New theoretical expressions for the five adsorption type isotherms classified by BET based on statistical physics treatment

New theoretical expressions to model the five adsorption isotherm types have been established. Using the grand canonical ensemble in statistical physics, we give an analytical expression to each of five physical adsorption isotherm types classified by Brunauer, Emett, and Teller, often called BET isotherms. The establishment of these expressions is based on statistical physics and theoretical considerations. This method allowed estimation of all the mathematical parameters in the models. The physicochemical parameters intervening in the adsorption process that the models present could be deduced directly from the experimental adsorption isotherms by numerical simulation. We determine the adequate model for each type of isotherm, which fixes by direct numerical simulation the monolayer, multilayer, or condensation character. New equations are discussed and results obtained are verified for experimental data from the literature. The new theoretical expressions that we have proposed, based on statistical physics treatment, are rather powerful to better understand and interpret the various five physical adsorption type isotherms at a microscopic level.