Brillouin spectrum

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...

Physically, the Brillouin spectrum arises from the inelastic interaction between a photon and the hydrodynamics modes of the fluid. The doublets can be regarded as the Stokes and anti-Stokes translational Raman spectrum of the liquid. These lines arise due to the inelastic collision between the photon and the fluid, in which the photon gains or loses energy to the phonons (the propagating sound modes in the fluid) and thus suffer a frequency shift. The width of the band gives the lifetime ( 2r)-1 of a classical phonon of wavenumber q. The Rayleigh band, on the other hand, represents the... 

In the present chapter we consider the effect of a mixture of species on the Brillouin spectrum. The theory will be described and examples will be presented which illustrate the theory. 

Figure 4. Brillouin spectrum of a quenched film of 75% PVFS 25% PMMA by weight at 20°C...

A Brillouin spectrum of commercial Mylar film is shown in Figure 8. The longitudinal (L) and transverse (T) Brillouin peaks are easily seen. 

Figure 7. Brillouin spectrum of a commercial cellulose-acetate film...

Figure 8. Brillouin spectrum of commercial Mylar film showing longitudinal (L), transverse (T), and unknown ( ) Brillouin peaks...

Measurement of the Brillouin spectrum of polymer films is now straightforward using multiple-pass Fabry-Perot interferometry. The use of Brillouin scattering to study polymer blends as films should be a very fruitful area for further study. 

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). 

Fig. 10.4.1. Brillouin spectrum of liquid argon (T = 84.97°K, 6 = 90° 14, laser wavelength = 5145 A). (From Fleury and Boon, 1969.)...

The longitudinal Brillouin spectrum appears when both the incident and scattered light are polarized vertically with respect to the scattering plane (/vv) The transverse Brillouin spectrum results when the incident polarization is perpendicular to the scattered polarization (Ihv =1vh). 

The instrument most commonly used to resolve the Brillouin spectrum is the Fabry-Perot interferometer. This device consists of a pair of highly reflective, optically polished mirrors. The transmission function for a plane parallel Fabry-Perot interferometer is ... 

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)...

Figure 15. Brillouin spectrum of a film of PMMA at 100° C. Two Fabry-Perot orders are shown.

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