Coarse-grained molecular simulation of penetrant diffusion in a glassy polymer using reverse and kinetic Monte Carlo
A coarse-grained method for simulating diffusion of a small molecule within a glassy polymer was developed and implemented. The method builds on our 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. In this work we first use a reverse Monte Carlo approach 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. Next we simulate diffusion of isolated penetrant molecules in these microstructures using kinetic Monte Carlo. Over small to moderate times, mean-squared displacement increases sublinearly (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 is 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, we attribute anomalous diffusion to situations in which a penetrant molecule is confined to regions of low connectivity similar to a percolation cluster. The infrequent jumps that occur over longer times allow the penetrant to move away from this confining region and experience regular diffusion. This phenomenon is present with a distribution of connectivity and uniform rate constants, and it is exaggerated by a distribution of rate constants. The regular diffusion regime is reached for displacements beyond 70 Å and below the edge length of the periodic cell employed, and the predicted diffusion coefficient is reasonable for methane diffusing in glassy atactic polypropylene.