from the coexistence [14]. The approach used for a bulk system in Ref. [9] have been modified to account for a spatial variation of the volume fractions and, consequently, of the dielectric permittivity of the binary mixture. In addition, a surface term describing the interactions between the charged solutes and confining charged surfaces has been included. Using a mean-field approximation the density profiles and osmotic pressure between charged interfaces have been calculated. In order to investigate the influence of critical adsorption of ion-containing binary mix- tures on the distribution of ions near a single charged wall, we propose here an approach that starts from the microscopic theory. Within such an approach the Landau functional is derived rather than postulated, and it should describe correctly all the collective phenomena in the system that are consistent with the assumed interaction potentials. Hence, we can control all the assumptions on the fundamental level of interactions. In Sec. II A we intro- duce the lattice-gas model of a four-component mixture describing two species of the solvent and the positive and negative ions. The generic for this model, short-ranged interactions between all the species and between the species and the surface are assumed. From the lattice model we derive the continuum Landau-Ginzburg functional which is then supple- mented by electrostatic bulk and surface contributions. Contrary to previous approaches all parameters of our functional are expressed in terms of microscopic interactions. Our Landau functional is similar to the functionals in Refs. [9, 14], but more terms are present, and all the approximations are based on assumptions concerning types of interparticle in- teractions. In Sec. II B we derive Euler-Lagrange (EL) equations that allow to calculate the density and charge profiles on a mean-field level. Next, in Sec. III we solve the linearized EL equations (Sec. III A) and calculate the leading-order correction to them (Sec. III B) under the assumption of weak interactions with the surface, small amount of ions and weak surface charge. A discussion of our results is included. The summary and outlook are given in Sec. IV. 4