Surface Stress and Electrocapillarity of Solid Electrodes

There are two fundamental excess thermodynamic parameters that characterize a surface, the surface free energy and the surface stress. The surface free energy is the reversible work per unit area to form new surface while maintaining a constant equilibrium density of surface atoms. The surface stress is the reversible work per unit area required to form new surface by elastic deformation of a preexisting surface, and thus the atom density is altered. For a fluid surface the surface free energy is equal to the surface stress, but for a solid this is in general not true. We develop thermodynamic arguments that describe proper interpretations of wafer curvature experiments that are typically used in electrocapillarity experiments of solid electrodes. Additionally, we consider stress evolution during underpotential deposition. The sources of stress relate to electrocapillarity differences between overlayer and substrate, interface stress, and coherency stress. Experimental results are presented for the systems Pb2+/Au(111), Pb2+/ Ag(111), and Ag+/Au(111). We show how it is possible to use the experimental data to extract results for the interface stresses in each of these systems. The following values of interface stress were determined: for the incommensurate Pb/Au(111) interface, 1.76 ± 0.04 N/m; for the incommensurate Pb/Ag(111) interface, 0.9 ± 0.04 N/m; and for the coherent Ag/Au(111) interface, −0.08 ± 0.04 N/m. Finally, we employ the thermodynamic arguments developed to consider two important problems in the electrocapillarity of solids. The first is a comparison of the magnitude of the change in surface free energy and surface stress that result from pure double − layer effects. The second is the potential-induced 23 × √3 ⇔ (111) reconstruction that occurs on Au surfaces. Here, we calculate the difference in surface stress between the reconstructed and unreconstructed surface, obtaining −0.43 N/m, which compares favorably with recently published experimental results.