Ultrasonic investigation of the glass transition in glycerol

We have measured, as a function of temperature and frequency, the velocity and attenuation of ultrasound near the glass transition of glycerol. The data are compared with that from frequency-dependent specific-heat measurements recently performed on the same sample. When the difference between adiabatic and isothermal processes is taken into account, we find that the relaxation time associated with the ultrasonic measurements is the same as that responsible for the dispersion seen in the specific-heat experiment. We also compare our results with recent hydrodynamic theories of the glass transition. The relaxation time that we measure can be fitted equally well either by a scaling form τ=${\tau }_0$[(T-$T_h$)/$T_h$ ${]}^{\mathrm{-}\alpha }$, as these theories predict, or by the Vogel-Tamman-Fulcher law τ=${\tau }_0$exp[E/$k_B$(T-$T_0$)], which has often been used to fit relaxation behavior in glasses. In the scaling-law fit, α=12.5, which is unexpectedly large. The recent theory of Marchetti, which includes the wave-vector dependence of the mode-coupling vertex, provides a good fit to the frequency dependence of the data at constant temperature.