Field theoretic calculation of the surface tension for a model electrolyte system

TL;DR

This paper presents a field theoretic calculation of the surface tension for a model electrolyte system, directly deriving the surface tension without thermodynamic integration, and recovers the Onsager-Samaras law with corrections.

Contribution

It introduces a direct field theoretic approach to compute electrolyte surface tension at first order, extending previous methods by avoiding thermodynamic integration.

Findings

Calculation regularized for epsilon_0 < epsilon

Recovers Onsager-Samaras law at h=0

Provides corrections for epsilon_0/epsilon ratio

Abstract

We carry out the calculation of the surface tension for a model electrolyte to first order in a cumulant expansion about a free field theory equivalent to the Debye-H\"uckel approximation. In contrast with previous calculations, the surface tension is calculated directly without recourse to integrating thermodynamic relations. The system considered is a monovalent electrolyte with a region at the interface, of width h, from which the ionic species are excluded. In the case where the external dielectric constant epsilon_0 is smaller than the electrolyte solution's dielectric constant epsilon we show that the calculation at this order can be fully regularized. In the case where h is taken to be zero the Onsager-Samaras limiting law for the excess surface tension of dilute electrolyte solutions is recovered, with corrections coming from a non-zero value of epsilon_0/epsilon.