Occupancy Dependency of Maxwell–Stefan Diffusivities in Ordered Crystalline Microporous Materials

Molecular dynamics simulation data for a variety of binary guest mixtures (H₂/CO₂, Ne/CO₂, CH₄/CO₂, CO₂/N₂, H₂/CH₄, H₂/Ar, CH₄/Ar, Ar/Kr, Ne/Ar, CH₄/C₂H₆, CH₄/C₃H₈, C₂H₆C₃H₈, CH₄/nC₄H₁₀, and CH₄/nC₅H₁₁) in zeolites (MFI, BEA, ISV, FAU (all-silica), NaY, NaX, LTA, CHA, DDR) and metal–organic frameworks (MOFs) (IRMOF-1, CuBTC, MgMOF-74) show that the Maxwell–Stefan (M–S) diffusivities, Đ₁, Đ₂, Đ₁₂, are strongly dependent on the molar loadings. The main aim of this article is to develop a fundamental basis for describing the loading dependence of M–S diffusivities. Using the ideal adsorbed solution theory, a thermodynamically rigorous definition of the occupancy, θ, is derived; this serves as a convenient proxy for the spreading pressure, π, and provides the correct metric to describe the loading dependence of diffusivities. Configurational-bias Monte Carlo simulations of the unary adsorption isotherms are used for the calculation of the spreading pressure, π, and occupancy, θ. The M–S diffusivity, Đ_i, of either constituent in binary mixtures has the same value as that for unary diffusion, provided the comparison is made at the same θ. Furthermore, compared at the same value of θ, the M–S diffusivity Đ_i of any component in a mixture does not depend on it partner species. The Đ_i versus θ dependence is amenable to simple interpretation using lattice-models. The degree of correlations, defined by the ratio Đ₁/Đ₁₂, that characterizes mixture diffusion shows a linear increase with occupancy θ, implying that correlations become increasingly important as pore saturation conditions are approached.