Physical origin of adsorption heat and its significance in the isotherm equation

Adsorption heat is a cornerstone concept underpinning almost all the existing theoretical isotherms for porous media. Yet, it remains elusive what this concept stands for and what are the physical sources for it. Here, a rigorous thermodynamic formulation is derived for the adsorption process with the aid of the law of mass action, leading to an expression of adsorption heat as the external chemical potential difference between two adjacent adsorbate layers. The interaction between adsorbent and adsorbates like van der Waals is theoretically identified as the intermolecular source for the change of adsorption heat. Thereby, adsorption heat is formulated as a spatially varied function of the distance to adsorbent surfaces. This adsorption heat function facilitates the establishment of a two-parameter sorption isotherm equation. The equation can be theoretically converted to two widely used adsorption isotherm equations, namely Brunauer-Emmet-Teller (BET) and GuggenheimAnderson-de Boer (GAB) equations, and shows excellent performance in capturing experimental isotherm data of a wide array of materials. The comparative analysis demonstrates that the derived two-parameter isotherm equation outperforms the two-parameter BET equation and the three-parameter GAB equation in most cases. Such performance verifies the generality of the derived isotherm equation, thus further confirming the validity of the derived formulation of adsorption heat.