Principles of Sum-Frequency Vibrational Spectroscopy

One of the principal analytical techniques used for surface-sensitive and orientational analysis is SFG [1, 22-26]. This nonlinear optical technique is based on a coherent photon emission process. It utilizes a combination of two laser beams, one in the visible and one in the IR range frequency, set at two possible polarizations, p - for light incident parallel to the plane of incidence, and s - for incidence perpendicular to it. The resulting SFG signals emitted from the surface are proportional to the interaction of the molecular vibrational modes with the incoming electric fields and their hyperpolarizabiHties. The emitted signals from the surface are analyzed and interpreted according to their intensities and intensity ratio at the four relevant polarization combinations [24, 27, 28]. 

The SFG technique probes the second-order nonhnear hyperpolarizability tensor this tensor includes the Raman and IR susceptibihty, which requires that the molecular vibrational modes are both Raman and IR active. Since Raman- and IR-dipole moment transition selection rules for molecules with a center of symmetry indicate that a vibrational mode is either Raman or IR active but not both, only molecules in a non-centrosymmetric environment on the surface interact with the electric fields molecules in the isotropic bulk phase show inversion symmetry where the third rank hyperpolarizability tensor goes to zero [25-27]. 

Signal intensity is proportional to the square of the induced polarization of the vibrational modes and depends on the second-order susceptibility It consists of nonresonant background signals and the resonant part that is related to the second-order hyperpolarizability as given by the following equations. 

I 7 Ionic Liquids at the Cas-Liquid and Solid-Liquid Interface - Characterization and Properties 

The term includes the Raman polariTability tensor elements as well the IR-dipole transition moment The variable N refers to the number of resonant modes on the surface and iT specifies the damping constant or lifetime of the vibration. From Eq. (7.2), it is obvious that signal intensities increase as the term — ft q) goes to zero as it approaches resonance. 

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