Homogeneously broadened Raman

FIGURE 5.5 (a) Components of the CARS signal. The last three terms in Equation 5.1 are plotted versus detuning A = C0p-co -O. O is the center frequency of a homogeneously broadened Raman line with linewidth F. The curves are calculated with an assumption that2 R = 1.2 = 0)- (b) Schematic of the FM CARS process. Solid curve, sum of the contribu-... 

The resonant susceptibility associated with a homogeneously broadened Raman transition, j, is,... 

Figure 19 The VE prediction of the diffusive component of the vibrational coherence decay CpiD as a function of the solvent viscosity (ij = 1, 2, 4, 8, 16, 32 and oo cP) for typical parameters. At low viscosity, the decay is exponential, its rate is inversely proportional to the viscosity, and the corresponding Raman line is homogeneously broadened. At high viscosity, the decay becomes Gaussian, its decay time reaches a limiting value, and the Raman line is inhomogeneously broadened. (From Ref. 8.)...

This expression describes the important case of an inhomogeneously broadened band with homogeneously broadened components. If the number of components is small or they are regularly spaced in frequency, a beat pattern for C(t) is obtained. Exjjerimentally, a time-resolved CARS experiment (which gives C(t) for t > tp) displays directly this oscillatory behavior, as was observed in an early study of (Fig. 5). The corresponding Raman... 

It is generally accepted that the linewidth 6v (in cm ) of the same Raman mode, Wy, as observed from spontaneous Raman scattering is related to T2 by 6v = (ircT2) provided that the Raman line is homogeneously broadened (see, e.g., Laubereau and Kaiser, 1978). 

The dimerization of 28 has also been studied by Prasad, who used Raman spectroscopy to monitor both changes in intermolecular vibrations and lattice phonon modes [73]. The Raman spectrum shows the disappearance of alkene stretches at 997, 1180, 1593, and 1625 cm-1 as expected, and the appearance of cyclobutane modes at 878,979, and 1001 cm-1. Phonon modes broadened as the reaction progressed, and bands around 15-40 cm-1 showed a shift in frequency. Between about 50 and 66% conversion it was difficult to define distinct bands, but after that point product bands grew in distinctly. This amalgamation behavior is good evidence for a homogeneous reaction mechanism. 

An example is illustrated in Fig. 2. In case 1, there are two mechanisms operating one in the fast modulation limit, and one in the slow modulation limit. This is the classic case of combined homogeneous and inhomogeneous line broadening. In case 2, there is a single mechanism, but it is in the intermediate modulation region. The Raman hnewidths are identical... 

It has been shown that spontaneous or even coherent Raman scattering cannot be used to distinguish between the fast homogeneous and the slow inhomogeneous broadening mechanisms in vibrational transitions [18. 

All vibrations present in the neat, ciystalline explosive seem to be enhanced by the same factor (non-selective enhancement). Moreover, the spectra resemble solid phase normal Raman (NR) spectra, with fully resolved, non-broadened peaks. The reproducibility in band intensities is slightly better than in SERS spectra ( 20-30%), but is prone to sample variation due to the lack of homogeneity in the sohd-solid mixtures. KBr-analyte pellets were used as reference, since no evidence of ERS was fotmd for this substrate. Experiments using cobalt (11) oxide did not result in observation of enhanced Raman signals under the experimental protocol followed (Figure 7). 

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