The two loop calculation of the disjoining pressure of a symmetric electrolyte soap film

TL;DR

This paper performs a two-loop calculation of the disjoining pressure in a symmetric electrolyte soap film, revealing finite results without cut-offs and identifying significant non-perturbative corrections at large film thicknesses.

Contribution

It introduces a two-loop calculation method for the disjoining pressure in electrolyte soap films, including a resummation technique and analysis of non-analytic contributions.

Findings

Disjoining pressure is finite without short distance cut-off.

Two-loop correction exceeds one-loop at large film thicknesses.

Identifies non-analytic g*ln(g) contribution.

Abstract

In this paper we consider the two-loop calculation of the disjoining pressure of a symmetric electrolytic soap film. We show that the disjoining pressure is finite when the loop expansion is resummed using a cumulant expansion and requires no short distance cut-off. The loop expansion is resummed in terms of an expansion in g=l_B/l_D where l_D is the Debye length and l_B is the Bjerrum length. We show that there there is a non-analytic contribution of order g*ln(g). We also show that the two-loop correction is greater than the one-loop term at large film thicknesses suggesting a non-perturbative correction to the one-loop result in this limit.