Modern Polymer Spect..

128 3 Vibrational Spectra as a Probe of Stvuctzirnl Order
known about the dipole transition moments (infrared intensities) or Raman or
neutron-scattering cross-sections unless specific calculations are carried out using
other models for the electronic distribution (dipole derivatives, polarizability derivatives,
and vibrational amplitudes respectively 1971). Care must then be taken in
carrying out the comparison between calculated g( v) and observed spectra.
3.10 What Do We Learn from Calculations?
We have just outlined the way theoreticians in polymer dynamics face the problem
of the understanding of the vibrational spectra of polymers in their realistic state.
The reader interested in the theoretical aspects will find in the references quoted all
indications which will enable him or her to grasp the theory and to carry out the
calculations.
However, a larger number of reader do not wish to play with calculations, but
simply to know what we have learned about polymer structure and spectra using
these calculations and to apply quickly and directly the knowledge acquired to their
own problems. We report here the concepts of general validity in polymer spectroscopy
which were derived from calculations and which can be applied to any polymer
(for a general discussion, see [ 16, 19, 661).
The reader is certainly familiar with the traditional group-frequency approach
generally used in the past 50 years for the chemical application of the infrared
spectra (Section 3.4). Correlation tables and books have been written which discuss
group-frequency correlations and provide the way to carry out a chemical diagnosis
from the vibrational spectrum (so far, the infrared spectra have enjoyed great
popularity; the reader is advised to extend their interest to the very useful and easily
available Raman spectra).
As already discussed in Section 3.4, from the dynaniical viewpoint chemical correlations
are based on the fact that there are a few vibrations (normal modes) which
are Imyely localized on the functional group and give rise to medium/strong absorption
bands in infrared (scattering lines in the Raman) at specific and wellisolated
frequencies. The occurrence of such bands in the spectrum implies the
existence of such a functional group in the molecule under study. On the other
hand, when the vibrations involve a large molecular domain (collectiue motions) the
observed bands are no longer so characteristic of a given group of atoms.
The vibrations of disordered polymer chains follow the same kind of conceptual
path which, on the other hand, was also found earlier by physicists in the study of
lattice dynamics of very simple disordered lattices [98].
Let us make the problem simpler by considering briefly the small molecular unit
which contains the defect as an isolated entity consisting of n atoms which generate
3n normal vibrations that occur somewhere in the vibrational spectrum. Next, we
insert just one defect unit into the otherwise perfect polymer chain and allow the
whole system to display its own new dynamics through the observed (or calculated)
vibrational spectra.
The dynamics (new frequencies and displacements, see Eq. (3-17)) of the defect