Weak and Strong Coupling Theories for Polarizable Colloids and Nano-Particles

TL;DR

This paper develops weak and strong coupling theories to accurately predict counterion density profiles around polarizable colloids and nanoparticles, incorporating ion-image interactions and validated by Monte Carlo simulations.

Contribution

It introduces a unified theoretical framework for both monovalent and multivalent ions, explicitly accounting for ion-image interactions and boundary conditions.

Findings

Excellent agreement with Monte Carlo simulations

Weak-coupling theory captures ion-image effects for monovalent ions

Strong-coupling theory accurately describes multivalent ion distributions

Abstract

A theory is presented which allows us to accurately calculate the density profile of monovalent and multivalent counterions in suspensions of polarizable colloids or nano-particles. In the case of monovalent ions, we derive a weak-coupling theory that explicitly accounts for the ion-image interaction, leading to a modified Poisson-Boltzmann equation. For suspensions with multivalent counterions, a strong-coupling theory is used to calculate the density profile near the colloidal surface and a Poisson-Boltzmann equation with a renormalized boundary condition to account for the counterion distribution in the far-field. All the results are compared with the Monte Carlo simulations, showing an excellent agreement between the theory and the simulations.