Polarons small polaron

The conductivity due to conduction by polarons (small polarons) in a disordered system depends greatly on the temperature [68]. At low temperature the polaron moving requires, in fact, two concomitant tunneling effects [28,69] one related to the charge displacement and the other to the transfer of atomic sites that are associated with the deformation. Because of the mass of atoms, which gives a very low overlap factor, the latter transport mechanism is negligible. 

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. 

In Fig. 1 the absorption spectra for a number of values of excitonic bandwidth B are depicted. The phonon energy Uq is chosen as energy unit there. The presented pictures correspond to three cases of relation between values of phonon and excitonic bandwidths - B < ujq, B = u)o, B > ujq- The first picture [B = 0.3) corresponds to the antiadiabatic limit B -C ljq), which can be handled with the small polaron theories [3]. The last picture(B = 10) represents the adiabatic limit (B wo), that fitted for the use of variation approaches [2]. The intermediate cases B=0.8 and B=1 can t be treated with these techniques. The overall behavior of spectra seems to be reasonable and... 

Because polarons are localized species, their natural transport mechanism is hopping. We shall now briefly describe the small polaron model, as developed by Holstein and Emin [26, 29, 46]. 

At very low temperatures, Holstein predicted that the small polaron would move in delocalized levels, the so-called small polaron band. In that case, mobility is expected to increase when temperature decreases. The transition between the hopping and band regimes would occur at a critical temperature T, 0.40. We note, however, that the polaron bandwidth is predicted to be very narrow ( IO Viojo, or lO 4 eV for a typical phonon frequency of 1000 cm-1). It is therefore expected that this band transport mechanism would be easily disturbed by crystal defects. 

The perturbation theory used by Holstein in his small-polaron model confines its validity to an upper limit for J of around hto0, which corresponds to a non-adiabatic process. The adiabatic process, for which J > has been studied less extensively. In the high temperature limit, Emin and Holstein [46] arrive at the result that... 

Emin stresses the point that, as in the non-adiabatic process, Eq. (14.66) is only valid for J < Eu/2 to preserve the small polaron character of the charge carrier. 

Many other time parameters actually enter - if the molecule is conducting through a polaron type mechanism (that is, if the gap has become small enough that polarization changes in geometry actually occur as the electron is transmitted), then one worries about the time associated with polaron formation and polaron transport. Other times that could enter would include frequencies of excitation, if photo processes are being thought of, and various times associated with polaron theory. This is a poorly developed part of the area of molecular transport, but one that is conceptually important. 

Importantly, deep oxidation of polyaniline leads to a material that becomes insulating and spinless. This phenomenon was demonstrated in case of poly(fV-methylaniline) by monitoring ESR signal and electric conductivity of the sample (Wei et al. 2007). Deep oxidation results in the formation of the so-called polaron pairs that are evidenced by optical spectra. Because the hopping probability of two polarons on a single chain is too small, polaron pairs do not contribute to electric conductivity and ESR signal. 

Schein LB, Glatz D, Scott JC (1990) Observation of the transition from adiabatic to nonadiabatic small polaron hopping in a molecularly doped polymer. Phys Rev Lett 65 472... 

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