Polaron motion

To investigate polaron motion we started on the stack, at t=0, a polaron obtained by solution of Eqs. 1-5 with A=0. To apply a constant electric field we took A=Aot. The field is then -AqIc. Aq was chosen to give a moderate field, 5x10 V/cm. For this field numerical integration of the equations of motion gave a polaron drifting smoothly, maintaining its shape, when the stack consisted of the same base pair repeated (Fig. 6). 

In crystalline materials a characteristic of polaron motion is a difference between E the activation for conduction, and s, that for the thermopower written as S=(kB/e) (EsjkBT+ const). We expect that Ea=Ec—EF+WH and Es=Ec-Ef, where Ee is the extremity of the band in which the carriers move. 

Fig. 25 The two paths between two sites A and C for polaron motion, which can give rise...

There are two different temperature regimes of diffusive behavior they are analogous to those described by Holstein [1959] for polaron motion. At the lowest temperatures, coherent motion takes place in which the lattice oscillations are not excited transitions in which the phonon occupation numbers are not changed are dominant. The Frank-Condon factor is described by (2.51), and for the resonant case one has in the Debye model ... 

Holstein, T. (1959) Studies of polaron motion Part II. The small polaron. Ann. Phys., 8, 343-389. 

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... 

DONOVAN AND WILSON Solitary Wave Acoustic Polaron Motion... 

Shortly after the concept of hopping was introduced, Holstein [14] developed the concept of polaron motion. This theory was introduced to describe charge transport in molecular crystals. As a result of electron—lattice interaction, the surrounding lattice particles will be displaced to new equihbrium positions. The induced displacements provide a weU for the electron. If the well is sufficiently deep, the electron will occupy a hound state unahle to move unless accompanied by the well. The unit consisting of the electron together with its induced lattice deformation is termed the polaron. ... 

In summary, using the electron—lattice dynamics theory, we have been able to explore the details of the intrachain polaron motion. In particular, we have shown that the velocity of the polaron can exceed the sound velocity of the system. This is achieved by the decoupling of acoustic phonons from the polaron. With this knowledge about the intrachain behavior of the polaron dynamics, we will now go on to discuss the interchain transport of polarons. 

Holstein, T. Studies of polaron motion. Part I. The molecular-crystal model. Ann. Phys. 8, 325-342 (1959)... 

Emin, D., Holstein, T., 1969. Studies of small-polaron motion IV. Adiabatic theory of the Hall effect. Annals of Physics 53, 439—520. 

Polaron motion along the polymer chain induces interactions between electron spins and between electron and proton spins, which depend on the frequency. The line width of the ESR spectral components of polarons immobilized and delocalized in, for example, PTTF-Et-Ph, increases from 2.8 to 3.8 G and then to 39 G, and from 10.2 to 11.5 and then to 175 G, when the microwave frequency increases from 9.5 to 37, and then to 140 GHz, respectively, at room temperature. " It is then possible to determine a real line width of these PCs at the rOe —> 0 hmit, 2.4 and 8.3 G, respectively. 

Figure 6 also shows the contribution of both ID and 3D polaron motions to the ac conductivity of the laser-modified PATAC. Its intrachain conductivity Oid was interpreted in terms of the model of the charge-carrier scattering on the lattice optical phonons proposed by Kivelson and Heeger for metal-Uke clusters in conjugated polymers, ... 

In ID the lattice deforms around the electron and loced.ises the electron to form a polaron. The ii portant deformation is acoustic, in udiich the density of the lattice changes optic deformations occur also but are not important in the polaron motion. The mathematical description of the polaron is like that of solitary waves. The Solitary wave Acoustic Polaron (SWAP) has a very large effective mass its kinetic velocity is small. Horeover it cannot move at a velocity greater than S as its kinetic velocity approaches S the acoustic deformation increases and the SNAP mass increases. In addition back scattering is very rare. So the SWAP kinetic and drift velocities are equal. 

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