Polyacetylene electronic states

In the weak-coupling limit unit cell a (, 0 7a for fra/u-polyacetylene) and the Peierls gap has a strong effect only on the electron states close to the Fermi energy eF-0, i.e., stales with wave vectors close to . The interaction of these electronic states with the lattice may then be described by a continuum, model [5, 6]. In this description, the electron Hamiltonian (Eq. (3.3)) takes the form ... 

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. 

Unlike (SN), most polymers correspond to closed-shell systems where all the electrons are paired. Such a configuration leads to insulating or semiconducting properties as noted previously. Polyacetylenes and related conjugated polymers, for example, have conductivities that classify them as semiconductors. The carbon atom in polyacetylene is sp hybridized, which leaves one p electron out of the bond-forming hybrid orbitals. In principle, such a structure might be expected to give rise to extended electronic states formed by overlap of the p (tt) electrons and thus provide a basis for metallic behavior in polymers. 

The high electronic conductivity of the 7c-conjugated polymers (e.g. polypyrrole, polyacetylene) determined by the presence of delocalized electronic states, puts those polymers into the category of synthetic metals. The lower electronic conductivity of the redox and ion-exchange polymers, compared with the 7r-conjugated polymers, is due to the presence of localized electronic states. The redox polymers, which contain redox electroactive centres, conduct current by electron self-exchange... 

The dimerized chain is the simplest model of semiconducting polymers, and is applied in particular to trans-polyacetylene. The noninteracting electronic structure of conjugated polymers with more complex unit cells, such as poly(para-phenylene), will be discussed in their relevant chapters. We emphasize that the noninteracting model is a simple model. It is not a realistic description of the electronic states of conjugated polymers, as it neglects two key physical phenomena electron-phonon coupling and electron-electron interactions. Despite these deficiencies it does provide a useful framework for the more complex descriptions to be described in later chapters. 

SoKtons produced in polyacetylene are delocalized over approximately 12 CH units, with the maximum charge density to the dopant counterion. Soliton formation results in the creation of a new localized electronic state which is in the middle of the energy gap. At a high level of doping the charged sohtons produce soliton bands that can merge to behave hke a metalhc conductor. 

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