{'fraction_non_alphanumeric': 0.018150388936905792, 'fraction_numerical': 0.0, 'mean_word_length': 5.327868852459017, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Mathematical Modeling of Solidification of Semi- crystalline Polymers under Quiescent Non-isothermal Crystallization: Determination of Crystallite’s Size

In this paper, a mathematical model for the solidification of the semi-crystalline polymers is proposed to predict the size of the crystallites. In addition to the degree of the crystallinity, the size of the crystallites is one of the structural variables, which can shape the mechanical properties of the polymer materials. During the quiescent non-isothermal processes, the mean radius of crystallites is a function of both nucleation and growth process. The density of the potential nuclei is assumed to follow the nucleation law. With the stochastic approach, the nucleation centers and the activation temperatures are randomly assigned to these potential nuclei. A radial front-tracking method is used to determine the evolution of the shapes of crystallites, according to the dependence of the growth rate on the temperature. In a realistic study of solidifying High Density Polyethylene, the simulation results allow us to predict the mean size of the crystallites at the various cooling rates.