Modern Polymer Spect..

122 3 Vibrational Spectra as N Probe of Structural Order
displacement C of atom n for the j-th normal mode of the r branch with frequency
wi. The sum is extended to all the atoms n in the unit cell and to all branches r in
the dispersion relation. The Debye-Waller factor W, of each atom n has an explicit
expression [83, 841 which again contains quantities defined in Eqs. (3-51) and (3-52).
In spite of the seemingly complex expressions given in Eqs. (3-51) and (3-52) for
the scattering cross-sections, all terms appearing in these equations are known from
dynamics and from experiments? and have been defined in the previous sections of
this chapter. Automated computer programs have been added to the classical programs
for normal coordinate calculations of polymers for the calculations of the
INS spectra.
The reason of requiring the experiments to be carried out on stretch-oriented
samples mounted with known geometry with respect to the incoming neutron beam
is the existence of the ek . Cy,r term which indicates that the scattering cross-section
is determined by the directional interaction of the neutrons with wave vector ko and
the direction of the atomic displacements. This situation is very similar in the experiments
of infrared spectroscopy in polarized light with a stretch-oriented material.
In dichroism experiments the absorption intensity is proportional to /pi. El’, i.e.,
to the square of the projection of the molecular dipole moment change p during the
i-th normal mode onto the electric field of the light beam.
The g(w) measured with INS experiments on stretch-oriented materials is then
‘amplitude-weighted’ and is ‘directional’. The directionality of the displacements
associated with a given normal mode can be determined by placing ko 11 and I to
the chain direction.
The history of polymer neutron spectroscopy can be divided in two different time
domains. The enthusiasm for INS experiments in polymers reached its highest peak
in the 1970s, but the experiments have been restricted to a few polymers with a
limited number of data [84, 851 which could hardly solve particular problems in
polymer dynamics. The availability of modern instruments with higher resolution
and with the possibility of removing most of multiphonon scattering has presently
revived the field and vibrational spectroscopists await with great interest for the
revival of this important field of research.
In Figure 3-13 we show the most recent INS results reported by Parker [86] on
oriented polyethylene at 30 K obtained with the high-resolution, broad-band spectrometer
(TFXA) at ISIS pulsed spallation neutron source at the Rutherford Appleton
Laboratory, Chilton, UK. Notice that the whole spectral range 0-4000 cnc‘
range has been explored with considerable resolution, especially in the lower-energy
region.
3.9 Moving Towards Reality: From Order to Disorder
3.9.1 Basic Concepts
In reality, polymeric materials never possess the perfect chemical stereochemical
and conforinational regularity which were assumed at the beginning of Section 3.5.