# Poisson-Fermi Formulation of Nonlocal Electrostatics in Electrolyte Solutions

## TL;DR

This paper introduces a nonlocal Poisson-Fermi electrostatic model that incorporates steric and correlation effects in electrolyte solutions, improving upon classical models for biological and chemical systems.

## Contribution

It develops a novel nonlocal electrostatic formulation using a Fermi-like distribution to account for steric and correlation effects in electrolyte solutions.

## Key findings

- Nonlocal Poisson-Fermi results better match experimental data.
- Model captures ion selectivity in potassium channels.
- Links atomic-scale structures with macroscopic electrostatics.

## Abstract

We present a nonlocal electrostatic formulation of nonuniform ions and water molecules with interstitial voids that uses a Fermi-like distribution to account for steric and correlation effects in electrolyte solutions. The formulation is based on the volume exclusion of hard spheres leading to a steric potential and Maxwell's displacement field with Yukawa-type interactions resulting in a nonlocal electric potential. The classical Poisson-Boltzmann model fails to describe steric and correlation effects important in a variety of chemical and biological systems, especially in high field or large concentration conditions found in and near binding sites, ion channels, and electrodes. Steric effects and correlations are apparent when we compare nonlocal Poisson-Fermi results to Poisson-Boltzmann calculations in electric double layer and to experimental measurements on the selectivity of potassium channels for K+ over Na+. The present theory links atomic scale descriptions of the crystallized KcsA channel with macroscopic bulk conditions. Atomic structures and macroscopic conditions determine complex functions of great importance in biology, nanotechnology, and electrochemistry.