Dependence of surface stress, surface energy and surface tension on potential and charge
- 16 November 2007
- journal article
- research article
- Published by Royal Society of Chemistry (RSC) in Physical Chemistry Chemical Physics
- Vol. 10 (1), 168-177
- https://doi.org/10.1039/b710065e
Abstract
A toy model and simple model functions are used to exemplify the relation between surface tension, surface energy and surface stress given by Shuttleworth’s equation. Variations of the surface tension of charged interfaces must obey Lippmann’s equation. Variations Δf of the surface stress of electrodes would be either equal to or proportional to and smaller than those variations Δγ of the surface tension, if the potential of zero charge (pzc) did not depend on the surface strain ε. However, since the pzc E0 is a function of strain ε, the basic dependence of the surface stress on the charge, f(q), is described by a sum of three terms: the first one is the surface stress of the uncharged surface. The second one varies linearly with the surface tension, γ(q), as long as the amount of specific adsorption remains constant, and is quadratic in E and q for a potential-independent double layer capacitance. The third summand that contributes to f(q) is linear in q and is a direct consequence of the potential dependence E0(ε) of the pzc. This result should help to resolve the seeming discrepancy between previous work on the surface stress changes of electrodes: Most experimental and theoretical results supported either the view that the variations of surface stress are identical or similar to that of surface tension, i.e. have essentially a quadratic dependence on the electrode potential, or that the basic dependence is a linear function of the charge. The more comprehensive model description presented here allows an explanation of the different results and their seeming discrepancies without assuming experimental errors or fundamental thermodynamic problems. Furthermore, an estimate of the potential dependence of the surface modulus can be obtained.Keywords
This publication has 62 references indexed in Scilit:
- Thermodynamic issues associated with combined cyclic voltammetry and wafer curvature measurements in electrolytesJournal of Solid State Electrochemistry, 2005
- Balance of Force at Curved Solid Metal−Liquid Electrolyte InterfacesLangmuir, 2005
- Simultaneous oscillations of surface energy, superficial mass and electrode potential in the course of galvanostatic oxidation of formic acidJournal of Solid State Electrochemistry, 2005
- Charge‐Induced Reversible Strain in a Metal.ChemInform, 2003
- Study of Adsorption of Iodide Ions on Gold Electrode by a Laser‐Beam Deflection Method Compared with a Piezoelectric TechniqueJournal of the Electrochemical Society, 1999
- The role of surface stress in reconstruction, epitaxial growth and stabilization of mesoscopic structuresSurface Science Reports, 1997
- A new interferometric method to investigate surface energies at solid electrodesElectrochimica Acta, 1994
- The study of specific adsorption of a polar solvent at solid electrodes by means of step elastic stretching under potentiostatic conditionsElectrochimica Acta, 1991
- Piezoelectric Response to Surface Stress Change of Gold Electrode in Sulfate Aqueous SolutionsJournal of the Electrochemical Society, 1987
- Anisotropy of the Electronic Work Function of MetalsPhysical Review B, 1941