Kink-solitons

In the continuum model, the motion of a kink occurs without energy barriers if Q is irrational. For rational fl the distribution of ground state must be discrete, which makes it impossible to transform the phases continuously without extra energy. The dynamic solutions of Eq. (33) exploit the isomorphism with nonlinear relativistic wave equations [107,108] and a moving kink (soliton) can be interpreted as an elementary excitation with energy k(u)... 

Various exact solutions to this problem are known. The most prominent one is the kink (soliton) for the case of polyacetylene being,... 

It is conceivable that diffusion of kinks, or overdamped solitons, along the DNA could act to relax the FPA with a time dependence similar to that predicted for torsional deformation/31 32) High levels of intercalated dyes would be expected to alter both the equilibrium population of kinks and their mobility along the DNA. Hence, this question is addressed by examining the effect of intercalating dyes on the torsional dynamics. 

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. 

Cation (soliton, phase kink, no spin) Cation (soliton, phase kink,... 

Such a kink is represented in Fig. 5, where the bond alternation has been supposed to take place on a single carbon atom. By counting the valence electrons on this carbon atom one can see that there is an odd electron left. Thus one unpaired spin is present. Indeed, the presence of spins was early detected by ESR in undoped /rans-(CH)x [62], with a spin concentration of about 1 spin per ca. 3000 CH units. However, with a theoretical soliton formation energy of 0.45 eV, one would expect a much smaller concentration of thermal solitons at room temperature. Very likely the spins in trans-po yacetylene, which essentially appear during the cis —> tram isomerization [63], are related to an odd number of tt electrons in conjugated segments accidentally formed during isomerization. 

The work of Su Shrieffer and Heeger (11) focussed on conjugated polymers having two valence bond structures, say A and B. In the case of trans polyacetylene, where A and B are degenerate, they showed intrinsic defects can occur, in which A phase goes continuously over to B phase, forming a soliton kink. 

---