Large polaron theories

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... 

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. 

On the basis of a definite analogy between e tx and F-centers we may expect the appearance under certain conditions of (e tr)2- particles of the type of F -centers. From the polaron model (57) it follows that the bipolaron (two electrons localized in a common polarization well) can not exist. In accordance with the work of Vinetskii and Giterman (63), in some cases the formation of the bipolarons becomes energetically possible in the result of interaction of the polarization wells of two separate polarons. However, the saving in energy for such bipolaron states is not large and hence they will not be stable in liquids under room temperature. Actually, up to the present time a series of attempts have been made to detect (e aq)2 in the irradiated liquid water but these attempts were not successful. The polaron theory (57) predicts that F -centers (two electrons in the anionic vacancy) may be stable. For this it is necessary that the ratio e/n2 (e and n2 are the static and optical dielectric constants, n—refraction index) should be more than 1.5. Evidently, in the glassy systems under consideration this requirement is fulfilled. 

Qian and Kholodenko [256] presented a new approach to the polyelectrolyte theory based on the Feynman variational method as used in the theory of large polarons. Unfortunately, the results are presented in a form which cannot easily be utilized for the interpretation of experimental results. One interesting result, however, is derived for the effective persistence length as... 

Fig. 3 An illustration of the transport mechanisms described in Sect. 2 for the one dimensional model of Eq. (1). The continuous line represents the density profile of the charge carrier at a given time and the lattice is idealized as an array of diatomic molecules whose bond distance uj can be modulated by the presence of the charge. In pure band transport (a) the carrier travels as a delocahzed wavepacket without deforming the underlying lattice. In polaronic band transport (b), the carrier and a deformation of the lattice form a quasiparticle that behaves as a heavier (and slower) charge carrier. In pure hopping (c), the charge is localized in one site and hops with a given rate to the neighboring sites. The intermediate case between (a) and (b) is studied by large polaion theories, while the transition between (b) and (c) is studied by smaU polaron theories...

That one cannot explain an ultra high mobility and a low saturated drift velocity with conventional theory cannot be over emphasised. The latter requires a large electron phonon interaction while the former requires low scattering and a concomitant low electron phonon interaction according to conventional wisdom. The resolution of this apparent paradox is found in the motion of the acoustic solitaacy mve polaron descri2>ed in the following article. 

In many oxides, and particularly those with large percentage ionic bonding, periodic fluctuations of the electric potential associated with each ion become too large (and energy bands too narrow) so that the band model provides an inadequate description or theory. In this case the electrons or holes may be considered to be localised at the lattice atoms. Such localised electronic defects are termed polarons and may from a chemical point of view be considered to constitute valence defects. 

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