Modern Polymer Spect..

112 3 Vibrutionnl Spectru as ci Probe of Strirctzirul Order
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WAVENUMBERS
Figure 3-8. Infrared absorption spectrum of highly crystalline polyethylene where crystal field
splitting is shown in the 1450 and 720 cm-' range due to crystal field splitting (crystallinity bands).
ber of chains in the unit cell is appropriate, and space-group selection rules are
favorable [67-691. Among the true crystallinity bands we have also to consider the
low-frequency lattice modes associated with the translation and librations of the
molecules which behave almost as rigid objects moving within the 3D lattice.
The classical case of crystalline polyethylene (Figure 3-8) may be mentioned in
reference also to the vibrational spectra of its model compounds consisting of a
series of n-alkanes. Relatively short alkanes with an odd number of C atoms crystallize
in the orthorhombic lattice with two molecules in the unit cell. Relatively
short n-alkanes with an even number of C atoms crystallize in monoclinic or triclinic
unit cells with one molecule per unit cell. Very few of the normal modes of
orthorhombic n-alkanes show in infrared and/or Raman doublets due to phonons
at r (i.e., true doublets due to weak intermolecular forces; such splitting is coinmonly
known and studied as correlation field splitting 1701); the spectra of monoclinic
(or triclinic) n-alkane do not show any splitting as if the molecules, in a first
approximation, were trans-planar, but in vuczio. Indeed, there exists only one molecule
per unit cell and no correlation field splitting can occur. Analogously, when
orthorhombic n-alkanes molecules are heated just before melting they transform
in a probably monoclinic unit cell (there may be different interpretation of the
so-called monoclinic modification). The classical doublets (phonons at r) observed
in infrared and Raman disappear and singlets (phonons at k = 0) are observed as
if the molecules were iiz ouc~io. This problem will be matter of extensive discussion
later in this chapter.