On the contact conditions for the charge profile in the theory of the electrical double layer for nonsymmetrical electrolytes

TL;DR

This paper derives exact expressions for the contact values of charge and density profiles in the electrical double layer for nonsymmetrical electrolytes, highlighting the roles of bulk and surface contributions.

Contribution

It introduces a new framework expressing contact values as sums of bulk, surface, and electrostatic stress contributions, extending understanding for nonsymmetrical electrolytes.

Findings

Contact value of charge profile is a sum of three contributions.

Bulk term dominates in charge asymmetry cases.

Exact expressions for coion and counterion profiles are derived.

Abstract

The contact value of the charge profile for nonsymmetrical electrolytes is presented as the sum of three contributions. One of them is the normal component of the Maxwell electrostatic stress tensor. The second one is the surface electrostatic property defined as the integral of the product of the gradient of the electrical potential and the density distribution function of coions. The third term is the bulk contribution defined by the sum for anions and for cations of the product of their charge and their partial pressure. For noncharged surfaces only the last two are present and have the same sign in the case of size asymmetry. In the case of charge asymmetry the contact value of the charge profile is the result of the competitions of bulk and surface terms in which the bulk term is dominant. Using both the contact theorems for the density and the charge profiles, the exact expressions for the contact values of the profiles of coions and counterions are obtained and some related properties are discussed.