Ion-ion correlations: an improved one-component plasma correction

TL;DR

This paper introduces an improved free energy correction for ionic correlations in plasma models, addressing stability issues and better matching molecular dynamics simulations for charged systems.

Contribution

It proposes a new thermodynamically stable free energy correction based on a modified Debye-Hückel approach, improving upon previous theories for ionic correlations.

Findings

The new correction avoids the structuring catastrophe of previous models.

It accurately accounts for correlations in a charged rod system.

The model aligns well with molecular dynamics simulation results.

Abstract

Based on a Debye-Hueckel approach to the one-component plasma we propose a new free energy for incorporating ionic correlations into Poisson-Boltzmann like theories. Its derivation employs the exclusion of the charged background in the vicinity of the central ion, thereby yielding a thermodynamically stable free energy density, applicable within a local density approximation. This is an improvement over the existing Debye-Hueckel plus hole theory, which in this situation suffers from a "structuring catastrophe". For the simple example of a strongly charged stiff rod surrounded by its counterions we demonstrate that the Poisson-Boltzmann free energy functional augmented by our new correction accounts for the correlations present in this system when compared to molecular dynamics simulations.