Adsorption of Large Ions from an Electrolyte Solution: A Modified Poisson-Boltzmann Equation

TL;DR

This paper introduces a modified Poisson-Boltzmann equation that accounts for ion size and solvent entropy, providing insights into large ion adsorption and surface charge interactions.

Contribution

It presents a new theoretical model incorporating steric effects into the Poisson-Boltzmann equation for electrolyte solutions near charged surfaces.

Findings

Steric effects lead to saturated ion layers near surfaces.

A modified Grahame equation relates surface charge to ion concentration.

The model explains adsorption behavior of large ions on charged monolayers.

Abstract

The behavior of electrolyte solutions close to a charged surface is studied theoretically. A modified Poisson-Boltzmann equation which takes into account the volume excluded by the ions in addition to the electrostatic interactions is presented. In a formal lattice gas formalism the modified Poisson-Boltzmann equation can be obtained from a mean-field approximation of the partition function. In an alternative phenomenological approach, the same equation can be derived by including the entropy of the solvent molecules in the free energy. In order to visualize the effect of the steric repulsion, a simple case of a single, highly charged, flat surface is discussed. This situation resembles recent adsorption experiments of large ions onto a charged monolayer. A simple criterion for the importance of the steric effects is expressed in terms of the surface charge density and the size of the ions. It is shown that when these effects are important a saturated layer is formed near the surface. A modified Grahame equation relating the ion concentration at the surface to the surface charge density is obtained.