Exact bounds for the complex, bulk, effective dielectric constant ${\epsilon }_e$ 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 ${\epsilon }_e$ diverges as $\omega \to 0$ while the dc conductivity ${\sigma }_e\ne 0$.

• Received 4 March 1980

DOI:https://doi.org/10.1103/PhysRevLett.44.1285