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In the previous paper (Gutman, JOSSEC 18:3217–3237, 2014), we have shown that the main problem in capillarity and electrocapillarity of solid surfaces is the lack of clarity in determining the surface stress and basic equations. Now, we continue the survey of efforts to solve this problem and show origins of erroneous results, accenting some important items: comparative analysis of Gibbs and Guggenheim approaches in surface thermodynamics (a geometrical dividing surface and finite-thickness surface layer, respectively), transformation of fundamental equations on per-unit-area basis to obtain Gibbs adsorption equation for finite-thickness surface layer, different attempts to derive the thermodynamic definition of “surface stress” in frames of Gibbs’ theory (including Shuttleworth’s approach), atomistic calculations of surface stress, surface stress in rational continuum mechanics, “modifications” of Gibbs–Duhem relations made for solid interface, and Maxwell relations in capillarity and electrocapillarity of solid interface. It is shown that the erroneous Shuttleworth’s approach is present in an explicit or implicit form in all efforts to introduce the surface stress in frames of Gibbsian theory (although Gibbs did not introduce surface stress). Therefore, “modernizations” or “generalizations” of the Gibbs–Duhem relation, the Gibbs adsorption equation, and the Lippmann equation to adopt them for a solid surface are unnatural and not necessary. Therefore, we recommend withdrawing the Shuttleworth equation and its consequences from circulation, including the IUPAC Recommendations.

The main problem in electrocapillarity of solid electrodes is the lack of clarity in determining the surface stress and basic equations. Within the framework of the Gibbs concept of geometrical dividing surface, the “surface stress” cannot be defined because methods of continuum mechanics can be applied to a physical surface layer (of finite thickness), but not to a mathematical surface. Gibbs never used the concept of surface stress, introducing only “surface tension” for a liquid electrode and “closely related quantity” for a solid electrode. Revisiting the derivation of the Gibbs adsorption equation, we prove its applicability to solid surfaces without the limiting requirement of constant state of strain, which was undeservedly interpreted by Eriksson as a shortcoming of the Gibbs theory caused to look for other approaches to surface stress problem. A critical analysis shows that the attempts (Shuttleworth, Eriksson, Couchman, Gokhstein, Weissmuller, etc.) to create a thermodynamic definition of the surface stress (as well as the formulation of fundamental thermodynamic equations and Maxwell relations operating with surface stresses) contain mathematical defects. It is shown that confusing interpretations of some Gibbs’ concepts encountered in the literature have led to “modifications” of the Lippmann equation based on the critical error in the Gibbs–Duhem relation due to the occurrence of an extensive variable, which is inadmissible. The famous Lippmann equation should not be modified, and it remains a unique electrocapillary relation applicable to liquid and solid electrodes.

It is shown that the so-called “equation of solid-state electrocapillarity” derived by Gokhshtein from the simplest thermodynamic model, earlier used by Lippmann, is an incorrect modification that is returned to the classic Lippmann equation if to take into account the usual definition of differential capacity of the electrical double layer. Consequently, Gokhshtein’s experiments can actually confirm only the validity of the Lippmann equation (with deviations caused by physicochemical processes in the double layer, which could not be taken into account in the thermodynamic equations). The thermodynamic model is insufficient for the interpretations of these experimental results, whose understanding requires physical models of the different phenomena occurring at the electrode surface.

Unknown phenomenon was observed on the oxidized surface of a number of metals in water solutions including nickel, palladium, and platinum. Elastic extension of the metal decreases the interface capacity in wide potential region which reaches 0.4 V in the case of palladium. Within such region, the oscillograms “estance vs. potential” disclose an unusually long and low flat section which may be considered as the expanded zero of the differential charge density. The decrease of the capacity points out strengthening the bond of the water molecules to the surface oxide under its elastic extension which thickens the hydrated envelops of the adsorbed ions. Along the flat section, the state of the interface is reversible without changing the structure of the surface oxide. The anodic boundary of the flat section can be used as a sign of reaching the oxide monolayer. In the equations of solid state electrocapillarity, the potential of zero charge is presented explicitly. Its derivative with respect to elastic deformation is independent of the electrode potential and shifts the reversible section of the estance curve along the ordinate.

Contrary to some recent publications, the trivial definition of the surface charge density q = Q/A does not give any information about the charge Q and area A. Therefore this definition cannot be used as a “simple check,” rejecting results of electrochemical experiments where the values Q and A are the independent variables. Experimental confirmation and practical applications can be the two self-contained checks for the equations of solid-state electrocapillarity. Along with thermodynamics, the kinetic aspect is important here since the charge and area can oscillate in the large frequency range. Cycling the surface charge gives the three different contributions to the alternating surface tension of solids, corresponding to the double layer charging, reversible chemisorption, and discrete transitions closed within the rigid surface layer. The derivative of the charge density with respect to elastic deformation represents chemisorption and can be decreased to negligibly small value at the point of zero charge by increasing the frequency. On the base of the solid-state electrocapillarity, the dependence between the adsorption energy and elastic deformation was measured for the first time. It was thus found that stretching reinforces the bonding of hydrogen to the platinum surface. Acting inside the rigid surface monolayer, the alternating surface tension of solids is an independent tool in solving some complex problems of electrochemistry and solid-state physics. Two consecutive transitions are discovered on platinum instead of two coexistent hydrogen states which earlier were associated with two waves of the charging current. There are three consecutive hydrogen states separated along the potential axis by transitions from one state to another. Similar surface transitions are observed also on iridium, rhodium, and palladium. The number of transitions coincides with the number of finite radial nodes of the wave functions formed by d-electrons of these metals.

This review describes the evolution of important concepts related to potential drops at interfaces in electrochemical systems. The role of the thermodynamic theory of electrocapillarity of perfectly polarizable electrodes in the development of interfacial electrochemistry is emphasized. A critical analysis of the phenomenological models of the electrical double layer on ideally polarizable electrodes is given. Certain trends in studying solid electrodes with well-defined surfaces brought into contact with electrolyte solutions are summarized. Attention is drawn to several unsolved problems crucial for the future development of electrochemical surface science. Finally, some recent experimental data are analyzed for selected models.

A thermodynamic framework has been provided for the interpretation of combined cyclic voltammetry and surface stress measurements, the latter being obtained from wafer curvature or beam deflection measurements of a solid electrode as a function of applied potential (so-called voltstressograms). Firstly, the derivation of electrocapillarity equations for solid electrodes has been critically reviewed by starting from the Gibbs adsorption equation appropriate for solid-electrolyte interfaces. This allowed us to demonstrate the critical importance of elastic surface strain in the thermodynamic boundary conditions of the partial derivatives intervening in the interpretation of voltstressograms. From these considerations, it was shown for the first time that the electrocapillarity equations for solid electrodes are not appropriate for describing the variation of surface stress with potential obtained from wafer curvature measurements, because such measurements are intrinsically incompatible with the constant strain condition implied in the electrocapillarity equations. An alternative explanation is provided for the experimentally observed proportionality between the current density, measured in cyclic voltammograms, and the first derivative of surface stress with respect to potential, obtained from voltstressograms.