Description beyond the mean field approximation of an electrolyte confined between two planar metallic electrodes

TL;DR

This paper develops a beyond mean field theoretical description of an electrolyte confined between metallic electrodes, analyzing the effects of different boundary models on disjoining pressure and internal profiles.

Contribution

It introduces a more realistic model for metallic boundaries considering thermal fluctuations, extending beyond the traditional mean field approximation.

Findings

Disjoining pressure is positive and scales as 1/W^3 for ideal conductors.

Disjoining pressure is negative with exponential decay for good conductors.

Density and potential profiles inside the electrolyte are identical in both boundary models.

Abstract

We study an electrolyte confined in a slab of width $W$ composed of two grounded metallic parallel electrodes. We develop a description of this system in a low coupling regime beyond the mean field (Poisson--Boltzmann) approximation. There are two ways to model the metallic boundaries: as ideal conductors in which the electric potential is zero and it does not fluctuate, or as good conductors in which the average electric potential is zero but the thermal fluctuations of the potential are not zero. This latter model is more realistic. For the ideal conductor model we find that the disjoining pressure is positive behaves as $1/W^3$ for large separations with a prefactor that is universal, i.e. independent of the microscopic constitution of the system. For the good conductor boundaries the disjoining pressure is negative and it has an exponential decay for large $W$. We also compute the density and electric potential profiles inside the electrolyte. These are the same in both models. If the electrolyte is charge asymmetric we find that the system is not locally neutral and that a non-zero potential difference builds up between any electrode and the interior of the system although both electrodes are grounded.