Frequency Brillouin scattering

The application of Brillouin scattering to the characterization of elastomers [281-283] is an interesting extension of earlier work on polymers in general [284-287]. It should be quite useful for looking at glassy-state properties of elastomers at very high frequencies. 

Figure 14 shows the result of a Brillouin scattering experiment in the vicinity of Tc [11]. Closed circles and open circles below Tc indicate the modes split from the doubly degenerated ferroelectric soft mode. The closed circles above Tc denote the frequency of the doubly degenerated soft u mode in the paraelectric phase. The results clearly show a softening of the soft mode toward zero frequency at Tc following the Curie-Weiss law. The soft mode remains underdamped even at Tc. Generally, a soft mode is heavily damped in the vicinity of Tc, e.g., as for PbTiOs, which are typical displacive-type... 

We have made classical calculations of the effect of water surrounding a helix on the acoustic velocity (5). The effects seem small at frequencies of 5GHz and higher which were found in the Brillouin scattering results. In our recent calculations the lowest optical mode occurs at 150 GHz in B conformation and is much higher for A conformation. 

Brillouin scattering provides information about the acoustic branches of the dispersion curves of the material under study. The measured frequency shift of the radiation is equal to that of the phonon under consideration (EQN (1)), and its wave vector is deduced from EQN (2), so the sound velocity may be calculated by ... 

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... 

Measurements and information. Signal processing allows both time- and frequency-domain information to be obtained depending on the type of specimen studied. In addition, the use of frequency-tunable laser to generate density variations within the sample results in thermal expansion by absorption of light. Compared to spontaneous Brillouin scattering, the SNR in this forced Brillouin spectrometry is substantially enhanced by the generation of coherent phonons within the sample. 

Recently, Brillouin scattering has proved useful in this area for studying the frequency dependence of hypersonic (GHz zone) absorption and dispersion velocity in liquid sulphur dioxide [91] the effect of isotopes on hydrodynamic fluctuations in self-associated fluids [92] and the elastic properties of polyethylene glycol solutions in water, benzene and toluene [93]. 

In the very high frequency range, Brillouin scattering may be used to measure the sound velocities of aerogels [53]. 

Fig. 5.3.11. Dependence of the sound velocities on the polar angle from Brillouin scattering experiments on (J-methyl butyl p((p-methoxy-benzylidene)amino) cin-namate. (a) Smectic A(T = 60.7 °C), (b) smectic B (F = 48.1 C). The dashed lines are calculated from theory. The presence of a third component in (b) indicates that the shear modulus does not vanish in smectic B at these very hi frequencies. Circles, triangles and squares represent measurements at different scattering angles. (After Liao, Clark and Pershan. )...

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