Modeling of high pressure adsorption isotherm using statistical physics approach: lateral interaction of gases adsorption onto metal–organic framework HKUST-1

A novel theoretical approach for description of high pressure isotherm is developed in the present study. This approach is based on the grand canonical formalism in statistical physics by taking into account the lateral interaction between the adsorbate molecules. This leads to five parameters equation describing the high pressure adsorption equilibrium. This model is applied to experimental adsorption data of hydrogen, nitrogen, methane and carbon dioxide on metal–organic frameworks HKUST-1. There is a good correlation between experimental data and those calculated by the new model at pressure up to 50 MPa. It was found that hydrogen molecules can be considered as a ideal gas over a wide temperature range and even at high pressures. Lateral interactions were found to be necessary to describe the adsorption of N₂, CH₄ and CO₂ at high pressures. The proposed model allows also prediction of some adsorption thermodynamic functions which govern the adsorption mechanism such as the entropy, the Gibbs free enthalpy and the internal energy.