amplitude n$_{1}$ of the decay of the ion density, η = n$_{1}$ exp( − z/ξ$_{b}$ ), and otherwise depends only on the dominant lengths in the system, the bulk correlation length ξ$_{b}$ and the Debye screening length 1 /κ . We find that due to the critical adsorption of that component of the solvent in which the ions are preferentially dissolved, the amount of counterions in the layer near the charged surface of the thickness of the Debye screening length is increased with respect to the one away from the critical point. Critical adsorption of the better solvent enhances screening whereas the critical adsorption of the poorer solvent leads to the opposite effect. This approach is quantitatively valid provided the Debye screening length is large, the surface-charge density is small, and the surface fields are weak. We expect the same trend beyond the approximate perturbation expansion solution. This will be studied further by the numerical treatment of the full EL equations. We should note that our theory shows that the leading-order correction to the Debye- H¨ uckel form of the charge profile is determined by the average dielectric constant, i.e., the spatial variation of the dielectric constant can be neglected when κ ≪ 1 (in units of inverse molecular size). Finally, the change of the charge distribution near the charged surface occuring upon ap- proaching the critical point of the binary solvent, indicates that in the confining geometries, i.e., for systems between two surfaces, the effective interactions between the confining sur- faces will be altered. Our predictions will be tested in the future work by explicit calculations and by comparison with the experimental data of Ref. [7]. Acknowledgments We would like to thank S. Dietrich, M. Bier, L. Helden and C. Bechinger for discussions. The work of AC was partially supported by the Polish Ministry of Science and Higher Education, Grant No NN 202 006034. [1] K. Binder, in Phase Transitions and Critical Phenomena , edited by C. Domb and J. L. Lebowitz (Academic, London, 1983), Vol. 8, p.1. [2] H. W. Diehl, in Phase Transitions and Critical Phenomena , edited by C. Domb and J. L. Lebowitz (Academic, London, 1986), Vol. 10, p. 76. [3] M. E. Fisher and P. G. de Gennes, C. R. Acad. Sci. Ser. B 287 , 207 (1978). [4] Supercritical Fluids – Fundamentals and Applications , edited by E. Kiran, P. G. Debenedetti 23