Density measurement, vibrational Raman

Complementary to other methods that constimte a basis for the investigation of molecular dynamics (Raman scattering, infrared absorption, and neutron scattering), NIS is a site- and isotope-selective technique. It yields the partial density of vibrational states (PDOS). The word partial refers to the selection of molecular vibrations in which the Mossbauer isotope takes part. The first NIS measurements were performed in 1995 to constitute the method and to investigate the PDOS of... 

The superionic phase has been explored with more extensive CPMD simulations.69 Calculated power spectra (i.e., the vibrational density of states or VDOS) have been compared with measured experimental Raman spectra68 at pressures up to 55 GPa and temperatures of 1500 K. The agreement between theory and experiment was very good. In particular, weakening and broadening of the OH stretch mode at 55 GPa was found both theoretically and experimentally. 

Figure 3. Schematic of turbulent combustor geometry and optical data acquisition system for vibrational Raman-scattering temperature measurements using SAS intensity ratios. Also shown are sketches of the expected Raman contours viewed by each of the photomultiplier detectors, the temperature calibration curve, and several expected pdf s of temperature at different flame radial positions. The actual SAS temperature calibration curve was calculated theoretically to within a constant factor. This constant, which accounted for the optical and electronic system sensitivities, was determined experimentally by means of SAS measurements made on a premixed laminar flame of known temperature. Measurements of Ne concentration were made also with this apparatus, based on the integrated Stokes vibrational Q-branch intensities. These signals were related to gas densities by calibration against ambient air signals.

A second advantage is that the frequency distribution or density of vibrational states can be obtained from these measurements. These data complement those determined from infrared and Raman measurements. 

The S diads in the vibrational Raman spectrum of CO2 and its isotopic variants were measured and their intensity distribution simulated [48,164-167]. In Fig. 17, a more recent recording of the Raman spectrum of natural CO2 in the Fermi resonance region is presented [53]. The structure of the Q branch of the (10 02) component at 1285 cm has been resolved by CARS [168], stimulated Raman [169], and photoacoustic Raman spectroscopy [106] see Fig. 10. The Q branches of the overtones of the Fermi diad were also observed [170] and the evaluation of their intensities yielded mean polarizability derivatives. In supersonic jet experiments on CO2, the density, condensation, and translational, rotational, and vibrational temperatures were investigated [171]. 

The statistic model of Bell and Dean [16] has often been used as a basis of vibrational spectra calculations. It leads to a distribution of the density of the modes able to be compared to infrared or Raman measurements [17]. It is, however, impossible to assign the observed bands to one vibrational mode or another the maxima in absorption correspond to additions of several modes in various proportions, depending on the shape of the density of vibrational states [18] see Fig. 15. For a mathematical approach of glass, see the work of Volf [19]. 

IR and Raman spectroscopy are both quantitative techniques, in that both the IR absorbance and the Raman scattered intensity are, to a first approximation, linearly proportional to the number density of vibrating species. Although quantitative information can be extracted from a single absorbance or scattered intensity (after calibration against absolute standards), it is more usual to measure the ratio of the analyte band of interest against an independent internal standard, in order to allow for variations in pathlength, deviations from ideality, detector nonlinearity, etc. The reader is referred elsewhere for a full discussion of quantitative methods (including multivariate techniques) [9, 10]. 

In the resonance Raman spectra of GO0X (125), vibrational modes have been assigned to both the tyrosinate ligand (Tyr 495) as well as the tyrosyl radical (Tyr 272). The spectrum does not provide evidence for the speculation that the tyrosyl radical is delocalized onto the jr-stacked tryptophan residue (Trp 290) (126, 127). Recent results of high-frequency EPR measurement (30) on the apogalactose oxidase radical are also consistent with the radical spin density being localized on the modified Tyr 272 moiety only. 

For our purpose, it is convenient to classify the measurements according to the format of the data produced. Sensors provide scalar valued quantities of the bulk fluid i. e. density p(t), refractive index n(t), viscosity dielectric constant e(t) and speed of sound Vj(t). Spectrometers provide vector valued quantities of the bulk fluid. Good examples include absorption spectra A t) associated with (1) far-, mid- and near-infrared FIR, MIR, NIR, (2) ultraviolet and visible UV-VIS, (3) nuclear magnetic resonance NMR, (4) electron paramagnetic resonance EPR, (5) vibrational circular dichroism VCD and (6) electronic circular dichroism ECD. Vector valued quantities are also obtained from fluorescence I t) and the Raman effect /(t). Some spectrometers produce matrix valued quantities M(t) of the bulk fluid. Here 2D-NMR spectra, 2D-EPR and 2D-flourescence spectra are noteworthy. A schematic representation of a very general experimental configuration is shown in Figure 4.1 where r is the recycle time for the system. 

The shape of the vibration-rotation bands in infrared absorption and Raman scattering experiments on diatomic molecules dissolved in a host fluid have been used to determine2,15 the autocorrelation functions unit vector pointing along the molecular axis and P2(x) is the Legendre polynomial of index 2. These correlation functions measure the rate of rotational reorientation of the molecule in the host fluid. The observed temperature- and density-dependence of these functions yields a great deal of information about reorientation in solids, liquids, and gases. These correlation functions have been successfully evaluated on the basis of molecular models.15... 

In Eq. (10), E nt s(u) and Es(in) are the s=x,y,z components of the internal electric field and the field in the dielectric, respectively, and p u is the Boltzmann density matrix for the set of initial states m. The parameter tmn is a measure of the line-width. While small molecules, N<pure solid show well-defined lattice-vibrational spectra, arising from intermolecular vibrations in the crystal, overlap among the vastly larger number of normal modes for large, polymeric systems, produces broad bands, even in the crystalline state. When the polymeric molecule experiences the molecular interactions operative in aqueous solution, a second feature further broadens the vibrational bands, since the line-width parameters, xmn, Eq. (10), reflect the increased molecular collisional effects in solution, as compared to those in the solid. These general considerations are borne out by experiment. The low-frequency Raman spectrum of the amino acid cystine (94) shows a line at 8.7 cm- -, in the crystalline solid, with a half-width of several cm-- -. In contrast, a careful study of the low frequency Raman spectra of lysozyme (92) shows a broad band (half-width 10 cm- -) at 25 cm- -,... 

Very few experiments have been performed on vibrational dynamics in supercritical fluids (47). A few spectral line experiments, both Raman and infrared, have been conducted (48-58). While some studies show nothing unique occurring near the critical point (48,51,53), other work finds anomalous behavior, such as significant line broadening in the vicinity of the critical point (52,54-60). Troe and coworkers examined the excited electronic state vibrational relaxation of azulene in supercritical ethane and propane (61-64). Relaxation rates of azulene in propane along a near-critical isotherm show the three-region dependence on density, as does the shift in the electronic absorption frequency. Their relaxation experiments in supercritical carbon dioxide, xenon, and ethane were done farther from the critical point, and the three-region behavior was not observed. The measured density dependence of vibrational relaxation in these fluids was... 

A theoretical determination of vibrational absorption and Raman spectra of 3-methylindole radicals has been carried out in comparison to experimentally measured spectra for 3-methylindole (Table 28) to provide specific spectroscopic markers for the detection of neutral or cationic tryptophan radicals in biological systems <2001CPH(265)13>. Among isatin derivatives, substitution at C-5 has relatively greater influence on the electron density and the force constant of the amide than of the ketone carbonyl group (Table 29) <2001SAA469>. 

Since the slope, E, of the Urbach absorption reflects the shape of the valence band tails, it follows that varies with the structural disorder. For example, one measure of the disorder is the average bond angle variation, which is measured from the width of the vibrational spectrum using Raman spectroscopy (Lannin 1984). Fig. 3.22 shows an increasing E with bonding disorder, which is caused by changes in the deposition conditions and composition (Bustarret, Vaillant and Hepp 1988 also see Fig. 3.20). The defect density is another measure of the disorder and also increases with the band tail slope (Fig. 3.22). A detailed theory for the dependence of defect density on is given in Section 6.2.4. 

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