Modern Polymer Spect..

tend to the limit of the infinite case and we expect to find in the spectra of the
finite, but long, chains clear (generally, but not always strong) quasi k = 0
phonons while the other members of the band progression will show quickly
decreasing intensity. This is the typical case observed in the series of n-alkanes
by Snyder and Schachschneider [9. 341.
(iv) It is obvious that if normal-mode calculations have permitted calculation of the
dispersion curves for the infinite polymer, the identification of the band progressions
in finite chains with identical structure is made easier. In contrast. if a
systematic study is carried out on a series of inolecules of the same chemical
class, but with increasing chain length, the experimental identification of the
band progressions allows experiinental determination of the phonon dispersion
branches from which a reliable force field can be derived. Vibrational spectroscopy
then becomes a complementary tool (sometimes unique) to the extremely
more expensive and elaborate neutron-scattering techniques. The whole work
has been very clearly and precisely explained and successfully applied by
Snyder and Schachschneider [9, 341.
3.9.3 Polymer Chains with Structural Defects
In order to model the reality of a polymeric material we need first to introduce in
the calculations the various energetically possible structural defects. The tjFes of’
defects to be considered are the following:
0 Clzenzical defects, e.g., head-to-head linking in an otherwise head-to-tail chain. A
typical case is the real structure of the chain of polyvinylfluoride ICHz-CFz),,
which contains a sizeable fraction of undesired head-to-head defects [89]. Once
the chemistry of a given polymer is approximately known, other kinds of defect
structures can be envisaged. A typical case is often found for isotopically substituted
chains when substitution is not ideally complete.
Stereocheiiiicnl defects, e.g., syndiotactic configurations in an otherwise isotactic
chain.
Cotiforwmtiond defects, e.g., gauche conformers in an otherwise all-trnizs chain
structure.
It is obvious that, because of intramolecular interactions, the introduction of
some kind of chemical and/or stereochemical defects forces also the introduction of
conformational defects.
Next, the model requires the definition of the concentrafion mid distribiitiori (e.g.,
Bernoullian, Markovian, etc.) of defects. If a small concentration of defects with a
random distribution is considered, defects most probably are isolated in the host
polymer ID lattice. When the concentration increases, even a random distribution
generates both isolated defects and a distribution of ‘islands’ of various lengths (see,
for instance, [90, 911).
When such variables are well defined, calculations require the construction of the
usual dynamical matrix and the solution of the corresponding eigenvalue equation.