Predicting adsorption selectivities from pure gas isotherms for gas mixtures in metal-organic frameworks

We perform Grand Canonical Monte Carlo simulations on a lattice of Mg²⁺ sites (GCMC) for adsorption of four binary A/B mixtures, CH₄/N₂, CO/N₂, CO₂/N₂, and CO₂/CH₄, in the metal-organic framework Mg₂(2,5-dioxidobenzedicarboxylate), also known as CPO-27-Mg or Mg-MOF-74. We present a mean field co-adsorption isotherm model and show that its predictions agree with the GCMC results if the same quantum chemical ab initio data are used for Gibbs free energies of adsorption at the individual sites and for lateral interaction energies between the same, A⋯A and B⋯B, and unlike, A⋯B, adsorbed molecules. We use both approaches to test the assumption underlying Ideal Adsorbed Solution Theory (IAST), namely approximating A⋯B interaction energies as the arithmetic mean of A⋯A and B⋯B interaction energies. While IAST works well for mixtures with weak lateral interactions, CH₄/N₂ and CO/N₂, the deviations are large for mixtures with stronger lateral interactions, CO₂/N₂ and CO₂/CH₄. Motivated by the theory of London dispersion forces, we propose use of the geometric mean instead of the arithmetic mean and achieve substantial improvements. For CO₂/CH₄, the lateral interactions become anisotropic. To include this in the geometric mean co-adsorption model, we introduce an anisotropy factor. We propose a protocol, named co-adsorption mean field theory (CAMT), for co-adsorption selectivity prediction from known (experiment or simulation) pure component isotherms which is similar to the IAST protocol but uses the geometric mean to approximate mixed pair interaction energies and yields improved results for non-ideal mixtures.