Modern Polymer Spect..

3.7 The Cuse of Isotactic Polypvop.vleiie - A Tevbook Case 1 15
ture which is known from calculations and experiments [77] to form a 1D periodical
lattice with the coiiformational sequence -GTGTGT- which defines a threefold
helix with $ = (3rr/3. d/3) and one turn (t = 1). The isolated chain belongs to the
point group C3. Each chemical unit contains nine atoms and three chemical units
(z = 3) are contained in the crystallographic repeat unit [77]. Thus, we expect
3 x 9 = 27 phonon branches in q space or 3 x 9 x 3 = 81 in k space.
Following the previous discussion we expect:
0 27-2 totally symmetric q = 0 nonzero frequency modes of A species, infrared
active with 1) dichroisni and Raman active in zz polarization.
0 54-2 doubly degenerate modes (thus 27-1 frequencies) at y = B = 2n/3 of E
species infrared and Ranian active (1). The phonons for q~ = 28 coincide with
the phonons at q = 0 because of the periodicity of the functions ~ (y) (see Figure
3-10a).
The observed infrared spectrum of an isotropic sample of IPP is shown in Figure
3-9a, and clearly identifies the regularity bands associated with 1 D periodicity. The
assignment of the observed infrared bands to vibrations of species A, B = 0" (11) and
E, B = 120" (1) is carried out on a stretch-oriented sample (Figure 3-9b).
Dispersion curves have been calculated (Figure 3-10a) [56] from which spectroscopically
active phonons have been derived for q = 0 and 27c/3. One-phonon density
of states have been calculated and compared with the few data experimentally
available from neuron-scattering spectroscopy (Figure 3-lob) (see Section 3.8). In
Figure 3- 1 Oa, the dispersion curves of isotactic polypropylene are reported in terms
of the phase coupling y; in the same figure the six high-energy branches (associated
with the C-H-stretching modes in the 3000 cnir' range are omitted. The C-H
branches are flat (i.e., C-H-stretching phonons practically do not show dispersion
with p).
Next, let IPP chains crystallize in a cell with space group isomorphous with the
point group C, with four molecules per unit cell in three dimensions. In principle,
one should expect (9 x 3 x 4 x 3) - 3 = 321 vibrations in the spectrum for the
spectroscopically active phonons at the symmetry point r (i.e. k, = k, = k, = 0).
This would mean that, in principle, each of the 25A + (2 x 26)E k = 0 bands of the
single chain should split into four lines if intermolecular Van der Waals-type forces
between atoms were strong enough to generate an observable splitting. Generally,
such forces are very weak, especially since interchain distances are relatively large.
If such splitting could be observed, true infrared crystallinity bands of crystalline
IPP would be identified. The search for such splitting has not been easy and we
made careful experiments at very low temperature aiming at shrinking the crystal,
thus increasing the interchain interactions which should increase the correlation
field splitting (i.e. k, = 0 line-group modes in 1D should show splitting into niultiplets
due to phonons with k, = k, = k, = 0 in 3D (phonons at the syinnietry point
r in the BZ). Moreover, bands should become sharper since 'multiphonon states'
are depopulated. After much work the experiments were finally successful and the
Ranian spectrum of IPP at liquid nitrogen temperature shows indeed multiplet
splittings due to crystallinity (Figure 3-1 1) [78].