Surface tension of electrolyte solutions: A self-consistent theory

Abstract

We study the surface tension of electrolyte solutions at the air/water and oil/water interfaces. Employing field-theoretical methods and considering short-range interactions of anions with the surface, we expand the Helmholtz free energy to first order in a loop expansion and calculate 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 the mean-field result. 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.

Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions

“…Note that α of Ref. [17] corresponds to α − of the present paper, and in order to make the comparison we should set α + = 0.…”

“…(11). The grand potential, Ω[ρ f , h ± ], is expanded in powers of ℓ, and to one-loop order, this expansion gives [17,18],…”

“…In order to test our model, the results are compared with our previous work [17], where the surface tension was calculated in a different way, directly from the free energy. The latter method is thermodynamically equivalent to the Gibbs adsorption isotherm.…”

Fluid-dynamical model for antisurfactants

“…Although the details of the electrochemical mechanisms that lead to the exclusion of particular species from the surface remain the topic of ongoing research [12,13], the qualitative mechanism by which they affect the equilibrium surface tension is clear. Solvent molecules in the bulk interact with the dissolved solute; those near the surface have less interaction with the solute, as well as with other solvent molecules, and hence have higher energy than in the bulk, the excess being exhibited as surface energy.…”

“…Incorporating other effects, such as a maximum surface concentration due to packing effects or a critical micelle concentration in the bulk [7], is straightforward in principle but in practice it introduces distracting complications and so is not discussed further here. Similarly, we do not attempt to represent the underlying molecular or ionic interactions that control the surface excess and its effects [13], but in the spirit of established surfactant models [4][5][6][7][8] we subsume these into a simple kinetic description.…”