# Structural interactions in ionic liquids linked to higher order Poisson-Boltzmann equations

## TL;DR

This paper derives generalized Poisson-Boltzmann equations from classical binary fluid mixture theories, linking microscopic interactions to macroscopic electrostatic models with potential applications in understanding ionic liquids.

## Contribution

It introduces a novel derivation of higher-order Poisson-Boltzmann equations using Legendre transforms, connecting microscopic fluid structure to electrostatic modeling.

## Key findings

- Reduction to a phenomenological equation under symmetry assumptions
- Structural interactions influence near-surface ion distributions
- Provides a theoretical framework for higher-order electrostatic equations

## Abstract

We present a derivation of generalized Poisson-Boltzmann equations starting {from} classical theories of binary fluid mixtures, employing an approach based on the Legendre transform as recently applied to the case of local descriptions of the fluid free energy. Under specific symmetry assumptions, and in the linearized regime, the Poisson-Boltzmann equation reduces to a phenomenological equation introduced by (Bazant et al., 2011), whereby the structuring near the surface is determined by bulk coefficients.