Stochastic approach to the evolution of some polycrystalline (bio) polymeric complex systems

The diffusion-migration concept, represented by the normal grain growth equation with the kinetic coefficient being time-dependent, has been used to gain the evolution rules for a polycrystalline (bio)polymeric complex system. The approach works in a time-dependent regime termed the long tail (fractal) kinetics. Two basic physical quantities of the process, i.e. the overall crystallization and adsorption rates are not simple exponentials, but the former follows Avrami kinetics whereas the latter is a stretched exponential. In our modeling, which holds for slow growth rates and suits a fluctuating viscous system, they are applied in a linear case. As the main result, the linear dependence of the crystallite radius against time has been recovered which is in good agreement with experimental data.