General theory of asymmetric steric interactions in electrostatic double layers

TL;DR

This paper extends the Poisson-Boltzmann framework to dense charged fluids by incorporating steric effects through a generalized lattice gas model with Flory-Huggins entropy, comparing it to other equations of state.

Contribution

It introduces a novel approach to model steric effects in electrostatic double layers using a generalized lattice gas theory with Flory-Huggins entropy, and compares it to existing models like Carnahan-Starling.

Findings

Strong differences in free energy shapes between models

Slow, power-law convergence at high potentials in Carnahan-Starling model

Constructed convex free energy functions for easier numerical minimization

Abstract

We study the Poisson-Boltzmann equation in the context of dense charged fluids where steric effects become important. We generalise the lattice gas theory by introducing a Flory-Huggins entropy for ions of differing volumes and then compare the effective free energy density to other approximations, valid for more realistic equations of state, such as the Carnahan-Starling approximation and find strong differences in the shapes of the free energy functions. We solve the Carnahan-Starling model in the high density limit, and demonstrate a slow, power-law convergence at high potentials. We elucidate how equivalent convex free energy functions can be constructed that describe steric effects in a manner which is more convenient for numerical minimisation.