Rayleigh-Brillouin spectra

Figure A3.3.1 Rayleigh-Brillouin spectrum from liquid argon, taken from [4],...

Fig. 1. Rayleigh-Brillouin spectrum of PEMA at room temperature showing several Fabry-Perot orders...

Figure 4. Rayleigh Brillouin spectrum ofBP-D20 mixture outside the coexistence curve.

The Rayleigh-Brillouin Spectrum of a Pure Monatomic Fluid, 233... 

In Section 10.2 we saw that the macroscopic relaxation equations can be used to determine correlation functions. In this section we summarize the traditional methods for deducing the macroscopic relaxation equations of fluid mechanics. In subsequent sections these equations are used to determine the Rayleigh-Brillouin spectrum. The first step in the derivation of the relaxation equation involves a discussion of conservation laws. 

THE RAYLEIGH-BRILLOUIN SPECTRUM OF A PURE MONATOMIC FLUID... 

A detailed study of the Rayleigh-Brillouin spectrum of liquid argon recently made by Fleury and Boon (1969) showed that the normalized spectrum, 5(q, cu)/5(q), is described by Eq. (10.4.30) to within experimental error. In their experiment q 2.1 x 105 cm-1, T = 85 °K and P = 592.5 mmHg. From Eq. (10.4.41), the sound speed is cs = 850 4 m/sec this compares very well with the low-frequency sound speed measured acoustically, cs = 853 m/sec. A typical spectrum is shown in Fig. (10.4.1). 

If the density p and ratio of specific heats y are known, measurements of A(0(i) can be used to obtain /3t- The ratio of specific heats for the case where t << 10" sec can be obtained from the Rayleigh-Brillouin spectrum of the fluid. The intensity of the central peak owing to the thermal expansion divided by the intensity of the two Brillouin peaks is equal to y — 1 (6). For n-hexadecane at 120°G (shown in Figure 1), this ratio yields y = 1.227. The density is 0.7036 (7). The Brillouin splitting is measured to be 0.131 cm" The isothermal compressibility is calculated to be 1.6 X 10" cm /dyn in good agreement with the directly measured value of (7). 

Figure 11. Depolarized (Ihv) Rayleigh-Brillouin spectrum of bisphenol-A polycarbonate at 14(f (upper left, 200 (lower left, and 240° C (top)...

The so-called fast relaxation limit in which coe cog. In this case the structural relaxation gives rise to a broad backgroimd scattering in the frequency scale, leaving the Rayleigh-Brillouin spectrum nearly unchanged. 

Fig. 5. Polarized Rayleigh-Brillouin spectrum of amorphous PnHMA taken with a Burleigh plane Fabry-Perot interferometer using a free spectral range of 12.4 GHz at 295 K. The two Brillouin peaks are shifted from the incident frequency by the product of the wave vector q and the sound velocity u. The line width of the Brillouin peaks is related to the attenuation of the sound waves. PnHMA.

This chapter has considered measurements of the dynamic structure factor S q, t) of polymer solutions. Here behaviors of the first cumulant, the polymer slow mode, and the high-frequency Rayleigh-Brillouin spectrum have been considered. Neutron spin-echo methods as supplements to light scattering spectroscopy were noted. Results on Ki and the Rayleigh-Brillouin spectrum are readily summarized. The discussion of the slow mode is considerably more extended, but leads to a comparison with modem models for glass formation. 

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