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Electrostatic correlations in inhomogeneous charged fluids beyond loop expansion

Electrostatic correlation effects in inhomogeneous symmetric electrolytes are investigated within a previously developed electrostatic self-consistent (SC) theory (R.R. Netz and H. Orland, Eur. Phys.J. E 11, 301 (2003)). To this aim, we introduce two computational approaches that allow to solve the SC equations beyond the loop expansion. Both approaches can handle the case of dielectrically discontinuous boundaries where the one-loop theory is known to fail. By comparing the theoretical results obtained from these schemes with the results of the MC simulations that we ran for ions at neutral single dielectric interfaces as well as with previous MC data for charged interfaces, we first show that the weak coupling (WC) Debye-Huckel (DH) theory remains quantitatively accurate up to the bulk ion density rhob=0.01 M, whereas the SC theory exhibits a good quantitative accuracy up to rhob=0.2 M. Then, we derive from the perturbative SC scheme the one-loop theory of asymmetrically partitioned salt systems around a dielectrically homogeneous charged surface. It is shown that correlation effects originate in these systems from a competition between the salt screening loss at the interface driving the ions to the bulk region, and the interfacial counterion screening excess attracting them towards the surface. In the case of weak surface charges, the interfacial salt screening loss is the dominant effect. As a result, correlations decrease the MF density of both coions and counterions. With increasing surface charge, the surface-attractive counterion screening excess starts to dominate, and correlation effects amplify in this regime the MF density of both type of ions. We also show that at a characteristic value of the electrostatic coupling parameter, electrostatic correlations result in a charge inversion effect.