Formulas for the analysis of surface sum-frequency generation spectrum by CH stretching modes of methyl and methylene groups

Abstract

Derivation has been made of the expressions of surface vibrational sum-frequency generation(SVSFG). The results include (a) the vibrational selection rule, (b) the expressions of the susceptibility tensors at the surfaces composed of functional groups with C3v and C2v local symmetry, (c) the formulas of the SFG tensor components which apply specifically to the vibrational resonance with the CH stretching modes of methyl and methylene groups, and (d) the interference effect by the nearby Fermi resonance band. Changes introduced by the slight distortion of C3v symmetry into Cs symmetry have also been discussed. Sample calculations have been made of the SVSFG of the CH stretch modes of oriented CH3 groups.

Vibrational Sum-Frequency Spectroscopic Investigation of the Structure and Azimuthal Anisotropy of Propynyl-Terminated Si(111) Surfaces

“…The fits of the azimuthal rotational anisotropy data, collected for inplane rotation intervals of 10° (Table S3, 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 The terminating CH 3 CC-group can be approximately described as having C 3v symmetry, with c being the C 3 symmetry axis and the ac plane lying on one of the σ v symmetry planes. 55,57 With respect to this molecule fixed coordinate system, the three C-H vibrational modes observed in the SFG spectra can be categorized into two different types of vibrations with different hyperpolarizability tensor elements. [58][59] The r + and the modes account for changes in the transition dipole moments along the c axis (perpendicular to the Si(111) surface plane), whereas the r -mode accounts for changes along a direction that is perpendicular to the c axis (parallel to β lmn (2) β lmn (2) β lmn,i …”

Molecular Structure of Hydrophobic Alkyl Side Chains at Comb Polymer-Air Interface

“…The theory behind SFG as a surface-sensitive spectroscopic technique and the analysis to obtain orientation of methyl and methylene groups has been discussed previously. [12][13][14][15][16][17][18][19] Here we summarize the main points to understand the work reported in this paper. The second-order nonlinear susceptibility can be expressed using a Lorentzian function with a resonance peak at ω q and width Γ q corresponding to a resonance mode q.…”

“…According to the dipole approximation, generation of a SFG photon at (ω 1 + ω 2 ) is forbidden in the centrosymmetric bulk and is nonzero at interfaces where the inversion symmetry is broken. [12][13][14][15][16] SFG intensities are resonantly enhanced when ω 2 overlaps with the resonant frequency of a molecular vibrational mode that is both infrared and Raman active. The intensity, polarization, and resonance frequency of the SFG signal yield chemical and orientational information on molecules at interfaces.…”

“…Theoretical predictions suggest that the for a methylene group is higher than a methyl group. 14 For an all-trans alkyl chain, a pair of methylene groups is approximately centrosymmetric, the methylene bands do not normally show up in the SFG spectrum. The appearance of the methylene bands is usually associated with an increase in gauche defects and an additional unpaired methylene unit in the case of octadecyl side chain.…”

“…The intensity, polarization, and resonance frequency of the SFG signal yield chemical and orientational information on molecules at interfaces. [12][13][14][15][16][17][18] Here, we compare the differences in the surface structure of 65 nm thick octadecyl polymer films prepared by spin-coating to a 7 nm polymer layer prepared by solution dipping on a mica substrate. In both cases, the SFG signals show strong methyl asymmetric and symmetric stretching vibrations indicating ordered methyl terminal groups.…”