Homogenization of Continuum-Scale Transport Properties from Molecular Dynamics Simulations: An Application to Aqueous-Phase Methane Diffusion in Silicate Channels

Silica-based materials including zeolites are commonly used for wide ranging applications including separations and catalysis. Substrate transport rates in these materials can significantly influence the efficiency of such applications. Two factors that contribute to transport rates include 1) the porosity of the silicate matrix and 2) non-bonding interactions between the diffusing species and the silicate surface. These contributions generally emerge from disparate length scales, namely 'microscopic' (roughly nanometer-scale) and 'macroscopic' (roughly micron-scale), respectively. Here, we develop a simulation framework to estimate the simultaneous impact of these factors on methane mass transport in silicate channels. Specifically, we develop a model of methane transport using homogenization theory to obtain transport parameters valid at length scales of hundreds to thousands of nanometers. These parameters implicitly reflect interactions taking place at fractions of a nanometer. The inputs to the homogenization analysis are data from extensive molecular dynamics simulations that incorporate atomistic-scale interactions, processed to yield local diffusion coefficients and mean force potentials. With this model, we demonstrate how nuances in silicate hydration and silica/methane interactions impact methane diffusion rates in silicate materials, including the effects of silicate surface chemistry such as the presence of silanol groups. The molecular dynamics simulations indicate that methane diffusivity at the silica surface is lower than the bulk-like rates observed at the center of channels of sufficient width. However, potentials of mean force generally evidence attractive methane/silica interactions that enhance diffusion overall. By simultaneously accounting for both of these effects, we show that the effective diffusion coefficient for the nanoporous silicate can be approximately double the value of estimates assuming fully bulk-like behavior in the channel. This study therefore demonstrates the importance of determining diffusion coefficients and potentials of mean force at an atomistic level when estimating transport properties in bulk materials. Importantly, we provide a simple homogenization framework to incorporate these molecular-scale attributes into bulk material transport estimates. This hybrid homogenization/molecular dynamics approach will be of general use for describing small molecule transport in materials with detailed molecular interactions.