An enhanced phase field model for the numerical simulation of polymer crystallization

An enhanced phase field model is proposed for the numerical simulation of crystallization in semicrystalline polymers. As with other models, it is based on coupling the heat equation with the Alle-Cahn equation, which is derived from the Gibbs-Thomson solid-liquid interface equation. Starting from spherulite nucleation, existing phase field models can simulate their evolution in a surrounding liquid and separate the amorphous and crystalline phases. However, the predictions of the morphological characteristics of the spherulites remain qualitative only. Moreover, the predicted spherulite evolution as a function of crystallization temperature is not consistent with experimental results. In this work, existing phase field models are enhanced in order to obtain experimentally consistent results. We target these characteristics to make them quantitative: spherulite growth, crystal morphology, and crystalline rate in spherulite. We show the importance of modeling the dependence of the model's parameters with respect to crystallization temperature, because, if assumed constants, the predicted results are not consistent with polymers physics. The model is numerically implemented using the finite difference method in a research version of the Digimat software so that 2D and 3D simulation results are presented and compared to experimental data, illustrating the quantitative adequacy of the predictions with experimental evidence.