Thermodynamics of interface elasticity

Abstract

We generalize and extend a series of articles on the thermodynamics of interface elasticity. The whole formulation is based on taking into account a finite elastic deformation. This leads to generalized forms of the equations for the surface excess of the internal energy, the Gibbs adsorption equation and the Shuttleworth equation. In all cases correction terms occur containing the strain tensor. Although the deformation might be small, the corrections are critical in performing derivatives with respect to the strain which are needed to obtain equations connecting measurable quantities. These consequences are demonstrated in detail for the simple case of the spherical electrode. In the traditional electrochemical treatment, the densities of extensive quantities are related to the deformed surface, which is usually not mentioned. In analogy to the theory of volume elasticity, where the densities are related to the unstrained solid, one can also relate the densities of surface excess quantities to the unstrained surface. This formulation gives at first an additional proof for some of the generalized equations. Moreover, within this formulation one can express the surface excess of the energy density by the superficial work of the unstrained surface and three surface elastic constants, two of them being the surface Lamé constants. In the alternative formulation, the Shuttleworth equation appears simply as the relation between a generalized force and a generalized potential.