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Reports: ND553404-ND5: Effects of Ions on Interfacial Tension and Electrical Double Layer

Zhen-Gang Wang, California Institute of Technology

Research Accomplishments and Scientific Significance The main objective of our proposed research is to include the self energy of ions in a coherent framework for studying water-air and water-oil interfacial tensions, as well as structure and interaction involving the electric double layers. Our efforts have focused on two aspects of this problem: (1) specific ion effects (Hofmeister series effects) in the interfacial tension of salt involving halogen ions; (2) proper treatment of image charges in the double layer structure. A continuous self-energy model for dielectric interfaces. The interfacial activities of salt ions are of great importance in physical chemistry, colloidal science and biophysics. Many interfacial phenomena, such as the surface tension of electrolyte solution and stability of proteins solutions and colloidal suspensions, exhibit strong dependence on the chemical identity of the ions. Although this "specific ion effect" has been known for over a century, a systematic, unified and predictive theory has been an outstanding challenge. A key factor that determines the ion distribution at the dielectric interface and other interfacial properties is the self energy of a single ion. The self energy consists of electrostatic and nonelectrostatic contributions, such as cavity energy, hydration and dispersion forces. While the effects and the theoretical treatments of these nonelectrostatic contributions are debatable, there is general agreement in recent years that the electrostatic contributions include the image force, the solvation energy and the polarization of the ions. However, previous treatments of these effects are ad hoc, inconsistent and often involve artificially "fixing" some pathological behaviors that arise due to the inconsistent assumptions.

Figure 1. (a) Self energy and (b) interfacial affinity of F-, Cl-, Br-, I- and Na+ at the water/air interface. e1=80, e2=1.

We proposed a new theory for the self-energy of salt ions across dielectric interfaces. By treating both the solvation and image force electrostatic forces as well as charge polarization induced by these forces in a consistent manner, we obtain a continuous self energy of an ion across the interface. Along with nonelectrostatic contributions, our theory enables, for the first time, a unified description of ions on both sides of the interface. Using intrinsic parameters of the ions, 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. Our work constitutes a major progress towards resolving a long-standing debate on the key contributing factors for the specific ion effects. In particular, our work indicates that hydration forces and dispersion forces, while playing quantitative roles, are not essential for explaining the specific ion effects. Effects of image charge on the double-layer structure for weakly charged surfaces. The study of the electric double layer is at the heart of colloid and interface science. The standard textbook description of the electrical double layer is based on the mean-field Poisson-Boltzmann (PB) theory. At large surface-charge density, high counter-ion valency and high ion concentration – the so-called strong coupling limit – it is recognized that PB theory fails to capture a number of qualitative effects, such as like-charge attraction and charge inversion. In the opposite limit – the weak-coupling regime – it is generally accepted that the electric double layer is well described by the PB theory. Figure 2. Ion concentration for the counterion-only system showing the presence of a boundary layer near the surface. The dielectric constants of the solvent and the plate are respectively eS=80, eP=2.5 and charge density s=1e/100nm2. The Gouy-Chapman length is kept constant for counterions of different valencies.

Text Box: Figure 2. Ion concentration for the counterion-only system showing the presence of a boundary layer near the surface. The dielectric constants of the solvent and the plate are respectively eS=80, eP=2.5 and charge density s=1e/100nm2. The Gouy-Chapman length is kept constant for counterions of different valencies.

The PB theory does not include image force that are ubiquitous when the surface has a different dielectric constant from the solvent. Previous researchers justified the negligence of the image charge interaction by a perturbation expansion in a smallness parameter proportional to the surface charge.  These studies concluded that, under the weak-coupling condition, the image force only enters as a small correction to the leading PB theory, which vanishes in the limit of zero coupling. We have reexamined the validity of the PB theory for weakly charged surfaces using a non-perturbative theory. Our work shows that the image charge repulsion creates a depletion boundary layer that cannot be captured by any regular perturbation approach involving a smallness parameter. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. In the presence of dielectric discontinuity, we show that there is no limiting condition for which the PB theory is valid. This work should fundamentally change the way electrical double layer is described in textbooks and is expected to have wide range of implications for any colloidal and interfacial phenomena involving electrical double layers. Figure 3. Charge inversion for a 0.05M 2:1 electrolyte solution near a positively charged plate. (a) Dimensionless electrostatic potential and (b) net charge density. The dielectric constants of the solvent and the plate are respectively eS=80, eP=2.5 and charge density s=1e/100nm2.

Text Box: Figure 3. Charge inversion for a 0.05M 2:1 electrolyte solution near a positively charged plate. (a) Dimensionless electrostatic potential and (b) net charge density. The dielectric constants of the solvent and the plate are respectively eS=80, eP=2.5 and charge density s=1e/100nm2.

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Impact on the Personnel

PI: The study of the interfacial properties of salt solutions is a relatively new direction for the PI. The work supported by the ACS-PRF has allowed him to be recognized, within a relatively short period of time, as one of the key researchers in the field.

Graduate Student: The projects in this research have formed an excellent platform for the education and training of the graduate student. Working on resolving some long-standing puzzles and on revising standard textbook knowledge has been tremendously motivating for the student. Critically understanding the existing theories, finding the key missing ingredients in them and ways to improve them, and making predictions based on the new theories, have proved an enriching and rewarding experience for the student. In addition, he had the opportunity to present his work in the American Physical Society Meeting and the ACS Symposium for Colloid and Interface Science.