%0 Journal Article %@ 1364-503X %A Manos, G %A Dunne, LJ %D 2018 %F discovery:10022699 %I Royal Society, The %J Philosophical Transactions of the Royal Society A %K Metal–organic framework, mixture adsorption isotherms, transfer matrix, osmotic ensemble, binary and co-adsorption, mechanical pressure %N 2115 %T Statistical Mechanics of Binary Mixture Adsorption in Metal-Organic Frameworks in the Osmotic Ensemble %U https://discovery.ucl.ac.uk/id/eprint/10022699/ %V 376 %X 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 CO2 and CH4 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 CO2 and CH4 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. %Z This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. © 2018 The Author(s) Published by the Royal Society. All rights reserved