Non-mean-field screening by multivalent counterions

TL;DR

This paper demonstrates that multivalent counterions form a strongly correlated liquid on macroions, creating an image charge effect that cannot be explained by mean field theories, confirmed through Monte Carlo simulations.

Contribution

It introduces a non-mean-field approach showing how multivalent counterions induce an image charge effect, with Monte Carlo simulations confirming the phenomenon.

Findings

Counterions form a strongly correlated liquid on macroions.

An image charge potential energy exists due to counterion correlations.

The effective metallic surface is located above the SCL by the screening length.

Abstract

Screening of a strongly charged macroion by its multivalent counterions can not be described in the framework of mean field Poisson-Boltzmann (PB) theory because multivalent counterions form a strongly correlated liquid (SCL) on the surface of the macroion. It was predicted that a distant counterion polarizes the SCL as if it were a metallic surface and creates an electrostatic image. The attractive potential energy of the image is the reason why the charge density of counterions decreases faster with distance from the charged surface than in PB theory. Using the Monte Carlo method to find the equilibrium distribution of counterions around the macroion, we confirm the existence of the image potential energy. It is also shown that due to the negative screening length of the SCL, $-2\xi$, the effective metallic surface is actually above the SCL by $|\xi|$.