Steric Effects in Electrolytes: A Modified Poisson-Boltzmann Equation

TL;DR

This paper introduces a modified Poisson-Boltzmann equation accounting for ion size, providing analytical solutions that explain ion saturation at high surface charges, aligning with experimental observations.

Contribution

It presents a generalized Poisson-Boltzmann model incorporating finite ion size, offering analytical expressions for potential and concentration at charged surfaces.

Findings

Ionic concentration saturates at high surface charge densities.

The model's predictions agree with recent experimental data.

Analytical solutions for electrostatic potential are derived.

Abstract

The adsorption of large ions from solution to a charged surface is investigated theoretically. A generalized Poisson--Boltzmann equation, which takes into account the finite size of the ions is presented. We obtain analytical expressions for the electrostatic potential and ion concentrations at the surface, leading to a modified Grahame equation. At high surface charge densities the ionic concentration saturates to its maximum value. Our results are in agreement with recent experiments.