Modern Polymer Spect..

3.16 Stnictural Znlioi~zogeneity and Ranmn Spectroscopy qf LAM Modes 161
Figure 3-35. Density of vibratioiial states for
a realistic model of configurationally disordered
PVC (Bernoullian paramater
P, = 0.47). Comparison with the experimental
spectrum (see text).
[lo81 suggested that the alkyl chains of fatty acids contain a few conformational
defects. This conclusion was shown not to agree with the conformational mapping
side-by-site obtained by defect-mode spectroscopy with the introduction of CD2
defects in the polymethylene alkyl chain.
Such discrepancy seemed either to weaken the relevance of LAM spectroscopy
for the measure of the length of the all-trans segment in a polyethylene chain, or to
cast doubts on the reliability of defect-mode spectroscopy. Some further studies
were in order.
Since dispersion curves have been clearly discussed in Sections 3.5 and 3.6, the
concepts which form the grounds of LAM spectroscopy can be easily defined. Let
us consider an all-tmizs polymethylene chain and focus our attention on the branch
(08 of the phonon dispersion curve. The branch starts as mostly C-C stretching and
ends as CCC bending. For a finite chain of N chemical units we expect to locate on
this branch a band progression of N vibrational modes characterized by the phase
coupling pJ = jn/N. The ‘most in-phase mode’ occurs at very mall frequencies; its
frequency approaches zero when the chain tends to be of infinite length. Let
1,2,3 . . . N label the components of the band progression of the modes which lie on
the Cllg branch.
Schaufele and Shimanouchi [ 13 I] have shown that for centrosymmetric all-from
polymethylene chains the lowest frequency mode performs an accordion-like motion
(LAM) with the atomic displacements describing a wave with one node at the