Potential of zero charge and surface charging relation of metal-solution interphases from a constant-potential jellium-Poisson-Boltzmann model

The potential of zero charge (pzc), a fundamental concept in interfacial electrochemistry, is revisited using a jellium-Poisson-Boltzmann model. Under constant-potential description of the metal-solution interphase, this model is able to calculate the surface charging relation (surface free charge density as a function of the electrode potential) and then to determine the pzc therefrom. The potential corresponding to the minimum of differential double-layer capacitance curve is shown to be lower than the pzc determined from surface charging relation, which is caused by free metal electrons entering the solution phase. The model further reveals that the pzc decreases when the vacuum gap between the solution phase and the metal surface, $d$, becomes narrower. This is consistent with the common observation that the pzc of metal-solution interphase is lower than that calculated from the work function of metal-vacuum interphase (the latter corresponds to $d=\ensuremath{\infty})$. Multifaceted roles played by the solvent, including electrostatic screening, polaron effect, and orthogonalizational repulsion, are analyzed. Also discussed are the effects of specific adsorption of ions and potential-dependent $d$ on the surface charging relation.