Polarons excitation

The states in the gap and the associated optical transitions for P" are shown in Figure 22.3a. The polaron energy states in the gap are SOMO and LUMO, respectively, separated by 2wo(P) [52]. Then three optical transitions Pf, P2, and P3 are possible [52-54]. In oligomers, the parity of the HOMO, SOMO, LUMO, and LUMO + 1 levels alternates they are g, u, g, and u, respectively. Therefore, the transition vanishes in the dipole approximation, and the polaron excitation is then characterized by the appearance of two correlated optical transitions below Eg. Even for long chains in the Hiickel approximation, transition P3 is extremely weak, and therefore the existence of two optical transitions upon doping or photogeneration indicates that polarons were created [51,54]. Unfortunately, polaron transitions have not been calculated for an infinite correlated chain. This is a possible disorder-induced relaxation of the optical selection rules that may cause ambiguity as to the number of optical transitions associated with polarons in real polymer films. 

FIGURE 22.26 (a) Transient PM spectrum of PDPA-nB solution at t = 0 that shows an SE and two correlated PA bands of excitons the onset of a third PA band is assigned. The inset shows the decay kinetics of the SE (full line) and two PA bands (dashed lines), (b) The steady state PM spectrum at 80 K that shows two other correlated PA bands and photoinduced IRAVs of polaron excitations. The inset shows the energy levels and optical transitions associated with a positively charged polaron excitation. (From Korovyanko, O.J., et al., Phys. Rev. B, 67, 035114, 2003. With permission.)... 

The role of the dopant potential on the stability and magnetic and optical properties of polarons and bipolarons in conducting polymers is shown with the aid of calculations of singlet and triplet states of a bipolaron [167] and by spectroelectrochemical and conductivity measurements [168-170]. The X-band optically detected magnetic resonance of PHT and PDDT shows that the distant intrachain polaron recombination is temperature-independent and identical in films and solutions. However, the triplet polaronic excitation decay is observable in films, but not in solutions [171], Electrochemical in situ conductivity and EPR measurements of PT films were performed in several solutions [172]. The results indicate that polarons merely seem to initiate the electrical conductivity. The electronic delocalization of polarons is restricted to a relatively short chain length at low potentials. As the polaron concentration increases (spin density maximum), bipolarons are generated immediately (probably too fast for the detection of polarons by EPR). Thus the bipolarons prevail in the fully conducting polymer films and as a consequence should be mainly responsible of the intrinsic conductivity [172]. Asymmetrically disub-stituted PBT display well-defined redox processes which are correlated to the consecutive formation of radical cations, dimerized radical cations, and dications [173]. 

According to a large number of experimental studies, the most stable phologen-erated species in the lowest excited stales of conjugated chains are electron-hole pairs bound by Coulomb attraction and associated to a local deformation of the backbone, i.e., polaron-excilons [18]. A good insight into the properties of these species can be provided by quantum-chemical calculations our recent theoretical... 

The decay of photogenerated chaiged excitations such as polarons and bipolar-ons should be bimolecular. In this case, the rate equation is written ... 

For spin-1/2 excitations such as electrons and holes in normal semiconductors or polarons in conjugated polymers, a single resonance is found centered at the Field... 

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-... 

Figure 7-27 shows the frequency dependency of the in-phase PA bands in a-6T, measured at the maxima of the various PA bands. As expected, the two polaron bands are correlated with one another, having virtually the same dynamics. In contrast, the bipolaron PA band at 1.1 eV is virtually flat from 10 to 1000 Hz, indicating that trapped pol is are longer lived than trapped bipolarons in -6T. The excitation lifetimes modeled by comparing the data in Figure 7-27 to... 

Sewell GL (1962) Polarons and Excitions. Plenum Press, New York... 

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. 

Because the extension of the polaron in polyene radical cations is finite (10-20 double bonds depending on the type of calculation), its electronic structure is independent of the number of double bonds attached to either side of it, so that the two lines in Figure 29 must bend at some point to meet the abscissa horizontally, as indicated by the dashed curves. Apparently, the point of inflection has not been reached for n = 15, but it is of interest that the curve for the first excited state could well extrapolate to 0.35 eV, which happens to be where the absorption of a polaron in polyacetylene has been observed300. If this is true, a second, more intense absorption band should occur between 0.5 and 0.7 eV, but the corresponding experiments have not yet been carried out. 

The realization of the polaronic nature of polyene radical cations leads naturally to the question, to what extent the pronounced relaxation of polyenes upon ionization affects their excited-state energies. Such changes can be assessed by comparing the ionization energy differences I) —I] obtained from PE spectra with the positions of the band maxima in the radical cation s EA spectra which measure the same quantities at the radical cation... 

Once the electrons and holes have been injected, they migrate into ETL and HTL to form excited states referred to as polarons by physicists or radical ions by chemists. These polarons or radical ions move, by means of a so-called charge-hopping mechanism, through the electron and hole transport materials (ETMs and HTMs), which typically possess good charge mobility properties, and eventually into the EML. 

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. 

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