Surface potentials of conductors in electrolyte solutions

When we place conducting bodies in electrolyte solutions, their surface potential Φs appears to be much smaller in magnitude than the applied one Φ0 and normally does not obey the classical electrostatic boundary condition of a constant potential expected for conductors. In this paper, we demonstrate that an explanation of these observations can be obtained by postulating that diffuse ions condense at the "wall" due to the reduced permittivity of a solvent. For small values of Φ0, the surface potential responds linearly. On increasing Φ0 further, Φs augments nonlinearly and then saturates to a constant value. Analytical approximations for Φs derived for these three distinct modes show that it always adjusts to salt concentration, which is equivalent to a violation of the constant potential condition. The latter would be appropriate for highly dilute solutions but only if Φ0 is small. Surprisingly, when the plateau with high Φs is reached, the conductor surface switches to a constant charge density condition normally expected for insulators. Our results are directly relevant for conducting electrodes, mercury drops, colloidal metallic particles, and more.