A definition of the ideally polarisable electrode which allows a general statistical mechanical treatment is given, comparisons with the usual thermodynamic approach being made. It is shown that, with this definition, the system behaves as a pure capacitance to an imposed alternating potential of sufficiently low frequency. The equilibrium states of the system are described by the grand canonical distribution. Thermodynamic functions, given in terms of the grand canonical partition function, can be computed in molecular terms: In particular, general expressions for the surface tension and the pressure are obtained, and compared to those proposed by various authors. The separation of the pressure into electrical and nonelectrical parts is analyzed. Expressions are given for the electrochemical potentials of charged and of dipolar species. With these microscopic definitions, the Gibbs adsorption isotherms and the Lippmann equation are derived. For several simple models, including that of Gouy and Chapman for an ionic solution and a metal electrode, these relations are explicitly considered. The inadmissability, in a coherent model, of reducing the solvent to a medium of fixed dielectric constant, is emphasized.
IntroductionThe ideally polarisable electrode (IPE) is the simplest electrochemical system. In spite of its ideality, it is possible to approach it experimentally, at least in a limited range of potential, in the mercury drop electrode. Because of this, the system has been the subject of many studies, which are summarized and discussed in the standard works on electrochemistry [1--4].From thermodynamic reasoning, one can show that certain quantities characteristic of the interface, such as the electrode charge or the amounts of adsorbed substances, are accessible through studies of the surface tension of the IPE as a function of parameters like the potential difference across the system or the chemical potentials of the various components. On the other hand, several authors have attempted to define the surface tension o directly, in terms of the mechanical equilibrium of the interface [5--10]. Various expressions have [End of page 151] been proposed for o. In a study of the interface between an electrolytic solution and its vapor, Buff [11] showed that the thermodynamic and mechanical approaches yield the same microscopic expression for o. Our study of the IPE is in part along these lines.In the first part of this work, we define precisely the system and its surroundings (measurement cell). Subsequently, we derive the Gibbs adsorption isotherm by statistical mechanical methods (grand partition function). This procedure affords microscopic definitions of the various intensive quantities which characterize the interface. Subsequently, we compare the expression for the surface tension with those proposed in the literature.