Bounds for the effective dielectric constant of a suspension of spherically symmetric particles

Abstract

The author evaluates explicit expressions for the third-order upper and lower bounds for the effective dielectric constant, as derived by Dederichs and Zeller (1973) and by Kroner (1977) for a suspension of identical spherically symmetric particles. The expressions involve two- and three-body integrals which in dipole approximation are identical with those appearing in the theory of Kirkwood and Yvon for the dielectric constant of a non-polar fluid. The author extends the theory of Kirkwood and Yvon to multipoles of arbitrary order to make the analogy complete.