Rayleigh scattering intensity

Rayleigh scattering is the re-emission by solvent molecules of a small fraction of the excitation radiation. This emission occurs at the same wavelength and is independent of the angle of observation (Fig. 12.6). The Rayleigh scattering intensity varies with the polarisability of solvent molecules. 

Assuming the laser intensity to be constant, variations in the Rayleigh scattered intensity are a result of both temperature and species variations. Hence, an unambiguous interpretation of the Rayleigh scattered intensity requires that experiments be contrived into one of three cases. These are ... 

Case 2 Constant Rayleigh Cross Section - In this case, variations in the Rayleigh scattering intensity are attributed to variations in temperature. A natural compliment to the isothermal mixing investigations identified in Case 1 would be to measure the time-resolved temperature in a submerged jet of heated air. For premixed flames, the variation of Rayleigh intensity is primarily due to variation in temperature, which can vary by a factor of 7. 

Case 3 Both temperature and species variation - In this case, additional information is required. This could be obtained from another diagnostic or a mathematical model. Smith (10) used an extensive mathematical model of a laminar hydrogen diffusion flame to predict the species distribution throughout the flame having this, the temperature could be inferred from the Rayleigh scattering intensity. 

At certain positions in the flame, the background flame luminescence received by the photomultiplier tube can be 15% of the Rayleigh scattered intensity. A large reduction of this noise would be achieved by replacing the 1 nm bandpass filter with a monochrometer. Use of a multipass cell (12) or intracavity laser (13) would raise the signal above the flame luminescence. In addition, the increased scattered photon count rate would increase the precision of each measurement. 

Equation (7.36) is known as the Debye plot. Figure 7.11a and Figure 7.11b show the excess Rayleigh scattering intensities of polyacrylamide from MALLSP (multi angle laser light scattering photometer) and LALLSP, respectively. 

FIGURE 7.11 Excess Rayleigh scattering intensities of a polyacrylamide from (a) MALLSP and (b) LALLSP. [Graphs reconstructed from data by Wyeth Corp. and Kim, Ph.D. dissertation, McMaster University, Hamilton, Ontario, 1984.]... 

Figure 5. Schematics of an experimentaj arrangement for the measurement of the Hyper Rayleigh Scattering intensity (HWP half-wave plate LPF low-pass filter, LI and L2 lens BD beam dutrrp A analyzer. HPF high-pass filter)...

Figure 11-17. Comparison of the Rayleigh scattering intensity ratio profiles eorresponding to plasma power 0 W, 33 W, 60 W. Strain rates are 87.1 s , 98.6 s, and 298.5 s, respectively.

Rank of G matrix, test for completeness of coordinate set, 145 Rayleigh scattering intensity, 48, 49 equilibrium polarizability in, 48 Rayleigli s principle, 218., 227 Rea matrix, 290 Rccijn-ocal matrix, 295 Recursion formuhi tor Hormite polynomials, 38... 

Due to the rather stringent requirements placed on the monochromator, a double or triple monocln-omator is typically employed. Because the vibrational frequencies are only several hundred to several thousand cm and the linewidths are only tens of cm it is necessary to use a monochromator with reasonably high resolution. In addition to linewidth issues, it is necessary to suppress the very intense Rayleigh scattering. If a high resolution spectrum is not needed, however, then it is possible to use narrow-band interference filters to block the excitation line, and a low resolution monocln-omator to collect the spectrum. In fact, this is the approach taken with Fourier transfonn Raman spectrometers. 

The second method to calculate the scattered intensity or R the Rayleigh ratio) is to square the sum in I... 

Thus Rg is a constant in any particular experiment where Rayleigh scattering is obtained, since the entire angular dependence of the light intensity is correctly contained in the 1 + cos 6 term. 

We assume that there exists a function which we represent by P(0)-in recognition of the fact that it is angle dependent-which can be multiplied by the scattered intensity as predicted by the Rayleigh theory to give the correct value for i, even in the presence of interference. That is. 

Since P(0) is Rayleigh observed scattering intensity at 0-the value that... 

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... 

In the low frequency region, the calculations predict nanotube-specifiic Eig and E g modes around 116 cm and 377 cm respectively, for (10,10) armchair naiiotubes, but their intensities are expected to be lower than that for the A g mode. However, these Eig and E2g modes are important, since they also show a diameter dependence of their mode frequencies. In the very low frequency region below 30 cm a strong low frequency Raman-active E2g mode is expected. However, it is difficult to observe Raman lines in the very low frequency region, where the background Rayleigh scattered is very strong. 

The force Rayleigh scattering method was developed by Nagashima s group. Thermal diffusivity can be measured in a contact-free manner within a time interval of 1 ms, with a small temperature rise of 0.1 K and with a small volinne of about 10 mm The sample needs to be colored by an admixture of a dye for suitable absorption of a heating laser beam. The principle is schematically shown in Fig. 32. Two beams of equal intensity divided by means of abeam splitter cross in the sample to create... 

If the scattering intensity can be measured with sufficient accuracy down to very small angles, the Rayleigh ratio at zero angle may be... 

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