Bipolaron conductivity

Figure 18.2 Bipolaron conduction of charge across fmlypyrrole chains...

The structure of ES is difficult to elucidate directly. Spin-relaxation studies, however, strongly suggest that the structure of ES depicted in Chart 12.Id, in which semiquinone radical cations are separated by individual mers, is favored over the structure in which cations are present on adjacent mer units." " The latter case would lead to bipolaronic conduction bands and would render the... 

Fig. 11.1 Optical transitions in (a) an undoped and (b) an oxidatively doped (bipolaron) conducting polymer.

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.

In principle, such propositions resemble the bipolaron model, which presents the physicist s view of the electronic properties of doped conducting polymers 53-159) The model was originally constructed to characterize defects in solids. In chemical terminology, bipolarons are equivalent to diionic spinfree states of a system (S = 0)... 

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. 

A bipolaron introduces two states in the gap, both now empty (see Figure 3.72(b)), 0.75eV above the valence band and 0.79eV below the conduction band. As a result of the bonding state being empty, only two transitions within the gap are now possible, hence the loss of the middle 1.4 eV absorption peak in Figure 3.71. 

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 authors postulated that the conductivity is proportional to the number of carriers in the film and that the mobility of polarons is equal to that of bipolarons, hence the conductivity is independent of carrier type. Thus, the conductivity increases steadily as polarons, and then both polarons and bipolarons, are generated but should attain a steady value when polaron recombination to give half as many bipolarons becomes important. 

The work of Christensen and Hamnett (1991) provided the first positive evidence for bipolarons and showed, for the first time, that the oxidation of polypyrrole was accompanied by a dramatic decrease in the film thickness, linking this with the generation of these carriers. Taken in addition to all the work discussed above their work provided some of the final pieces in a workable theory of the conduction mechanism in polypyrrole. 

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. 

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