Brillouin peaks

In real fluids, low-frequency light-scattering reveals a central Rayleigh peak, due to heat diffusion, and two symmetrically displaced Brillouin peaks, due to sound waves, such that... 

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

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

Figure 9.14. Brillouin spectrometer using fibre optics to increase the signal-to-noise ratio. (1) Light source consisting of a master laser (1a) a slave with matched frequency (1b) and control unit (1c) for sensitive stabilization of the difference frequency Sv. (2) Signal splitter. (3) Fibre coupler. (4) Polarizer. (5) Chopper. (6) Lens. (7) Cuvette placed on a goniometer. (8) Termination. (9) Slit. (10) Broad-band (10 GHz) APD. (11) Photodiode with a smaller bandwidth (1 GHz). (12) Spectrum analyser (10 GHz) for controlling the intermediate frequency Sv. (13) Spectrum analyser (1 GHz) for the measurement of the half-power bandwidth, Av, of the Brillouin peak. (14) Amplifier system. (15) Process control computer. (Reproduced with permission of Elsevier, Ref [96].)...

The last two terms in Eq. (10.4.39) represent a non-Lorentzian correction which shifts the apparent Brillouin peaks toward the center slightly and renders the doublets asymmetric (the whole spectrum is, nevertheless, still symmetric about co= 0) about co(q). This last term is usually very small. 

The spectrum associated with a binary solution consists of four contributions. The two Brillouin peaks are centered at +a> q) with a width q2r. The central component consists of a superposition of two Lorentzians with a height that depends on many parameters (cf. our preceding discussion). 

The spectrum of amorphous bisphenol-A polycarbonate showing both longitudinal and transverse Brillouin peaks is shown in Figure 2. 

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). 

When Ts < < 10" sec, the transverse phonon velocity is imaginary and no transverse Brillouin peaks are observed. However, shear fluctuations do occur and they can couple with other modes of motion such as molecular reorientation. The spectrum that results is given by ... 

The basic experiment consists of measuring the spectrum of the scattered light. It consists of a strong elastic peak at one frequency with additional components whose frequency has been shifted by the inelastic scattering processes. The frequencies of these much weaker phonon peaks are measured relative to the elastic peak. From observation of the shifted Brillouin peak with respect to the central elastic peak, the longitudinal Brillouin splitting, A >i is given by... 

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.

The above method uses the position and width of the Brillouin peak, rather than the complete spectrum, to determine viscoelastic parameters of the polymer. It is useful to consider the relation of the spectral intensity of scattered light to these viscoelastic parameters. This gives one an alternate method for finding relative values of M (o) as a function of temperature. In addition, it allows one to measure the temperature dependence of the isothermal compressibility, Pj- q. 

Here, we briefly summarize the results for the dynamic structure factor. The dynamic sfiucture factor exhibits three peaks, a central Rayleigh peak caused by the thermal diffusion, and two symmetrically placed Brillouin peaks caused by sound. The width of the central peak is determined by the thermal diflfusivity, Dj, while that of the two Brillouin peaks is related to the sound attenuation coefficient, r. For the SRD algorithm [57],... 

Fig. 2 Normalized dynamic structure, Spp k0 )fXpp k)< for k = 2tr(l, 1)/L and a X/a = 1.0 with a = 120°, and b A/a = 0.1 with a = 60°. The solid lines are the theoretical prediction for the dynamic structure factor (see (36) of [57]) using values for the transport coefSdents obtained with the expressions in Table 1. The dotted lines show the predicted positions of the Brillouin peaks, 0) = ck, with c = a/2ksT jm. Parameters L/u = 32, M = 15, and At = 1.0. From [57]...

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