Optical Sum Rules and Effective Medium Theories for a Polycrystalline
Material: Application to a Model for Polypyrrole
D. Stroud and A. Kazaryan,
Department of Physics, Ohio State University, Columbus,
Ohio 43210, USA
We derive sum rules for the effective dielectric function epsilon_e(omega)
of a polycrystalline material, under the assumption of macroscopic isotropy.
If the material comprising the polycrystal is a quasi-one-dimensional or
quasi-planar Drude metal, we predict that part of the oscillator strength of
the polycrystal is pushed up in frequency to form an ``impurity'' band of
confined plasmon-like excitations. Under an additional
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 function,
-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 isotropy. It does, however,
obey the only sum rule which is valid for any microstructure, namely,
the sum rule on the spectral density.
As an application, we
describe a simple effective-medium model which qualitatively accounts for the
a. c. electromagnetic properties of polypyrrole, over a broad range of
frequencies, based on the assumption of polycrystallinity.
Many features of the
observed optical constants are found consistent with the existence of a
broad localized plasmon band arising from polycrystallinity.
PACS numbers: 78.50.-w, 78.50.Jg, 78.65.-s, 78.65.Hc