Modern Polymer Spect..

eyularity), e.g.,
2. During the polymerization process the catalysts is chosen in such a way that
.stereo-rrgzilur.itJi is assured [45], e.g.,
isotactic: CH3 CH3
I
-C-CH?-C-CH2
I
H
I
I
H
3. Upon solidification from solution (or from the melt), inacromolecules coil in an
energetically preferred minimum energy conformation and form long chains
along which roriforniatioiznl periodicity is assured [46-48). Chains are considered
long enough to be considered ‘infinite’. For isotactic polypropylene, the conforniational
sequence is TGTGTG. The overall shape of the chain can be described
as a regular helix with a threefold screw axis [45].
4. The process of solification proceeds with the formation (when possible) of crystalline
material in which chains pack in a lattice with tri-diinensional periodicity.
The conditions for perfect packing are that chains possess chemical regularity,
configurational periodicity, and conforinational regularity.
Since interniolecular Van der Waals-type forces which hold molecules in a crystalline
lattice are very weak, when compared with intramolecular covalent forces,
lattice dynamics of polymers is made easy by considering firstly the vibrations of
infinite isolated polymer chains [ 16- 181. Three-dimensional order is considered
later as a sinall perturbation of the normal modes of the one-dimensional chain
by the weak intermolecular forces [49]. In other words, we are considering the
dynamics of one chain ‘in ziacuo’.
The structural characteristics of the polymer chain constructed as described
above are that translational or roto-translational symmetry can be found along the
chain in addition to the traditional point group symmetry operations (rotation axes,
symmetry planes, inversion center, and identity) [18].
In a dynamical treatment the labeling of the internal coordinates starts froin the
reference repeat unit and proceeds along the chain by applying the one-dimensional
translational operator which identifies the translationally equivalent internal coordinates.
The structural situation is clarified if one considers that a polymer chain
can be generated by application to a chemical repeat unit of a certain rototranslational
operator $(Q, 1) which corresponds to a rotation of an angle 8 about the
chain axis and a translation of a fraction 1 = d/n of the crystallographic unit length
(repeat distance) d. In general, the crystallographic repeat unit can contain L
chemical units coiled in a helix with t turns [47].