Electrocapillary equations of solid electrodes

Some remarks to the derivation of the “generalized Lippmann equation”

In the present communication, an attempt is made to demonstrate (once again) some of the problems with the derivation of the “generalized Lippmann equation” considered to be valid by many researchers for solid electrodes and to address the problems in the framework of the Gibbs model of the interface by using only the basic principles of thermodynamics. By surveying the relevant literature, it has been shown that during the derivation of the equation, it was completely ignored that the Gibbs-Duhem equation (i.e., the electrocapillary equation) is a mathematical consequence which follows directly from the homogeneous degree one property of the corresponding thermodynamic potential function; consequently, the resulting expression cannot be correct. Some alternative approaches have also been considered. The adequacy of the open system and the partly closed system approach has been critically discussed, together with the possibility of introducing new thermodynamic potential functions.

Electrocapillary coupling during electrosorption

The electrocapillary coupling coefficient, ς, measures the response of the electrode potential, E, to tangential elastic strain at the surface of an electrode. Using dynamic electro-chemo-mechanical analysis, we study ς(E) simultaneously with cyclic voltammetry. The study covers extended potential intervals on Au, Pt, and Pd, including the electrosorption of oxygen species and of hydrogen. The magnitude and sign of ς vary during the scans, and quite generally the graphs of ς(E) emphasize details which are less obvious or missing in the cyclic voltammograms (CVs). Capacitive processes on the clean electrode surfaces exhibit ς < 0, whereas capacitive processes on oxygen-covered surfaces are characterized by ς < 0 on Au but ς > 0 on Pt and Pd. The findings of ς < 0 during the initial stages of oxygen species adsorption and ς > 0 for hydrogen electrosorption agree with the trend that tensile strain makes surfaces more binding for adsorbates. However, the large hysteresis of oxygen electrosorption on all electrodes raises the question: is the exchange current associated with that process sufficient for its measurement by potential response during small cyclic strain?

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.

Microcantilever-Based Sensors: Effect of Morphology, Adhesion, and Cleanliness of the Sensing Surface on Surface Stress

The surface stress response of micromechanical cantilever-based sensors was studied as a function of the morphology, adhesion, and cleanliness of the gold sensing surface. Two model systems were investigated: the adsorption of alkanethiol self-assembled monolayers at the gas-solid interface and the potential-controlled adsorption of anions at the liquid-solid interface. The potential-induced surface stress, on a smooth and continuous polycrystalline Au(111)-textured microcantilever in 0.1 M HClO4, is in excellent agreement with macroscopic Au(111) single-crystal electrode results. It is shown that ambient contaminants on the sensing surface dramatically alter the surface stress-potential response. This observation can be misinterpreted as evidence that for polycrystalline Au(111) microcantilever electrodes, surface stress is dominated by surface energy change. Results for anions adsorption on gold are in contrast to the gas-phase model system. We demonstrate that the average grain size of the gold sensing surface strongly influences the magnitude of the surface stress change induced by the adsorption of octanethiol. A 25-fold amplification of the change in surface stress is observed on increasing the average gold grain size of the sensing surface from 90 to 500 nm.