Beyond Poisson-Boltzmann: A self-consistent theory for electrical double layers

One outstanding challenge in the physical chemistry of electrolyte solutions is to capture the inhomogeneity in electrostatic correlation where either the ionic strength or the dielectric permittivity is spatially varying. A solution to this problem is critical to understanding many complex interfacial phenomena such as like-charge attraction and charge inversion, among many others. The standard mean-field Poisson-Boltzmann (PB) theory fails to explain even qualitatively these as it does not take electrostatic correlations and excluded volumes of molecules into account. Using the Gaussian Renormalized Fluctuation theory, we have developed a new method to self-consistently solve for inhomogeneous ionic fluctuations and dielectric variations via a self-energy term and the effect of excluded volume of ions and solvent through an incompressibility constraint. The first system we investigated using this method is the vapor-liquid interface of ionic fluids. For symmetric salts, the surface tension predicted by our theory is in quantitative agreement with the simulation data. Ours is also the first self-consistent theory to successfully explain the phenomena of charge inversion and like charge attraction in multivalent electrolytes. In quantitative agreement with experiments, the value of zeta potential is found to depend non-monotonically on the bulk salt concentration. For a system of two like-charged surfaces immersed in a multivalent salt solution our theory again correctly predicts an attractive electrostatic force. In agreement with simulations, we show that the strength of attraction varies non-monotonically with respect to bulk salt concentration. Our work provides the first explanation of the re-solubilization of charged colloidal aggregates consistent with the non-monotonic nature of the effective surface charge after inversion. In the future, we and our collaborators aim to understand polyelectrolyte brushes, ionic liquids, and surface tension at the air-water interface with this new method.