Density Functional Theory for Adsorption of Gas Mixtures in Metal-Organic Frameworks

In this work, a recently developed density functional theory in three-dimensional space was extended to the adsorption of gas mixtures. Weighted density approximations to the excess free energy with different weighting functions were adopted for both repulsive and attractive contributions. An equation of state for hard-sphere Mixtures and a modified Benedict-Webb-Rubin equation for Lennard-Jones Mixtures were used to estimate the excess free energy of a uniform fluid. The theory was applied to the adsorption of CO2/CH4 and CO2/N-2 mixtures in two metal-organic frameworks: ZIF-8 and Zn-2(BDC)(2)(ted). To validate the theoretical predictions, grand canonical Monte Carlo simulations were also conducted. The predicted adsorption and selectivity from DFT were found to agree well with the simulation results. CO2 has stronger adsorption than CH4 and N-2, particularly in Zn-2(BDC)(2)(ted). The selectivity of CO2 over CH4 or N-2 increases with increasing pressure as attributed to the cooperative interactions of adsorbed CO2 molecules, The composition of the gas mixture exhibits a significant effect oil adsorption but not oil selectivity.