Modern Polymer Spect..

center of the chain [ 1321. Such a mode has been labeled as LAM 1 mode. The higher
frequencies components have been indicated analogously as LAM?, LAM3, etc.
The odd modes give origin to a strong band progression in the Raman spectrum,
with LAMl extremely strong and the other components with intensity rapidly
decreasing as the number of nodes increases.
Schaufele and Shiinanouchi have considered the longitudinal stretching motion
of an elastic rod of length L, elastic modulus E and density p and have shown that
the frequency of its ‘according’ motion can be written as
(3-53)
The same authors have shown that if E and p are suitably chosen for polymethylene
chains, VLAM~ of tram-planar finite polymethylene chains also follows the
same law. In this case L is the length of the all-miis polymethylene chain which can
be approximated as
L(A) z 1.25(A)(N - 1) (3-54)
where N is the number of CH2 units of the chain.
LAM spectroscopy gained much popularity in polymer characterization and
morphology since it has been possible to measure from Raman spectra the length of
the tmns-planar stems in polyethylene laniellae and in many other relevant cases.
As mentioned above, these concepts were applied in a straightforward manner
to the case of fatty acids by the French group [108], but the results were highly
controversial, thus casting some serious doubts on the applicability of LAM
spectroscopy.
The dynamical problem has been re-examined with the purpose of evaluating the
effects of chain ends on LAM modes. Simplified models were employed which
consider chemical repeat units as point masses joined by elastic springs. Various
cases of perturbations of the LAM modes were considered namely:
(i) The effect of heavier masses at one or at both ends of the polymethylene chain
mimicking systems such as X-(CH2),-X where X = -CH3, F, C1, Br, I, etc. It
transpires that \’LAMI decreases when the mass of X increases [133].
(ii) The effect of joining a polymetliylene chain with another chain with varying
length and with different and variable spring constants. The realistic case
studied was the class of eniifluorinated n-alkanes F(CFZ)~ . (CHZ)~H where N
and M change in a broad range of values. Contrary to expectations, the two
segments do not generate two independent LAMl modes, nor can a simple
heavy mass (X as (i)) at the end of a chain account for the observed spectra.
Calculations show that the molecule vibrates as a whole and generates only one
LAMl mode whose frequency is critically dependent on the length of both
segments. Moreover, the node of such LAMl inode shifts along the chain
depending on the length N and M of the two arms [134].
(iii) The above results opened the way to the study of dimeric systems where the
two monomers are joined head-to-head by springs with varying spring con-