Understanding depletion induced like-charge attraction from self-consistent field model

TL;DR

This study develops a self-consistent field model to explain like-charge attraction in electrolytes, revealing it results from electrostatic entropic forces enhanced by dielectric depletion, and depends on material and ionic parameters.

Contribution

The paper introduces an efficient algorithm based on self-consistent equations to accurately model like-charge attraction, incorporating electrostatic correlation and dielectric effects beyond mean-field theories.

Findings

Like-charge attraction is driven by electrostatic entropic forces.

Attraction is enhanced by dielectric depletion of mobile ions.

Interaction forces depend on permittivity, ionic size, valence, and salt concentration.

Abstract

The interaction force between likely charged particles/surfaces is usually repulsive due to the Coulomb interaction. However, the counterintuitive like-charge attraction in electrolytes has been frequently observed in experiments, which has been theoretically debated for a long time. It is widely known that the mean field Poisson-Boltzmann theory cannot explain or predict this anomalous feature since it ignores many-body properties. In this paper, we develop efficient algorithm and perform the force calculation between two interfaces using a set of self-consistent equations which properly takes into account the electrostatic correlation and the dielectric-boundary effects. By solving the equations and calculating the pressure with the Debye-charging process, we show that the self-consistent equations could be used to study the attraction between like-charge surfaces from weak-coupling to mediate-coupling regime, and that the attraction is due to the electrostatics-driven entropic force which is significantly enhanced by the dielectric depletion of mobile ions. A systematic investigation shows that the interaction forces can be tuned by material permittivity, ionic size and valence, and salt concentration, and that the like-charge attraction exists only for specific regime of these parameters.