Bipolaron formation

So far, electrochemical measurements have not provided any direct proof for the formation of a bipolaron state in oligbmers or polymers which is significantly more stable than the polaron state. In general, in terms of energy the redox potentials E° for bipolaron formation should be much lower than the potentials Ej for polaron formation (/E / < /E /). However, more recent electrochemical and ESR spectroscopic studies by Nechtschein et al. indicate that the bipolaron state is not much more stable than the polaron state... 

Figure 3.69 Schematic representations of the nature and energetics of (a) polaron and (b) bipolaron formation (see text for details).

Thus, it appears that the transition represented by the anodic peak in the cyclic voltammogram of polypyrrole is due to a changeover in the dominant carrier type and is accompanied by a dramatic contraction of the film. The authors strongly suspected that this contraction was due to electro-striction associated with bipolaron formation. As a further test they also carried out experiments intended to test if proton expulsion from the film occurred on oxidation. They found that it did indeed occur but monotonically at alt potentials > -0.6 F, in agreement with the extremely elegant work of Tsai et at. (1987), and so could not be responsible for the relatively sudden contraction at potentials > —0.2 V. 

Nature of charge carriers. Once injected, an electron and a hole must be brought at small enough distance to allow their recombination. This will depend on the nature and transport properties of the charge carriers. All CPs used in EL are nondegenerate ground-state polymers. The relevant notions of polaron and bipolaron and their relative stability were introduced in Chapter 11, Section IV.C. Some characteristic times pertinent to polaron or bipolaron formation will be discussed first, then the influence of traps. 

Furthermore, in addition to the temperature-independent term, disorder has the effect of favoring bipolaron formation rather than polarons. Consider, for instance, U > 0 and q = 1 (Nc = N, i.e., one charge per unit cell in average). In the absence of disorder, essentially the polaron states will be populated (for kT U). With enough disorder (Ae U), some doubly occupied sites (bipolarons) will be located below the singly occupied states (polarons), giving rise to an increase in the bipolaron number, and thus to a decrease in the spin susceptibility. 

Bipolarons Problems with Two or More Electrons 4.1 Bipolaron Formation... 

The formation of a bipolaron (or a bound pair of two polarons) is established, if the ground-state energy of the two-electron system is lower than twice the ground-state energy of a polaron. This issue has been studied rather intensively for the Holstein bipolaron [78], but it is not the case for the JT bipolaron. In [96], the electron-electron correlation function and the effective mass of an (gi e bipolaron was studied in one dimension in comparison with the corresponding results for the Holstein bipolaron [107]. In Fig. 5, we plot the phase diagram for the bipolaron formation, from which we find that the JT bipolaron is less stable than the Holstein one. 

Fig. 5 Phase boundary for the bipolaron formation [96,107]. The spatial dimension of the system is indicated by d...

A revisal of the equilibrium between polarons and doubly charged states of the polymer chains shows that the previous assumptions on the extension of polaron, bipolarons and polaron pairs were not justified. A more general formulation is presented for the equilibrium concentrations and the kinetics. But the differences are almost negligible up to the maximum charge concentrations that can be achieved in accumulation layers. The resulting rate constants for formation and dissociation of (immobile) bipolarons can be estimated using a rate constant for the bipolaron formation determined recently by Salleo and Street, and indicate that these processes can cause the hysteresis on the time scale of the measurements. 

Figure 1.4 Polaron and bipolaron formation on the conjugated backbone of PPy/...

ESR data of the intrazeolite PANI show the presence of ca. 0.0025 Curie-type spins per aniline loaded (comparable to bulk spin densities if the lower polymer content in the zeolites is considered), with g-values (g=2.0034) similar to bulk polymers. ESR spectra of intrazeolite PPy confirm the low spin count expected for bipolaron formation and g-values (2.0027) characteristic of polypyrrole. Large linewidths in both cases (8-10 G) could indicate strong dipolar interactions with the zeolite host. 

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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