Modern Polymer Spect..

3.18 Band Bvoaderiing arid Conjonnationril Flexibility 177
tional relaxation contribution can be easily evaluated. For all antisymmetric modes
a = 0 and p = $; only the contribution from coupled vibrational-reorientational
motions can then be obtained from Raman experiments. The evaluation of the pure
reorientational contribution can be obtained by suitably subtracting the contribution
from vibrational relaxations (Eq. (3-59)).
3.18.2 Short and long n-alkanes
The Raman spectra of a series of n-alkane suitably chosen have been studied [137]
with the precise aim of extracting from d- (antisymmetric, - depolarized) and d'
(symmetric - polarized) modes of the CH2 group information of general validity on
intra- and intermolecular dynamics using the techniques discussed in Section 3. IS. 1.
The following molecules have been studied [ 1371 in the solid and liquid states:
propane-d6 (CD3CH2CD3) butane-d6 (CD3CH2CH2CD3), and pentane-dlo
(CD~CH~CHZCH~CD~) and n-nonadecane. The following conclusions, which may
be of general interest, have been derived:
1. For d+ p = 0, thus allowing us to distinguish the contribution by vibrational
relaxation processes; for d- CI = 0 and p = %, thus the coupled vibrationalreorientational
processes are active simultaneously. The reorientational contribution
was derived by suitable deconvolution methods (Eq. (3-59)).
2. The temperature independence of the band width of d+ modes has been verified
and provides an average value of T(VIBR) - 1.3 x 10l2 s for the three small
deuterated molecules. An amplitude-dependent vibrational dephasiiig process
(inhomogeneous broadening) best accounts for the observed temperatureindependent
broadening.
3. A ~ J of ~ / d- ~ is strongly teniperature-dependent and increases rapidly with
increasing temperature (Figure 3-41); correspondingly, r(RE0RIENT) decreases
by at least one order of magnitude from low to higher temperatures (see
Table 3-3). It is found that, at a given temperature, identical for the three deuterated
molecules, the band width increases with increasing chain length. Moreover,
at a constant temperature, the reorientational relaxation time increases
with increasing chain length. This trend is consistent with the view that the contribution
of reorientational relaxation decreases with increasing chain length, as
might be expected based on inertial and frictional effect. Indeed, it is conceivable
that while the molecule of propane in the liquid phase may easily tumble in
all directions about its axes, for longer molecules the end-over-end tumbling
becomes progressively less likely while some sort of rotation about the long
molecular axis may still occur even for longer n-alkanes.
4. For chains larger than propane (for which no torsional motion about
(CHl)-(CH?) bonds exists) it is quite conceivable that the increasing hinderance
to molecular reorientation which broadens d- mode comes from torsional
motions of the molecular skeleton, i.e., its overall torsional flexibility. In other
words, when a flexible molecule tries to tumble it necessarily drives the motions
of the torsional angles. We expect these contributions to increase with iiicrcasing