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

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-Hückel 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 ϵ₀ is smaller than the electrolyte solution’s dielectric constant ϵ 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 nonzero value of ϵ₀∕ϵ.