Poisson-Boltzmann theory with non-linear ion correlations

TL;DR

This paper introduces a new non-linear Poisson-Boltzmann model incorporating ion correlations via Green's function, improving agreement with molecular dynamics simulations over traditional linear self-energy approaches.

Contribution

A novel non-linear self-energy formulation for the Poisson-Boltzmann equation that better captures ion correlations and aligns with molecular dynamics results.

Findings

The non-linear model matches MD simulations for ion distributions.

Linear self-energy equations deviate significantly from MD results.

The new approach improves modeling of ionic systems with high concentration or charge valence.

Abstract

The Poisson-Boltzmann (PB) theory is widely used to depict ionic systems. As a mean-field theory, the PB theory neglects the correlation effect in the ionic atmosphere and leads to deviations from experimental results as the concentration or charge valance increases. A modified PB theory including ion correlation effect while retaining its simplicity is critical for many important applications in which ion correlation effect can be significant. In this paper, we present a new model to incorporate ion correlations into the original PB equation by utilizing the Green's function with a non-linear form of the self-energy, which is different from the linear self-energy equation obtained by the Field-Theoretic (FT) approach. Both equations are solved numerically and compared with our molecular dynamics (MD) simulation. The co-ion distribution calculated by the FT approach deviates significantly from the MD simulation, while our results for both counter-ion and co-ion distributions are justified by the MD simulation.