Supercooled Liquid Dynamics Studied via Shear-Mechanical Spectroscopy

We report dynamical shear-modulus measurements for five glass-forming liquids (pentaphenyl trimethyl trisiloxane, diethyl phthalate, dibutyl phthalate, 1,2-propanediol, and m-touluidine). The shear-mechanical spectra are obtained by the piezoelectric shear-modulus gauge (PSG) method. This technique allows one to measure the shear modulus ($10^{5} -10^{10}$ Pa) of the liquid within a frequency range from 1 mHz to 10 kHz. We analyze the frequency-dependent response functions to investigate whether time-temperature superposition (TTS) is obeyed. We also study the shear-modulus loss-peak position and its high-frequency part. It has been suggested that when TTS applies, the high-frequency side of the imaginary part of the dielectric response decreases like a power law of the frequency with an exponent -1/2. This conjecture is analyzed on the basis of the shear mechanical data. We find that TTS is obeyed for pentaphenyl trimethyl trisiloxane and in 1,2-propanediol while in the remaining liquids evidence of a mechanical $\beta$ process is found. Although the the high-frequency power law behavior $\omega^{-\alpha}$ of the shear-loss may approach a limiting value of $\alpha=0.5$ when lowering the temperature, we find that the exponent lies systematically above this value (around 0.4). For the two liquids without beta relaxation (pentaphenyl trimethyl trisiloxane and 1,2-propanediol) we also test the shoving model prediction, according to which the the relaxation-time activation energy is proportional to the instantaneous shear modulus. We find that the data are well described by this model.Comment: 7 pages, 6 figure

Shear modulus in viscoelastic solid 4^4He

The complex shear modulus of solid $^4$He exhibits an anomaly in the same temperature region where torsion oscillators show a change in period. We propose that the observed stiffening of the shear modulus with decreasing temperature can be well described by a viscoelastic component that possesses an increasing relaxation time as temperature decreases. Since a glass is a viscoelastic material, the response functions derived for a viscoelastic material are identical to those obtained for a glassy component due to a time delayed restoring back-action. By generalizing the viscoelastic equations for stress and strain to a multiphase system of constituents, composed of patches with different damping and relaxation properties, we predict that the maximum change of the magnitude of the shear modulus and the maximum height of the dissipation peak are independent of an applied external frequency. The same response expressions allow us to calculate the temperature dependence of the shear modulus' amplitude and dissipation. Finally, we demonstrate that a Vogel-Fulcher-Tammann (VFT) relaxation time is in agreement with available experimental data.Comment: 8 pages, 4 figures. Revision has expanded the result section. To appear in Journal of Low Temperature Physic

Shear modulus of neutron star crust

Shear modulus of solid neutron star crust is calculated by thermodynamic perturbation theory taking into account ion motion. At given density the crust is modelled as a body-centered cubic Coulomb crystal of fully ionized atomic nuclei of one type with the uniform charge-compensating electron background. Classic and quantum regimes of ion motion are considered. The calculations in the classic temperature range agree well with previous Monte Carlo simulations. At these temperatures the shear modulus is given by the sum of a positive contribution due to the static lattice and a negative $\propto T$ contribution due to the ion motion. The quantum calculations are performed for the first time. The main result is that at low temperatures the contribution to the shear modulus due to the ion motion saturates at a constant value, associated with zero-point ion vibrations. Such behavior is qualitatively similar to the zero-point ion motion contribution to the crystal energy. The quantum effects may be important for lighter elements at higher densities, where the ion plasma temperature is not entirely negligible compared to the typical Coulomb ion interaction energy. The results of numerical calculations are approximated by convenient fitting formulae. They should be used for precise neutron star oscillation modelling, a rapidly developing branch of stellar seismology.Comment: 10 pages, 3 figures, accepted to MNRA

Rheology and ultrasonic properties of Pt57.5Ni5.3Cu14.7P22.5 liquid

The equilibrium and nonequilibrium viscosity and isoconfigurational shear modulus of Pt57.5Ni5.3Cu14.7P22.5 supercooled liquid are evaluated using continuous–strain-rate compression experiments and ultrasonic measurements. By means of a thermodynamically-consistent cooperative shear model, variations in viscosity with both temperature and strain rate are uniquely correlated to the variations in isoconfigurational shear modulus, which leads to an accurate prediction of the liquid fragility and to a good description of the liquid strain-rate sensitivity