Mesoscale modelling of penetrant diffusion in computer-generated polyethylene-spherulite-like structures

Penetrant diffusion in semicrystalline polyethylene was simulated by first generating model spherulitic systems, and then, in the same systems, generating penetrant trajectories. Spherulitic growth was mimicked with an algorithm able to generate structures comparable to those observed in polyethylene. Current limitations in the number of lattice points of the system restricted the minimum amorphous layer thickness, which in turn limited the volume crystallinity range attainable to 0-35% and the crystal width-to-thickness ratio to ≤15. An on-lattice Monte-Carlo simulation assessed penetrant diffusion and the geometrical impedance factor was calculated and compared with the results obtained by the analytical method according to the Fricke theory. The combined effect of volume crystallinity and the crystal width-to-thickness ratio on the diffusivity was studied. A linear relationship was obtained between the geometrical impedance factor and the volume crystallinity at constant crystal width-to-thickness ratio, in accordance with the Fricke theory. The Fricke theory, however, underestimated the blocking effect of crystals of a given crystal width-to-thickness ratio, simply because it did not encounter the anisotropic lateral shape of the crystals and the continuous character of the branched lamellar crystals.