Polaron-bipolaron band model

It is assumed that with oxidation new bands form within the band gap, which could explain the metal-like conductivity. The energetic details of these bands are basically obtained from spectro-electrochemical measurements (Section 11.5.5). The polaron-bipolaron band model for polypyrrole is shown in Figure 11.26 as an example. 

Fig. 4. Energy level diagrams showing possible electronic configurations for positively-charged polaron (a) and bipolaron (b) defects and (c) a schematic bipolaron band model. The negatively-charged polaron would carry three electrons and the bipolaron four. Also shown is the neutral polaron-exciton (d) which would decay to restore the chain 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. 

Figure I3.Z6. Schematic representation of successive (a) p-doping, and (b) n-doping in a band model. From left to right undoped state, polaron states (here symmetric) for lightly doped anT, bipolaron states (above, here symmetric) or polaron bands (below) for intermediate to strongly doped anT, bipolaron bands for strongly doped anT. The polaron and bipolaron states originate from the valence and conduction band near edgestates of the undoped material. The dashed areas mark occupied bands.

The concept of electric conduction in 7r-conjugated polymers used to be explained in terms of polaron , bipolaron , soliton , and band model [14e]. The iodine-doping of crystalline PTh prepared by the... 

At present it would appear that the polaron-bipolaron model is fully accepted by the scientific community. The main conductivity features of PPPs can easily be explained on the basis of this band energy scheme, and several experiments based on spectroscopic determinations have confirmed the theory. In particular, electron energy loss spectroscopy (EELS) of PPPs doped by AsFs [219] clearly showed the presence of two peaks near 1 eV and 2 eV, corresponding to transitions from the valence band to two states in the gap [219b], in fair agreement with the predictions of Bredas et al. [224]. 

Simply put, a conductive organic polymer, or for that matter any organic polymer, is not a metal, although many of the theories used to explain the electrical nature of ICPs are based on our understanding of conduction mechanisms in metals and semiconductors. Band theory, polarons, bipolarons, thermopower, etc., are but a few examples of the models borrowed from solid-state chemistry and physics to explain the observed electronic behavior of these materials. Lattice distortions that... 

Fig. 21.7 (a) Band diagram scheme for n-type doped PPP according to the polaronic-bipolaronic model, (b) Transitions in the Mott-Davis model of an amorphous semiconductor. 

From model calculations performed using the VEH technique for a 100% doping level, the new states appearing in the previously forbidden energy gap are assigned to two doping-induced bipolaron bands. Also, the lack of significant density of states at the Fermi level, as would be expected for a polaron situation, indicates that the formation of bipolaron bands is most likely. 

Figure 7-27 shows the frequency dependency of the in-phase PA bands in a-6T, measured at the maxima of the various PA bands. As expected, the two polaron bands are correlated with one another, having virtually the same dynamics. In contrast, the bipolaron PA band at 1.1 eV is virtually flat from 10 to 1000 Hz, indicating that trapped pol is are longer lived than trapped bipolarons in -6T. The excitation lifetimes modeled by comparing the data in Figure 7-27 to... 

Whereas the intermediate existence of polarons has been unequivocally proved by ESR measurements and optical absorption data, up to now, the existent of bipolarons has been only indirectly deduced from the absence of the ESR signal and the disappearance of the visible polaron bands from the optical absorption spectrum On the other hand, spinfree — diionic-charge — states in aromatics, whose optical properties bear a remarkably resemblence to the predictions of the bipolaron model, have long been known Further evidence of bipolarons is the fact that doped... 

Polaron — Polarons are charged quasiparticles with spin lf. This term has been introduced by physicists as one of the possible solutions to the equations of the relevant defect model of solids in order to describe an electron in a dielectric polarizing its environment (electron-phonon coupling), electrically situated below the conduction band, and transported together with its polarized environment. Polarons and -> bipolarons are the charge carriers in oxidized or reduced (doped) -> conducting polymers. A polaron is defined as a neutral and a charged -> soliton in the same... 

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