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Polarization-dependent sum frequency generation (SFG) spectroscopy was applied to study the adsorption of carbon monoxide (CO) on the well-ordered (annealed) Ir(111) single-crystal surface at various CO coverages. Coverage was adjusted by varying the substrate temperature (300–575 K) and/or gas pressure (10 –7 to 1.0 mbar). Under all conditions investigated, only a single absorption band at 2038–2094 cm –1 was observed, characteristic of linearly bonded (on-top) CO. Using different polarizations, PPP and SSP spectra were acquired with a high signal-to-noise ratio, whereby tilt angles of CO on Ir(111) could be determined for the first time by SFG. It was found that not only the vibrational frequency of on-top CO but also the tilt angle was strongly coverage-dependent. The higher the coverage was, the larger the vibrational frequency and the tilt angle were. At about 0.7 ML coverage, a CO tilt angle of at least 20° was observed, which is in good agreement with density functional theory (DFT) calculations. In addition, the molecular hyperpolarizability ratio ( R ) of CO (at 0.13 ML in UHV) was determined to be 0.08. Based on the combined SFG/DFT results, it may change to 0.29 at 0.77 ML coverage.

Polarization-dependent sum frequency generation (SFG) vibrational spectroscopy was employed to examine CO overlayers on Pt(111) and Pd(111) single crystal surfaces at room temperature. Utilizing different polarization combinations (SSP and PPP) of the visible and SFG light allows to determine the molecular orientation (tilt angle) of interface molecules but the analysis of the measured is involved and requires a proper optical interface model. For CO/Pt(111), the hyperpolarizability ratio is not exactly known and varying R in the range 0.1–0.5 yields tilt angles of 40°–0°, respectively. Based on the known perpendicular adsorption of CO on Pt, an exact R-value of 0.49 was determined. Polarization-dependent SFG spectra in the pressure range 10−4 to 36 mbar did not indicate any change of the tilt angle of adsorbed CO. Modeling also indicated a strong dependence of on the incidence angles of visible and IR laser beams. Complementing previous low temperature/low pressure data, room temperature CO adsorption on Pd(111) was examined from 10−6 to 250 mbar. The absolute PPP and SSP spectral intensities on Pt and Pd were simulated, as well as the expected ratios. Although CO on Pt and Pd should exhibit similar intensities (at high CO coverage), the higher ratio for Pd (48 vs. 27 on Pt) renders the detection of adsorbed CO in SSP spectra difficult. The presence or absence of CO species in SSP spectra can thus not simply be correlated to tilted or perpendicular CO molecules, respectively. Careful modeling, including not only molecular and interface properties, but also the experimental configuration (incidence angles), is certainly required even for seemingly simple adsorbate–substrate systems.

Sum frequency generation (SFG) vibrational spectroscopy is applied to ambient pressure surface science studies of adsorption and catalytic reactions at solid/gas interfaces.

The interfacial behavior of the benchmark zwitterionic phospholipid molecule dipalmitoylphosphatidylcholine (DPPC) has been extensively investigated by surface-selective vibrational sum frequency generation spectroscopy (VSFG). However, there is still a lack of agreement between various orientational measurements of phospholipid monolayers at the air/water interface, mainly because of the difficulty in assigning congested VSFG features. In this study, polarization-dependent VSFG measurements reveal a frequency shift between the in-plane and out-of-plane antisymmetric stretching modes of the terminal methyl groups in the DPPC alkyl tails, favoring the model of C local symmetry rather than the previously assumed C symmetry. Further VSFG experiments of isotopically labeled DPPC successfully capture the vibrational signatures of the glycerol backbone. With the newly derived VSFG polarization selection rules for C symmetry and the refreshed spectral assignments, the average tilt angles of the alkyl tail groups, choline headgroup, and glycerol backbone of DPPC molecules can all be determined, showing the powerful capability of VSFG spectroscopy in revealing the structural details at interfaces. The VSFG polarization dependence rules and the orientational analysis procedures developed for C symmetry in this work are applicable to other bulky molecules in which the methyl group cannot freely rotate, and they therefore have general applications in future VSFG studies.

The multiterm fractional differential equation has a wide application in engineering problems. Therefore, we propose a method to solve multiterm variable order fractional differential equation based on the second kind of Chebyshev Polynomial. The main idea of this method is that we derive a kind of operational matrix of variable order fractional derivative for the second kind of Chebyshev Polynomial. With the operational matrices, the equation is transformed into the products of several dependent matrices, which can also be viewed as an algebraic system by making use of the collocation points. By solving the algebraic system, the numerical solution of original equation is acquired. Numerical examples show that only a small number of the second kinds of Chebyshev Polynomials are needed to obtain a satisfactory result, which demonstrates the validity of this method.

A new custom-designed ultrahigh vacuum (UHV) chamber coupled to a UHV and atmospheric-pressure-compatible spectroscopic and catalytic reaction cell is described, which allows us to perform IR-vis sum frequency generation (SFG) vibrational spectroscopy during catalytic (kinetic) measurements. SFG spectroscopy is an exceptional tool to study vibrational properties of surface adsorbates under operando conditions, close to those of technical catalysis. This versatile setup allows performing surface science, SFG spectroscopy, catalysis, and electrochemical investigations on model systems, including single crystals, thin films, and deposited metal nanoparticles, under well-controlled conditions of gas composition, pressure, temperature, and potential. The UHV chamber enables us to prepare the model catalysts and to analyze their surface structure and composition by low energy electron diffraction and Auger electron spectroscopy, respectively. Thereafter, a sample transfer mechanism moves samples under UHV to the spectroscopic cell, avoiding air exposure. In the catalytic cell, SFG spectroscopy and catalytic tests (reactant/product analysis by mass spectrometry or gas chromatography) are performed simultaneously. A dedicated sample manipulation stage allows the model catalysts to be examined from LN temperature to 1273 K, with gaseous reactants in a pressure range from UHV to atmospheric. For post-reaction analysis, the SFG cell is rapidly evacuated and samples are transferred back to the UHV chamber. The capabilities of this new setup are demonstrated by benchmark results of CO adsorption on Pt and Pd(111) single crystal surfaces and of CO adsorption and oxidation on a ZrO supported Pt nanoparticle model catalyst grown by atomic layer deposition.

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