Modern Polymer Spect..

1700
- CIO
--- ca
c 22
_- c 12
l l l l l l l l l
Figure 3-5. Effect of the long-range interactions (s in equation 3.45) on the dispersion curves of the
frequency branch v3 (associated with the in-phase skeletal stretching) of trms polyacetylene calculated
for the unsimplified and realistic equilibrium geometry. The force field has been derived by ‘LI~J
initio’ calculations on polyene oligoinei-s with n = 2,4,5,6, and 11 double bonds [%I. Attention
should be paid to the fact that the ‘softening’ of the ~ ( = 90) mode iiiodulated by the distance of
iriteraction generates a ‘dispersion’ with chain length of a very strong and very characteristic
Ranian line ([41, 421).
These observations are essential when the dynamics of disordered chains will be
discussed later in this chapter.
3.6 From Dynamics to Vibrational Spectra of
One-Dimensional Lattices
The experiments which provide direct information on the vibrations of one- and
tridimensional lattices are infrared absorption (reflection) spectra, Ranian scattering
and neutron scattering. For a general discussion on the theoretical principles and
experimental methods the reader is referred to the abundant literature on these