Charge inversion of colloids in an exactly solvable model

TL;DR

This paper presents an exactly solvable two-dimensional model demonstrating charge inversion in colloids, where divalent counterions overscreen a negatively charged macroion, with implications for understanding electrostatic interactions in electrolytes.

Contribution

It provides an exact analytical solution for the effective charge of a macroion in a charge-asymmetric electrolyte, revealing conditions for charge inversion.

Findings

Charge inversion occurs at high Coulombic coupling.

Counterion condensation threshold shifts to lower absolute values.

Effective charge can become positive despite macroion's negative charge.

Abstract

We study a two-dimensional model for a long cylindrical stiff charged macroion immersed in a charge-asymmetric electrolyte with charge ratio +2/-1. The model is integrable and it allows an exact analytical determination of the effective charge of the macroion, which characterizes the electrostatic potential at large distances (compared to the screening length) from the macroion. At at high coulombic coupling, this model predicts charge inversion: for a highly negatively charged macroion, the effective charge could become positive, indicating an overscreening of the macroion by the divalent counterions. By studying the behavior of the coions and counterions density profiles close to the macroion, we show that the counterion condensation threshold is shifted to a lower value in absolute value. This plays an important role in the charge inversion phenomenon.