Modern Polymer Spect..

3. I7 Fernii Resoiiances 17 1
tering has been shown experimentally to have A, symmetry [28, 1231 and originates
from a convolution of a large population of overtone and combination levels which
are in Fermi resonance with the symmetric CH?-stretching mode which, in principle,
should occur as an unperturbed strong level near 2880 cm-', but has been
pushed downward by Fernii resonances with the manyfold of overtones and combinations
to which it has also lent intensity (Figure 3-41). Floating on top of such
a broad A, scattering we find the strong and sharp line associated with the CH?
antisymmetric stretching which remains unperturbed because it does not enter in
any Fermi resonance coupling.
3.17.2 Applications
We need now to translate the above theoi-etical results into practice. First, let us
start from an orthorhombic lattice with two molecules per unit cell and lower the
symmetry to a supermolecular organization in which the cell can be considered as
isolated and decoupled from its neighbors. This situation can be achieved in the
following case: (i) isotopic solid solutions; (ii) molecule as a guest in a chemically
different host lattice (e.g., urea clathrates) [ 1431: (iii) liquid crystalline-like systems;
and (iv) systems with confomiationally distorted chain ends, but with an ordered
bulk [1031. The following changes of the Raman spectrum are expected (and
observed):
(i) The triplet of lines in the bending region becomes almost a singlet (@), since the
crystal field splitting disappears and the convolution of overtone and conibination
bands for finite chains (two phonon states for polyethylene) in Fermi
resonance with the crystal field split fundamentals are removed (Figure 3-40).
(ii) As the number of overtone and conibination states in Fermi resonance with the
A, fundamental state (CH2 symmetric stretch) decreases we expect the lowering
of the total A, scattering and possibly a shift toward higher frequencies
of the A, fundamental. Generally, the scattering in the valley between the
antisymmetric and symmetric CH? stretch 2980 and 2850 cm-' respectively)
is observed to decrease and the two fundamental lines sharpen somewhat.
Attention should be paid to the fact that for chains with CH3 end groups
the symmetric CH-stretching mode shows up as a weak line within the same
frequency range.
The next step is to interrupt the long trans chain by gauche defects. The following
changes are expected (and observed) in the Rainan spectrum [ 141, 1421.
(iii) As both P and 6 inodes of CH? groups in gauche conformation occur at different
frequencies the population of vibrational levels which enter Fernii resonances
in the trans interaction scheme decreases. We expect changes of the
Raman spectrum both in the CH?-stretching and bending regions. Qualitatively,
the vibrational spectrum should change from that of a full. all-fr~nis
single chain molecule toward that of a fully decoupled structure, thus tending