Solitons domain wall

Fig. 28. Soliton lattice solution of the FvdM model with regularly spaced, distance 1, domain walls. The dashed line corresponds to the incommensurate phase with negligible potential modulation (K = 0). The plateaus represent the commensurate domains.

The switching or memory phenomena induced by electric field application or photo irradiation have been studied on Mott insulators, charge ordered insulators, and N-I transition systems and were found to be fast phase transitions in general. For the former two systems, the phase transitions caused a pronounced change in reflectance and conductivity from insulating to metallic features. The third system also exhibited a change in conductivity and dielectric response connected with the transports of solitons and/or domain walls, dynamic dimerization, and... 

The effect of this is that the charged defects are independent of one another and can form domain walls that separate two phases of opposite orientation and identical energy. These are called solitons and can sometimes be neutral. Solitons produced in polyacetylene are believed to be delocalised over about 12 CH units with the maximum charge density next to the dopant counterion. The bonds closer to the defect show less amount of bond alternation than the bonds away from the centre. 

Figure 3-2. Soliton a domain wall between the two different dimerized phases shown in Figure 3-1. The dot indicates the unpaired electron which is localized near the domain wall in case it is neutral.

More than two decades ago Pople and Walmsley (1962) discussed the existence of an unpaired ir electron in the trans-(CH)x as shown in Fig. 12a, which accompanies a localized nonbonding MO level. This has been actually confirmed by ESR analyses (Shirakawa et al., 1978) and ENDOR (Kuroda and Shirakawa, 1982) observations. The lineshape of the ESR shows the motional narrowing from a highly mobile tt electron in the (CH), chain even down to 10 K (Goldberg et al., 1979 Weinberger et al., 1980). It has been concluded that there is one unpaired electron per approximately 3000 carbon atoms. This unpaired tt electron in the trans-(CH), chain is frequently referred to as the bond alternation domain wall, phase kink, or soliton. 

One can show that the Cl transition occurs at uc = n2n2a2/16y2. The incommensurate phase (for v < uc) consists of a periodic arrangement of regions where the phase is nearly constant, separated by walls where p(x) increases by 2njn (see fig. 24 for n = 1). One describes this structure as a domain wall lattice or soliton lattice , whose lattice constant ld... 

A soliton is a localized collective excited state likely to arise in nonlinear dispersive media. The soliton is capable of migrating over relatively long distances with very little energy dissipation. It may be electrically charged or may be neutral such as a kink in a polymeric chain, or a domain wall. 

Further oxidation of the polymer creates a dication. However, because of the two-fold degeneracy of PAc, these cations are not bound to each other by any lattice distortion and can freely separate along the chain. In the case of PAc, it is reported that solitons are delocalised over about 12 (CH) units [26]. Therefore, solitons are isolated, non interacting charged defects that form domain walls separating two phases of opposite orientation with identical energies. 

As a result of the degenerate ground state, an immediate and fascinating consequence of bond-alternation are bond-defects, or solitons. Solitons separate a dimerized region A from a dimerized region B, and thus they resemble domain walls in ferromagnets. 

Domain walls are defined as topological solitons, that is, 2-D membranes formed by spontaneously breaking a discrete symmetry at a phase transition. 

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