Connection of the generalized Shuttleworth equation for the elastic spherical electrode with the Laplace formula and the Gibbs adsorption equation

Abstract

The surface strain of a solid is related to the surface free energy (interfacial superficial work) by the Shuttleworth equation. Its generalization for the case of a finite surface strain has been derived only recently by one of the present authors (B.M.G). Now consequences are derived for the case of an elastic spherical electrode. At first, it is shown that this generalized form is in accordance with the Laplace formula connecting the capillary pressure with the surface stress. Further, the generalized Shuttleworth equation leads to an additional term in the Gibbs adsorption equation, which is of first order in the elastic strain. Whereas this first order term may be negligible in the adsorption equation itself even for non-infinitesimal strain, it leads to a significant modification when considering second order derivatives of surface charge and surface stress which are directly accessible in experiments. A reformulation is presented for changing variables and the applicability to small particles is discussed.