Non-equilibrium steady states of electrolyte interfaces

TL;DR

This paper analytically investigates non-equilibrium steady states of electrolyte interfaces using Poisson-Nernst-Planck theory, deriving explicit expressions for electric fields, charge densities, and capacitance, and addressing unphysical solutions.

Contribution

It provides exact analytical solutions for electrolyte steady states under electric currents and establishes criteria to identify unphysical solutions.

Findings

Derived current-dependent differential capacitance expressions.

Reduced to Gouy-Chapman results at zero current.

Identified boundary conditions leading to unphysical negative ion densities.

Abstract

The non-equilibrium steady states of a semi-infinite quasi-one-dimensional univalent binary electrolyte solution, characterised by non-vanishing electric currents, are investigated by means of Poisson-Nernst-Planck (PNP) theory. Exact analytical expressions of the electric field, the charge density and the number density are derived, which depend on the electric current density as a parameter. From a non-equilibrium version of the Grahame equation, which relates the total space charge per cross-sectional area and the corresponding contribution of the electric potential drop, the current-dependent differential capacitance of the diffuse layer is derived. In the limit of vanishing electric current these results reduce to those within Gouy-Chapman theory. It is shown that improperly chosen boundary conditions lead to non-equilibrium steady state solutions of the PNP equations with negative ion number densities. A necessary and sufficient criterion on surface conductivity constitutive relations is formulated which allows one to detect such unphysical solutions.