Mechanical spectra of glass-forming liquids. II. Gigahertz-frequency longitudinal and shear acoustic dynamics in glycerol and DC704 studied by time-domain Brillouin scattering

Abstract

This paper presents and discusses the temperature and frequency dependence of the longitudinal and shear viscoelastic response at MHz and GHz frequencies of the intermediate glass former glycerol and the fragile glass former tetramethyl-tetraphenyl-trisiloxane (DC704). Measurements were performed using the recently developed time-domain Brillouin scattering technique, in which acoustic waves are generated optically, propagated through nm thin liquid layers of different thicknesses, and detected optically after transmission into a transparent detection substrate. This allows for a determination of the frequency dependence of the speed of sound and the sound-wave attenuation. When the data are converted into mechanical moduli, a linear relationship between longitudinal and shear acoustic moduli is revealed, which is consistent with the generalized Cauchy relation. In glycerol, the temperature dependence of the shear acoustic relaxation time agrees well with literature data for dielectric measurements. In DC704, combining the new data with data from measurements obtained previously by piezo-ceramic transducers yields figures showing the longitudinal and shear sound velocities at frequencies from mHz to GHz over an extended range of temperatures. The shoving model's prediction for the relaxation time's temperature dependence is fairly well obeyed for both liquids as demonstrated from a plot with no adjustable parameters. Finally, we show that for both liquids the instantaneous shear modulus follows an exponential temperature dependence to a good approximation, as predicted by Granato's interstitialcy model.

Time-domain Brillouin scattering for the determination of laser-induced temperature gradients in liquids

“…Note that the twofold change in Brillouin frequency with temperature in Fig. 2(c) is mainly due to the significant change in speed of sound over the examined temperature range (200 K -400 K) [22], rather than the change of the index of refraction which varies only a few percent over the same temperature range [18]. A slight Brillouin frequency shift of about 0.8 GHz in between our experimental data and the calculated calibration curve can be observed in Fig.…”

“…At such relatively low fluence, the overheating caused by the multiple laser pump pulses is moderate. (c) Temperature dependent Brillouin frequency in glycerol, from our measurements, and calculated from Comez et al [22] and Klieber et al [18]. The temperature calibration curves displayed in (c) can be used to estimate the absolute liquid temperature from the measured Brillouin frequency.…”

“…The experimental temperature calibration of the Brillouin frequency has been further fitted by a smooth polynomial function in order to extract an even more reliable temperature behavior of the Brillouin scattering frequency of glycerol under our experimental conditions at 395 nm probe wavelength and a normal incidence scattering angle. Since we did not have the possibility to record the Brillouin scattering frequency at higher temperatures than 320 K, we have used a calculated calibration curve from literature data obtained from Comez et al [22] and Klieber et al [18] as a reference function to link the Brillouin frequency to the absolute glycerol temperature. Note that the twofold change in Brillouin frequency with temperature in Fig.…”

“…The optical experiment is based on the TDBS technique, suitable for the investigation of the frequency and temperature dependences of ultrafast acoustic dynamics in liquids at GHz frequencies [16][17][18][19][20][21]. Measurements were made using an ultrafast optical pump-probe experimental setup as illustrated in Fig.…”

“…In this situation, well suited for the investigation of mechanical properties of ultrathin solid or liquid samples, the occurrence of time-domain Brillouin scattering (TDBS) phenomena in transparent materials has been used to investigate viscoelastic properties of matter at ultrasound GHz to THz frequencies [6]. Recently, several examples have shown that TDBS is sensitive to diverse phenomena, including spatial mechanical, optical or acousto-optical inhomogeneities [7][8][9][10][11][12][13], non-linear acoustic waves or weak shock waves [14,15], and even GHz transverse acoustic phonons in viscoelastic liquids [16][17][18][19].…”