Electrostatic correlations in inhomogeneous electrolytes

The field-theoretic approach is used to obtain the self-consistent equations for inhomogeneuos symmetric electrolytes. The perturbative Green's function method is used to solve these self-consistent equations for an electrolyte in contact with a charged dielectric membrane wall up to one-loop level. We show that the perturbative solution includes the nonlinear correlation effects originating from the competition between the salt screening deficiency close to the membrane surface and charge uctuations in the ionic cloud. At biologically relevent model parameters, the correlation corrections give rise to the charge inversion phenomenon where the average electrostatistic potential changes its sign and the negatively charged membrane wall acquires an effective positive charge.