A coarse-grained method for simulating diffusion of a small molecule within a glassy polymer was developed. The method built upon previous work in which molecular-level jump rates between likely sorption states were calculated with multidimensional transition-state theory incorporating explicit chain motions that accompany each jump. A reverse Monte Carlo approach was first used to generate large microstructures of sorption states and jump paths whose size, connectivity and rate constant distributions match those found in detailed molecular simulations of methane in glassy atactic polypropylene. Diffusion of isolated penetrant molecules in these microstructures was next simulated by using kinetic Monte Carlo. Over small to moderate times, mean-square displacement increased sub-linearly (anomalous diffusion) in structures of either low or moderate connectivity and with either uniform rate constants or a distribution of rate constants. At long times, regular diffusion was observed in all systems except the low-connectivity structure with a distribution of rate constants. Through examination of the fraction of jumps that return to the initial state, anomalous diffusion was attributed to situations in which a penetrant molecule was confined to regions of low connectivity similar to a percolation cluster. The infrequent jumps that occurred over longer times permitted the penetrant to move away from this confining region and experience regular diffusion. This phenomenon was present with a distribution of connectivity and uniform rate constants, and it was exaggerated by a distribution of rate constants. The regular diffusion regime was reached for displacements beyond 70Å and below the edge length of the periodic cell employed, and the predicted diffusion coefficient was reasonable for methane diffusing in glassy atactic polypropylene.

Coarse-Grained Molecular Simulation of Penetrant Diffusion in a Glassy Polymer using Reverse and Kinetic Monte Carlo. M.L.Greenfield, D.N.Theodorou: Macromolecules, 2001, 34[24], 8541-53