Brillouin spectroscopy

The elastic properties of PS depend on its microstructure and porosity. The Young s modulus for meso PS, as measured by X-ray diffraction (XRD) [Ba8], acoustic wave propagation [Da5], nanoindentation [Bel3] and Brillouin spectroscopy [An2], shows a roughly (1-p)2 dependence. For the same values of porosity (70%), micro PS shows a significantly lower Young s modulus (2.4 GPa) than meso PS (12 GPa). The Poisson ratio for meso PS (0.09 for p=54%) is found to be much smaller than the value for bulk silicon (0.26) [Ba8]. 

A full theory of light scattering from a viscoelastic medium has been presented by Rytov17). This theory has been extensively discussed in the context of Rayleigh-Brillouin spectroscopy of bulk polymers18"21). In the present paper the results of that work will be presented and extended to include relaxation near the glass transition. 

Whalley (1980) presented a theoretical argument to suggest that both the thermal expansivity and Poisson s ratio should be similar to that of ice. With the above two estimates, Whalley calculated the compressional velocity of sound in hydrates with a value of 3.8 km/s, a value later confirmed by Whiffen et al. (1982) via Brillouin spectroscopy. Kiefte et al. (1985) performed similar measurements on simple hydrates to obtain values for methane, propane, and hydrogen sulfide of 3.3, 3.7, and 3.35 km/s, respectively, in substantial agreement with calculations by Pearson et al. (1984). 

Shimizu et al. (2002) extended the previous Brillouin spectroscopy measurements by performing in situ measurements on a single crystal methane hydrate. They examined the effect of pressure on shear (TA) and compressional (LA) velocities, and compared these results to that for ice. The shear velocities of methane hydrate and ice were very similar, showing a slight decrease (about 2 to 1.85 km/s) with increasing pressure (0.02-0.6 GPa). Conversely, the compressional velocities of ice and methane hydrate were different. The... 

The discrepancy between the first determination of the elastic constants and the following ones is not surprising, due to the very indirect way utilised in [33]. The difference between the Brillouin spectroscopy results on the one hand and those obtained with resonance ultrasonic spectroscopy on the other one is mostly due to the difference in C33. Although the authors claim that the most precise measurements of elastic moduli are obtained using ultrasonic techniques, the samples should have a... 

Brillouin Spectroscopy on Thermal Phonons and Other Elementary Excitations... 

Fig. 9.2 Typical scattering geometries used for Brillouin spectroscopy, (a) 90N-scattering geometry (b) 90A-scattering geometry (c) a combination of the 90A- and the 90R-scatter-ing geometry (d) back scattering geometry.

Whiffen, B.L. Kiefte. H. Clouter. M.J. Determination of acoustic velocities in xenon and methane hydrates by Brillouin spectroscopy. Geopliys. Res. Lett. 1982. 9. 645. 

As an experimental approach to investigate the temperature behavior of extremely slow structural glass relaxation processes (a-relaxation) we resently presented measurements with time domain Brillouin spectroscopy (TDBS) performed... 

Experimental bulk moduli can be obtained from the measurement of lattice parameters and volumes as a function of pressure [30]. The single crystal elastic moduli can be measured using the Brillouin spectroscopy, inelastic neutron scattering, ultrasonic measurements or the Schaefer-Bergmann method [31]. Once the single crystal moduli are known one can derive the bulk B and shear G moduli of a polycrystalline material [32]. 

Brillouin spectroscopy can also be used to study the change of sound velocity with deformation. Anders et al. reported the longitudinal sound velocity in stretched poly (urethane) and poly (diethylsiloxane) (PDFS, Figure 60.8) networks [15]. They used the lattice-model to determine the force constants [11]. The samples showed different deformation-dependent behavior of the force constants. For the... 

Spectroscopic methods for hydration of ions were reviewed for structural aspects and dynamic aspects of ionic hydration by Ohtaki and Radnai (150). They discussed X-ray diffraction, neutron diffraction, electron diffraction, small-angle X-ray (SAXS) and neutron-scattering (SANS), quasi-elastic neutron-scattering (QENS) methods, extended X-ray absorption fine structure (EXAFS), X-ray absorption near-edge structure (XANES) spectroscopies, nuclear magnetic resonance (NMR), Mdssbauer, infrared (IR), Raman, and Raleigh-Brillouin spectroscopies. The clay interlayer molecular modeling where clay surface is interfaced with aqueous solution also includes ions that are also solvated by interlayer water. 

Brillouin spectroscopy enables the elastic constants of pol3oners to be determined at frequencies of several gigahertz, i.e. three orders of magnitude higher than those pertaining to ultrasonic measurements, which are known as h3qiersonic frequencies. 

The technique of Brillouin spectroscopy (Section 5.3.3 above) has been applied to determine the elastic constants of oriented polymer fibres. Early studies of this nature were undertaken by Kruger and co-workers [26, 27] on oriented polycarbo-... 

Recent Brillouin spectroscopy measurements include those of Kumar, Renisch and Grimsditch [30] on uniaxially and biaxially stretched polypropylene films. Using the Ward aggregate model with a modified definition of molecular alignment enabled elastic anisotropy and refractive index data to be related quantitatively to molecular orientation. 

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