Modern Polymer Spect..

124 3 Vibvcrtinntrl Spectvci as ci Prohe qf Stvzicturrrl Order
100, II I I I
Figure 3-14. Comparison of the calculated
g(v) of single-chain polyethylene with the
infrared spectrum of an e\rtended chain of
polyethylene.
sider the experimental infrared spectrum of high-density crystalline polyethylene
(Figure 3-14). The infrared active phonons at r for an orthorhonibic lattice with
two chains per unit cell show the predicted crystallinity bands as doublets originating
from the k = 0 modes of the former regularity bands for a chain with a ID
symmetry operator $(Q = n, d/2). In Figure 3-14, the infrared spectrum is superposed
to the singularities of the calculated g(v) while the Ranian active peaks are
indicated in the figure. It is quite clear that not all the peaks in the observed vibrational
infrared or Ranian spectrum find a one-to-one correspondence with the
singularities in the calculated g(v). It follows that, in addition to the ‘perfect’ part of
the all-trans polyethylene chain, extra structural features must exist whose existence
is indicated by the additional peaks in the infrared or Raman spectra. It will be
shown that the extra absorption or scattering are associated with various kinds of
conformational defects.
In this section we proceed as follows.
1. First, we take the perfect and infinite polymer chain and truncate the chain in
increasingly shorter segments and predict theoretically and watch experimentally
the effects of such truncation. The structural perfection is retained.
2. Any kind of chemical and/or structural disorder can be introduced into the
chain. We chose the various plausible kinds of disorder, their population and
distribution, and try to predict the infrared, Raman and neutron-scattering
spectra by suitable theories and computational techniques.
3. Calculated theoretical and experimental cases will be presented.
3.9.2. Finite Chains
The theoretical modeling of the vibrations of molecular chains with finite length has
been nicely treated by Zbinden [18] and by Snyder and Schachschneider [9, 341.
While the approach by Zbinden is mathematically complete, but it applies to simplified
monoatomic chains, quite away from chemical reality, the model by Snyder
and Schachschneider is more directly applicable to real molecules and will be