Modern Polymer Spect..

130 3 Vibratiod Spectru as LL Probe of Structural Order
Phonon mode
a
Resonance mode
b
Figure 3-16. Dynamics of a one-dimensional lattice containing one defect. Vibrational displacements
of each unit are rotated of 90” for a better display of the normal modes. (a) uiiperturbcd
phonon of the host lattice; (b) resonance mode: and icj gap/local mode if!-om [66]).
1. Some of the normal modes of the defect strongly couple with the normal modes
(phonons) of the polymer and generate collective motions which lose all the
characteristic of the motion of the isolated unit. These normal modes are generally
labeled as ‘resomince ~zodes’ (Figure 3- 16) because their frequencies are close
enough to those of the host lattice that they generate mechanical resonance with
some of the normal modes of the polymer. This is generally found when the
frequency of the separated unit happens to occur within the range of frequencies
spanned by one of the dispersion curves of the perfect host polymer 1D lattice.
2. When the frequency of the separated unit differs strongly from the frequencies
spanned by the dispersion branches of the polymer chain, the motion of the unit
cannot couple with the motions of the host lattice, it cannot be propagated and
generates a mode strongly localized in space (at the site of the defect within the
polymer) and in energy (at a characteristic specific frequency). These modes are
generally labeled as ‘yap modes’ or ‘out-oflbancl modes’, since the frequency of
the isolated units occurs either in a gap between dispersion branches 01- above
the highest frequency branch respectively. Out-of-band modes in organic polymers
can only be observed in the case of perdeuterated polymers which contain
H atoms as defects. In this case, C-H stretching modes occur at frequencies
higher than any other normal modes of the polymer.
3. Compared with the results from the dynamics of simple impure 3D lattices, in
the case of 1D lattices (polymers) localized modes (or quasi-localized modes) can
sometimes also be generated if the frequency of the defect unit occurs within the
frequencies spanned by a dispersion branch of the perfect host lattice. As the