Multilayer sorption parameters: BET or GAB values?

The differences between the sets of values for the monolayer capacity and the energy constant obtained by sorption data regressions using two related multilayer sorption isotherms, the two-parameter BET (Brunauer–Emmett–Teller) and the three-parameter GAB (Guggenheim–Andersen–de Boer) isotherms, are analysed. Experimentally, it is found that the GAB monolayer value is always higher than the BET value and the GAB energy constant results always lower than the BET constant. Mathematical and physical reasons are given which explain these differences. The third GAB parameter determines the greater versatility of the GAB equation, which has a quite larger range of applicability than the BET isotherm. It is shown that in terms of the three GAB constants, the two BET parameters are qualitatively and quantitatively reproduced as well as their dependence on the regression interval used in the BET regression, justifying in this way the above-mentioned inequalities. The typical upswing in the BET plots after a (pseudo) linear range at lower activities of the sorbate is also explained. All these findings are exemplified using experimental sorption data of several systems of very distinct chemical nature. A complete regression procedure for sorption data in terms of the GAB isotherm is advanced.