Modern Polymer Spect..

3.6 Froin Dynaiiiics to T’ihratioiial Sjlectra of Onr-DiriimsioriLII Lattices 1 1 1
neglected the possible existence of a tridimensional arrangement of the polymer
chains in the solid. Experimentally, it transpires that for most of the polymers the
entire observed spectrum can be accounted for in terms of the k = 0 modes of the
single infinite chain [65]. When the material is melted, oi- is dissolved in some suitable
solvents, k = 0 modes disappear and the spectrum becomes typical of a conformationally
disordered ‘liquid-like’ molecule with the classical ‘group frequency’
modes which can be interpreted using the classical spectroscopic correlations (see
Section 3.2).
The fact that, in going from the solid to the liquid state, maiiy bands disappear
has been taken by authors as an indication that these bands must be associated with
the material in the Crystalline state. In spite of the existence of clear and easy
dynamical theories on polymer vibrations, a whole body of literature has accepted
the direct correlation between k = 0 modes of the single chain and content of
material in the crystalline (3D) state.
This view is wrong both in principle and in practice. In spite of strong warning
and extensive discussions (theoretical and experimental [65, 661) the general definition
of ‘crystallinity bands’ has been widely and uncritically accepted by the chemical
polymer community and even analytical determinations on the concentration
of crystalline material have been carried out on polymers which show no direct
spectroscopic indications of crystallinity [65, 661. The disappearance of such bands
upon melting is simply due to the fact that the conformational regularity of the
chain collapses and no 1 D-translational periodicity can be found anymore over a
reasonable chain length. Chemical and stereo regularities are not modified in the
melt or in solution, but all optical selection rules are removed because of the lack
of phase coupling between adjacent units. From the above discussion it becomes
apparent that the k = 0 bands previously discussed (generally and reasonably
called ’regularity bands’ [65, 661) arise from a polymer molecule organized as a onedimensional
crystal iiz uacuo, as if there were no intermolecular lattice forces. It
becomes apparent that their labeling as crystallinity bands is a conceptual error.
Certainly, the dynamical treatment can be and has been carried out for a few
cases by taking into account the tridimensional arrangement of polymer chains [49].
A model of suitable intermolecular nonbonded atom-atom potential has to be
chosen critically [49, 671 and calculations can be carried out using the same principles
discussed previously in this chapter. The number (q) of atoms per tridiniensional
unit cell increases, the complexity of the BZ increases, many more phonon
branches are calculated for different directions of the wave-vectors, and special
symmetry directions and symmetry point in the BZ can be found depending on the
syiiinietry of the whole lattice [60, 641. Typical examples are given in Figures 3-3
and 3-6.
Since intermolecular forces in polymers are weak, their effects on the phonons
of the whole lattice are relatively small, thus originating small splitting of few of
the regularity bands [68]. Rigorously speaking, the limited splitting of the regularity
bands observed for a few polymers originate from phonons at the point ik, =
k, = k, = 0) of the tridimensional BZ. Such splitting can indeed be considered as
crystallinity band and certainly originate from material organized in a tridimensional
lattice. This occurs when intermolecular forces are strong enough, the nuin-