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

In this paper, we generalize a recently derived expression of the contact value of the charge profile for the case of nonsymmetrical electrolytes. For the electrolytes with a single type of cation and anion, this relation can be 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, which is 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, which is 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 terms 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. A semiempirical expression of the contact value of the charge profile is discussed in relation to our exact result.