A quantitative theoretical analysis of the enthaplic effects accompanying ion adsorption at the oxide/electrolyte interface, based on a model of energetically heterogeneous surface oxygens, is presented. The triple layer complexation model is accepted, along with the 2-pK charging mechanism. For the purpose of illustration a set of experimental data is subjected to that quantitative analysis including titration curves, radiometrically measured individual iostherms of ions, and calorimetric titration data for the alumina/NaCl electrolyte system. Two models of energetic heterogeneity were taken into consideration. One of them assumes that the binding-to-oxygen energies of the surface complexes vary but are highly correlated when going from one to another surface oxygen. The other model of surface heterogeneity assumes that these correlations are very small. Our numerical simultaneous analysis of the titration data, of the individual isotherms of Na+ and Cl- adsorption, and of the accompanying heat effects advocates strongly for the model of surface heterogeneity assuming small correlations to exist. A good simultaneous fit of all three kinds of experimental data is obtained, with a small uncertainty as for the values of the estimated adsorption parameters. A simultaneous fit of the measured enthalpic effects appears to be an especially strong criterion for a proper choice of adsorption parameters.

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A profound theoretical analysis is presented of the four-layer complexation model assuming that adsorbed anions and cations are located in two distinct layers. The theoretical relations between the intrinsic complexation constants developed in our previous paper (Langmuir 1995, 11, 3199) are subjected to an exhaustive numerical analysis, along with the newly developed relation between PZC and IEP. That analysis shows that the dependence of the electrical capacitances in the system on the activity of the bulk electrolyte is of crucial importance for the behavior of these systems.

The theory based on the complexation model has been used to derive the adsorption isotherm equation describing proton adsorption at the solid/electrolyte interface. The present equation applies to the 1-pK theory developed by Hiemstra and co-workers to describe oxide/electrolyte interfaces. Development has also been performed to take into account the local surface heterogeneity (i.e., the local pK distribution). It has then been shown that whatever the assumption, all the equations degenerate into a single derivative isotherm equation as the local surface potential and the heterogeneity parameters merge into one parameter. The obtained derivative equation has been used to model experimental high-resolution titration curves realized on anatase and goethite by using the titration derivative isotherm summation (TDIS) method proposed by Prelot and co-workers. The comparison between the fits obtained with this model and the Bragg-Williams-Temkin model shows that very similar quantitative results (peak position, adsorbed amounts) can be obtained. The present approach is, however, considered to be more realistic from a physical point of view.