Surface Tension of Acid Solutions: Fluctuations beyond the Non-linear Poisson-Boltzmann Theory

TL;DR

This paper develops an analytical theory for the surface tension of acid solutions, incorporating ion-surface interactions and fluctuations beyond the non-linear Poisson-Boltzmann framework, aligning well with experimental data and the reverse Hofmeister series.

Contribution

It introduces a loop-expansion method to account for fluctuations beyond mean-field in surface tension calculations for acids and salts.

Findings

Theory fits a wide range of acids and salts.

Results agree with the reverse Hofmeister series.

Provides a generalized Onsager-Samaras result.

Abstract

We extend our previous study of surface tension of ionic solutions and apply it to the case of acids (and salts) with strong ion-surface interactions. These ion-surface interactions yield a non-linear boundary condition with an effective surface charge due to adsorption of ions from the bulk onto the interface. The calculation is done using the loop-expansion technique, where the zero-loop (mean field) corresponds of the non-linear Poisson-Boltzmann equation. The surface tension is obtained analytically to one-loop order, where the mean-field contribution is a modification of the Poisson-Boltzmann surface tension, and the one-loop contribution gives a generalization of the Onsager-Samaras result. Our theory fits well a wide range of different acids and salts, and is in accord with the reverse Hofmeister series for acids.