Using the spreading pressure to inter-relate the characteristics of unary, binary and ternary mixture permeation across microporous membranes

The primary objective of this article is to investigate the possibility of inter-relating the characteristics of unary, binary, and ternary mixtures across microporous zeolite membranes. Towards this end, we performed Configurational-Bias Monte Carlo (CBMC) simulations of mixture adsorption equilibrium, and Molecular Dynamics (MD) simulations of guest diffusivities in unary (CO₂, CH₄, N₂, and H₂), binary (CO₂/CH₄, CO₂/N₂, CH₄/N₂, CO₂/H₂), and ternary (CO₂/CH₄/N₂, CO₂/CH₄/H₂, CO₂/N₂/H₂) mixtures in four zeolites: CHA, DDR, MFI, and FAU. The combined CBMC and MD data are used to obtain fundamental insights into the adsorption, diffusion, and permeation characteristics of the variety of guest/host combinations. Application of the Myers-Prausnitz theory shows that the adsorption selectivity for the i-j pair, S_ads,ij, in ternary mixtures has practically the same value as for the binary i-j mixture, provided the comparison is made as the same surface potential Φ, a convenient and practical proxy for the spreading pressure π, that is calculable on the basis of the data on the unary isotherms of the constituent guests. For the mixtures investigated, departures from thermodynamic idealities do not cause deviations from the uniqueness of the S_ads,ij vs Φ dependence because the ratios of the activity coefficients γ_i/γ_j also appear to uniquely depend on Φ. The surface potential Φ is also the thermodynamically correct metric to describe the loading dependence of diffusivities. Compared at the same Φ, the diffusion selectivity for the i-j pair, S_diff,ij, in ternary mixtures has practically the same value as for the binary i-j mixture. Consequently, the permeation selectivity, S_perm,ij=S_ads,ij×S_diff,ij is also uniquely dependent on Φ. When compared at the same Φ, the component permeabilities, Π_i for CO₂, CH₄, and N₂ are found to be independent of the partners in the binary and ternary mixtures investigated and have practically the same as the values for the corresponding unary permeabilities.