Virial analysis of low-coverage physical adsorption data on heterogeneous surfaces

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Abstract
The general treatment of the McMillan–Mayer theory of solutions is applied to low-coverage adsorption on heterogeneous surfaces. Expressions are derived for the second and third gas/solid virial coefficients for adsorption on model heterogeneous surfaces. The gaussian, log-normal, exponential and Maxwell–Boltzmann functions are examined as possible models for the site energy distribution function and it is found that, of these, only the gaussian gives a suitable expression. A method of analysis is given that can be used to fit experimental second gas/solid virial coefficients to a model with a gaussian site energy distribution. Equations for the analysis of the third gas/solid virial coefficient are obtained for a model that incorporates the gaussian site energy distribution with either a random or a patchwise pair distribution function. The methods of analysis described here are applicable over the range of temperature for which the second and third gas/solid virial coefficients are normally determined either by adsorption or gas-chromatographic measurements (3 ⩽ε*/kT⩽ 8). The approximations inherent in the analysis are less than the usual experimental uncertainty in the virial coefficients. The limited available data are analyzed and the potential of the method for the characterization of heterogeneous surfaces is discussed.

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