Polaron molecular

The experiments just discussed made it clear that the motion of the hole on the series of As represents a different mechanism of transport than tunneling. Giese [13] and Bixon and Jortner [18] suggested that this mechanism is incoherent hopping of the hole between neighboring bases. This means that the hole wavefunction is Hmited to one base. The wavefunctions of the remaining electrons on that base would of course be distorted by the presence of the hole. Thus in this view of the transport process the base on which the hole sits could be called a molecular polaron, or a small polaron because it is limited to one site. 

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. 

Fig. 23 (a) A molecular polaron and (b) the excited state that must be formed before an... 

SUinsh, E.A., Khmkans, A., Larsson, S., and Capek, V., Molecular polaron states in polyacene crystals. Eormation and transfer processes, Chem. Phys., 198, 311, 1995. 

The great interest of the molecular polaron model is that it can account for the apparent contradiction between the band-like temperature-dependent mobility and a small mean-free path. The weak point of the approach developed by Silinsh and coworkers is that it is phenomenological. It is worth mentioning that a more consistent analytical theory has been formulated by Kenkre and coworkers [22]. The presentation of this model would go to far outside the scope of this chapter and will not be developed here. 

A generalization of the Marcus theory establishes an important criterion for activationless ( band-like ) or localized transport namely, the former occurs when 2t>X, while the latter dominates when 2t model developed before can be derived from the fact that the reorganization energy is linked to the the molecular polarization time, and the transfer integral to the residence time, so the first inequality can also write and the... 

In order to give a physical meaning to the concept of molecular polaron, Silinsh introduces an interaction time r which characterizes the time needed for the formation of the polarization cloud around the carrier [24], In Fig. 6, the value of r is given for various kinds of interactions. 

Here, rjj is the distance between nearest neighbor molecules. A typical mobility in molecular crystals such as naphthalene, anthracene, tetracene or perylene, ranges between 1 and lOcm V s at room temperature. Silinsh traces a border line between the electronic polaron (i.e. the nearly free electron) and the molecular polaron at lOOcm V s . Above this value, the charge carrier moves faster than the time necessary for the formation of the polarization cloud. 

A very interesting issue of the theory of the molecular polaron is that, unlike the small polaron, its transport occurs via stepping by tunneling without activation energy. Accordingly, the mobility is not thermally activated rather, it follows a power law mT , like in the band theory. The temperature dependence of the mobility can hence be used as a criterion to discriminate between the lattice (small) polaron and the MP. 

Complementary to electronic polarization, a charge carrier in a molecular solid also polarizes the vibration modes of the molecule on which it resides as well as dipole active modes of the neighboring molecules, thus forming an extended ionic state. The corresponding relaxation time Tv is estimated from the frequency of the vibration mode ( l,000cm ) toca. 10 s, comparable to the residence time Xres-The quasi-particle associated with this process is the molecular polaron. 

Due to the action of molecular polaron condensation, spinel LiMn204 undergoes disordered/ordered phase transition at low temperature (-173°C), which does not affect the intercalation and deintercalation of lithium. 

---