Modern Polymer Spect..

180 3 Vibrational Spectra as ci Probe of Strtrctirrcil Ordu
modes shifts very selectively upward, while the frequency of d+ mode remains
unchanged. There must be some specific process which should be discovered.
With this purpose various dynamical possibilities have been considered [ 1451.
It has been concluded that a rational explanation is that there exists a selective
intramolecular coupling between d- modes and the torsional modes of the carbon
backbone. Symmetry consideration tell us that for a trans-planar molecule
the existence of such coupling will affect d- and not d+ modes. In other words,
within the quadratic approximations interactions of the type fCH stretch/C-C torhions
seem to exist and are modulated by the amplitude of the collective torsional
flexibility.
Another contribution to the upper shift may come from a complex scheme
of Fermi resonances which are activated because of the lowering of the instantaneous
symmetry during the libro-torsional motion. This difficult problem
remains unsolved.
5. The final observation, relevant for the discussion which follows in Section 3.19,
is that in crystalline a-alkanes the band width of d- is relatively narrow and the
frequency does not change throughout the temperature range of existence of the
crystalline lattice. This suggests that libro-torsional motions are not allowed in
the crystal and only small amplitude collective librational phonons seem to be
allowed. Some additional observations will be added in Section 3.19.
3.19 A Worked Example: From n-Alkanes to
Polyethylene Structure and Dynamics
3.19.1 Description of the Physical Phenomena
We wish to guide the reader through a realistic case worked out step-by-step using
most of the concepts and methods discussed in this chapter. We consider the case of
n-nonadecane (CH~-(CH~)I~-CH~) as a prototypical case and try to derive from
the vibrational spectra all possible information about its structure and dynamics.
Both order and disorder will be considered. The methods applied and the conclusions
reached form the background knowledge to be used for the understanding ot
(i) the structural properties of many molecules containing long-chain alkyl derivatives;
and (ii) the structural features of polyethylene or other polymers containing
polymethylene segments.
The basic physics we wish to understand is the mechanism at the molecular level
which generates the phase transitions of relatively short n-alkanes. The experimental
nonspectroscopic facts to be accounted for are the following (for a collection of
references and a full discussion of many of the data presented in the first part of this
section see [ 1031): orthorhombic n-alkanes first undergo a solid-solid phase transition
(Toicc) to a phase variously described as 'rotatory phase' or 'c1' phase whose
structure has been matter of controversy in the literature. This phase characterizes a