Surface potentials of conductors in electrolyte solutions

Abstract

When we place conducting bodies in electrolyte solutions, their surface potential $\Phi_s$ appears to be much smaller in magnitude than the intrinsic one $\Phi_0$ and normally does not obey the classical electrostatic boundary condition of a constant surface 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 a reduced permittivity of a solvent. For small values of $\Phi_0$ the surface potential responds linearly. On increasing $\Phi_0$ further $\Phi_s$ augments nonlinearly and then saturates to a constant value. Analytical approximations for $\Phi_s$ 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 $\Phi_0$ is small. Surprisingly, when the plateau with high $\Phi_s$ 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.