OFFPRINT Surface tension of electrolyte solutions: A self-consistent theory

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. Copyright c © EPLA, 2014 Introduction. – When salts are added in small quantities to an aqueous solution, its surface tension generally increases [1,2]. Wagner [3] was the first to connect this finding with the dielectric discontinuity at the air/water surface, suggesting dielectric image interactions as a possible explanation. This idea was implemented in the pioneering work of Onsager and Samaras (OS) that was built upon the work of Debye and Hückel [4]. In their model, OS found a universal limiting law for the dependence of the excess surface tension on the salt concentration [5]. However, the OS 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 [6]. This led to numerous investigations of non-electrostatic ion-specific interactions between ions and surfaces [6,7], and their role in modifying surface tension of electrolyte solutions [2]. However, even nowadays a fundamental understanding of surface tension of electrolyte solutions is still missing. On a broader scope, ion-specific effects date back to the late 19th century, when Hofmeister [8] measured the amount of protein precipitation from solution in the presence of various salts, and found a universal (Hofmeister) series of ionic activity. The same ionic series emerged in a large variety of chemical and biological experiments [9–11], such as forces between mica or silica surfaces [12–14], osmotic pressure in the presence of (bio)macromolecules [15,16], and quite notably in the surface-tension measurements at the air/water and oil/water interfaces [17,18]. For simple monovalent salts the air/water surface tension depends strongly on the type of anion, while the dependence on the cation type is weaker [19], and is consistent with the fact that anion concentration exceeds that of cations at the air/water interface. For halide ions, the lighter ones lead to a larger excess in surface tension in a sequence that is precisely the reverse of the Hofmeister series. The OS treatment of electrolyte surface tension attracted much interest and generated a vast number of modifications to the original model, in particular more recent ones [20–26] that are relevant for our approach advocated below. Specifically, Dean and Horgan [20] calculated the ionic solution surface tension to first order in a cumulant expansion, where the zeroth order is equivalent to the Debye-Hückel approximation [4]. The surface-specific interactions were included via an ionic surface-exclusion layer in the vicinity of the dielectric