Modern Polymer Spect..

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3.11 A Very Siriiple Ccrse: Lattice Dyriurriics of HCI-DCI Mi-xed CrjistLiIs 131
polymer chain is conformationally flexible it may well occur that, for a certain
geometrical arrangement of the atoms. the motion of the defect unit happens to
be orthogonal (or quasi-orthogonal) to the displacements of the atoms during a
certain vibration of the host lattice. It has been shown [99] that in an n-alkane
chain the CH: wagging of the central unit in a conformational sequence such as
-(G)-CH?-(G)- generates a pseudo-localized CH2 wagging motion almost fully
decoupled from the vibrations of the host lattice, even if the frequency occurs in
the frequency range spanned by the CH? wagging dispersion branch [99].
The observation of characteristic gap modes in disordered polymers becomes
then the basis for the use of the vibrational spectra as useful probes for the structural
characterization of these systems.
It should be remembered that the above discussion has been presented by considering
only one single defect embedded in a host polymer chain. When a distribution
of defects is considered, defects may occur close enough to couple mechanically.
Splitting and changes of the gap modes (frequencies and intensities) may occur and
are indicated by the calculations (see, for instance [ 1001).
3.11 A Very Simple Case: Lattice Dynamics of
HCl-DCl Mixed Crystals
It is considered that the simplest possible realistic case on which our theories can be
tested, and which could act as a guide to the reader for the discussions which follow,
are the studies of mixed crystals of HC1 and DCl [97]. Solid HCl and DC1 undergo
a first-order phase transition at 98.4 OK, and 105.0 OK, respectively. Below the transition
temperature, X-ray and neutron diffraction studies show the existence of an
ordered face-centered orthorhombic structure which contains planar zigzag chains
consisting of HCl (DCl) molecules linked to each other by hydrogen bonds (for a
list of references on the physical properties of solid HCl, see [97]). Our model of the
chain consists of a pure infinite isolated chain of the type ... H-Cl.-.H-Cl...H-Cl...
(Figure 3-17). Using the techniques presented in the previous sections we have
Figure 3-17. Geometry and internal
coordinates (in-plane and out-of-plane) for
crystalline HCI or DC1 in the orthorhombic
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modification. Only one single chain has been
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considered. =z - + + -