Free-Energy Density Functional of Ions at a Dielectric Interface

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's permittivity....

In the region where two bulk phases meet, an intricate electric charge distribution arises due to charge transfer, ion adsorption, molecular orientation, and charge distortion. This complex distribution is commonly referred to as the electrical double layer.When a solid electrode interfaces with ions in an electrolyte solution, the speed of electron transfer dictates the rates of oxidation and reduction. The electrode acquires a charge through the escape of atoms into the solution as cations or...

When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of the bound and free charge densities, while the total charge density can also be written in terms of the total electric field. The bound charge density can be measured in terms of polarization, leading to the relationship between electric displacement and polarization.

The interionic forces of the strong electrolytes depend on the solvent's dielectric constant, which is the ability of a solvent to store electrical energy, based on its polarizability. and the solution's concentration. In high-dielectric solvents and in dilute solutions, weak electrostatic forces keep ions apart. However, in low-dielectric solvents or concentrated solutions, stronger interionic forces may cause ions to pair up as ionic doublets despite being fully ionized. The theory of strong...

The electrode interacts with ions in the electrolyte solution at its interface. The rate of oxidation and reduction depends on the speed at which electrons can transfer through this interface. As ions attach to or leave the electrode surface, the electrode acquires a charge, and an electrical potential forms across the interface, making the process more difficult to reach equilibrium. The charge on the electrode affects the local ion concentrations in the solution, though thermal motion...

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...