Bloch-type conduction

Looking at Tables 9 and 10 one can see that the valence and conduction bands of the stacked bases and of the polySP chain are several tenths of an eV in width (values between 0.16 and 0.86 eV) indicating that there is the possibility of a Bloch-type conduction in these systems if free charge carriers are generated in them. On the other hand, the gap in all cases is more than 10 eV. Although one knows that the Hartree-Fock calculation gives too large a gap for conduction, this rules out the possibility of intrinsic semiconduction in DNA. 

The investigation of the localization properties (Anderson localiza-tion ) of the eigenstates of disordered chains is important primarily from the standpoint of their transport properties. If the Fermi eneigy (ep) falls into a more or less continuous region of allowed energy levels, one has to know whether the states around p are localized or delocalized. If the wave functions are delocalized, a coherent, Bloch-type conduction is still possible. If, however, they are localized, one can expect only incoherent, hopping-type chaise transport. 

If a periodic polymer chain has a very narrow bandwidth [like the so-called narrow-band (widths of order 10" eV) periodic nucleotide base stacks or base pair stacks in Table 9.11) or a polymer consists of a nonperiodic sequence of different types of units, then the electronic states become localized molecular states and coherent Bloch-type conduction is no longer possible. 

The gap in alternating trans-polyacetylene is described on the basis of its quasi-particle band structure and the question of the Bloch-type conduction in DNA (either through doping or the possibility of intrinsic conduction due to charge transfer from the sugar rings to the nucleotide bases) is discussed. This is followed by a brief discussion of the electronic structure of disordered polypeptide chains. 

At low temperatures, the small-polaron moves by Bloch-type band motion, while at elevated temperatures it moves by thermally activated hopping mechanism. Holstein (1959), Friedman and Holstein (1963), Friedman (1964) performed the theoretical calculations of small-polaron motion and showed that the temperature dependencies of the small-polaron mobility in the two regimes are different. In the high-temperature hopping regime, the electrical conductivity is thermally activated and it increases with increasing temperature. As shown by Naik and Tien (1978), its temperature dependence is characterized by the following equation... 

Yafet (1963) calculated the relaxation of the conduction electrons to the lattice <5 l due to spin-orbit scattering. Set can be separated into (intrinsic) and S eB-X. Hereby x denotes the concentration of the extrinsic scattereis. Has awa (1959) analyzed the situation which is shown in fig. 1 by Bloch-type equations. In this scenario the paramagnetic ions are... 

The Theory of Bloch-Type Electric Conduction in Polymers and Its Applications... 

In other words if the Fermi level falls into such a region of states which are still delocalized (the Fermi level is above the mobility edge) Bloch-type (coherent) conduction is possible, while in the opposite case (the Fermi level is below the mobility edge) only hopping-type conduction occurs /44/. For this reason the investigation of localization properties of the states in a disordered system like a protein chain is of utmost importance for which a Green matrix technique has been developed /44,45/. 

Bloch electrons in a perfect periodic potential can sustain an electric current even in the absence of an external electric held. This infinite conductivity is limited by the imperfections of the crystals, which lead to deviations from a perfect periodicity. The most important deviation is the atomic thermal vibration from the equilibrium position in the lathee however, electric perturbations can also promote this type of vibration. A quantitative treatment of the external electric perturbation of a crystal, therefore, starts with the observation of the change in the lattice vibrations [1] ... 

Since various rr-electron Hamiltonians have already been applied very extensively to the polyene problem, it is also of interest to ask what part of the correlation originates from purely r-electron interactions. (Both the highest filled and lowest unfilled bands have n symmetry. This question is therefore decisive for doping and conductive properties.) Owing to symmetry, the a- and r-type Bloch functions can be completely separated, so we can evaluate XYitn — n,a — a, and n —o contributions to El individually. Almost independently of the atomic basis set, we found that iff contributes only 15 to 20%, showing that for this kind of polymer the whole valence shell must be treated as an entity a simple model separating bands with r-type symmetry would not work. 

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