OPTICAL SUM-RULES AND EFFECTIVE-MEDIUM THEORIES FOR A POLYCRYSTALLINEMATERIAL - APPLICATION TO A MODEL FOR POLYPYRROLE

We derive sum rules for the effective dielectric function epsilon(e)(o mega) of a polycrystalline material, under the assumption of macroscop ic isotropy. If the material comprising the polycrystal is a quasi-one -dimensional or quasiplanar Drude metal, we predict that part of the o scillator strength of the polycrystal is pushed up in frequency to for m an ''impurity'' band of confined plasmonlike excitations. Under an a dditional condition of ''strong isotropy,'' we calculate the center of gravity of this band, in terms of the zero-frequency conductivity of the polycrystal. Analogous predictions are given for the energy-loss f unction, -Im epsilon(e)(-1)(omega). The effective-medium theory for a polycrystal composed of approximately spherical crystallites is shown to satisfy this condition of strong isotropy. A more general effective -medium theory for ellipsoidal crystallites does not satisfy strong is otropy. It does, however, obey the only sum rule which is valid for an y microstructure, namely, the sum rule on the spectral density. As an application, we describe a simple effective-medium model which qualita tively accounts for the ac electromagnetic properties of polypyrrole, over a broad range of frequencies, based on the assumption of polycrys tallinity. Many features of the observed optical constants are found c onsistent with the existence of a broad localized plasmon band arising from polycrystallinity.