A Nonlocal Poisson-Fermi Model for Ionic Solvent

TL;DR

This paper introduces a nonlocal Poisson-Fermi model that incorporates ion size and water polarization effects, providing a more comprehensive approach to calculating electrostatic potentials in ionic solvents.

Contribution

It extends previous Poisson-Fermi models by including nonlocal dielectric effects and demonstrates the Fermi distribution as an energy-minimizing ionic concentration solution.

Findings

Numerical results show differences between Poisson-Fermi and Poisson solutions.

The model captures ion size effects and polarization correlations.

The solution involves a convolution with a Yukawa-type kernel.

Abstract

We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-type kernel function. Moreover, the Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy. Finally, numerical results are reported to show the difference between a Poisson-Fermi solution and a corresponding Poisson solution.