# Comments on the linear modified Poisson-Boltzmann equation in electrolyte solution theory

## TL;DR

This paper presents three analytic solutions for a linearized modified Poisson-Boltzmann equation in electrolyte solutions, comparing predictions with experimental data and other theoretical models to understand electrostatic potential behavior at varying concentrations.

## Contribution

It introduces three analytic results for a linear form of the modified Poisson-Boltzmann equation and compares them with mean spherical approximation and experimental data.

## Key findings

- Electrostatic potential transitions from exponential to oscillatory with increasing concentration.
- Screening length decreases as concentration increases in the oscillatory regime.
- Comparison with experimental data shows qualitative agreement.

## Abstract

Three analytic results are proposed for a linear form of the modified Poisson-Boltzmann equation in the theory of bulk electrolytes. Comparison is also made with the mean spherical approximation results. The linear theories predict a transition of the mean electrostatic potential from a Debye-H\"{u}ckel type damped exponential to a damped oscillatory behaviour as the electrolyte concentration increases beyond a critical value. The screening length decreases with increasing concentration when the mean electrostatic potential is damped oscillatory. A comparison is made with one set of recent experimental screening results for aqueous NaCl electrolytes.