Multiscale simulation of gas transport in mixed-matrix membranes with interfacial polymer rigidification

We investigate permeation in non-ideal mixed-matrix membranes (MMMs) having interfacial defects based on a multiscale simulation approach, involving sequential nanoscale and macroscale simulations. Our approach combines insight from equilibrium molecular dynamics (EMD) simulation of the transport in the individual phases, and in the interfacial region, with macroscopic simulation of the transport through solution of coupled 3-D partial differential equations (PDEs) via a finite-element method (FEM). Thus, unlike existing adaptations of classical effective medium theory (EMT), our approach avoids the empirical fitting of filler-polymer interfacial properties, such as interfacial thickness and permeability, against experimental permeation data. While the proposed multiscale simulation approach is general and applicable to any MMM system, it is illustrated in the context of single CO2 and CH4 permeation in two different polyimide-based MMMs; with one using MFI-type zeolite as filler phase and the other using carbon molecular sieves (CMS). For both systems, our nanoscale simulations reveal an interfacial region with rigidification of the polymer and reduced permeability at the polymer-adsorbent interface. Comparison of permeability predictions of classical EMT-based models considering interfacial rigidification, with our macroscale simulations, demonstrates the former to be best at low particle loadings. Further, our macroscale simulations reveal the existence of an optimum filler particle size, never discussed before, which maximizes the permeability in non-ideal MMMs; this arises from the competing effects of decrease in permeability and decrease of the relative interfacial resistance with increase of filler particle size. Moreover, the CO2/CH4 perm-selectivity is found strongly sensitive to the interfacial resistance for both finite uniform and non-uniform particle size distributions, an effect not captured by existing EMT models and over-looked in prior fundamental approaches.