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 p revious work in which molecular-level jump rates between likely sorption st ates were calculated with multidimensional transition-state theory incorpor ating explicit chain motions that accompany each jump. In this work we firs t use a reverse Monte Carlo approach to generate large microstructures of s orption states and jump paths whose size, connectivity, and rate constant d istributions match those found in detailed molecular simulations of methane in glassy atactic polypropylene. Next we simulate diffusion of isolated pe netrant molecules in these microstructures using kinetic Monte Carlo. Over small to moderate times, mean-squared displacement increases sublinearly (a nomalous diffusion) in structures of either low or moderate connectivity an d with either uniform rate constants or a distribution of rate constants. A t long times, regular diffusion is observed in all systems except the low-c onnectivity structure with a distribution of rate constants. Through examin ation of the fraction of jumps that return to the initial state, we attribu te anomalous diffusion to situations in which a penetrant molecule is confi ned to regions of low connectivity similar to a percolation cluster. The in frequent jumps that occur over longer times allow the penetrant to move awa y from this confining region and experience regular diffusion. This phenome non is present with a distribution of connectivity and uniform rate constan ts, and it is exaggerated by a distribution of rate constants. The regular diffusion regime is reached for displacements beyond 70 Angstrom and below the edge length of the periodic cell employed, and the predicted diffusion coefficient is reasonable for methane diffusing in glassy atactic polypropy lene.