Low-frequency Raman spectrum

The low frequency Raman spectrum of 5CB in the nematic phase and several solid polymorphs is shown in Fig. 13. 

The low frequency Raman spectrum of the 6-coordinate models is distinctly different from the low frequency spectrum of the 5-coordinate sites of the Ni gjobins. In fact only one line, a very weak shoulder on the 300-cm line, is obserYed in the expected metal-ligand stretching region below 300 cm. Further no predominately Ni stretches are found in the 100-500-cm region. Instead, in both the 6- and 5-coordinate c mp xes many of the low frequency Raman lines show small (< 1 cm ) Ni isotopic shifts indicating some pyppole... 

Fig. 4. Microphotometrie record of low frequency Raman spectrum of formic acid crystal...

Fig. 5.16 Low-frequency Raman spectrum of a PP07PE075PP07 triblock at -10 °C (Viras et al. 1988). The band between 8 and 12 cm 1 is assigned to the longitudinal acoustic mode (LAM) of the copolymer.

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- -,... 

An alternate approach is to perform coherent Raman spectroscopy in the time domain rather than in the frequency domain. In this case, a single laser that produces short pulses with sufficient bandwidth to excite all of the Raman modes of interest is employed. One pulse or one pair of time-coincident pulses is used to initiate coherent motion of the intermolecular modes. The time dependence of this coherence is then monitored by another laser pulse, whose timing can be varied to map out the Raman free-induction decay (FID). It should be stressed at this point that the information contained in the Raman FID is identical to that in a low-frequency Raman spectrum and that the two types of data can be interconverted by a straightforward Fourier-transform procedure (12-14). Thus, whether a frequency-domain or a time-domain coherent Raman technique should be employed to study a particular system depends only on practical experimental considerations. 

F. D. Medina and W. B. Daniels. Low frequency Raman spectrum of methane at high densities. J. Chem. Phys., 66 2228-2229 (1977). 

The presence of the third peak in the low frequency Raman spectrum, radial breathing mode, testifies to the presence of SWNTs in the arrays. Moreover, it contains the quantitative characteristic information on SWNTs structure. The SWNTs diameter d was calculated as v= 6.5+223.75/al, where v(cm ) is the frequency of the radial oscillation modes of the SWNT hexagonal lattice. SWNTs were observed in both types of arrays synthesized with 1.0% and 10% of ferrocene in the feeding solution. CNT arrays obtained with 1.0% of ferrocene have V =183.1cm (Fig. 3a), and the calculated d value is 1.2 nm, which... 

Dihydropyrrole is a pseudo-four-membered ring molecule. Its structural relationship to trimethylene imine is the same as that of 2,5-dihydrofuran to trimethylene oxide. Again, both the parent and N-d compounds were studied. Figure 4.22 shows the far infrared spectrum of the light compound reported by Carreira and Lord89 The low-frequency Raman spectrum was reported later by Carreira et al.9°). Transitions with both Av = 1 and Av = 2 were observed. Table 4.14 summarizes the... 

F. Additional Condition to Overall Permittivity Provided by Low-Frequency Raman Spectrum... 

The dielectric spectrum (DS), pertaining to the T-band region, arises also in a certain specific form in the low-frequency Raman spectrum (RS). Comparison of both spectra allows us to improve the parameterization of our molecular model. Namely, in view of recent works (Gaiduk et al. [24], Gaiduk [25], we may write down the following relationships for the so-called R(v) and Bose-Einstein (BE) representations of the RS, denoted, respectively, Ir(v) and /hi (v) ... 

In this section we calculate the water spectrum in the range 0-1000 cm-1. This calculation is based on an analytical theory elaborated in 2005-2006 with the addition of a new criterion (38), related to the 50-cm 1 band in the low-frequency Raman spectrum. The calculation scheme was briefly described in Section II. One of our goals is to compare the spectra of liquid H20 and D20 and the relevant parameters of the model. Particularly, we consider the isotopic shift of the complex permittivity/absorption spectra and the terahertz (THz) spectra of both fluids. Additionally, in Appendix II we take into account the coupling of two modes, pertinent to elastically vibrating HB molecules. 

The evolution with the temperature of the calculated overall loss spectrum e"(v) is illustrated for seven temperatures by Figure lOg and by the left column in Figure 1 la. In the right column of Figure 1 la the partial loss curves, governed by the mechanisms (b) and (c), are depicted for each temperature. In Fig. lib the dielectric loss in the T-band region is compared with the low-frequency Raman spectrum calculated from the formula (38b). 

Fig. 2.36. Low-frequency Raman spectrum of a single crystal of PbeOiOHje (004)4 H2O at -HOC (632.8nm excitation) [1468].

The second manifestation of disorder in KNCS is the breakdown of translational invariance near Tc this is shown in Figure 22. Here the low-frequency Raman spectrum is replaced by a density-of-states type spectrum above Tc- The Raman spectrum of KN3 in this temperature region is also included for reference. No highly temperature-sensitive mode was found for KNCS, but it was observed that the product of the squares of the Raman-active modes decreases linearly with temperature in the low-temperature phase. Such a relationship was found by Rao et al, [98] for NaC103. The plot for KNCS is reproduced in Figure 23. 

A rhombohedral-to-monoclinic phase transition has been observed in NaNa using X-ray diffraction techniques [62]. This is confirmed by the low-frequency Raman spectrum which shows splitting of the librational line (Figure 24) at r 280°K [63,64]. 

Fig. 20. Time evolution of low-frequency Raman spectrum of the deoxy photoproduct Hb generated from HbACO (pH 6.4 plus IHP, 35°). For comparison purposes an equilibrium R-state deoxyHb spectrum derived from Hb Kempsey at pH 9 is also shown. Photolysis of the HbACO was accomplished with a 10 nsec excitation pulse (4050 A, 1 mj). The Raman spectra were generated with an electronically delayed second 10 nsec pulse (4350 A, 5 mJ). The sample was maintained at 35° in order to reduce geminate recombination. (From Scott and Friedman.

Measurements of the low-frequency Raman spectrum of TIN3 at various temperatures are consistent with the existence of a low-temperature phase transition, involving distortion of the ion, at 225 K. Salicylato-(l,10-phenanthroline)thallium(i) exists in dimeric form with five-co-ordinate Tl. The phenanthroline is bidentate, with T1—N distances of 2.65 and 2.71 A, as is the salicylato ligand, although it is here markedly unsymmetrical (with Tl—O distances of 2.65, 2.98 A). Further, the former oxygen undergoes a weak bridging interaction with the second Tl atom of the dimer (Tl O = 3.00 A). ... 

Johari. G.P. Molecular inertial effects in liquids Poley absorption, collision-induced absorption, low-frequency Raman spectrum and Boson peaks. J. Non-Cryst. Solids 2002. 307-310. 114. 

Single element laser line rejection filters reject more of the low-frequency Raman spectrum, but... 

The application of high polymers as insulating materials at low temperatures, as is well known, is limited by their brittleness. Consequently, it is highly desirable to develop methods of checking quickly and simply if a certain polymer can be used at low temperatures or not. In this paper, we propose the use of spectroscopy as a testing procedure. From simple considerations of the molecular structure of polymers, it appears that spectroscopy in the low frequency range of lattice vibrations, i.e., the far infrared (FIR), or the low frequency Raman spectrum, is an appropriate tool for this purpose. 

Ito and Shigeoka (1966) investigated the lattice vibrational Raman spectrum of solid pyrazine and compared their measurements to calculations which the same authors carried out. They correlated their work with the matrix method calculations of Harada and Shimanouchi (1966). Of particular interest was the N-H hydrogen bond force constant. Also Gerbaux and Hadni (1968) studied the lattice vibrations of solid pyrazine. Colombo (1967) reported the low-frequency Raman spectrum of p-toluidine solid. 

Janik and co-workers (1969) carried out incoherent inelastic neutron scattering studies on solid methane. They studied the lattice vibrations and molecular rotation in this solid near the melting point. Ito (1964) reported the lattice vibrational Raman spectrum of solid methyl iodide. Durig, Craven, and Bragin (1970) studied the low-frequency vibrations in the solid phases of two classes of molecules (CH3)jMCl and (CH3)3MBr where M was C, Si, and Ge. The infrared spectra of solid CCI4, benzene, and CS2, pure and activated by the impurities I3 and HCl, were studied by Munier and Hadni (1968). Colombo (1968) described the low-frequency Raman spectrum of single crystals of imidazole. 

Fig. 8. Low frequency Raman spectrum of TPBD at 110 K, using an iodine absorption cell. Bandpass, 3 cm" laser power, 150 mW at 5145.42 °A.

Based on relative intensity and, particularly, bandshape of skeletal bands, it has become possible to obtain the relative energy difference between various rotational isomeric states. In the first study of this type, Snyder and co-workers analyzed low frequency (0-600 cm ) Raman spectra of re-alkanes in the liquid state (35). The method was subsequently applied to analysis of the low frequency Raman spectrum of molten state isotactic polypropylene. The vibrational spectroscopic analysis was successfully used to differentiate the correct model governing the chain (80) and has been extended to analysis of higher frequency vibrations (0-1500 cm" ) of liquid re-alkanes (36). 

The low frequency Raman spectrum can provide information on the density of states g(co) in the low frequency region. In the quasi-harmonic approximation the specific heat is given by... 

As an example, the Stokes/anti-Stokes low-frequency Raman spectrum of L-cystine is shown in Figure L-Cystine is commonly used for testing the low-frequency capability of a Raman spectrometer. The 9.8 cm Raman bands are measurable in as short as 0.2 s fFig. 8.31. If the laser power is raised, faster measurements with 10 ms exposure time are possible. 

Figure 37 Low-frequency Raman spectrum of vitreous Si02 o, experiment solid line, theory using density of vibrational states from a-quartz A neutron data dotted line, molecular dynamic simulation, (From Ref. 56.)...

The use of different representations of the low-frequency Raman spectrum has been and is still widely discussed. Some relevant references are found in Refs. 2-5. The intensities obtained by use of these representations are often referred to as reduced intensities, and the representations are sometimes named reduced representations. 

Four different representations of the low-frequency Raman spectrum are used. The so-called R(v) representation is... 

Another way of comparing low-frequency Raman and far-IR data is to compare the absorption coefficient a(P) with the Raman spectrum in the R(P representation. Examples are shown in Fig. 3 for benzene and hexafluorobenzene [14,15]. The approximate expression, Ra(P) in Eq. (2) was used. Both molecules do not posses permanent molecular dipole moments, so the infrared spectrum is caused solely by induced dipole moments. Accordingly, the band shapes for the absorption coefficient and the R(P) representation are very similar [5]. When a permanent molecular dipole moment is present, the librational motion of this will give the main contribution to the far-IR intensity, whereas the intensity in the low-frequency Raman spectrum is determined by the anisotropy of the static molecular polarizability. In this case, it should be taken into account that the band shape in IR... 

Eq. (1)] and I v) [Eq, (3)] spectral representations. A comparison of Figs. 4 and 5 clearly shoves that the OHD-RIKES spectrum and the low-frequency Raman spectrum in the I v) representation are very similar, as expected for spectra obtained by the two different experimental techniques. 

Figure 5 (a) The low-frequency Raman spectrum of NMF obtained at room temperature in the... 

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