SFG Intensities

Second-order NLO processes, including SFG, are strictly forbidden in media with inversion symmetry under the electric dipole approximation and are allowed only at the interface between these media where the inversion symmetry is necessarily broken. In the IR-Visible SFG measurement, a visible laser beam (covis) and a tunable infrared laser beam (cOir) are overlapped at an interface and the SFG signal is measured by scanning cOir while keeping cOvis constant. The SFG intensity (Isfg) is enhanced when coir becomes equal to the vibration levels of the molecules at the interface. Thus, one can obtain surface-specific vibrational spectra at an interface... 

Previously, we have proposed that SFG intensity due to interfacial water at quartz/ water interfaces reflects the number of oriented water molecules within the electric double layer and, in turn, the double layer thickness based on the p H dependence of the SFG intensity [10] and a linear relation between the SFG intensity and (ionic strength) [12]. In the case of the Pt/electrolyte solution interface the drop in the potential profile in the vicinity ofelectrode become precipitous as the electrode becomes more highly charged. Thus, the ordered water layer in the vicinity of the electrode surface becomes thiimer as the electrode is more highly charged. Since the number of ordered water molecules becomes smaller, the SFG intensity should become weaker at potentials away from the pzc. This is contrary to the experimental result. 

The SFG intensity decreased when PVA gel was in contact with the quartz surface. Weakening of SFG intensity is mostly due to the change in the Fresnel coefficients upon contact with the PVA gel [99]. 

Figure 8. Rate of carbon monoxide oxidation on calcined Pt cube monolayer as a function of temperature [27]. The square root of the SFG intensity as a function of time was fit with a first-order decay function to determine the rate of CO oxidation. Inset is an Arrhenius plot for the determination of the apparent activation energy by both SFG and gas chromatography. Reaction conditions were preadsorbed and 76 Torr O2 (flowing). (Reprinted from Ref. [27], 2006, with permission from American Chemical Society.)...

Fig. 17. PM-IRAS and SFG spectra of CO on Pd(l 1 1) at CO pressures of 170 and lOOmbar at 190 K, respectively. A comparison of the experimentally observed and calculated intensity ratios of peaks characterizing CO in hollow positions relative to CO in on-top positions is included (see text), (b) Dependence of the SFG intensity on coverage in the range 0.5 to 0.65 ML adapted from (755) with permission from Elsevier.

We emphasize, however, that although SFG intensities are normalized to the intensity of the incident light, variations in the optical alignment of the various detectors (which can hardly be avoided) still make it difficult to compare exactly experiments with different samples on different days. 

Fig. 16. (a) SFG spectra of CO adsorbed on the polycrystalline Pt foil recorded at different substrate temperatures at a CO pressure of 10 mbar. SFG intensity is plotted versus the frequency of the tunable IR laser. Experimental data points are represented by crosses, the solid lines represent results of least-squares fits. Details of the fitting procedure are described in the text. The depicted SFG spectra are on the same vertical scale, (b) TPD spectra of CO obtained under molecular flow conditions recorded after the corresponding SFG measurements shown in (a). Desorption was started at different substrate temperatures at the same CO pressure of 10 mbar. All TPD spectra are also on the same vertical scale. 

Fig. 17. Plot of the values of the resonant amplitude An ( ) and the meiximum value of the resonant part of the SFG intensity (B), Fsfg( co)i derived from the SFG spectra depicted in Fig. 16(a), versus the relative coverage determined from the corresponding TPD spectra of Fig. 16(b). The values of Ar and /sfg( uco) were normalized to unity at saturation coverage.

In Fig. 17, the values of the resonant amplitude Ar and the maximum value of the resonant part of the SFG intensity, /sfg(wco), obtained from the corresponding parameters Ar, ujco and F, are plotted versus the relative CO coverage of the Pt foil. As can be seen in Fig. 17, /sfg (< co) is the spectroscopic quantity which correlates linearly with CO surface coverage. 

Figure 5 shows the SFG vibrational spectra of carbon monoxide obtained at 10 -700 Torr of CO and at 295 K. When the clean Pt(lll) surface was exposed to 10 L (1 L=10 Torr sec) of CO in UHV, two peaks at 1845 cm and 2095 cm were observed which are characteristic of CO adsorbed at bridge and atop sites. LEED revealed that a c(4 X 2) structure was formed in which an equal number of carbon monoxide molecules occupied atop and bridge sites [15]. Such results are in agreement with previous HREELS [16] and reflection-absoiption infrared spectroscopy (RAIRS) [17] studies. ITie much higher relative intensity of atop bonded CO to bridge bonded CO in the SFG spectra is due to the specific selection rule for the SFG process [18]. As mentioned earlier, SFG is a second order, nonlinear optical technique and requires the vibrational mode under investigation to be both IR and Raman active, so that the SFG intensity includes contributions from the Raman polarizability as well as the IR selection mle for the normal mode. 

Here Uab is the Raman transition moment, fic is the infrared transition moment, g and V refer to ground and excited vibrational states, coir is the input infrared frequency, coq is the resonance frequency of the adsorbate, and T is a damping factor [8, 14—17]. Thus, the SFG intensity is related to the product of an (anti Stokes) Raman transition and an infrared transition. The SFG intensity is enhanced when the input infrared wavelength coincides with a vibrational mode of the adsorbate and the result of an SFG spectrum corresponds to the vibrational levels of the molecule. This situation is shown schematically in Fig. 5.1. From (5), non-zero SFG intensity will occur only for transitions that are both Raman and IR allowed. This situation occurs only for molecules lacking inversion symmetry [19]. 

Since it is the orientational average, (), of the molecular hyperpolarizability that gives SFG intensity, this average clearly cannot go to zero. This means that SFG is sensitive to the presence of order at the interface, and surface molecules must have a net polar orientation to be observed in SFG. For multiple oscillators, q (vibrational modes)... 

The final SFG intensity is the square of the sum of the non-linear susceptibilities and the input electric fields, as shown in (3). In general, the second-order polarizability is a complex quantity, as shown in (7)... 

It should be mentioned here that these nonlinear polarizations are important only when an intense electric field is applied V m ), which is usually generated by a pulsed laser. Generally, the SFG intensity in terms of photon per pulse can be expressed by [12] ... 

Since SFG intensity is inversely proportional to the pulse duration, the fs ultrashort laser pulse is expected to give even better performance in SFG measurements [12]. However, as the pulse duration is as short as fs, the frequency bandwidth becomes too wide, which cannot be ignored for vibrational spectroscopy. The pulse duration (Af, FWHM) and spectral width (Av, FWHM) of an ultrashort pulse with the Gaussian shape are related to each other by the uncertainty principle in quantum mechanics as [59] ... 

SFG intensity in the spectral region that is associated with an increase in the ordering of hydrogen-bonded water molecules.The increase in the SFG intensity was attributed to an increase in the ordering of water molecules caused by the formation of an ionic double layer at the interface. 

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