Electronically conducting polymer band structure

The electronic band structure of a neutral polyacetylene is characterized by an empty band gap, like in other intrinsic semiconductors. Defect sites (solitons, polarons, bipolarons) can be regarded as electronic states within the band gap. The conduction in low-doped poly acetylene is attributed mainly to the transport of solitons within and between chains, as described by the intersoliton-hopping model (IHM) . Polarons and bipolarons are important charge carriers at higher doping levels and with polymers other than polyacetylene. 

In real tran -polyacetylene, the structure is dimerized with two carbon atoms in the repeat unit. Thus the tt band is divided into occupied tt and unoccupied n bands. The bond-alternated structure of polyacetylene is characterishc of conjugated polymers. Consequently, since there are no partially filled bands, conjugated polymers are expected to be semiconductors, as pointed out earlier. However, for conducting polymers the interconnection of chemical and electronic structure is much more complex because of the relevance of non-linear excitations such as solitons (Heeger, 2001). 

Conjugated conducting polymers consist of a backbone of resonance-stabilized aromatic molecules. Most frequently, the charged and typically planar oxidized form possesses a delocalized -electron band structure and is doped with counteranions (p-doping). The band gap (defined as the onset of the tt-tt transition) between the valence band and the conduction band is considered responsible for the intrinsic optical properties. Investigations of the mechanism have revealed that the charge transport is based on the formation of radical cations delocalized over several monomer units, called polarons [27]. 

The TB MO calculation on the 15N chemical shift of polypyrrole in the solid state allows useful information to be extracted from the observed spectra, namely that the two peaks obtained are correctly assigned to the quinoid and aromatic structures.(l 1,38) ( The quinoid structure is closely to the electric conductivity.) A decrease in the band gap leads to a downfleld shift. These results on conducting polymers demonstrate that the chemical shift behavior provides information about the band gap which, in turn, is a measure of the electric conductivity. It can be said that TB MO calculations offer useful perspectives in interpreting the results of NMR nuclear shieldings in polymers, both in terms of the structure in the solid state and in understanding the effect of intermolecular interactions on nuclear shieldings. The latter are shown to operate through the electronic structures of the polymers considered. 

Fig. 12 a, b Electronic band structure of the rhombohedral C60 polymer with a ACB stacking and b ABC stacking, respectively. In each case, the electronic density of states is shown (in arbitrary units) energy is measured from the valence band top. The two systems show very similar valence-band dispersions, while the conduction-band states show a little difference in their dispersion. The fundamental gap of the ABC stacking polymer (lower panels) is found to be narrower than that of the ACB stacking polymer (upper panels) [39]... 

Scheme 3. Band-structure and electronic transitions for conducting polymers in the neutral and charged state...

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