Exact matrix treatment of the statistical mechanics of adsorption of large aromatic molecules on graphene

Experimental studies of adsorption from solution of the large aromatic molecules 1,2-dihydroxybenzene (catechol) and phenyl hydroquinone on graphene nanoplatelets show that at low coverage adsorption is followed by a transition which occurs from adsorbed molecules in flat to more vertically oriented states. Catechol adsorption isotherms exhibit 2 plateaus while phenyl hydroquinone shows 3 plateaus indicating 2 and 3 active conformers respectively participating in the adsorption process. Modelling such adsorption isotherms presents a challenge. Here, an exact matrix treatment of the statistical mechanics of a one-dimensional model of adsorption of catechol and dihydroquinone on graphene nanoplatelets is presented. The theoretical adsorption isotherms successfully reproduce all the features of both the catechol and dihydroquinone experimental adsorption isotherms. As suggested by the experimentalists, our theoretical model demonstrates that adsorbed phenyl hydroquinone molecules adopt a flat orientation at low concentrations and an edge orientation at higher coverage before eventually adopting a vertical configuration. Both catechol and phenyl hydroquinone can be described by our interconvertible monomer-dimer-trimer model. The theoretical adsorption isotherms obtained show several plateaus reflecting the types of conformer on the graphene surface.

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

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.This article is part of the theme issue 'Modern theoretical chemistry'.