Bipolarons levels

Figure 28. Energetic transitions in neutral and oxidized polaronic and bipolaronic levels. Energy transitions fit UV and visible photons, respectively.

Emersed electrode, 12 Energy scales and electrode potentials, 7 Energy transitions via polaronic and bipolaronic levels, 362 Engineering models, for fluorine generation cells, 539 Esin and Markov plots, 259-260 Experimental data comparison thereof, 149 on potential of zero charge, 56... 

At higher doping levels the polaron states interact the authors calculated that a bipolaron level is 0.49 eV more stable than two polaron levels so unfavourable polaron interactions are avoided via the formation of a more stable bipolaron, in agreement with the epr data of Scott and colleagues (1983). 

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. 

The occurrence of bipolaronic states in the polymer chains promotes optical absorption prior to the n-n gap transitions. In fact, referring to the example (9.30) of the band structure of doped heterocyclic polymers, transitions may occur from the valence band to the bipolaronic levels. These intergap transitions are revealed by changes in the optical absorptions, as shown by Fig. 9.8 which illustrates the typical case of the spectral evolution of polydithienothiophene upon electrochemical doping (Danieli et al., 1985). 

As the polymer is oxidized further, a dication is formed, a bipolaronic charge carrier with the cations coupled to one another, that is delocalized over the same polymer segment. These bipolaron levels are unoccupied, only electronic transitions from the top of the valence band can occur, which is shown in Figure 20.1c [5,16,26]. 

FIGURE 21.15 Schematic drawing of the energy level alignment at interfaces of PFO and different metallic substrates. In all cases, the Fermi level of the substrate ( p) is situated between the negative and positive bipolaron levels. 

Equation 22.2 shows that we can determine U from a single transition (5S ) if is known and charge conjugation symmetry exists. In more general case in which S is replaced by a polaron level, this transition should be associated with the SOMO level in the gap. We used this relation to determine Uin NDGS polymers from the optical transitions associated with the polaron and bipolaron levels in the gap [49]. 

Table 1.3 VEH-Calculated Polaron Transition Energies Between the HOMO Level and the Lower Polaronic Level (H — POLl) and Between the Two Polaron Levels (POLl - P0L2) and Bipolaron Excitation Energies Between the HOMO Level and the Lower Bipolaronic Level (H -> BlPl) in Thiophene Oligomers Containing Three, Five, Seven, and Nine Rings ...

Another important feature to note regarding the bipolaron levels in particular is that they are either empty (p-type doping) or fiilly occupied (n-type doping), and thus spinless. An important reason why a model different from that of conventional semiconductors was sought for CPs is that in highly doped CP samples, which had high intrinsic conductivity, there was no evidence for unpaired electrons from experiments such as electron spin resonance (esr) measurements, or correlation of conductivity with esr absorption, but rather, spinless charge carriers were indicated [16]. 

Figure 13. Schematic hybridization of soli ton energy levels at midgap to form poison or bipolaron levels at coi. It is illustrated here for S + as for example in rans-polyacetylene.

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