A new adsorption model based on generalized van der Waals partition function for the description of all types of adsorption isotherms

A new adsorption model is proposed based on the Generalized van der Waals partition function by introducing the concept of attractive region, which integrates the effects of the adsorption sites of adsorbent and represents pore space where adsorbates concentrate. A theoretical expression for the chemical potential of adsorbates in the attractive region is derived and used to calculate the adsorbate density in each attractive region. The model can generate all the six types of isotherms classified by the International Union of Pure and Applied Chemistry (IUPAC) report including those with hysteresis and is easy to use. It is a generalized model that can be applied to various types of porous materials. With the fitted parameters, the model can predict the adsorption isotherms even for adsorbents with wide pore size distributions. It also well captures the isotherm-type transition as temperature changes and can estimate the hysteresis when capillary condensation exists.