Modeling domain growth of polymer melt crystallization

The crystallization of a subcooled polymer melt, described by a local scalar internal variable ϕ, is modeled by non-equilibrium thermodynamics, specifically using a dissipation argument. The formulation yields a pair of nonlinear differential equations: a thermal energy balance coupled to a Fisher-type rate law for melt to solid conversion. The simplest non-dimensional forms of these equations have two parameters: the Stefan number λ, quantifying the relative importance of latent heat release to conductive heat transport, and a dispersion coefficient β for secondary melt nucleation. Traveling wave solutions for the temperature and ϕ result in both 1 and 2 dimensions for realistic λ and β. The prediction of sharp solidification fronts controlled by crystallization kinetics is consistent with experiments on polymer melts. Specifically, the undercooling at the solid/melt interface scales with the front speed. The equilibrium extent of solidification is controlled by λ and thermal constraints, while β determines the front speed. The model predictions are robust in that neither the details of temperature dependencies in the source/nucleation terms nor the inclusion of solid/melt interfacial energy qualitatively affects the predictions. Together with a specification of primary nucleation kinetics, the model can successfully simulate the overall crystallization kinetics.