Energy polaron

As a result of the LF we get a shift of the onsite energies (polaron shift or reorganization energy in electron transfer theory) and a renormalization of... 

The energy spectrum of the exciton polaron as a function of k is obtained by the solution of an equation... 

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. 

It is possible to make elastic scattering corrections to the algorithm (24) in the case of an Einstein phonon spectrum and purely local exciton-phonon coupling. If we calculate the energy of the polaron state at the value E ss nuio only the matrix elements 5 " should be considered in Eqs.(16). In this case... 

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... 

Figure 7-23. Schematic diagram of energy levels and optical irunsiciits of neutral molecule, polaron (P+) and bipolar. HP2+).

Our results also shed light on the long-lived PA3 band detected in transient PM measurements of P3BT (see Fig. 7-19) and can explain changes in the PA spectra observed in several ps transient measurements of films of PPV derivatives at energies around 1.8 eV [9, 25, 60J. In good PPV films the transient PA spectrum shows a PA band of excitons at 1.5 eV whose dynamics match those of the PL and stimulated emission (SE) [9J. However, in measurements of oxidized [25] or C60-doped films 60, there appears a new PA band at about 1.8 eV whose dynamics are not correlated with those of the PL and SE. Based on our A-PADMR results here, we attribute the new PA band at 1.8 eV to polaron pair excitations. These may be created via exciton dissociation at extrinsic defects such as carbo-... 

Using a variety of transient and CW spectroscopies spanning the time domains from ps to ms, we have identified the dominant intrachain photoexcitations in C )-doped PPV films. These are spin-correlated polaron pairs, which are formed within picoseconds following exciton diffusion and subsequent dissociation at photoinduced PPV+/Cw> defect centers. We found that the higher-energy PA band of polaron pairs is blue-shifted by about 0.4 eV compared to that of isolated polarons in PPV. 

In molecular doped polymers the variance of the disorder potential that follows from a plot of In p versus T 2 is typically 0.1 eV, comprising contributions from the interaction of a charge carrier with induced as well as with permanent dipoles [64-66]. In molecules that suffer a major structural relaxation after removal or addition of an electron, the polaron contribution to the activation energy has to be taken into account in addition to the (temperature-dependent) disorder effect. In the weak-field limit it gives rise to an extra Boltzmann factor in the expression for p(T). More generally, Marcus-type rates may have to be invoked for the elementary jump process [67]. 

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