Polaron states

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... 

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... 

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). 

On the basis of their results the authors concluded that the crossover from the neutral to oxidised form of poly pyrrole, and vice versa, requires the number of spins to pass through a maximum, i.e. the creation and anihilation of bipolarons involves the passage through the polaron state. They expressed this as a two-step redox reaction ... 

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,... 

Transport in DNA samples with all bases the same could be either by free carriers, i.e., band transport, or by polarons. As will be further discussed in the next section, the polarons are expected to be large polarons, not small. In the conducting polymers there is overwhelming evidence that electrons (holes) from a metal contact are injected directly into polaron states in the polymer, because the polaron states have lower energies than the LUMO (HOMO) or conduction (valence) band edge. As has recently been shown theoretically [30], the injection takes place preferably into a polaron state made available when a polaron-like fluctuation occurs on the polymer chain close to the interface, rather than into a LUMO state, with subsequent deformation to form the polaron. It could also be expected for DNA that injection... 

It has been shown theoretically that an extra electron or hole added to a one-dimensional (ID) system will always self-trap to become a large polaron [31]. In a simple ID system the spatial extent of the polaron depends only on the intersite transfer integral and the electron-lattice coupling. In a 3D system an excess charge carrier either self-traps to form a severely locahzed small polaron or is not localized at all [31]. In the literature, as in the previous sections, it is frequently assumed for convenience that the wavefunction of an excess carrier in DNA is confined to one side of the duplex. This is, of course, not the case, although it is likely, for example, that the wavefunction of a hole is much larger on G than on the complementary C. In any case, an isolated DNA molecule is truly ID and theory predicts that an excess electron or hole should be in a polaron state. 

In all cases, formation of a bipolaron state coincides with a complete bleaching of the original tt-tt polyene transition, which in effect moves the optical absorption "window" several hundred nm to the red. More recently we have discovered that polaronic state formation (EDG = MeO) can be preferentially controlled if the quantity of oxidizing agent is carefully monitored (25). 

One can conclude from this data that although polaron states are present, they are present to the extent of 1% or less. Thus it is not surprising that the dominant optical absorption is bipolaronic. Since Han and Elsenbaumer (26) do not report a quantitative spin concentration for their protonically doped PPV,... 

The studies presented in this section indicate that the presence of a complex environment, which induces decoherence and dissipation, can dramatically modify the electronic response of a nanowire coupled to electrodes. Electron transport on the low-energy sector of the transmission spectrum is supported by the formation of (virtual) polaronic states. Though strongly damped, these states manifest nonetheless with a finite density of states inside the bandgap and mediate thermally activated transport. 

Two recent and detailed three-dimensional band calculations on trans-PA [93] and on PPV [94] yield similar results tjtn is at least 3 x 10 2, so three-dimensional behavior should be observed and no polaron state should... 

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. 

Scheme 13. A schematic picture of a ferromagnetic coupling unit between two polaronic states aax>rding to the Fukotome model...

Figure VE-1 Ultrafast relaxation of photoexcited carriers into polaronic states with their associated midgap electronic states. We show schematically the band diagrams and corresponding absorption spectra for a non-degenerate ground state polymer.

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