Interactions Between Charged Spheres in Divalent Counterion Solution

TL;DR

This study uses simulations to explore how charged spheres interact in divalent counterion solutions, revealing a phase transition and density fluctuations driven by electrostatic and hard core forces.

Contribution

It introduces a minimal model simulation approach to analyze effective interactions and phase behavior of charged spheres in divalent counterion solutions, connecting to recent experimental findings.

Findings

Strong attraction at high concentration

Global repulsion at dilute concentration

Indication of a first order phase transition

Abstract

We simulate model systems of charged spherical particles in their counterion solution and measure the thermodynamic pressure and the pair distribution function from which we derive effective potentials of mean force. For a system with only electrostatic and hard core interactions, we investigate the effective potential between two like-charged spheres in divalent counterion solution as a function of concentration. We find a strong attractive interaction for high concentration and a global repulsive effective interaction for dilute systems. The results indicate a first order phase transition in sphere-counterion density as a function of global concentration and the effective sphere-sphere potentials in the dilute (solvated) regime suggest significant density fluctuations due to short range local minima in the effective energy surface. Our results arise from a minimal approach model of several recent experiments on polystyrene latex particles in monovalent counterion solution.