Analytical Isotherm Equations for Multicomponent Adsorption to Heterogeneous Surfaces

Adsorption on heterogeneous surfaces may be influenced not only by the heterogeneity but also by lateral interactions. For multicomponent solutions competition increases the complexity even further. In practice such complex systems frequently occur and to investigate the behavior of these systems it is rather useful to have analytical equations available which can describe the adsorption. Existing analytical mono- and multicomponent binding equations for heterogeneous surfaces are briefly reviewed. These equations are based on a high degree of ideality with respect to both the local isotherm and the affinity distribution for the different components. A new more generally valid analytical competitive binding equation is derived, using a nonideal local isotherm equation. In this local isotherm all component-specific nonideality is incorporated; i.e., it includes both lateral interactions and component-specific heterogeneity contributions. Under these conditions the remaining adsorbate-surface interactions can be characterized by an "intrinsic" affinity distribution that applies for all components. The features of the new equation are discussed and illustrated on the basis of some model calculations. The model is tested in practice using cadmium ion binding to fulvic acid at various pH values (data of Saar and Weber, Can. J. Chem. 57, 1263, 1979). These data cannot be modeled satisfactorily with the classical equation for multicomponent adsorption on heterogeneous surfaces. The newly derived equation gives excellent results.