A reply to the question of whether the internal energy of solid interfaces can be of a non-homogeneous nature

Update on current state and problems in the surface tension of condensed matter

The dual concept of surface energy formally allows application of Gibbs thermodynamics to the surface tension of solids and is unlimited using the classical Lippmann equation for solids that is shown to contradict all available in situ experimental data. At present, the generalized Lippmann equation is believed to be the most universal, since the classical Lippmann equation, the Shuttleworth and Gokhshtein equations could be derived from it. Lately it was evaluated in two opposite ways: the first--the experimental verification of the Gokhshtein equation supports correctness of the generalized Lippmann and Shuttleworth equations; the second--the incompatibility of the Shuttleworth equation with Hermann's mathematical structure of thermodynamics makes invalid all its corollaries, including the generalized Lippmann and Gokhshtein equations. Both approaches are shown here to be incorrect, since the Gokhshtein equation cannot be correctly derived from any of the above-mentioned equations. The Frumkin derivation of the first and second Gokhshtein equations follows from one thermodynamic relationship general for the surface tension of both solid and liquid electrodes. The classical Lippmann equation is also derived from this general relationship as a particular case of the second Gokhshtein equations. We have considered the hierarchy of these equations and discussed the straightforward application of the classical Lippmann equation for solids with an account for elasticity of the surface structured layers of liquids. The partial charge transfer during anion adsorption cannot be measured in electrochemical experiments or reliably estimated by quantum-chemical and DFT calculations. However, it is directly involved in the adsorbate charge that is experimentally accessible by in situ contact electric resistance technique. We present the first quantitative evaluation of charge transfer during halides adsorption on silver from aqueous solutions in dependence on the electrode potential.