A close look into the excluded volume effects within a double layer

TL;DR

This paper investigates how steric interactions influence ionic distributions near charged surfaces, revealing limitations of local density functionals and deriving an analytical expression for the double layer's differential capacitance.

Contribution

It introduces a weighted density approximation to better account for steric effects and provides an analytical formula for contact electrostatic potential and capacitance.

Findings

Local density functionals fail near charged walls with large ions

Weighted density approximation improves modeling of steric effects

Derived analytical expression for differential capacitance

Abstract

We explore the effect of steric interaction on the ionic density distribution near a charged hard wall. For weakly charged walls, small particles, and monovalent ions the mean-field Poisson-Boltzmann equation provides an excellent description of the density profiles. For large ions and large surface charges, however, deviations appear. To explore these, we use the density functional theory. We find that local density functionals are not able to account for steric interactions near a wall. Based on the weighted density approximation we derive a simple analytical expression for the contact electrostatic potential which allows us to analytically calculate the differential capacitance of the double layer.