Computer-built polyethylene spherulites for mesoscopic Monte Carlo simulation of penetrant diffusion: Influence of crystal widening and thickening

An algorithm able to mimic crystal lengthening, branching, widening and thickening was developed in order to build spherulites similar to those observed in polyethylene. The ranges of volume crystallinity and crystal width-to-thickness ratio attainable were ≤40% and 8-35, respectively. An on-lattice Monte Carlo-based algorithm was used to generate penetrant trajectories in the built spherulites. Diffusivity was assessed from the mean-square displacement of the penetrant molecules, normalized with respect to the mean-square displacement of the penetrant molecules in a crystal-free system, and compared with the geometrical impedance factor calculated from the Fricke theory using morphological data samples in the simulated spherulites. The crystal blocking effect was greater in the tangential plane than along the spherulite radius. All data, except that for the highest crystallinity system (40%), conformed to a linear relationship between the geometrical impedance factor obtained from the diffusivity data and the geometrical impedance factor calculated from morphological data; the latter being calculated according to the Fricke model using averages based on the squares of the crystal width-to-thickness ratio data. This finding suggests that wide crystals had a more pronounced effect on the geometrical impedance factor than was indicated by their number fraction weight. The system with the highest volume crystallinity (40%) showed a markedly higher geometrical impedance factor than predicted by the Fricke theory using the two aforementioned modifications.