Disorder-Induced Kinks

In the previous section we assumed that disorder results in random fluctuations of the order parameter around some average value Aq. Such an approach is, essentially, a mean field treatment of the lattice. It requires sufficiently strong interchain interactions, whose role is to establish a coherence between the phases of the order parameter in different chains. 

For explicitness, let us assume that off-diagonal disorder is caused by chain twists, which randomly diminish the overlap between the 7r-orbitals of neighboring carbon atoms (see Fig. 3-7). The electron hopping amplitudes that depend both on the interatomic distances and on the relative orientation of the electronic orbitals on neighboring atoms can then be written in the form  

the second term describes the change of the hopping amplitudes due to the displacement of the atoms parallel to the chain [cf. Eq. (3.5)] and the third term is a random contribution resulting from the conformational disorder (chain twists). While the lattice displacements are dynamic variables, the fluctuations due to disorder are assumed to be frozen ( quenched disorder). 

F re 3-7. A simplified picture of a rran -polyacetylene chain with conformational disorder the right part of the chain is rotated with respect to its left part over the angle p. The electron hopping amplitude on the twisted bond is reduced by a factor of cos (j . 

The Peierls order parameter is the alternating part of the hopping amplitudes [see Eq. (3.11)] and now consists of two parts 

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As regards the nature of the so-called dissociation sites referred to above, it may be noted that generally any kind of disorder-induced kink may play an activating... 

Conformational disorder and kink-bands structures have recently been found also in random copolymers of syndiotactic polypropylene with small amounts of ethylene.192 193 The ethylene units are included in the crystalline regions193 and induce the crystallization of the metastable form II of sPP with conformationally disordered chains characterized by kink bands. Portions of chains containing the ethylene units tend, indeed, to assume a trans planar conformation, producing the kink-band defects in chains in the prevailing twofold helical conformation.192193... 

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