Bipolarons Bands

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.

Bi-layer angular movement during current flow, 348, 349, 350 Biological processes, mimicked, 425 Bipolaronic bands as a function of oxidation depth, 342 Bipolar iron-selective film, 226 Bismuth... 

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 3.72 Electronic structure diagrams for a polypyrrole chain containing (a) a polaron and (b) a bipolaron (c) The band structure obtained for highly oxidised (33 mol.0,, ) polypyrrole showing the presence of two broad bipolaron bands in the gap. After Bredas et al. (1984).

The authors also calculated the band structure expected for the fully oxidised form, taken as 33% doping or 2 charges per 6 rings, and the result is depicted in Figure 3.72(c). Continued removal of the states from the valence and conduction bands widens the gap to 3,56eV, with the two intense absorptions in the gap observed in the optical spectra now accounted for by the presence of wide bipolaron bands. The authors stated that, on the basis of other workers calculations, the lowest energy absorption should have the most intense oscillator strength, as is indeed observed. 

The bipolarons are energetically described as spinless bipolaron levels (scheme (9.30a)) which are empty and which, at high doping levels, may overlap with the formation of bipolaronic bands (9.30b). Finally, for polymers with band gap, values smaller than that of polypyrrole - such as polythiophene - the bipolaronic bands may also overlap with the valence and conduction bands, thus approaching the metallic regime. 

Removal of Removal of second electron n ore electrons forms bipolaron forms bipolaron bands... 

Concerning the cuprates it is now clear that a nonrigid basic electron spectrum must be used. Doping creates not only carriers but prepares the whole background (incorporating also structural changes) for the appearance of superconductivity. Under corresponding approaches there are ones which take as the basis a narrow defect (bipolaron) band above the itinerant band [23,40-48], or stripe-induced minibands [11,42],... 

Removal of more electrons forms bipolaron bands... 

Neutral Polymer Polaron Bipolaron Bipolaron Bands... 

Figure 6. Band structure of polypyrrole as a function of doping level (schematic). (A), neutral polymer (B) polaron (+), spin = 1/2, 3 new transitions (C) bipolaron (++), spin = 0, 2 transitions (D) Heavily doped, bipolaron bands.

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...

In (2), (3) the non-degenerate approximation (4) is valid up to more than a 10% oxidation degree [8], Such high concentrations are not achieved in space eharge layers in organie devices. The formation of bipolaron bands at larger oxidation degrees will not be considered here. 

FIGURE 3.7 Calculated electronic levels or bands for PPy s with increasing doping (CB = conduction band, VB = valence band) (a) neutral polymer, (b) polaron orbitals form, (c) bipolaron orbitals form, and (d) bipolaron bands form. 

A typical UV-visible spectrum obtained for PPy/DNA is shown in Figure 3.8. This reveals a n-n band and bipolaron bands at ca. 525 and 1000 nm. 

The absorption bands in the 300-500 nm range are assigned to transitions from the valence band to the uppermost bipolaron band [34,72]. The absorption bands due to the counter-anions (see Table 12.6) are absent in the spectra. This is due to the relatively low molar extinction extinction coefficients [73,74] of these counter-anions. The main absorption bands of FeEDTA occur outside the range of the spectrophotometer employed in this work. 

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.

Neutral polymer Polaron Bipolaron Bipolaron bands... 

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