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 and CH 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 and CH 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'.

Predicting the Features of Methane Adsorption in Large Pore Metal-Organic Frameworks for Energy Storage

“…Some time ago, we proposed an exactly solvable transfer matrix treatment of a statistical mechanical lattice theory of a MOF which allows mixture and single component adsorption isotherms and the compression of these soft materials to be theoretically described [ 30 ]. There is a broadly held view [ 27 ] that the OE is the most appropriate theoretical formalism to model adsorption in soft porous materials.…”

“…Modelling these transformations [ 20 , 21 , 22 , 23 , 24 , 25 ] in MOFs is challenging and has attracted wide attention. During the past few years [ 28 , 29 , 30 ], we have developed several solvable pseudo one-dimensional statistical mechanical lattice theories of adsorption of gas on MOFs. Previously, we considered [ 29 ] a pseudo-one dimensional statistical mechanical theory of adsorption in a metal-organic framework (MOF) with both narrow and large pores which is solved exactly by a transfer matrix method in the Osmotic Ensemble (OE).…”

“…Previously, we considered [ 29 ] a pseudo-one dimensional statistical mechanical theory of adsorption in a metal-organic framework (MOF) with both narrow and large pores which is solved exactly by a transfer matrix method in the Osmotic Ensemble (OE). More recently, [ 30 ] we considered a theory treated in the OE to describe pure component and mixture adsorption in MOFs in structures which can undergo pore transformation from narrow to large pores. The theory successfully describes the form of adsorption of gas isotherms in MOFs which reflect structural transformations induced by adsorption.…”

Thermodynamic Modeling of the Selective Adsorption of Carbon Dioxide over Methane in the Mechanically Constrained Breathing MIL‐53(Cr)

“…Finally, the same authors also investigated the impact of an additional mechanical pressure on the shape of the adsorption isotherms. [33] In this work, we extend the semi-analytical mean-field model, which was originally developed for single-component adsorption in MOFs, [20] toward adsorption of binary mixtures in a breathing MOF. This model is then used for the investigation of the breathing behavior of the 1D channel like carboxylate MIL-53(Cr) [14] when exposed to a mixture of methane and carbon dioxide under varying conditions, by constructing the full phase diagram of MIL-53(Cr) as a function of the independent CH 4 and CO 2 vapor pressures.…”

Addressing hysteresis and slow equilibration issues in cavity-based calculation of chemical potentials

“…The osmotic ensemble method calculates the composition of the saturated solution phase by imposing the chemical potential of the corresponding solid phase in a grand canonical approach. The osmotic ensemble has typically been applied to small solutes, both in solution and metal-organic frameworks [27][28][29] , as the initial and final states need to be similar. Moving away from particle-based methods, analytical models have been developed to investigate the solubility of large solutes in non-aqueous solvents and can accurately predict the solubility of PAHs in a range of solvents [30][31][32] .…”