Optical dispersion, lattice vibrations dynamics

The molecules treated in this chapter are indeed large systems with complex chemical structures. Moreover, in going from the oligomers to the polymers it becomes necessary to consider the systems as one-dimensional crystals. The optical transitions (both vibrational and electronic) are determined by one-dimensional periodicity and translational symmetry. Collective motions (phonons) that extend throughout the chain need to be considered and are characterized by the wave vector k, and their frequencies show dispersion with k. Lattice dynamics in the harmonic approximation are well developed [12,13J, and vibrational frequency spectroscopy has reached full maturity and has been widely applied in polymer science [8,9,14]. 

In a non-exhaustive literature search, a brief account is given here on the study of phonon and its vibrations. Corso et al. did an extensive study of density functional perturbation theory for lattice dynamics calculations in a variety of materials including ferroelectrics [93]. They employed a nonlinear approach to mainly evaluate the exchange and correlation energy, which were related to the non-linear optical susceptibility of a material at low frequency [94], The phonon dispersion relation of ferroelectrics was also studied extensively by Ghosez et al. [95, 96] these data were, however, related more with the structure and metal-oxygen bonds rather than domain vibrations or soliton motion. In a very interesting work, a second peak in the Raman spectra was interpreted by Cohen and Ruvalds [97] as evidence for the existence of bound state of the two phonon system and the repulsive anharmonic phonon-phonon interaction which splits the bound state off the phonon continuum was estimated for diamond. 

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