(1) Department of Physics, (2) Department of Chemistry, University of Illinois at Chicago, Chicago, IL 60607, USA. (3) Center for Advanced Radiation Sources, University of Chicago, Chicago, IL 60637, USA. (4) Department of Chemistry, University of California, Santa Cruz, CA 95064, USA. (5) Department of Chemistry and Biochemistry, Northern Illinois University, DeKalb, IL 60115, USA.
Mean field theories of ion distributions, such as the Gouy-Chapman theory that describes the distribution near a charged planar surface, ignore the molecular-scale structure in the liquid solution. The predictions of the Gouy-Chapman theory vary substantially from our x-ray reflectivity measurements of the interface between two electrolyte solutions. Molecular dynamics simulations, which include the liquid structure, were used to calculate the potential of mean force on a single ion. We used this potential of mean force in a generalized Poisson-Boltzmann equation to predict the full ion distributions. These distributions agree with our measurements without any adjustable parameters.