Simplified Model for Penetrant Hopping through Polymer Grafted Nanoparticles

Polymer grafted nanoparticles (GNPs) have enhanced gas transport properties compared to those of neat polymer matrices, which are often used in industrial separations. Activation energy of penetrant transport in GNPs exhibits a uniquely segmented trend compared to the single unifying trend found in neat polymer melts. These two distinct trends in the GNP systems alludes to possible differences in the transport mechanism of variously sized penetrants. The proposed mechanism for GNP membrane transport is hypothesized to stem from microscopic structure of GNPs with high grafting density and intermediate graft lengths. In this work, we investigate the proposed mechanism of hopping by constructing a simplified hard sphere Monte Carlo model, from which activation energy trends are successfully reproduced at little computational expense. Our results allow the mapping of parameters with physical significance to experimental materials, such as the molecular stiffness of a monomer, which permits us to compare materials from these properties, as well as provides the ability to track particle movement as a function of its size.