  Recently a variety of $\pi$-conjugated polymers have been developed and
essayed for a number of applications such as organic light-emitting diodes,
organic field-effect transistors, organic photovoltaics, and sensors. Is
central for these applications the semiconductor character of the pure
materials, which can turn into metallic conductivity by local oxydation or
reduction. Many very recent experiments show two characteristic peaks in the
UV-Vis excitation spectra of the conjugated polymers of interest, both lying in
the gap between the energies of the bonding $\pi$ and antibonding $\pi^*$ bands
and having excitation energies in a ratio ranging from 1.4 to 1.7. The issue is
that $\pi$-electrons are paired in covalent orbitals which interact strongly
between them and with the ionic cores, thus being far from the extended
quasi-free independent one-electron states assumed by the theory of inorganic
semiconductors. A model yielding a mechanism for many-body conduction of charge
and semiconducting properties of the undoped material is introduced here. The
model yields two new flat bands of excited bonding states of Bose-Einstein
statistics able of charge transport. The two bands explain well the
characteristic pair of maxima of the UV-Vis excitation spectra of the
conductive conjugated polymers.
