Effects of ion solvation on phase equilibrium and interfacial tension of liquid mixtures

Abstract

We study the bulk thermodynamics and interfacial properties of electrolyte solution mixtures by accounting for electrostatic interaction, ion solvation, and inhomogeneity in the dielectric medium in the mean-field framework. Difference in the solvation energy between the cations and anions is shown to give rise to local charge separation near the interface, and a finite Galvani potential between two coexisting solutions. The ion solvation affects the phase equilibrium of the solvent mixture, depending on the dielectric constants of the solvents, reflecting the competition between the solvation energy and translation entropy of the ions. Miscibility is decreased if both solvents have low dielectric constants and is enhanced if both solvents have high dielectric constant. At the mean-field level, the ion distribution near the interface is determined by two competing effects: accumulation in the electrostatic double layer and depletion in a diffuse interface. The interfacial tension shows a nonmonotonic dependence on the salt concentration: it increases linearly with the salt concentration at higher concentrations and decreases approximately as the square root of the salt concentration for dilute solutions, reaching a minimum near 1 mM. We also find that, for a fixed cation type, the interfacial tension decreases as the size of anion increases. These results offer qualitative explanations within one unified framework for the long-known concentration and ion size effects on the interfacial tension of electrolyte solutions.

On the theoretical description of weakly charged surfaces

“…The PB theory predicts a monotonic decrease of f s that scales approximately with (c b ) −1/2 , which arises from the electric field contribution in the free energy due to the surface charge. 41,42 With the inclusion of image charge interaction, our theory shows that f s changes nonmonotonically. At low salt concentration (c b < 10 −3 M), f s calculated by our theory follows closely the PB result; this is because the region affected by the image charge repulsion is relatively narrow compared to the screening length, giving a relatively small contribution to the surface excess energy when integrated over the entire solution.…”

Ion Solvation in Liquid Mixtures: Effects of Solvent Reorganization

“…(6) reduces to dc ðrÞ=dr ¼ Àzl 0 =½"ðrÞr 2 by integrating once with respect to the radial distance r. This equation is to be solved together with Eqs. (7) and (8).…”

“…However, recently it has been shown that the solvation energy of the salt ions can significantly affect the phase behavior [3,4] and interfacial properties of liquid mixtures [5][6][7][8]. For example, Ref.…”

“…In Refs. [3][4][5][6]8], the solvation energy is modeled phenomenologically at the linear dielectrics level by a crude Born expression: ÁG Born ¼ ½ðzeÞ 2 =ð8 a 0 Þ ð1=" À 1Þ, where e is the elementary charge, a is the radius of the ion, and z is the valency. The local dielectric constant is taken to be given by a simple composition weighted average " ¼ " A A þ " B B .…”

“…[4] showed that the dramatic increase in the order-disorder transition temperature of (polyethylene oxide)-b-polystyrene block copolymers upon adding a small amount of lithium salt can be explained on the basis of the preferential solvation energy of the anions. Physically, the tendency of an ion to be preferentially solvated by the more polarizable component in a two-component mixture provides a significant driving force for phase separation [3], as well as differential adsorption between the cation and anion at the interface [5][6][7][8].…”