Extrinsic dimerization

The MBPs are extrinsic proteins localized exclusively at the cytoplasmic surface in the major dense line (Fig. 4-11), a conclusion based on their amino acid sequence, inaccessibility to surface probes and direct localization at the electron microscope level by immunocytochemistry. There is evidence to suggest that MBP forms dimers, and it is believed to be the principal protein stabilizing the major dense line of CNS myelin, possibly by interacting with negatively charged lipids. A severe hypomyelination and failure of compaction of the major dense line in MBP deficient shiverer mutants supports this hypothesis (Table 4-2). 

Let us imagine now that for some reason, either intrinsic or extrinsic, the linear chain from Fig. 1.28(a) dimerizes but preserves its ID structure. The new distribution is illustrated in Fig. 1.29(a). The first consequence is that the period... 

Solutions of chlorophyll have been shown to be photoconductive even in the absence of extrinsic acceptors [256]. In acetonitrile as solvent, ions were formed from two molecules in the triplet state. In petroleum ether, red light yielded ions from dimers if the concentration exceeded 10"4 M, the dimerization point [257]. In chlorophyll solutions containing ascorbic... 

Fig. 4.1. The ground state energy per site as a function of the dimerization parameter, S. The electron-phonon parameter, A = 0.2. (As discussed in Section 4.8, the dashed curve is the groimd state energy with an extrinsic bond dimerization, te = O.lt.)...

Trans-polyacetylene has the unusual property of exhibiting no extrinsic dimerization, and thus has no extrinsic band gap. The dimerization arises entirely from TT-electrons coupling to the lattice. Consequently, the A and B phases are degenerate. Most polymers, however, have an extrinsic semiconducting band gap as a result of their stereochemistry independent of the of 7r-electrons. Examples of polymers that are extrinsically semiconducting include, cis-polyacetylene (because of the structure caused by the a orbitals), polydiacteylene (because of the... 

The detailed effects of the stereochemistry vary from polymer to polymer -the details of particular polymers will be described in their relevant chapters. However, to understand the qualitative consequences of extrinsic dimerization we can use the linear chain to model its effects. In this model the 7r-electrons are coupled to the extrinsic dimerization via the bond integral (Bishop et al. 1981 Brazovoskii and Kirova 1981),... 

Fig. 4.10. The intrinsic bond dimerization, Sq, and the total bond dimerization, Jo = Jo + <5 a-s a function of the extrinsic bond dimerization, J = te/t. X = 0.2.

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 4.11 shows the probability density of the Wannier orbitals associated with the mid-gap states. Although the relative separation of Wannier orbitals is small with an extrinsic dimerization of = 0.1, the fact that there are two... 

Fig. 4.11. Probability distribution functions of the soliton defects in the noninteracting limit on a 102-site chain for the 1B state. Left defect, or soUton (filled symbols), right defect, or antisoliton (open symbols) extrinsic dimerization, = 0 (circles), Je = 0.1 (squares) and A = 0.1.

These become confined in the presence of extrinsic dimerization. 

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. 

Fig. 4.12. The normalized, staggered bond dimerization, <5 , of the state for various extrinsic dimerizations, te. (The plotted results are scaled by the te = 0 values of So and. ) A = 0.2.

The variables and parameters in eqns (7.2) - (7.5) are defined in Chapter 4. Vmn (defined in eqn (2.55)) is the Ohno potential for the undistorted structure. For generality, we also include an extrinsic dimerization, represented by the term... 

Figure 4.11 shows the probability density of the Wannier orbitals associated with the mid-gap states. Although the relative separation of Wannier orbitals is small with an extrinsic dimerization of = 0.1, the fact that there are two distinct Wannier orbitals implies that the argument employed in Section 4.6 -concerning the different characters of the 1 B and 1 B+ states after electron-lattice relaxation - is a general one. Thus, the 1 B state is comprised of spinless electron-hole pairs, while the l B state is comprised of two spin-1/2 objects. These become confined in the presence of extrinsic dimerization. We would therefore expect that, as before, the different character of the PB and 1 S+ states will be evident by the different type of geometrical distortions when electron-electron interactions are included. 

Figure 7.10(a) and (b) shows the geometric structures of the 1 B and l B states, respectively. As the extrinsic dimerization causes a confinement of the soliton-antisoliton pair, the geometrical structures are polaronic in the noninteracting limit for both cases. For the l B state, as before, increased Coulomb interactions bind the particle-hole pair into an exciton, resulting in very little change to the geometrical structure. For the state, however, electronic... 

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