Thermodynamically Consistent Methodology for Estimation of Diffusivities of Mixtures of Guest Molecules in Microporous Materials.

The Maxwell-Stefan (M-S) formulation, that is grounded in the theory of irreversible thermodynamics, is widely used for describing mixture diffusion in microporous crystalline materials such as zeolites and metal-organic frameworks (MOFs). Binary mixture diffusion is characterized by a set of three M-S diffusivities: , , and . The M-S diffusivities and characterize interactions of guest molecules with pore walls. The exchange coefficient quantifies correlation effects that result in slowing-down of the more mobile species due to correlated molecular jumps with tardier partners. The primary objective of this article is to develop a methodology for estimating , , and using input data for the constituent unary systems. The dependence of the unary diffusivities and on the pore occupancy, θ, is quantified using the quasi-chemical theory that accounts for repulsive, or attractive, forces experienced by a guest molecule with the nearest neighbors. For binary mixtures, the same occupancy dependence of and is assumed to hold; in this case, the occupancy, θ, is calculated using the ideal adsorbed solution theory. The exchange coefficient is estimated from the data on unary self-diffusivities. The developed estimation methodology is validated using a large data set of M-S diffusivities determined from molecular dynamics simulations for a wide variety of binary mixtures (H/CO, Ne/CO, CH/CO, CO/N, H/CH, H/Ar, CH/Ar, Ne/Ar, CH/CH, CH/CH, and CH/CH) in zeolites (MFI, BEA, ISV, FAU, NaY, NaX, LTA, CHA, and DDR) and MOFs (IRMOF-1, CuBTC, and MgMOF-74).