When salts are added in small quantities to an aqueous solution, its surface tension increases due to the dielectric discontinuity at the air/water surface. This idea was implemented in the pioneering work of Onsager and Samaras, who found a universal limiting law for the dependence of the surface tension on the salt concentration. However, the result implies an increase in the surface tension that is independent of the ion type, which turned out to be violated in many physical realizations.

Employing field-theoretical methods to calculate the grand partition function and considering short-range interactions of anions with the surface, We expand the Helmholtz free energy to first-order in a loop expansion and obtain the excess surface tension. Our approach is self-consistent and yields an analytical prediction that reunites the Onsager-Samaras pioneering result (which does not agree with experimental data), with the ionic specificity of the Hofmeister series. We obtain analytically the surface-tension dependence on the ionic strength, ionic size and ion-surface interaction, and show consequently that the Onsager-Samaras result is consistent with the one-loop correction beyond mean-field. Our theory fits well a wide range of concentrations for different salts using one fit parameter, reproducing the reverse Hofmeister series for anions at the air/water and oil/water interfaces.