Exactly Solvable Microscopic Geometries and Rigorous Bounds for the Complex Dielectric Constant of a Two-Component Composite Material

Abstract

Exact bounds for the complex, bulk, effective dielectric constant ${\ensuremath{\epsilon}}_{e}$ of a two-component macroscopic composite that depend on the available information about the composite are presented and discussed. Some of these bounds are readily ascribable to special, exactly solvable, microscopic geometries. As a consequence, it is shown that there can exist composites where the real part of ${\ensuremath{\epsilon}}_{e}$ diverges as $\ensuremath{\omega}\ensuremath{\rightarrow}0$ while the dc conductivity ${\ensuremath{\sigma}}_{e}\ensuremath{\ne}0$.