# Continuum theory of electrostatic correlations at charged surfaces

## TL;DR

This paper develops a continuum electrostatic correlation theory at charged surfaces, extending existing models to better predict ion behavior in complex electrolytes beyond the Poisson-Boltzmann approximation.

## Contribution

It introduces a boundary condition and scaling laws within the Bazant-Storey-Kornyshev framework, improving predictions for correlated electrolytes at charged interfaces.

## Key findings

- Accurately reproduces Monte Carlo simulation results across coupling regimes.
- Provides a predictive continuum model for correlated electrolytes.
- Extensible to complex electrolyte and ionic liquid models.

## Abstract

The standard model for diffuse charge phenomena in colloid science, electrokinetics and biology is the Poisson-Boltzmann mean-field theory, which breaks down for multivalent ions and large surface charge densities due to electrostatic correlations. In this paper, we formulate a predictive continuum theory of correlated electrolytes based on two extensions of the Bazant-Storey-Kornyshev (BSK) framework: (i) a physical boundary condition enforcing continuity of the Maxwell stress at a charged interface, which upholds the Contact Theorem for dilute primitive-model electrolytes, and (ii) scaling relationships for the correlation length, for a one-component plasma at a charged plane and around a cylinder, as well as a dilute z:1 electrolyte screening a planar surface. In these cases, the theory accurately reproduces Monte Carlo simulation results from weak to strong coupling, and extensions are possible for more complex models of electrolytes and ionic liquids.