Statistical mechanics of multilayer sorption: Extension of the Brunauer-Emmett-Teller (BET) and Guggenheim-Anderson-de Boer (GAB) adsorption isotherms

Adsorption isotherms have important practical applications, including in solution chemistry where they have been used to model solvent and solute activities in liquid mixtures at extreme concentrations, such as pure melts. The conventional Brunauer-Emmett-Teller (BET) and Guggenheim-Anderson-de Boer (GAB) models are less successful for dilute solutions (high water activities), for which most data are available. In this work we extend these models to include arbitrary numbers of additional adsorbed monolayers and, using statistical mechanics, derive expressions for the Gibbs energies of solutions and for solute and solvent activities. We demonstrate consistency with results that can be obtained by other methods, and show how a particular simple case is equivalent to Raoult's law. Test applications of the equations to water activity data for aqueous solutions over very wide ranges of concentration show that the addition of a single extra adsorbed layer to the fitted adsorption model greatly increases its accuracy, especially for low concentrations.