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.

Synchrotron x-ray reflectivity is used to study the interface between bulk water and bulk n-alkanes with carbon numbers 6 through 10, 12, 16, and 22. For all interfaces, except the water-hexane interface, the interfacial width disagrees with the prediction from capillary-wave theory. The variation of interfacial width with carbon number can be described by combining the capillary-wave prediction for the width with a contribution from intrinsic structure. This intrinsic structure is determined by the gyration radius for the shorter alkanes and by the bulk correlation length for the longer alkanes.