Polaron and Bipolaron

When a polymeric chain having a polaron is subjected to further oxidation, an electron is removed from either the polaron or the rest of the chain. In the former case, a polaron radical is removed and two new positive charges resnlt, which are coupled through lattice distortion. In the latter case, two polarons are formed. However, the formation of a bipolaron causes a further decrease in ionisation compared to two polarons, indicating that bipolaron formation is thermodynamically more favourable. It has been reported through quantum chemical calculations that bipolaron energies are lower than those of polarons by 0.4 eV [13]. 

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Eig. 2. Lattice distortions associated with the neutral, polaron, and bipolaron states in poly(p-phenylene). 

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.

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... 

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. 

The model initially proposed by Genoud and coworkers (1985) was very simple, e.g. it did not take into account intcrparticle interactions. In their later papers, the authors did take into account such interactions but the conclusions remained essentially the same bipolarons and polarons are almost degenerate and can coexist. At low doping, only polarons are produced and then both polarons and bipolarons until the latter dominate at very high doping levels. They also found that their data were best understood in terms of bipolarons that are 5 monomer units long and polarons c. 4.5 units long. 

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. 

Clearly there are two sets of absorptions, as shown in Table 3.7, which were attributed to polarons and bipolarons by the authors. All the IRAV bands are relatively narrow and so suggest that the carriers occupy a well-defined number of monomer units. The highest frequency IRAV has been attributed to a combination of the intra-ring OC vibration and the inter-ring C-C stretch which increases in frequency as the conjugation length decreases, consistent with the bipolaron being somewhat shorter than the polaron. 

A plot of the polaron and bipolaron electronic band intensities as a function of charge injected (as electrons removed per monomer ring) is shown in Figures 3.85(a) and (b). The point at which the polaron intensity attains a plateau and the bipolaron intensity starts to dominate, at the anodic peak... 

Table 3.7 Polaron and bipolaron absorptions in polypyrrole (after Christensen and Hamnett, 1991) ...

From photoinduced absorption, luminescence and electron spin resonance observations, the dominant photocarriers generated in the polymer were shown to be polarons and bipolarons [189-191]. It was found that the magnitude of photoinduced absorption is rather independent of the condition of sample preparation whereas the photoluminescence intensity is strongly influenced. The results suggest that the luminescent exciton does not play a primary role in the photogeneration of polaronic species. 

We investigated the ultrafast dynamics in a Na-NaBr melt at 1073 K by fs pump probe absorption spectroscopy. A simple model was used to simulate the dynamics of polaron-, bipolaron- and Drude-type electrons. The relaxation times for polarons and bipolarons are 210 fs and 3 ps, respectively. The existence of an isosbestic point at 1.35 eV indicates an inter-conversion between bipolarons and Drude-type electrons. 

Within the pulse duration, polarons and bipolarons dissociate into Drude-type electrons and the subsequent bleach recovery at various probe wavelengths indicates the reformation of those species. On the other hand, the equilibrated absorption spectrum of Drude-type electrons is substantially red-shifted [7] compared to the F-centre absorption band. According to our mechanism polarons and bipolarons form Drude-type electrons after ultrafast excitation which leads to an increase of the transient absorption in the NIR region. 

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