Modern Polymer Spect..

3.19 A Worked Example 197
existence of the c( phase and for the longitudinal motion. First, the general idea
was that in the a phase chains rotate rigidly [152-1541. Next, models of rotational
diffusion coupled with longitudinal translations of one CH2 were proposed based
on NMR data [ 161, 1621. Elastic neutron-scattering experiments introduced the
idea of diffusional cooperative rotations or of independent translational motions
with jump length of one CH;! unit followed by 180" rotational jump [163]. A
translation of two CH? units was proposed [164] in agreement with calculations
by McCallough [165]. Most of the models proposed consider that in the solid state
chains perform large-amplitude collective rototranslational motions. McCullough
has presented an interesting model which shows by calculations that chain can find
a favorable energy path if they librate rigidly with large amplitude librations and
translate along the chain axis.
The knowledge at the molecular level of the mobility of chain molecules in the
solid state is of basic importance for the understanding of the general processes of
annealing of chain molecules. Attempts have been made to derive information using
band shapes in the Ranian spectra, especially focusing on the CH-stretching vibrations
(Section 3.18).
As already stated at the end of Section 3.18, we have measured the temperaturedependent
band widths and the frequency of the CH2 d- mode for several crystalline
n-alkanes and polyethylene and found no sizable broadening or upward frequency
shifts until they approach the melting point. All the theoretical models that
imply large amplitude librotorsional motions are not supported by the spectroscopic
criteria discussed in Section 3.18. We found evidence of large-amplitude
libro-torsional oscillations only when the n-alkane chains are included as clathrates
in various systems.
Conclusion no. 8
Based on the analysis of teniperature-dependent Ranian band shape and frequency
shift of the Raman active antisymmetric CH1-stretching modes (Section 3.18),
contrary to the case of urea clathrates, in the solid crystalline state (including the CI
phase), n-alkane chains do not perform large-amplitude libro-torsional motions.
We must search for alternative molecular models which may account for longitudinal
diffusion with transport of matter without implying large amplitude librotorsional
oscillations. A conceptually and, at least, intellectually exciting model
which may help in this search has been presented by Mansfield and Boyd [166] who
attempted to account for molecular relaxation phenomena. We label this model as
Utah-twist. The main message by these authors is that calculations suggest that an
orthorhombic lattice of n-alkanes can host a chain distorted by a gentle and long
twist. The long twist is achieved with a uniform succession of small torsions about
the C-C bonds which is extended over approximately 12-15 CH2 units. At the end
of the gentle twist the chain is flipped by 1800 with respect to the head of the twist.
Such a long twist (which we label as 'twiston') can propagate along the polymethylene
chain without finding a barrier to its propagation. Based on the aton-atom
potential chosen by the two above authors the activation energy for generating a