Stokes vibrational Raman

The mechanism for Stokes and anti-Stokes vibrational Raman transitions is analogous to that for rotational transitions, illustrated in Figure 5.16. As shown in Figure 6.3, intense monochromatic radiation may take the molecule from the u = 0 state to a virtual state Vq. Then it may return to u = 0 in a Rayleigh scattering process or to u = 1 in a Stokes Raman transition. Alternatively, it may go from the v = state to the virtual state Fj and return to V = (Rayleigh) or to u = 0 (Raman anti-Stokes). Flowever, in many molecules at normal... 

Figure 6.3 Stokes and anti-Stokes vibrational Raman scattering...

Figure 6.9 The 1-0 Stokes vibrational Raman spectrum of CO showing the 0-, Q-, and 5-branch rotational structure...

Fig. 7.1. Two equivalent ROA experiments involving Stokes vibrational Raman scattering at angular frequency oj — ojv in incident light of angular frequency oj far from resonance, a The ICP ROA experiment measures JR - JL, where JR and JL are the scattered intensities (shown here as unpolarized) in right- and left-circularly polarized incident light, respectively, b The SCP ROA experiment measures hi-h., where Jr and JL are the intensities of the right- and left-circularly polarized components, respectively, of the scattered light using incident light of fixed polarization (shown here as unpolarized)...

Figure 3. Calculated band profiles of Stokes vibrational Raman scattering from Nt at 2000 K assuming a triangular slit function with FWHM = 5.0 cm 1. The bottom curve includes the isotropic part of the Q-branch only. The top curve is a more exact calculation including O- and S-branch scattering, the anisotropic part of the Q-branch and line-strength corrections owing to centrifugal distortion. The base lines have been shifted vertically for clarity.

Nitrogen Stokes vibrational Raman signal from pulsed multipass cell (5)... 

Figure 1. Relative Stokes vibrational Raman intensity jor nitrogen for a trapezoidal slit function and various center positions...

Figure 2. Intensity ratio of anti-Stokes to Stokes vibrational Raman scattering for a trapezoidal slit function. Center position of Stokes bandpass at 6072 A.

For most purposes only the Stokes-shifted Raman spectmm, which results from molecules in the ground electronic and vibrational states being excited, is measured and reported. Anti-Stokes spectra arise from molecules in vibrational excited states returning to the ground state. The relative intensities of the Stokes and anti-Stokes bands are proportional to the relative populations of the ground and excited vibrational states. These proportions are temperature-dependent and foUow a Boltzmann distribution. At room temperature, the anti-Stokes Stokes intensity ratio decreases by a factor of 10 with each 480 cm from the exciting frequency. Because of the weakness of the anti-Stokes spectmm (except at low frequency shift), the most important use of this spectmm is for optical temperature measurement (qv) using the Boltzmann distribution function. 

A small fraction of the molecules are in vibrationally excited states. Raman scattering from vibrationally excited molecules leaves the molecule in the ground state. The scattered photon appears at higher energy, as shown in Figure lb. This anti-Stokes-shifted Raman spectrum is always weaker than the Stokes-shifted spectrum, but at room temperature it is strong enough to be useful for vibrational frequencies less than about 1500 cm 1. The Stokes and anti-Stokes spectra contain the same frequency information. 

For any vibrational mode, the relative intensities of Stokes and anti-Stokes scattering depend only on the temperature. Measurement of this ratio can be used for temperature measurement, although this application is not commonly encountered in pharmaceutical or biomedical applications. Raman scattering based on rotational transitions in the gas phase and low energy (near-infrared) electronic transitions in condensed phases can also be observed. These forms of Raman scattering are sometimes used by physical chemists. However, as a practical matter, to most scientists, Raman spectroscopy means and will continue to mean vibrational Raman spectroscopy. 

The inelastic processes - spontaneous Raman scattering (usually simply called Raman scattering), nonlinear Raman processes, and fluorescence - permit determination of species densities as well as temperature, and also allow one, in principle, to determine the temperature for particular species whether or not in thermal equilibrium. In Table II, we categorize these inelastic processes by the type of the information that they yield, and indicate the types of combustion sources that can be probed as well as an estimate of the status of the method. The work that we concentrate upon here is that indicated in these first two categories, viz., temperature and major species densities determined from vibrational Raman scattering data. The other methods - fluorescence and nonlinear processes such as coherent anti-Stokes Raman spectroscopy - are discussed in detail elsewhere (5). 

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.

Figure 1. Rotational—vibrational line strength correction factors for pure rotational Raman scattering (fM)0 and for O-, S-, and Q-branch vibrational Raman scattering (foh fots, and folQ). The value J is the rotational quantum number of the initial level (O), Stokes (A), anti-Stokes.

When the sample is illuminated by a giant pulse of frequency v, the scattered radiation contains frequencies of 2v (hyper-Rayleigh scattering) and 2v vm (Stokes and anti-Stokes hyper-Raman scattering), where vM is a frequency of a normal vibration of the molecule. Clearly, this is Raman scattering caused by two incident photons (2v) of the laser. Experimentally, this... 

Fig. 11.1 Schematics of vibrational Raman process. Stokes process gives scattered lights that are lower in energy than the incident light, and anti-Stokes process gives scattered lights that are higher in energy than the incident light...

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