  The study of the electrical double layer lies at the heart of colloidal and
interfacial science. The standard mean-field Poisson-Boltzmann (PB) theory is
incapable of modeling many phenomena originated from ion correlation. An
important example is charge inversion or overcharging of electrical double
layers in multivalent electrolyte solutions. Existing theories aiming to
include correlations cannot capture the nonmonotonic dependence of charge
inversion on salt concentration because they have not systematically accounted
for the inhomogeneous nature of correlations from surface to the bulk and the
excluded volume effect of ions and solvent molecules. In this work, we modify
the Gaussian renormalized fluctuation theory by including the excluded volume
effect to study ion condensation and charge inversion. A boundary layer
approach is developed to accurately model the giant difference in ion
correlations between the condensed layer near the surface and the diffuse layer
outside. The theory is used to study charge inversion in multivalent
electrolytes and their mixtures. We predict a surface charge induced formation
of a three-dimensional condensed layer, which is necessary but not sufficient
for charge inversion. The value of the effective surface potential is found to
depend non-monotonically on the bulk salt concentration. Our results also show
a non-monotonic reduction in charge inversion in monovalent and multivalent
electrolyte mixtures. Our work is the first to qualitatively reproduce
experimental and simulation observations and explains the underlying physics.

Soft Condensed Matter;Materials Science;Statistical Mechanics