Large polarons

Figure 35. Total conductivity, a, and oxygen stoichiometry, 3-d, at 1000 °C of Lao.9Sro.iMn03-(5, from measurements by Kuo et al. The model calculations are based on a large polaron model with equilibrium constants as given in ref 216. Thick line calculated stoichiometry, thin line calculated conductivity. (Reprinted with permission from ref 216. Copyright 2000 Elsevier.)...

The formation and transport properties of a large polaron in DNA are discussed in detail by Conwell in a separate chapter of this volume. Further information about the competition of quantum charge delocalization and their localization due to solvation forces can be found in Sect. 10.1. In Sect. 10.1 we also compare a theoretical description of localization/delocalization processes with an approach used to study large polaron formation. Here we focus on the theoretical framework appropriate for analysis of the influence of solvent polarization on charge transport. A convenient method to treat this effect is based on the combination of a tight-binding model for electronic motion and linear response theory for polarization of the water surroundings. To be more specific, let us consider a sequence... 

Keywords Large polarons Diffusion Conduction Hole traps Solvation... 

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. 

Up to this point we have discussed the formation of polarons in ionic crystals. Polarons of another type can also form in elements and other systems, such as the valence bands of alkali and silver halides, where the polarizability is not the relevant factor. In fact Holstein s (1959) original discussion of the small polaron was of this form. This kind of polaron is sometimes called a molecular polaron, and is illustrated in Fig, 2.3(a), and in Fig. 2.3(b) in the activated configuration of the atoms when the electron can move from one site to another. There is nothing analogous to the large polaron in this case in three-dimensional systems either a small polaron is formed or there is little effect on the effective mass from interaction with phonons. 

On the other hand, we have observed while studying even stoichiometries that JTD do not imply strict localization but, on the contrary, seem to survive rather easily in the metallic state. Trapping in CsC60 is then more probably due to defects than to a large polaron-like effective mass that would be intrinsic to a JT-dis-torted C q. One can then wonder about other types of influence of JTD in metallic compounds. 

In order to obtain the temperature dependence of rim, we consider the situation where small polarons coexist with large polarons of effective mass m [27], The equilibrium condition between large polarons and small polarons may be given by... 

However in the case of large polarons, the overlap of potential wells of neighbouring sites decrease the polaron formation energy which may be represented approximately as... 

SP), quantum mechanical tunneling (QMT) and overlapping large polaron (OLP)... 

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