Polaron-bipolaron model

Bipolaron — Bipolarons are double-charged, spinless quasiparticles introduced in solid state physics [i]. A bipolaron is formed from two -> polarons (charged defects in the solid). For chemists the double-charged states mean dications or dianions, however, bipolarons are not localized sites, they alter and move together with their environment. By the help of the polaron-bipolaron model the high conductivity of -> conducting polymers can be explained. 

At present it would appear that the polaron-bipolaron model is fully accepted by the scientific community. The main conductivity features of PPPs can easily be explained on the basis of this band energy scheme, and several experiments based on spectroscopic determinations have confirmed the theory. In particular, electron energy loss spectroscopy (EELS) of PPPs doped by AsFs [219] clearly showed the presence of two peaks near 1 eV and 2 eV, corresponding to transitions from the valence band to two states in the gap [219b], in fair agreement with the predictions of Bredas et al. [224]. 

Rodriguez et al. [693] reported infrared data obtained with the subtractively normalized interfacial Fourier transform infrared spectrascopy (SNIFTIRS) method for PPy films exposed to aqueous solutions containing various anions. In the range between 1000 and 1700 cm reversible changes in the range of electrode potentials below the onset of overoxidation were found. They are consistent with the polaron-bipolaron model. During overoxidation, hydroxyl and carbonyl groups attached to the polymer backbone... 

Exclusively with respect to electrode potential and charge transfer Amemiya et al. [718] studied UV-vis spectra of PPy as a function of electrode potential by considering the polaron-bipolaron model and the monomer unit model. Results favor the latter model. 

Recently Zuppiroli and coworkers [117-119] proposed a polaron/bipolaron model involving correlated hopping and mutiphonon processes as an explanation for the exponential temperature dependence of conductivity. 

Fig. 21.7 (a) Band diagram scheme for n-type doped PPP according to the polaronic-bipolaronic model, (b) Transitions in the Mott-Davis model of an amorphous semiconductor. 

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 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. 

These ideas developed by chemists resemble the bipolaron model, which presents the solid-state physicist s view of the electronic properties of doped conducting polymers [96]. The model was originally constructed to characterize defects in inorganic solids. In chemical terminology, bipolarons are equivalent to diionic states of a system (S = 0) after oxidation or reduction from the neutral state. The transition from the neutral state to the bipolaron takes place via the polaron state (= monoion, S = 1/2,... 

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. 

An important part of Andre and Bredas s work during the 1980s was to analyze and extend the soliton, polaron and bipolaron models to a number of cases [54] polypyrrole, polyparaphenylene, poly anilines, polythiophenes, etc. More details on the theory of conducting polymers can be found in specialized monographs [55]. 

It is assumed that with oxidation new bands form within the band gap, which could explain the metal-like conductivity. The energetic details of these bands are basically obtained from spectro-electrochemical measurements (Section 11.5.5). The polaron-bipolaron band model for polypyrrole is shown in Figure 11.26 as an example. 

Next, we discuss the electronic transitions due to polarons, bipolarons, and soli-tons in a polymer chain on the basis of a theoretical study reported by Fesser et al. [48] on a continuum electron-phonon-coupled model. The electronic energy levels of a neutral infinite polymer and those of polarons, bipolarons, and solitons are shown schematically in Figure 4-5. 

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