Fourier transform vibrational spectrum

Herman, M., Abbouti-Temsamani, M., Lemaitre, D., and Vander Auwera, J. (1991), The Fourier-Transform Vibrational Spectrum of Acetylene in the Visible Range, Chem. Phys. Lett. 185, 220. 

During the performance test, unfiltered vibration measurements and a Fast Fourier Transform (FFT) spectrum shall be made at each test point except shutoff. The measurements shall be as follows ... 

The electronic and vibrational spectra of benzoquinones are very diagnostic. Of the two possible isomers remaining, the 2,5-substituted quinone (5) would be expected to give two different electronic transitions of equal intensity around 280 nm, and only one carbonyl stretching band. The Fourier transform infrared spectrum (CH2CI2) of the haustorial Inducer showed strong absorptions at 1698 (vC=0), 1646 (vC=0) and 1597 cm (vC=C). These spectroscopic data established the haustorial inducer as 2,6-diraethoxy-2"benzoquinone (2,6-DMBQ, 4). 

In order to test the predictions of the model, plates were made up from selected formulations and tested in air. The thicknesses of the various layers were as stated previously, while the length was one meter and the width was one-third meter. Damping measurements were made by two different methods. In both cases, the plates were suspended in a shock chord and accelerometers placed at different locations on the plate. The first used a reverberation meter and the half-power method (16). In the second, an impact hammer was used to tap the structure and the outputs of the accelerometers fed into a Fourier transform based spectrum analyzer to examine the envelope of vibration (17). The results presented here are based upon the second method. 

Figure 22 Vibrational spectra of human stratum comeum. FTIR Fourier transform infrared spectrum FT-Raman Fourier transform Raman spectrum. (From Ref. 185. Reprinted from International Journal of Pharmaceutics, 81 (2-3), Williams et al. Fourier transform Raman spectroscopy A novel application for examining human stratum comeum, pp. R11-R14,1992, with kind permission from Elsevier Science, ML, Sara Burgerhartstraaat 25, 1055 KV, Amsterdam, The Netherlands.)...

The As-HAO system presents special difficulties for IR and XAFS spectroscopic analysis. In an XAFS spectrum, the magnitude of peaks in the Fourier transformed EXAFS spectrum is a function of several variables, two of which are atomic number (z) and distance from the central As atom. With only half as many electrons as Fe, the scattering power of Al is weak, therefore peaks representing As-Al scattering in the Fourier-transformed EXAFS are smaller and more difficult to interpret. IR and Raman spectra of As(V) sorbed on gibbsite are difficult to interpret for an entirely different reason substantial overlap of peaks representing Al(V)-0/Al-OH vibrations and As(V)-0/As(V)-OH vibrations (Myneni et al, 1998). 

Two NR samples (cured and uncured) were studied. In all studies, the samples were stretched to 500% elongation. The Fourier-transform Raman spectrum of NR is presented as a function of time of cold soaking at -25C and of strain with respect to laser polarisation. Under both sets of conditions, changes occur in the spectra that can be attributed to crystallisation. Difference spectra showing only those bands due to crystallisation (i.e. spectra of crystalline NR) are presented, which allows the crystallisation process to be discussed with respect to the conditions under which crystallites are formed. A combination of Fourier-transform Raman and Fourier-transform IR depolarisation spectra was used to deduce preliminary assignments for some of the vibrational bands of natural rubber. 40 refs. 

As mentioned, we also carried out IR studies (a fast vibrational spectroscopy) early in our work on carbocations. In our studies of the norbornyl cation we obtained Raman spectra as well, although at the time it was not possible to theoretically calculate the spectra. Comparison with model compounds (the 2-norbornyl system and nortri-cyclane, respectively) indicated the symmetrical, bridged nature of the ion. In recent years, Sunko and Schleyer were able, using the since-developed Fourier transform-infrared (FT-IR) method, to obtain the spectrum of the norbornyl cation and to compare it with the theoretically calculated one. Again, it was rewarding that their data were in excellent accord with our earlier work. 

In order to analyze the vibrations of a single molecule, many molecular dynamics steps must be performed. The data are then Fourier-transformed into the frequency domain to yield a vibrational spectrum. A given peak can be selected and transformed back to the time domain. This results in computing the vibra-... 

Frequency-domain data are obtained by converting time-domain data using a mathematical technique referred to as Fast Fourier Transform (FFT). FFT allows each vibration component of a complex machine-train spectrum to be shown as a discrete frequency peak. The frequency-domain amplitude can be the displacement per unit time related to a particular frequency, which is plotted as the Y-axis against frequency as the X-axis. This is opposed to time-domain spectrums that sum the velocities of all frequencies and plot the sum as the Y-axis against time... 

The phrase full Fast Fourier Transform (FFT) signature is usually applied to the vibration spectrum that uniquely identifies a machine, component, system, or subsystem at a specific operating condition and time. It provides specific data on every frequency component within the overall frequency range of a machine-train. The typical frequency range can be from 0.1 to 20,000 Hz. 

Ifourth(fd, 2 Q) was multiplied with a window function and then converted to a frequency-domain spectrum via Fourier transformation. The window function determined the wavenumber resolution of the transformed spectrum. Figure 6.3c presents the spectrum transformed with a resolution of 6cm as the fwhm. Negative, symmetrically shaped bands are present at 534, 558, 594, 620, and 683 cm in the real part, together with dispersive shaped bands in the imaginary part at the corresponding wavenumbers. The band shapes indicate the phase of the fourth-order field c() to be n. Cosine-like coherence was generated in the five vibrational modes by an impulsive stimulated Raman transition resonant to an electronic excitation. 

Figure 6.5 Vibrational coherence at a Ti02(l 10) surface covered with TMA monolayer, (a) The raw SH intensity, (b) the modulated component, and (c) the Fourier-transformed spectrum. The TMA-covered surface was irradiated in air with p-polarized pump (14mjcm ) and p-polarized probe (6mjcm ) pulses.

With the boundary conditions that the chain ends are free of forces, Eq. (13) is readily solved by cos-Fourier transformation, resulting in a spectrum of normal modes. Such solutions are similar, e.g. to the transverse vibrational modes of a linear chain except that relaxation motions are involved here instead of periodic vibrations. 

The initial observation is that PMMA is essentially completely degraded to monomer by heating to 375°C in a sealed tube while heating a mixture of red phosphorus and PMMA under identical conditions yields a solid, non-deqraded, product as well as a lower yield of monomer. One may observe, by 3C NMR spectroscopy, that the methoxy resonance is greatly decreased in intensity and methyl, methoxy phosphonium ions are observed by 31P NMR. Additional carbonyl resonances are also seen in the carbon spectrum, this correlates with a new carbonyl vibration near 1800 cm 1 in the infrared spectrum and may be assigned to the formation of anhydride. The formation of anhydride was also confirmed by assignment of mass spectra obtained by laser desorption Fourier transform mass spectroscopy, LD-FT-MS. 

The interpretation of a spectrum from a dynamical point of view can also be applied to a spectrum containing a broad feature associated with direct and/or indirect dissociation reactions. From such spectra dynamics of a dissociating molecule can also be extracted via the Fourier transform of a spectrum. An application of the Fourier transform to the Hartley band of ozone by Johnson and Kinsey [3] demonstrated that a small oscillatory modulation built on a broad absorption feature contains information of the classical trajectories of the vibrational motion on PES, so-called unstable periodic orbits, at the transition state of a unimolecular dissociation. 

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