We report the coexistence of metallic and non-metallic states within d
ifferent portions of samples of heavily iodine-doped stretched polyace
tylene based upon the measurements of a huge negative dielectric const
ant at microwave frequency (epsilon(mw)) for the center portions and a
relatively small and positive epsilon(mw) for the neck and end portio
ns. A Drude model in the low frequency limit is applied to estimate a
transport time and a plasma frequency for the metallic portions of the
samples. A modified Drude model including one-dimensional localizatio
n effects is used to account for the temperature dependence of the mic
rowave dielectric constant and conductivity. For the non-metallic port
ions, an interrupted metallic strand model, which represents the mater
ial as a bundle of metallic wires or polymer chains interrupted by ins
ulating defects, is applied to analyze the localization behavior probe
d by the positive dielectric constant. The variation of dielectric res
ponse of samples stretched before doping and with aging after doping p
oints to the key role of inhomogeneous disorder in charge transport fo
r these fibrillar materials with incomplete crystallinity.