Modern Polymer Spect..

15
Figure 3-41. Calculated Raman spectrum for crystalline polyethylene in the CH-stretching region.
The spectrum is a convolution of numerous combination and overtone levels in Ferini resonance
with the nonresonant CH2 antisyinmetric stretchings. This spectrum should be compared with the
experimental one of Figure 3-37.
levels; moreover, in addition to the overtone levels, we should also consider their
combinations. For the space group we can use the observed experimental frequencies:
(2P-)-, B3u x B3,, = A,, 2 x 731 = 1462 an-'; 2(P-)+, B?,, x Bzu = A,,
2 x 719 = 1438 cm-'; (P-)- + (P-)', B3u x B?, = Bl,, 731 + 719 = 1450 cn-'. It
follows that for the space group the mode (af)+ can couple with 2(P-)- and
2(P-)+ while (6')- can interact with the combination (P-)- + (P-)'. Raman
spectra of stretch-oriented (extruded rods) in various polarization directions 128,
1231 show that the symmetry species of the lines at 1464 and 1440 cm-' is certainly
Big, while the line at 1416 cm-' is certainly A,.
The full treatment needs to consider in addition to the k 40 modes also the
k # 0 modes (throughout the whole BZ) due to either the finiteness of the chain, or
to the whole continuous dispersion curve for an infinite chain. The population of
overtones and combinations becomes extremely large and many of these levels can
enter Fermi resonances with a large transfer of intensity from the fundamental
strong modes.
Once the bending region has been understood the same approach must be taken
by considering all line-group or space-group overtones and combinations of the d
modes which are in Fermi resonance with the CH2-stretching modes. All details of
the calculations are provided in [140]. Figure 3-41 gives the result for crystalline
polyethylene.
The most important and useful feature in the Raman spectra of polymethylene
chains is that reported in Figure 3-37, which is easily observed every time a sequence
of CH2 units occurs in a molecule. If the system forms an orthorhombic
lattice, generally one observes a broad and strong line near 2850 cn-' with a broad
wing which extends towards higher frequencies foiming a broad background scattering
that reaches -2950 cm-'. Broad and sometimes ill-defined bands appear
near 2930 and 2900 cin-l. For the orthorhoinbic system, such a background scat-