Analysis of adsorption on a uniform surface using the quasi-chemical theory of interaction shows that the hypotheses of the BET theory lead to substantially no adsorption beyond the first layer if E2 = EL, and stepwise isotherms if E1>E2>E3>···>EL. For the monolayer adsorption of gases on silver, platinum, and steel, the heterogeneous nature of the adsorbing surface is clearly indicated. Cooperative adsorption on the non-uniform surface is treated, and the cooperative analog of the Freundlich equation derived. The typical multi-layer isotherm is shown to be composed of three regions: non-cooperative adsorption on a strongly heterogeneous surface; cooperative adsorption on a still heterogeneous surface; and cooperative multi-layer adsorption induced by small van der Waals perturbations some distance from the surface. The isotherm p/p0=exp{—a/θr} is derived and shown to be a good representation of adsorption data that conform to the BET Type I, II, or III shapes.

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