Potential theory for gate adsorption on soft porous crystals

We demonstrate that an adsorption potential at the gate adsorption pressure of soft porous crystals (SPCs) based on the Polanyi's potential theory of adsorption shows a constancy to temperature. This was done using grand canonical Monte Carlo simulations and free energy analysis, which were carried out with a simplified stacked-layer SPC model. This finding implies that the characteristic curve obtained from an experimental gate adsorption isotherm on SPCs can be used to predict the temperature dependence of the gate-opening pressure, even though the potential theory of adsorption does not take into account the deformation of porous solids during the adsorption. We develop a modified potential theory for gate adsorption and show that the derived relation has a form that the Gibbs free energy change due to the host framework deformation per guest molecule, -Delta G(host)/N, and a correction term, C, are added to the expression of the original potential theory of adsorption. The term C is not an empirical correction factor but is the difference of intermolecular interaction potential and entropy between the bulk liquid phase at the saturated state and the adsorbed phase, originating from spatial constraint of adsorbed guest molecules in the host. By evaluating the modified expression for gate adsorption using the simulation results, we demonstrate that the constancy of the adsorption potential to temperature results from a compensation effect between three terms: guest-host interaction potential per guest molecule, -Delta G(host)/N and C, which have a temperature dependence.