Like-charge colloidal attraction: a simple argument

TL;DR

This paper presents a simple length scale analysis demonstrating how like-charge colloidal particles can attract each other due to counter-ion unbinding at high Coulombic couplings, providing an accessible explanation of this counterintuitive phenomenon.

Contribution

It offers a minimal formalism and exact treatment to explain like-charge attraction through counter-ion unbinding at strong Coulombic interactions.

Findings

Counter-ion unbinding occurs at large Coulombic couplings.

Attractive interactions emerge from unbinding phenomena.

The approach simplifies understanding of colloidal attraction mechanisms.

Abstract

By a length scale analysis, we study the equilibrium interactions between two like-charge planes confining neutralising counter-ions. At large Coulombic couplings, approaching the two charged bodies leads to an unbinding of counter-ions, a situation that is amenable to an exact treatment. This phenomenon is the key to attractive effective interactions. A particular effort is made for pedagogy, keeping equations and formalism to a minimum.