Gibbs paradox and a possible mechanism of like-charge attraction in colloids

TL;DR

This paper revisits the Gibbs paradox to propose an entropic mechanism that could explain like-charge attraction in colloids, highlighting a residual entropy effect that influences macroion interactions.

Contribution

It introduces a novel entropic explanation for like-charge attraction based on residual entropy from the Gibbs paradox, applicable to colloidal systems.

Findings

Residual entropy contributes to free energy decrease.

The entropic effect is on the order of a few thermal energies.

This mechanism may explain observed like-charge attractions.

Abstract

Based on a reconsideration of the Gibbs paradox, we show that a residual, non-extensive term in entropy turns up upon mixing identical particles, whether they are indistinguishable or not. The positive contribution from this residual entropy leads to a decrease in free energy, and we suggest that this entropic mechanism may serve as a source of like-charge attractions between a pair of colloidal particles or other macroions. For a system of two colloidal particles along with their neutralizing counterions, such decrease in free energy is of a few thermal energies and therefore crucial to the effective interaction between the particles.