Surface Area Estimation: Replacing the Brunauer-Emmett-Teller Model with the Statistical Thermodynamic Fluctuation Theory

Abstract

Surface area estimation using the Brunauer-Emmett-Teller (BET) analysis has been beset by difficulties. The BET model has been applied routinely to systems that break its basic assumptions. Even though unphysical results arising from force-fitting can be eliminated by the consistency criteria, such a practice, in turn, complicates the simplicity of the linearized BET plot. We have derived a general isotherm from the statistical thermodynamic fluctuation theory, leading to facile isotherm fitting because our isotherm is free of the BET assumptions. The reinterpretation of the monolayer capacity and the BET constant has led to a statistical thermodynamic generalization of the BET analysis. The key is Point M, which is defined as the activity at which the sorbate-sorbate excess number at the interface is at its minimum (i.e., the point of strongest sorbate-sorbate exclusion). The straightforwardness of identifying Point M and the ease of fitting by the statistical thermodynamic isotherm have been demonstrated using zeolite 13X and a Portland cement paste. The adsorption at Point M is an alternative for the BET monolayer capacity, making the BET model and its consistency criteria unnecessary. The excess number (i) replaces the BET constant as the measure of knee sharpness and monolayer coverage, (ii) links macroscopic (isotherms) to microscopic (simulation), and (iii) serves as a measure of sorbate-sorbate interaction as a signature of sorption cooperativity in porous materials. Thus, interpretive clarity and ease of analysis have been achieved by a statistical thermodynamic generalization of the BET analysis.