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.

A number of adsorption models have been considered corresponding to various combinations of the 1-pK and 2-pK charging models, with various models of the oxide/electrolyte interface structure. The corresponding theoretical descriptions have been developed, along with the relations between the equilibrium constants, suggested by the appearance of the common intersection point. The equations developed for various adsorption models have been applied then to analyze the behavior of the surface charge, individual isotherms of ions, and electrokinetic data reported by Sprycha for the anatase/NaCl solution system. No decisive proof has been deduced in favor of either the 1-pK or 2-pK charging mechanism, but certain important conclusions have been drawn concerning the applicability of various adsorption models. It was shown that to arrive at a reasonable theoretical description, the assumed model of surface charging must necessarily be combined with a certain model of the oxide/electrolyte interface structure.

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The equations developed by us for the triple layer surface complexation approach, taking into account energetic heterogeneity of surface oxygens, are applied here to study the heterogeneity influences on the enthalpic effects accompanying ion adsorption at the silica/NaCl aqueous solution interface. That study is accompanied by the parallel experimental/theoretical study of the energetic heterogeneity of surface oxygens for adsorption of argon molecules which are known to interact practically only with surface oxygens. Such studies provide a simpler interpretation for information of the surface energetic heterogeneity. That additional study confirms a proper choice of the model of surface heterogeneity, accepted by us in our description of ion adsorption at the oxide/electrolyte interfaces. Our quantitative analysis also confirms quite different features of the silica/electrolyte interface, compared to those formed by other metal oxides. Namely, in the case of the silica/electrolyte interface, the adsorption of water molecules on the surface oxygens SO- is a process highly competitive with proton adsorption leading to that of formation of the neutral surface complexes SOH0.

The theoretical quantitative analysis of the temperature dependence and enthalpic effects of ion adsorption, developed in our earlier publications, was applied here to study the features of hematite/electrolyte interfaces. This is the first time that our set of experimental data could be used to carry out a simultaneous analysis of both the temperature dependence of the titration isotherm and directly measured enthalpic effects. To draw possible general conclusions about the features of the hematite/electrolyte interfaces, we considered two sets of experimental data measured in two laboratories, using the hematite samples prepared in different ways. The differences in sample preparations are manifested by substantially different values of the monitored surface charges and related calorimetric effects. The present quantitative analysis in Part I of this publication was carried out by using the model of an energetically homogeneous solid surface, which is still commonly accepted. Certain inconsistencies were found in the parameter values leading to a good fit of titration isotherms and those that are best to fit directly measured enthalpic effects. Thus, the general conclusion was drawn that this popular model is too crude for a quantitative analysis.