Modern Polymer Spect..

3.1 9 A Worked Example 199
The soliton solution gives the values of Oi which describes a twist in the chain
which, in the absence of friction, propagates keeping the same shape and velocity v.
The Utah-twist (twiston) is then approximated to a solitonic wave whose velocity
of propagation is estimated by Mansfield (using some molecular parameters) to be
- 10j cm s-I.
The final concept which emerges is that in the orthorhonibic crystal one can
conceive the existence of conforniational collective excitations thermally generated
which extend over approximately 20 CH2 units and move along the chain with a
certain velocity.
The main problem is to prove the existence of such mobile twistons. The idea of
using spectroscopy implies the fact that we should be able to detect somewhere in
the vibrational spectrum absorption and/or scattering associated to vibrations
localized on the twiston. Calculations have been made (i) of the density of vibrational
states of a long polymethylene chain containing a random distribution of
twistons and (ii) of the infrared spectrum (frequencies and intensities) of the molecule
C19 containing a twiston. A comparison has been made with the infrared
spectrum of C19 in the all-frans structure [169] (Figure 3-62).
in these calculations the twiston is assumed not to be mobile, but pinned at a
given site of the chain. The fact that the twiston is mobile along the chain in principle
does not deny the possibility, under certain conditions, to observe its vibration
in the infrared/Raman spectra. The conditions are the following:
(a) Since the band width is inversely proportional to the vibrational lifetimes of
each normal vibration, if the velocity of the twiston is small the vibrational
lifetime is long enough to allow the formation of its own vibrational mode and
can give rise to an observable IR or Raman band. if the twiston moves too fast,
the vibrational lifetimes are too short and the band broadens and flattens in
a broad continuum. Simple calculations show that if a band of the twiston has
to be observed with Ai~,p M 20 cin-' it sets an upper limit to the velocity of the
twiston of = lo4 cm-' which is not too different from the velocity estimated by
Mansfield.
(b) The concentration of twistons has to be large enough to generate a detectable
absorption in IR or scattering in the Raman. The concentration of twistons
depends on their energy of formation which has to be low if twistons are to
be seen spectroscopically. The energies calculated for the Utah-twist [ 1661 are
much too high and would make the twiston undetectable by spectroscopic
techniques.
The results of the theoretical calculations of the spectra of twistons and a few
attempts to catch spectroscopic signals possibly associated to twistons are reported
in [169]. The evidence collected so far is neither compelling nor completely negative.
The model needs to be supported or dismissed by other physical techniques.
The model of twistons which move as 'solitary waves' was also proposed by
Dwey-Aharon et al. [ 1701 in the case of polyvinyljdene fluoride (CHz-CF?),, which
upon poling transforms from the helical structure (TGTG') (labeled either as p
form or form 11) into a planar all-tram one (a, or form I). Form I is technologically