Modern Polymer Spect..

172 3 Vibrutionul Spectra as n Pvohe of StrirctLiral Order
to the situation described in Figure 3-38 for hexadeuteriopropane. It should
be noticed that necessarily the 2850 cn1-l line should move towards higher
frequencies approaching the unperturbed value near 2880 cni-' and the 2s line
near 2930 cm-' should eventually become stronger as it does not share with the
manyfold of binary combinations and overtones the intensity borrowed from
the fundamental originally observed near 2850 cm-'.
(iv) A drastic increase in concentration of gaziche structures occurs when the polymethylene
system melts. In that case one can assume that the statistics of
Flory's Rotational Isomeric State Model [48] works and we can describe the
system as coiisisting of a distribution of gauche and short trans sequences.
Upon melting, the d+ band near 2850 cm-' becomes the strongest feature in
the spectrum and d- collapses into a very broad band with its maximum
shifted upward of 4-10 cni-I. The overtone level near 2940 cm-l increases
in intensity. This is a very useful marker when the chain is confoimationally
collapsed (liquid like) (Figure 3-37b).
(v) There are two possible interpretations of the broadening of d- band observed in
the liquid phase. The first is that the broadening is the result of a convolution
of many transitions associated to d- mode of CH? groups in constrained nonequilibrium
near gauche conformations [143, 1441. Another explanation of the
broadening refers to the overall dynamics of the whole chain which may occur
in the liquid (see Section 3.18) [145].
(vi) A detailed study has been carried out by Abbate et al. on the molecule
CD3-CH2-CHa-CD3 11411 as a model in which (a) the possible coupling with
the methyl end groups are removed by deuteration and (b) only one degree of
torsional freedom between CH? groups is allowed. It is immediately apparent
that in gauche conformation the symmetry of the molecule is lowered, thus
changing the resonance schemes which may involve also the d- mode which
is unperturbed in the truns case. Calculations show that both d- and d+
are allowed to mix, thus reshuffling the intensities in a way that is difficult to
predict.
(vii) The experimental intensity ratio R = I2~50/12940 has been proposed as an experimental
way to determine the relative concentration of trans versus gauche
conformers in a sample. R has been matter of strong debate (see for instance
[ 1401). As a result of the calculations by Abbate on hexadeuteriobutane [141],
because of a mixing of the modes and the unpredictable changes of the extent
of Feimi resonance, we do not advise the use of R as analytical probe in liquid
polymethylene systems or in partially disordered solid polyethylene samples.
3.18 Band Broadening and Conformational Flexibility
The experimental spectroscopic facts which need to be accounted for in a comprehensive
way in relation to order-disorder are the following (we report here the
most striking manifestations, recorded in various ways, for oligo and polyniethylene
systems):