Polarons lattice

As for the molecular polarization, it forms in a time comparable to the residence time, so the situation varies from one compound to the other. Finally, the formation time of the lattice polaron is too long, so its occurrence is unlikely under all circumstances. 

Fig. 6. Temperature dependence of the PDF peak height at 2.75 A for Laj Ca MnOj compared to the expected temperature dependence (solid line) [22]. Anomalous depression near and above Tc indicates formation of lattice polarons...

The electron polaron corresponds to the nearly free electron of the conventional band model, whereas the lattice polaron is more or less the above discussed small polaron. By using the Heisenberg uncertainty principle, the interaction time r may be evaluated from the overlap integral 7 as r = H/J. In a molecular crystal, the overlap integral J is of the order of 0.01 eV. r is also connected to the mobility through Eq. (22). 

Such renormalization can be obtained in the framework of the small polaron theory [3]. Scoq is the energy gain of exciton localization. Let us note that the condition (20) and, therefore, Eq.(26) is correct for S 5/wo and arbitrary B/ujq for the lowest energy of the exciton polaron. So Eq.(26) can be used to evaluate the energy of a self-trapped exciton when the energy of the vibrational or lattice relaxation is much larger then the exciton bandwidth. 

Semiconductivity in oxide glasses involves polarons. An electron in a localized state distorts its surroundings to some extent, and this combination of the electron plus its distortion is called a polaron. As the electron moves, the distortion moves with it through the lattice. In oxide glasses the polarons are very localized, because of substantial electrostatic interactions between the electrons and the lattice. Conduction is assisted by electron-phonon coupling, ie, the lattice vibrations help transfer the charge carriers from one site to another. The polarons are said to "hop" between sites. 

Eig. 2. Lattice distortions associated with the neutral, polaron, and bipolaron states in poly(p-phenylene). 

The electrical conductivity in the solid state is determined by the product of the carrier concentration and the carrier mobility. In conjugated polymers both entities are material dependent and, i.e., are different for electrons and holes. Electrons or holes placed on a conjugated polymer lead to a relaxation of the surrounding lattice, forming so-called polarons which can be positive or negative. Therefore, the conductivity, o, is the sum of both the conductivity of positive (P+) and negative polarons (P ) ... 

In (1), Hq yields the total energy of system in which the molecules and the lattice are excited, yet there are no interactions between molecules and the lattice. The transfer of an electron from site m to site n is given by //j. Polaronic effects, i.e., effects due to the interaction of the electronic excitation and the lattice, are given by H2 and H. hi H2, the energy of the site is reduced by the interaction with the lattice vibration. In H, the lattice vibration alters the transition probability amplitude from site m to n. The term lattice vibration may refer to inter-molecular or intra-molecular vibrations. Static disorder effects are considered in H4, which describes the changes to the site energy or transition probabihty amplitude by variations in the structure of the molecular sohd. 

---