Polarons mobility

Turning to the calculations of polaron mobility in Sect. 2.5, we find that, although a stationary polaron can form with the wavefunction extending over an arbitrary sequence of bases, in the absence of an electric field, or in a small electric field, the polaron cannot move far unless the DNA is made up of the same base pair repeated. This result is for zero temperature, of course, not allowing thermal energy that makes possible the transition dis-... 

Schein et al. (1990) measured hole mobilities of TTA doped PC. The temperature dependence was described by an Arrhenius relationship. The results were described by a small-polaron argument, as proposed earlier by Schein and Mack (1988). The dependence of the activation energy on intersite distance is illustrated in Fig. 54. The authors argued that for p < 15 A the results are consistent with adiabatic small-polaron theory while for p > 15 A the results can be described by a nonadiabatic small-polaron argument. Schein et al. derived an expression for the zero-field polaron mobility as... 

Another approach has been proposed in Ref. 191. The approach is based on the model of small polaron and makes it possible to extend the range of the model. In particular, it includes the influence of vibration wave functions on the tunnel integral and provides a way of the estimation of diagonal and off-diagonal phonon transfers on the proton polaron mobility. It turns out that the one phonon approximation is able significantly to contribute to the proton mobility. Therefore, we will further deal with matrix elements constructed on... 

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... 

The ab initio calculations of polaron mobility on the basis of the Holstein-Peierls model including a nonlocal electron-lattice coupling (Hannewald and Bobbert [12,13] see references to earlier work therein) reproduced the temperature-... 

Rosso, K.M., Dupuis, M. Reorganization energy associated with small polaron mobility in iron oxide. J. Chem. Phys. 120, 7050-7054 (2004)... 

Figure 7 shows the temperature dependence of the relaxation times of polarons in P30T determined from its dispersion spectrum terms presented in Fig. 4 of the spin diffusion constants Did and D3D and of the conductivity due to polaron mobility along OiD and between Oid polymer chains. ... 

The transport of small polarons in an ionic solid may take place by two different mechanisms. At low temperatures small polarons may tunnel between localised sites in what is referred to as a narrow band. The temperature dependence of the mobility is determined by lattice scattering and the polaron mobility decreases with increasing temperature in a manner analogous to a broad band semiconductor. 

At high temperatures, the exponential temperature dependence of small polaron mobilities can thus in principle be used to distinguish it from the other mechanisms. 

Souza et al. examined the influence of plasticizers, such as dioctyl phthalate (DOP) and cashew nut shell liquid (CNSL), on the electrical properties of blends based on PANI (doped with dodecylbenzene sulfonic acid) and SBS (styrene-butadiene-styrene) copolymer [106,107]. EPR experiments revealed an increase in polaron mobility (a decrease of AHpp) as the amount of plasticizer in the blend was increased, with the effect being more pronounced for CNSL (Figure 23.25). This phenomenon is known as a second doping, and is achieved without any additional protonation of PANI rather, it is due to an enhanced conformational... 

A polaronic mobility is expected if sufficient configurational relaxation is stimulated by the transiting carrier during its residence on each transport site. Polaron models need to be developed further to account for the observed field dependence. 

As discussed by Travers [102], this can be due to either (1) an increase in the intrachain diffusion rate or (2) a decrease in the electron-proton coupling constants. In case 1, hydration has an effect on the polaron mobility, i.e., the latter is enhanced in case 2, hydration modifies the polaron electronic wave function. In addition, T p shows that the low frequency contribution to the proton relaxation is not affected, which is not consistent with a change in the coupling constant. It can be concluded that the increase in the macroscopic conductivity observed on hydration is related to an increase of the on-chain polaron mobility. A possible explanation can be proposed in terms of a solvation effect of the counterions resulting in a depinning of the polarons. 

The variation of conductivity O of GeOg-x at a fixed temperature (1000 °C) is shown as a function of xin Fig. 12.10. Even though Og is known to be proportional to dn the vicinity of stoichiometry (up to x 10" ) saturation occurs at x= 0.04 and a has a broad maximum with a peak value at x 0.1. The activation energy of the small polaron mobility FA, varies with xfrom about 0.2 eV near stoichiometry to about 0.5 eV at a vacancy concentration of x= The... 

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