Exact bounds for the complex, bulk, effective dielectric constant εₑ 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 εₑ diverges as ω→0 while the dc conductivity σₑ≠0.
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David J. Bergman (1980) studied this question.