Gaussian distribution of adsorptive potentials

The interpretation of adsorption isotherms in terms of a surface displaying a symmetrical (Gaussian) distribution of adsorptive potentials to the adsorbate has been successfully applied to a number of systems but marked exceptions have been found, particularly with crystals that were selected as likely to have completely homotattic surfaces. These exceptional adsorption isotherms are readily interpreted, however, as the result of a sum of two, or occasionally three, distinctly different Gaussian distributions, presumably deriving from the same number of surface constituents. Among these constituents the expected homotattic substrate, which is associated with a particular crystal face, can always be identified. 

A previous paper of this series (13) describes the analysis of adsorption iso- therms for heterogeneous surfaces in terms of a Gaussian distribution of adsorptive potentials. The distribution of adsorptive potential energies may not, however, have a form that is symmetrical about a mean it could possess enough asymmetry so that the adsorption isotherm could not be described by a model that assumed a Gaussian distribution. 

The first such solutions were carried out by Ross and Olivier [1, p. 129 6,7]. Using Gaussian distributions of adsorptive potential of varying width, they computed tables of model isotherms using kernel functions based on the Hill-de Boer equation for a mobile, nonideal two-dimensional gas and on the Fowler-Guggenheim equation [Eq. (14)] for localized adsorption with lateral interaction. The fact that these functions are implicit for quantity adsorbed was no longer a problem since they could be solved iteratively in the numerical integration. 

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