The renormalized jellium model for spherical and cylindrical colloids

TL;DR

This paper introduces a renormalized jellium model for spherical and cylindrical colloids that simplifies the mean-field description by using a homogeneous background, accurately predicting pressure and effective charge with good agreement to simulations.

Contribution

The paper presents a self-consistent renormalized jellium model that improves upon traditional approaches by accurately capturing the density-dependent effective charge of colloids.

Findings

Good agreement with Monte Carlo simulations.

Provides an analytical expression for the equation of state.

Offers an alternative to the Poisson-Boltzmann cell model.

Abstract

Starting from a mean-field description for a dispersion of highly charged spherical or (parallel) rod-like colloids, we introduce the simplification of a homogeneous background to include the contribution of other polyions to the static field created by a tagged polyion. The charge of this background is self-consistently renormalized to coincide with the polyion effective charge, the latter quantity thereby exhibiting a non-trivial density dependence, which directly enters into the equation of state through a simple analytical expression. The good agreement observed between the pressure calculated using the renormalized jellium and Monte Carlo simulations confirms the relevance of the {renormalized} jellium model for theoretical and experimental purposes and provides an alternative to the Poisson-Boltzmann cell model since it is free of some of the intrinsic limitations of this approach.