sizes (f and v), so that three regions (unstable, metastable and stable)are divided.