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.

New insights on the interfacial tension of electrochemical interfaces and the Lippmann equation

The Lippmann equation is considered as universal relationship between interfacial tension, double layer charge, and cell potential. Based on the framework of continuum thermo-electrodynamics, we provide some crucial new insights to this relation. For general interfaces such that the local curvature radius is large compared to the Debye length, we apply asymptotic analysis methods to obtain the Lippmann equation. We give precise definitions of the involved quantities and show that the interfacial tension of the Lippmann equation is composed of the surface tension of our general model, and contributions arising from the adjacent space charge layers that can only lower the interfacial tension. Moreover, it turns out that surface reactions can be consistently incorporated into the Lippmann equation, provided that there is no charge transfer from one side of the interface to the other. We apply the model to curved liquid metal electrodes and compare our model to experimental data of several mercury–electrolyte interfaces. We obtain qualitative and quantitative agreement in the 2 V potential range for various salt concentrations.

Thermodynamics of the Polymer-Concrete Interface

Property of polymer-concrete in the interface has been dealt with from the view of thermodynamics. Gibbs function or free enthalpy was applied to characterize the binding ability of the interface. AC impedance spectroscopy was used to measure the electrical capacitance of the interface between the polymer particle and mortar. Lippmann equation was used to estimate the thermodynamic functions for the estimation of the binding ability. A typical example was given.