Solitons soliton-antisoliton pair

The main scheme is shown in Fig. 17. The photogenerated electron hole pairs transfer to the soliton-antisoliton pairs in 10 13s. Two kinks appeared in the polymer structure, which separates the degenerated regions. Due to the degeneration, two charged solitons may move without energy dissipation in the electric field and cause the photoconductivity. The size of the soliton was defined as 15 monomer links with the mass equal to the mass of the free electron. In the scheme in Fig. 17, the localized electron levels in the forbidden gap correspond to the free ( + ) and twice occupied ( — ) solitons. The theory shows the suppression of the interband transitions in the presence of the soliton. For cis-(CH)n the degeneration is absent, the soliton cannot be formed and photoconductivity practically does not exist. 

Fig. 17a, b. Band scheme (a) and chemical structure (b) of trans-(CH) . The polymer chain contains the charged soliton-antisoliton pair. In the middle of the forbidden gap there are levels connected with two solitons not occupied ( + ) and twice occupied ( —) [106]... 

Three IR bands at 1370, 1260, and 500 cm-1 are also seen in Fig. 2.5. These energies are in the gap between the Raman mode of pure r-PA and are predicted by theory for the photoinduced solitons. The band near 500 cm-1 is attributed to the pinned soliton-antisoliton pair. The IR vibrational bands are also observed at 900, 1270, and 1370 cm-1 in the doped crystals. The band at 1270 cm-1 is rather weak. One possible explanation of the existence of the IR bands is that the coupling of the n electrons with the C-atom vibration along the chain increases the dipole-moment of the C vibrations making them infra-red active. The soliton vibrations in the Coulomb field of the impurity can also give rise to the infra-red active modes [14], A more detailed discussion of these bands is given in [6],... 

FIG. 3.4. (a) Neutral bipolaron (confined soliton-antisoliton pair) in polyOrara-phenylene) and (b) bipolaron charged with charge 2 e [8]. 

The situation in the polymers as been described in Section IV.C.l. There is a rich excitation spectrum solitons, polarons, and bi-polarons. The effect of three-dimensional coupling would be to confine soliton-antisoliton pairs... 

The photo-generation of soliton-antisoliton pairs implies formation of states at mid-gap. Time resolved spectroscopy (2) has been used to observe the predicted absorption due to photogenerated intrinsic gap states in li aii -(CH)x. Moreover, the time scale for photo-generation of these gap states has been... 

Solid-state devices usmg PANl, 111 Soliton-antisoliton pair, 11 Soliton hopping, 288 Soliton length, 278 Solitons, 6, 13, 252, 263... 

Fig. 2 Polyenes and the 2 state, (a) Schematic representation of the singlet 2Ag state in a polyene, showing its equivalent description either as a triplet-triplet or as soliton-antisoliton pair. Adapted from ref. 33. (b) Polyene-type structures discussed in the text. 1 Polydiacetylene [34,35], 2 Poly(diethyldipropargylmalonate) 136], 3 Poly(3-dodecylthienyl-enevinylene) [37], 4 Polyibenzodithiophene thiophene dioxide) [38]. R-groups denote solubilizing chains, (c) Models of singlet fission in polyenes, mediated by formation of 2Ag (left) or directly from IBu (right).

The small separation of the soliton-antisoliton pair means that there is no change of dimerization, merely a reduction in the dimerization in the locality of the doped particle. This is behaviour is shown in Fig. 4.9. 

The extrinsic dimerization has two effects. First, it causes an increased intrinsic dimerization, as shown in Fig 4.10. Second, it lifts the degeneracy of the A and B phases, as shown in the plot of the ground state energy in Fig. 4.1. This causes a linear confinement of the soliton-antisoliton pair, because the energy to create a B phase relative to the A phase increases linearly with the soliton-antisoliton separation. This new property of soliton-antisoliton confinenment is illustrated by the localized Wannier orbitals associated with the soliton, and antisoliton, These are obtained from the molecular orbitals associated with the mid-gap electronic states, V n > (described in Section 4.5) by inverting eqn (4.33). Thus,... 

Figure 4.12 shows the soliton-antisoliton pair for various extrinsic dimerizations. We see that even for relatively small extrinsic dimerizations the confinement energy is large enough to prevent a phase reversal between the soliton and antisoliton. 

---