Incorporation of excluded volume correlations into Poisson-Boltzmann theory

TL;DR

This paper enhances the Poisson-Boltzmann theory by incorporating non-local excluded volume effects, improving predictions of electrolyte distributions around macroions compared to traditional local density approaches.

Contribution

It introduces a non-local excess free energy method for excluded volume interactions, outperforming local density functionals and standard PB theory in accuracy.

Findings

Non-local weighted density approach agrees well with Monte Carlo simulations.

Standard local density theories deviate more from simulation results.

The new method captures layering effects in electrolyte distributions.

Abstract

We investigate the effect of excluded volume interactions on the electrolyte distribution around a charged macroion. First, we introduce a criterion for determining when hard-core effects should be taken into account beyond standard mean field Poisson-Boltzmann (PB) theory. Next, we demonstrate that several commonly proposed local density functional approaches for excluded volume interactions cannot be used for this purpose. Instead, we employ a non-local excess free energy by using a simple constant weight approach. We compare the ion distribution and osmotic pressure predicted by this theory with Monte Carlo simulations. They agree very well for weakly developed correlations and give the correct layering effect for stronger ones. In all investigated cases our simple weighted density theory yields more realistic results than the standard PB approach, whereas all local density theories do not improve on the PB density profiles but on the contrary, deviate even more from the simulation results.