Statistical mechanics of binary mixture adsorption in metal–organic frameworks in the osmotic ensemble

Abstract

Although crucial for designing separation processes little is known experimentally about multi-component adsorption isotherms in comparison with pure single components. Very few binary mixture adsorption isotherms are to be found in the literature and information about isotherms over a wide range of gas-phase composition and mechanical pressures and temperature is lacking. Here, we present a quasi-one-dimensional statistical mechanical model of binary mixture adsorption in metal–organic frameworks (MOFs) treated exactly by a transfer matrix method in the osmotic ensemble. The experimental parameter space may be very complex and investigations into multi-component mixture adsorption may be guided by theoretical insights. The approach successfully models breathing structural transitions induced by adsorption giving a good account of the shape of adsorption isotherms of CO 2 and CH 4 adsorption in MIL-53(Al). Binary mixture isotherms and co-adsorption-phase diagrams are also calculated and found to give a good description of the experimental trends in these properties and because of the wide model parameter range which reproduces this behaviour suggests that this is generic to MOFs. Finally, a study is made of the influence of mechanical pressure on the shape of CO 2 and CH 4 adsorption isotherms in MIL-53(Al). Quite modest mechanical pressures can induce significant changes to isotherm shapes in MOFs with implications for binary mixture separation processes. This article is part of the theme issue ‘Modern theoretical chemistry’.