Polaronic band models

The temperature variation of the mobility in the polaron hopping and band regimes is shown in Fig. 5. It is worth pointing out that, till now, definitive evidence for a small polaron band conduction has not yet been reported. It has been argued by Yamashita and Kurosawa that, because Ihe small polaron band width is extremely narrow, the small polaron band model cannot be regarded as suitable when impurities are present to a sufficient degree. 

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... 

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.

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.

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. 

Heeger, A.J. 1997. Nature of the primary photoexcitations in polyfarylene-vinylenes) Bound neutral excitons or charged polaron pairs. In Primary photoexcitations in conjugated polymers Molecular excitons versus semiconductor band model, ed. N.S. Sariciftci. Singapore World Scientific. 

Several models can explain the carrier transport in organic semiconductors. However, none of them can be independently employed to explain the carrier transport phenomena and the mechanism at the same time. Among the theoretical models, the most often used models are the band transport model (Warta and Karl, 1985 Pemstich et al., 2008 Karl et al., 1991), polaron transport model (Holstein, 1959 Emin and Holstein, 1969 Marcus, 1960), hopping transport model (Vissenberg and Matters, 1998), and multiple trapping and release model (Horowitz et al., 1995 Le Comber and Spear, 1970). 

The relevance of the studies discussed to electrochemical charge transport is that similar models can also be applied to the electrochemical situations. Our concern in the electrochemical context is the moderately doped state, in which our applications are envisaged. For the moderately doped state at room temperature, bipolaron or polaron bands are theoretically not expected to form. Hence the conduction is expected to be activated. 

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]. 

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