Raman scattering depolarization spectrum

Figure 7. Two-body depolarized scattering Stokes spectrum of the Vi Raman band of gaseous CF4 in absolute units at 294.5 K. Full circles ( ) indicate experimental data together with error bars.

There is an indirect way to detect intermittent local collective motions. In the case of depolarized Raman scattering, the depolarization ratio is sensitive to low-frequency fluctuations in water. Depolarization is the scattering of the polarization of the electric field of light in a direction perpendicular to the original direction of polarization. Each fluctuating state has a distinct depolarization ratio. The intermittent character of the dynamics is known to appear as a so-called 1,/ frequency (f) dependence in a power spectrum. The power spectmm is obtained by Fourier transforming a time correlation function. 

On the basis of transferability properties for intensity parameters in the hydrocarbon series, Martin [309] has predicted depolarization ratios, scattering coefficients and absolute differential Raman scattering cross sections for propane in the gas-phase employing electro-optical parameters determined for ethane. A good correspondence between the predicted and experimental data has been achieved. A survey of calculated Raman spectra of other hydrocarbons is presented in the book of Gribov and Orville-Thomas [155]. Gussoni and co-workers [300,319] have predicted the Raman spectrum of polyethylene and perdeutero-polyethylene by transferring electro-optical parameters evaluated for methane and cyclohexane. 

The Raman spectrum can be used to give additional information regarding the symmetry properties of vibrations. This information derives from the measurement of the depolarization ratio p for each Raman band. The quantity p is a measure of the degree to which the polarization properties of the incident radiation may be changed after scattering... 

Besides being always Raman active, the totally symmetric vibrational modes can also be readily identified in the spectrum. As shown in Fig. 7.3.2, the scattered Raman radiation can be resolved into two intensity components, /l and 7. The ratio of these two intensities is called the depolarization ratio p ... 

The Gas Phase Polarizability Anisotropy. Murphy50 has measured the depolarization ratio for Rayleigh scattering, pR, and analysed the intensity distribution in the rotational Raman spectrum of the vapour at 514.5 nm. The ratio R20 of the invariants of the a,-,aA/ tensor can be determined by fitting the rotational Raman distribution, and a is known (from the Zeiss-Meath formula). Knowledge of the three quantities, a, pR and R2o, allows the polarizability anisotropy, Aa, and the three principal values of the tensor to be calculated. The polarizability anisotropy invariant is numerically equal to the quantity,... 

Finally, M is introduced for convenience and represents the integral function of polarizability. It is the only function, the value of which depends on the polarizability characterizing the scattering medium. /iso( u) Raman spectrum depends only on the vibration motion and /aniso( y) depends on both vibration and reorientation motions of the molecule. In addition to the familiar qualitative use of the depolarization ratio, P = - Hv/. vv, to identify symmetric modes (i.e. p < 0.75), the quantitative studies of /iso and /aniso may provide detailed information about the vibration and reorientation relaxation. 

What are the consequences of these considerations for depolarized light scattering In a dilute gas where reorientation is predominantly inertial, we expect the spectrum to be what is normally called the pure rotational Raman spectrum of the molecule. As higher densities are approached, the discrete spectral lines broaden and overlap to form a continuous band. We show how the band shape can be computed for freely rotating linear molecules and spherical top molecules and then indicate the assumptions that have been used by several authors to include collisions in the theory. 

Thus the Raman spectrum shows only the fundamental and the REP shows two peaks, corresponding to = 0 and v= 1. In the absence of degeneracies, the scattering tensor has no diagonal elements for nontotally symmetric modes, i.e., p depolarization ratio is then, according to Eq. (3),... 

By polarizing the incident light or in other ways, it is possible to find the degree of depolarization of each frequency shift in the Raman spectrum, a quantity which will be important in the interpretation of the experimental results. This quantity is the ratio, for the scattered light, of the intensities of the components polarized perpendicular and parallel, respectively, to the direction of polarization of the incident illumination. 

Scattering in the range of lattice vibrations from 280 to 790 cm" was found to persist in the Raman spectrum after melting NaNH2- Deconvolution of the depolarized, broad band gave three peaks which were attributed to hindered rotational modes of the amide ion about its three principal axes [28]. 

Calculated depolarization ratios and differential scattering cross sections (do/dn)i for propyne are presented in Table 9.10. The simulated Raman spectrum is compared with the experimental gas-phase spectral ciuve [317] in Fig. 9.4. The band half-widths are taken from the experiment. The lines of A] transitions have sharp features, while E-vibrations are characterized with much broader bands. Since no quantitative intensity data for this molecule exist, a qualitative assessment of the results obtained can be done only. Fig. 9.4 reveals that the overall shape of the Raman spectrum is reproduced correctly. The most intense Raman lines are calculated to be those positioned at 2941, 2142 and 930 cm with intensities decreasing in the same order in agreement with the experimental spectrum. These lines are highly polarized. The other vibrational transitions giving rise to low- or medium-intensity lines in the spectrum are predicted to have intensities of the same order. The most significant difference between calculated and... 

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