Charge polarization near dielectric interfaces and the multiple-scattering formalism

Interfacial charge polarization is ubiquitous in systems with sharp dielectric contrast. Fully resolving the interfacial charges often relies on demanding numerical algorithms to solve the boundary value problem. The recent development of an analytical multiple-scattering formalism to solve the interfacial charge polarization problem for particles carrying monopolar, dipolar, and multipolar charges is reviewed. Every term produced in this formalism has a simple interpretation, and terms for spherical particles can be rapidly evaluated using an image-line construction. Several practical applications of this formalism are illustrated. A dielectric virial expansion for polarizable particles based on this formalism is also described. The origins of singular polarization charges for particles in close contact are explained and evaluated for both dielectric and conducting spheres.