Charge ordering in ionic fluids mediate repulsive surface interactions

Recent experiments on ionic fluids, such as surface force measurements in organic ionic liquids \footnote[3]{Smith, A. M., Lee, A. A. \& Perkin, S., J. \emph{Phys. Chem. Lett.}, {\bf 7 (12)}, 2157 (2016)} and the observation of colloidal stability in inorganic molten salts \footnote[4]{Zhang, H. \emph{et al.}, accepted at \emph{Nature} (2016)}, suggest the presence of long-ranged repulsive forces. These cannot be explained within the classical Debye-H{\"u}ckel theory for dilute electrolytes. We argue that such repulsive interactions can arise from long-range (several \emph{nm}) charge density oscillations induced by a surface that preferentially binds one of the ionic species in an ionic fluid. We present a continuum theory that accounts for such charge layering based on a frustrated Ising model that incorporates both long-range Coulombic and short-range steric interactions. The mean-field analytic treatment qualitatively matches results from molecular simulations. A careful analysis of the ionic correlation functions arising from such charge ordering may also explain the long electrostatic screening lengths observed in various ionic fluids and their non-monotonic dependence on the electrolyte concentration.