Negative soliton

Figure 6.48 (a) Effect of doping on the electrical conductivity (solid line) and thermopower (broken line) of polyacetylene. (Following Etemad et al, 1982.) (b) solitons in trans-polyacetylene (i) neutral, (ii) positive and (iii) negative solitons. Arrow marks the boundary between the two symmetric configurations. A, acceptor D, donor. (Following Subramanyam Naik, 1985.)... 

Fig. 9.12 Energy level schemes of solitons and polarons in polyacetylene (a) soliton, (b) anti-soliton, (c) negative soliton, (d) positive soliton, (e) negative polaron and (f) positive polaron.

The band diagram for positive and negative solitons is shown in Fig. IVD-lc, with the optical transitions (in the near infrared) indicated. In addition, molecular vibrations that are not infrared-active in the neutral polymer become active in the presence of charged defects these infrared active vibrational modes (IRAV) are discussed in greater detail in the next section. 

The positive and negative solitons are here illustrated diagrammatically for simplicity as residing only on one CH unit they are actually delocalized over circa 15 CH units. They disappear rapidly because of the recombination of electrons and holes when irradiation is discontinued. If a potential is applied during irradiation, then the electrons and holes separate and photoconductivity is observed. 

Figure 13.24 A soliton in franj-polyacetylene. The shaded ellipse in the centre of the soliton may represent either an electron hole (creating a positively charged soliton), a single electron (creating a neutral soliton) or two electrons (creating a negative soliton)...

FIGURE 5.20 Formation from (a) a neutral soliton, (b) a positive soliton and (c) a negative soliton by controlled addition of p- and -doping agents, respectively. 

Figure 3. a. A negative soliton in t/ans-polyacetylene. b. The filled midgap state has no spin and carries a negative charge. 

Figure 4-5. Schematic electronic band structures, (a) Neutral polymer (b) positive polaron ic) negative polaron (d) positive bipolaron (e) negative bipolaron (f) neutral soliton (g) positive soliton (h negative soliton. CB, conduction band VB, valence band , electron arrow, electronic transition.

When a soliton is formed, a nonbonding electronic level is formed at the center of the band gap (Figure 4-5f-h). For a neutral soliton, the nonbonding electronic level is occupied by one electron, while for a positive soliton and a negative soliton, the level is occupied by null and two electrons, respectively. Thus, all the neutral, positive, and negative solitons are expected to have only one intragap transition, ojs, as shown in Figure 4-5f-h. 

FIGURE 1.22. (a) Schematic representation of soliton structures in polyacetylene, (b) Schematic band structure for neutral, positive, and negative solitons. 

Another approximate scheme, MNDO, has been applied to the study of defects (10,26) in long polyenes. This self-consistent method allows the inclusion of electron interactions in an approximate way and leads to predictions similar to those of the SSH model. For example, the neutral defect is studied by exaining a 41 carbon atom polyene with a center of symmetry. This forces the defect to be centered in the middle of the chain. The MNDO results show the standard tanh structure but with t=3 (instead of t=7 from the Huckel model). The charged defects were treated in the same manner and it was found that t=5 for the positive and t<3 for the negative solitons. Note however that the tanh form was... 

Fig. 11. Schematic representations of (a) neutral soliton, (b) negative soliton, and (c) positive soliton.

Fig. 28.13 Lattice polarization (net charge per CH unit) for (a) positive soliton, (b) negative soliton, (c) positive po-laron, (d) negative polaron in C40H42 from MNDO calculations. (From Ref. 114.)...

For poly (pyrrole), positively charged polarons and bipolarons have already been illustrated above, (Fig. 2-71. Negatively charged polarons and bipolarons can be visualized which are analogous to those of poly(p-phenylene), but in practice they do not exist, as poly(pyrrole) cannot be n-doped stably. For trans-poly(acetylene) (P(Ac)) (Fig. 2-13 ). one may have a neutral soliton and "antisoliton" possessing spin (a), and spinless positive and negative solitons (b) two adjacent, positive solitons would be the equivalent of a bipolaron, which for reasons cited earlier degenerates... 

---