The Polarons

Let us first consider a case of the polaron spectrum when condition (20) is fulfilled so that the nondiagonal matrix elements of the operator F can be neglected, we denote as Vinei the coherent potential in which only the inelastic scatterings are accounted. It is easy show by explicit calculations that... 

It is possible to make elastic scattering corrections to the algorithm (24) in the case of an Einstein phonon spectrum and purely local exciton-phonon coupling. If we calculate the energy of the polaron state at the value E ss nuio only the matrix elements 5 " should be considered in Eqs.(16). In this case... 

Semiconductivity in oxide glasses involves polarons. An electron in a localized state distorts its surroundings to some extent, and this combination of the electron plus its distortion is called a polaron. As the electron moves, the distortion moves with it through the lattice. In oxide glasses the polarons are very localized, because of substantial electrostatic interactions between the electrons and the lattice. Conduction is assisted by electron-phonon coupling, ie, the lattice vibrations help transfer the charge carriers from one site to another. The polarons are said to "hop" between sites. 

The final remark of this section concerns the polaronic transition of m-LPPP around 1.9 eV, where we can observe P2 with its vibronic replica P3 at 2.1 eV. In Figure 9-20 we show this polaronic absorption in m-LPPP as detected by photoin-duced absorption (a), chaige-induced absorption in conventional light-emitting devices (b), and chemical redox-reaction (c). Only under pholoexcilation, which creates both neutral and charged species, the triplet signal at 1.3 eV is also observed. 

In molecular doped polymers the variance of the disorder potential that follows from a plot of In p versus T 2 is typically 0.1 eV, comprising contributions from the interaction of a charge carrier with induced as well as with permanent dipoles [64-66]. In molecules that suffer a major structural relaxation after removal or addition of an electron, the polaron contribution to the activation energy has to be taken into account in addition to the (temperature-dependent) disorder effect. In the weak-field limit it gives rise to an extra Boltzmann factor in the expression for p(T). More generally, Marcus-type rates may have to be invoked for the elementary jump process [67]. 

The polaron is characterized by the reversal of bond alternation, which, in the case of polythiophene, extends over five monomer units [30-32], and the appearance of two localized stales in the band gap ). These states have been indeed observed by UV-V1S absorption of both oligomers and polymers, in solution [33— 40] and in the solid state [41-45]. 

At very low temperatures, Holstein predicted that the small polaron would move in delocalized levels, the so-called small polaron band. In that case, mobility is expected to increase when temperature decreases. The transition between the hopping and band regimes would occur at a critical temperature T, 0.40. We note, however, that the polaron bandwidth is predicted to be very narrow ( IO Viojo, or lO 4 eV for a typical phonon frequency of 1000 cm-1). It is therefore expected that this band transport mechanism would be easily disturbed by crystal defects. 

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.

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... 

In a second possibility, the polaron-like hopping model, a structural distortion of the DNA stabilizes and delocalizes the radical cation over several bases. Migration of the charge occurs by thermal motions of the DNA and its environment when bases are added to or removed from the polaron [23]. 

Fig. 10 Two schematic representations of a polaron-like species in DNA. In the top drawing, the base pairs of DNA are represented by the horizontal lines the sugar diphosphate backbone is represented by the vertical lines. The polaronic distortion is enclosed in the box and extends over some number of base pairs. This is shown schematically by drawing the base-pair lines closer together. In the lower figure, a specific potential po-laron is identified, AAGGAA, and the radical cation is presented as being delocalized over this sequence. Movement of the polaron from one AAGGAA sequence to the next requires thermal activation...

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