Surface tension of strong electrolytes

– We present a theory which accounts for the increase in interfacial tension of water due to the presence of 1:1 electrolyte. The agreement between the theory and experiment is excellent, extending all the way to relatively high salt concentrations of 1 M. For low concentrations of electrolyte the theory reduces to the Onsager-Samaras limiting law. Contrary to surfactant solutions, aqueous electrolytes possess surface tensions higher than pure water. An explanation of this curious phenomenon has been advanced by Wagner [1] based on then recently introduced Debye-Hückel theory of strong electrolytes [2]. This work was further extended by Onsager and Samaras (OS) [3], who were able to derive a limiting law for surface tension similar to the one obtained by Debye and Hückel for bulk properties of electrolyte solutions. The OS limiting law is universal in the sense that it does not depend on specifics of electrolyte [4–7]. For low concentrations, good agreement has been found between the OS theory and the experiments [5, 6]. However, at larger concentrations the OS theory strongly underestimates the value of surface tension as compared to experiments [8]. Since the original work of Wagner and OS, the route to surface tension has relied on the Gibbs adsorption isotherm [9,10]. This equation relates the derivative of surface tension with respect to chemical potential to the number of ions adsorbed into the interfacial region [8, 11, 12]. The calculation is intrinsically grand canonical, since the interface is thought to be in contact with a reservoir of solute, i.e. bulk electrolyte. It has been argued, however, that a canonical calculation, besides being conceptually simpler, might actually lead to better results as it relies on fewer approximations [13]. Within the canonical formalism the Helmholtz free energy is directly related to the surface tension, bypassing use of the Gibbs adsorption isotherm. To see how this work, consider a neutral electrolyte solution of Nt = N+ + N− ions and Ns solvent molecules confined to a cylinder of height H and a cross-sectional area A. The interface can be idealized as the Gibbs dividing surface for which the surface excess of solvent is zero [14]. At fixed volume and temperature, the differential Helmholtz free energy is dF = σ dA+ μt dNt + μs dNs, where σ is the surface tension and μt and μs are the solute