Modern Polymer Spect..

176 3 Lri/ibvational Spectrci cis (1 Probe c?f'Stncc.tLiral Ovtlev
conformation [ 1461. Some additional or alternative processes then must exist. We
wish to discuss the results of band-broadening studies which may shine more light
on the conformatioiial dynamics in systems where order-disorder may exist.
A full discussion of the theory and experiments on band-broadening effects in
n-alkanes is reported in [137]. We wish to outline here a few basic concepts which,
in a first approximation, are the tool to be used in the understanding of the complex
dynamics in conforinationally flexible systems.
Band broadening [147] both in infrared and Raman spectra of polyatomic molecules
in the liquid phase may arise from vibrational relaxations (VIBR) (i.e., some
kind of process dissipates the vibrational energy stored in a vibrational transition)
and/or from reorientational motions of molecules (REORIENT) (i.e., the energy
stored in a vibrational transition is used to generate a reorientation in space of
the molecule). Vibrational relaxation can be due to vibrational energy dissipation
to the rotational-translational degrees of freedom of the thermal bath, to intramolecular
energy transfer between vibrational modes, or to several intermolecular
phenomena such as resonance vibrational energy transfer and vibrational
dephasing. Theory states that the amplitude-dependent vibrational relaxations are
temperature-independent, while the angular-dependent reorientational relaxations
depend strongly on temperature.
Raman scattering provides a nice way to gather information on these processes.
For liquid samples, it is possible to separate experimentally the isotropic spectrum
(ISOT) from the anisotropic one (ANIS), namely
I(IS0T) = I(ll) - (4/3)I(i)
(3-55 j
I(AN1S) = I(i) (3-56)
From these measurable quantities, under certain approximations [ 1371, it is also
possible to give precise expressions for the relaxation times:
where
z(V1BR) = 1 /(KcAu~~)(ISOT) (3-57)
z(RE0RIENT) = ~/(KcAv~/~)(REORIENT) (3-58)
It is coinnionly known that the depolarization ratio for linearly polarized light is
given by
p = I(I)/I(II) 1 3P2/(45C(' + 4p2j (3-60)
where a is the mean polarizability describing the isotropic component of the Ranian
polarizability tensor and P, the anisotropy, describes the anisotropic component.
It follows that for totally symmetric modes p 5, 0, I(il)= IfISOT), and the vibra-