Fundamental new results in the energetics and thermodynamics of charged metal surfaces

There should be close scientific relationships between the following: the bonding energy of an atom or molecule at a curved surface; the Laplace–Young equation (the ‘equation for pressure difference across a curved surface’); the Kelvin equation (the ‘equation for vapour pressure above a curved surface’); and the thermodynamics of surface diffusion. This paper briefly reports some surprising new theoretical results obtained by reviewing these relationships, and inserting ‘atomic-type’ surface electrostatic energy terms into the expression for system potential energy. The two main results are as follows. First, the field dependence of atomic bonding energy is shown to be associated with a change in the electrical capacitance between the specimen and its surroundings, when the atom is removed. Good agreement is found between old experiments and the new theory. Second, when atomic-type effects are taken into account, new terms appear in the formula for pressure difference across a charged curved surface. These describe a field-dependent correction to the ‘surface tension’ term and a curvature-dependent correction to the Maxwell field stress term. The main consequences are: the concepts of ‘surface tension’ and ‘surface free energy’ become no longer equivalent; a small correction is needed to the Raleigh criterion for the stability of charged droplets; and a mathematical Taylor cone is no longer a hydrodynamic equilibrium shape.