(218j) Effects of Ion Self-Energy on the Double Layer Structure and Properties at the Dielectric Interface

A systematic, unified and predictive theoretical framework that is able to capture all the essential physics of the interfacial behaviors of ions, such as the Hofmeister series effect, Jones-Ray effect and the salt effect on the bubble coalescence remains an outstanding challenge. The most common approach is the Poisson-Boltzmann (PB) theory; however, there are many systems for which the PB theory fails to offer even a qualitative explanation, especially for ions distributed in the vicinity of an interface with dielectric contrast between the two medium. A key factor missing in the PB theory is the self-energy of the ion. We develop a self-consistent theory that treats the electrostatic self-energy (including both the short-range Born solvation energy and the long-range image charge interactions), the nonelectrostatic contribution of the self-energy, the ion-ion correlation and the screening effect systematically in a single framework. The theory gives a continuous self-energy across the interface, which allows ions on the water side and the vapor/oil side of the interface to be treated in a unified framework. Using the theory, we demonstrate three essential effects, the image charge effect, the inhomogeneous screening effect and the specific ion effect, for the ions near the dielectric interfaces. First, we show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as like-charge attraction and charge inversion. Then, we show that the double layer structure and interfacial properties is drastically affected by the inhomogeneous screening due to the nonuniform ion distribution particularly at high salt concentrations when the bulk Debye screening length is comparable to the Bjerrum length. The characteristic length of the depletion layer scales with the Bjerrum length instead of the Debye screening length, resulting in a linear increase of the negative adsorption of ions with concentration, in agreement with experiments. Finally, we study the self-energy of a single ion across the dielectric interface. Using intrinsic parameters of the ions, such as the valency, radius, and polarizability, we predict the specific ion effect on the interfacial affinity of halogen anions at the water/air interface, and the strong adsorption of hydrophobic ions at the water/oil interface, in agreement with experiments and atomistic simulations.