Moving Bands and Moving Boundaries in an Hybrid Model for the Crystallization of Polymers

Abstract

Crystallization is a mechanism of phase change in polymeric materials; it consists of at least two processes, a nucleation (birth) process describing the time and the location of spots in the material where crystals start growing, and a growth process of the nucleated crystals. Both processes are coupled to temperature, and viceversa the temperature field is coupled with the crystallization process due to the production of latent heat. All the processes described above are of a random nature, since the birth process and the consequent geometry of the crystalline phase are random. However, under typical industrial conditions (many and small crystals), a multiple scale assumption can be made so that a deterministic approximation (homogeneization) for the spatial density of the crystalline phase at the (macro)scale of the temperature field is possible. Thus, at the macroscale the whole crystallization process may be modelled as a reaction-diffusion system in which a deterministic ODE for the crystalline density is coupled with a deterministic PDE for the temperature field via the kinetic parameters of birth and growth on the one hand and the latent heat on the other hand. Numerical simulations of this reaction-diffusion system show that the solution exhibits an advancing moving band of crystallization in the mass distribution, accompanied by a moving boundary in the temperature field, both advancing with a decreasing velocity.