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.

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