Polaron bands

At very low temperatures, Holstein predicted that the small polaron would move in delocalized levels, the so-called small polaron band. In that case, mobility is expected to increase when temperature decreases. The transition between the hopping and band regimes would occur at a critical temperature T, 0.40. We note, however, that the polaron bandwidth is predicted to be very narrow ( IO Viojo, or lO 4 eV for a typical phonon frequency of 1000 cm-1). It is therefore expected that this band transport mechanism would be easily disturbed by crystal defects. 

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... 

Figure 16. Evolution of the population of the polaronic and bipolaronic bands during polymer oxidation. CB, conducting band, P.B., polaronic band, V.B., valence band, B.P.B., bipolaronic band.

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... 

The disappearance of the sharp Verwey transition was discussed by Mott (1979), who suggested that at low temperatures the material is a Wigner glass , the electrons (Fe2 + ions) being frozen into random sites and the whole system stabilized by the fluorine. Discussion of the thermopower measurements show, according to Mott (1979), that a hopping mechanism is operative at low T. Ihle and Lorenz (1985), however, consider that the electrons in the wrong sites move by a small polaron band mechanism. 

However, the available theories have still been restricted to selected parameter orderings. In particular, it has been assumed in theories of exciton transport that the exciton bandwidth is narrower than the phonon bandwidth, and this assumption has been carried over to theories of carrier transport. In fact, carrier bandwidths may well be much larger than phonon bandwidths at low temperatures, becoming smaller than phonon bandwidths as the temperature is raised, owing to polaron band narrowing... 

The UV-Vis spectrum of nanostructured PDMA-PSS film shows a strong peak in the region around 800 nm due to the polaron —> band transition for emeraldine salt form of... 

Figure 18. Hopping motion of the excess proton in the system of polaron wells. 2J is width of the narrow polaron band is the pulling electric held. (From Ref. 37.)...

Figure 11.1 Electronic band diagrams of a nondegenerate Jt-conjugated polymer related to different doping levels, (a) Undoped (neutral state) (b) Slightly doped polymer with localized polaronic levels (c) Moderately doped polymer with polaronic bands (d) Heavily doped polymer with bipolaronic bands. The benzenoid (e) and...

Semiempirical molecular orbital calculations,58 and more recently, ab initio calculations59 on the conducting emeraldine salt form of PAn predict, in contrast to PPy and polythiophene, the presence of a single broad polaron band deep in the band gap. This band is half-filled, giving rise to an ESR signal.60... 

These band-structure calculations are in agreement with the observed UV-vis-ible-NIR spectra. In their compact coil conformation, emeraldine salt typically exhibit three peaks a n-n (band gap) band at ca. 330 nm and two visible-region bands at ca. 430 and 800 nm that may be assigned as n —> polaron band and polaron -> 7t band transitions, respectively61 (see Figure 5.6). 

The differences between the spectra recorded in benzyl alcohol and m-cresol must be attributed to different polymer chain conformations in both solvents [66]. In the phenolic type of solvents, polyemeraldine protonated with CSA has an expanded coil-like conformation which facilitates interactions between adjacent polarons. As a result, the absorption observed in benzyl alcohol at around 800 nm, which is due to isolated polarons, is replaced by the intraband transitions within the half-filled polaron band (free carrier tail). 

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.

When EB is protonated leading to ES, a continuous shift of the exciton band from 2 to 1.5 eV is observed, together with the growth of the polaron band, due to the formation of within-gap new defects levels. The polaron state with unpaired spin, (that is to say the isolated polaron) has been determined by Electron Spin Resonance at 2.75 eV when the level of protonation increases up to the formation of two associated polarons, the spin resonance disappears, while the peak shifts up to 3.1 eV [51]. In ES, beside the polaron lattice peak at (on an average) 2.9 eV, a new absorption centred at 1.0 eV attributed to intrachain ffee-carrier excitation appears also [52]. The near-UV absorption weakens, since the metallic character of ES is inconsistent with the keeping of a 7t —> tt transition. 

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