A Rigorous Justification of the Point B Method for Determination of Monolayer Capacity from a Type II Adsorption Isotherm

Abstract

A mathematical justification of the Point B method, based in a new, simple, two-layered isotherm is given. The sharp decrease of surface affinity near Point B is simulated mathematically using the new isotherm. A parameter c which is closely related to the constant c of a BET isotherm is found to characterize the distinctness of the layered structure of an adsorbed phase. Excluding the last two types, the empirical BDDT classification of adsorption isotherms is explained in terms of the distinctness of layered structures. The suspicion that monolayer capacity as determined by a BET plot is not reliable unless the isotherm has a distinctive Point B is supported mathematically and explained physically. Rather than providing a qualitative description over a wide range of fractional coverage, as does the BET model, the present isotherm is intended to give a quantitative description over a small neighborhood of Point B in the hope of improving monolayer capacity measurement. The number of parameters in the isotherm can be increased systematically to account for new physical effects. A rigorous justification of the present model is constructed by means of a cluster series for a classical system of interacting particles in an external field.