Polaron transport activation energy

Similarly the temperature dependence of a has been derived as a oc 7, where a = 1 - 5 In (l/(toTo)). In the case of small polarons there is a strong local polarization and an associated polaron formation energy, Wp. Due to the strongly localized nature of the distortions, there may not be any overlap between small polarons and the corresponding activation energy is simply Wn Wp/2, which is independent of the inter-site separation R. The small polaron transport is therefore characterized by a modified s value, which is given by. 

Similar to the case of transition to supersonic velocities discussed above, this interchain transport process is also nonadiahatic. To pass through the barrier, the electron has to undergo an electronic transition from the polaron level localized to chain 1 to the TT -level localized to chain 2. The energy needed for this transition, the activation energy, is taken from the phonon system. Actually, the process is very similar to that treated by the Holstein theory discussed in Section 2.2 the electronic coupling between the chains is weak enough to force the electronic states to localize on individual chains. 

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. 

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