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the effect based on anharmonic potentials, and predicted the shifts seen
in polydiacetylene single- crystal fi bers (see Figure 4.5). Considerable
work has been undertaken by Tashiro [88] upon the prediction of spec-
troscopic (particularly Raman) band shifts, including work on polyoxy-
methylene (POM) and polyethylene (PE) chains. Using general
expressions for the strain energy and potential functions of asymmetric
and symmetric vibrations, Tashiro [88] was able to obtain good pre-
dictions of the rate of his experimentally determined Raman band
shifts. This type of approach was later applied to a PBO chain by
Kitagawa et al. [91] and more rigorously for the case of a semicrystal-
line structure [92] .
This approach is generally adequate in the case where nonbonded
interactions do not signifi cantly contribute toward the deformation of
the structure. Little or no work exists, however, on modeling Raman
band shifts using molecular force fi elds. This type of approach uses a
normal mode analysis to predict vibrations of minimized structures.
Normal mode analyses on static theoretical cellulose structures have
been previously performed [93], but not for deformed polymer chains.
In recent times, Eichhorn and others [90,94] have used a commercial
force fi eld, a molecular mechanics approach, and normal mode analysis
to predict band shifts in cellulose polymorphs (both I and II). Each
structure was taken from recently published atomic coordinates [74 - 76]
and minimized within a commercial force fi eld (COMPASS
) under
restraint. The normal mode analysis used predicted infrared intensities,
and by a process of elimination a number of bands were chosen which
best represented the experimentally observed Raman band shifts. Good
agreement with the experimental data was obtained, and also with
chain stiffness data obtained from X-ray diffraction, a subject to which
we will now turn.
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4.5 COMPOSITES
4.5.1 Fiber-Reinforced Composites
The observation of Raman band shifts indicating the molecular defor-
mation of polydiacetylene single- crystal fi bers was the fi rst report of its
kind [30] and it opened up the possibility of using Raman spectroscopy
to study composite micromechanics. This was followed a few years later
by Galiotis et al. [95], who showed that it was possible to follow the
interfacial adhesion between two lap-jointed polydiacetylene fi bers
made using an epoxy resin adhesive. They found that strong well-
defi ned Raman spectra could be obtained from the fi bers and that the
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