Nonlinear vibrational spectroscopy of surfactants at liquid interfaces Page: 42 of 229
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parameter R describes how anisotropic the polarizability derivative of a single CH bond
is and can be taken from theoretical calculations23 (R = 0.14) or determined from Raman
Ba
spectra of polymethylene24 (R = 0.18). The aQ elements for the CH3 and CH2 groups
are then determined by adding the contributions from all CH bonds. Similarly, for
each group is determined by adding the contribution of individual bonds. Finally aq is
determined by Eq. (2.17).
For the CH3 group with C3V symmetry, we take the symmetry axis as 4, and is
such that one CH bond is in the 4C plane. For the symmetric stretch mode the normal
coordinate is Q = (r +r2 + r3), where r; is C-H bond distance for the i'i' H atom. We
then have
ap _ ap r, p r2 + rp Br (3p, cos8)= p 1 (2.18)
Q r Q -2 -Q -3 oQ (. 8
where 8 is the angle between a CH bond and the axis (cos 8 = 1/3) and po is the dipole
moment derivative for a single CH bond. For the polarizability derivative we note that
with C3v symmetry its nonvanishing elements are aQ , "" and a . They are
calculated as follows
a4 - aa. ar aa r aa r
aQ arl cQ ar2 aQ ar3 aQ (2.19)
= 1(3 ao cos2 8+3Rao sin2)= 31 (1+8R)ao28
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Miranda, P.B. Nonlinear vibrational spectroscopy of surfactants at liquid interfaces, thesis or dissertation, December 14, 1998; California. (https://digital.library.unt.edu/ark:/67531/metadc702752/m1/42/: accessed April 17, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.