Weak non-linear surface charging effects in electrolytic films

TL;DR

This paper develops a Gaussian field theory model for electrolytic soap films, incorporating non-linear surface charge effects and fluctuations, revealing how surface charge and disjoining pressure depend on film thickness and parameters.

Contribution

It introduces a novel theoretical framework combining mean-field and fluctuation effects to analyze surface charge regulation in electrolytic films with a Stern layer.

Findings

Surface charge vanishes as film thickness approaches zero.

Fluctuation-induced Casimir-like attraction influences disjoining pressure.

Surface charge and pressure depend strongly on Stern layer thickness and parameters.

Abstract

A simple model of soap films with nonionic surfactants stabilized by added electrolyte is studied. The model exhibits charge regularization due to the incorporation of a physical mechanism responsible for the formation of a surface charge. We use a Gaussian field theory in the film but the full non-linear surface terms which are then treated at a one-loop level by calculating the mean-field Poisson-Boltzmann solution and then the fluctuations about this solution. We carefully analyze the renormalization of the theory and apply it to a triple layer model for a thin film with Stern layer of thickness $h$. For this model we give expressions for the surface charge $\sigma(L)$ and the disjoining pressure $P_d(L)$ and show their dependence on the parameters. The influence of image charges naturally arise in the formalism and we show that predictions depend strongly on $h$ because of their effects. In particular, we show that the surface charge vanishes as the film thickness $L \to 0$. The fluctuation terms about this class of theories exhibit a Casimir-like attraction across the film and although this attraction is well known to be negligible compared with the mean-field component for thick films in the presence of electrolyte, in the model studied here these fluctuations also affect the surface charge regulation leading to a fluctuation component in the disjoining pressure which has the same behavior as the mean-field component even for large film thickness.