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The temperature dependence of the thermal conductivity is linked to the nature of the energy transport at a frequency omega, which is quantified by thermal diffusivity d(omega). Here we study d(omega) for a poorly annealed glass and a highly stable glass prepared using the swap Monte Carlo algorithm. To calculate d(omega), we excite wave packets and find that the energy moves diffusively for high frequencies up to a maximum frequency, beyond which the energy stays localized. At intermediate frequencies, we find a linear increase of the square of the width of the wave packet with time, which allows for a robust calculation of d(omega), but the wave packet is no longer well described by a Gaussian as for high frequencies. In this intermediate regime, there is a transition from a nearly frequency independent thermal diffusivity at high frequencies to d(omega) ~ omega^(-4) at low frequencies. For low frequencies the sound waves are responsible for energy transport and the energy moves ballistically. The low frequency behavior can be predicted using sound attenuation coefficients.
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The history dependence of the glasses formed from flow-melted steady states by a sudden cessation of the shear rate $dotgamma$ is studied in colloidal suspensions, by molecular dynamics simulations, and mode-coupling theory. In an ideal glass, stresses relax only partially, leaving behind a finite persistent residual stress. For intermediate times, relaxation curves scale as a function of $dotgamma t$, even though no flow is present. The macroscopic stress evolution is connected to a length scale of residual liquefaction displayed by microscopic mean-squared displacements. The theory describes this history dependence of glasses sharing the same thermodynamic state variables, but differing static properties.
There is growing evidence that the flow of driven amorphous solids is not homogeneous, even if the macroscopic stress is constant across the system. Via event driven molecular dynamics simulations of a hard sphere glass, we provide the first direct evidence for a correlation between the fluctuations of the local volume-fraction and the fluctuations of the local shear rate. Higher shear rates do preferentially occur at regions of lower density and vice versa. The temporal behavior of fluctuations is governed by a characteristic time scale, which, when measured in units of strain, is independent of shear rate in the investigated range. Interestingly, the correlation volume is also roughly constant for the same range of shear rates. A possible connection between these two observations is discussed.
The temperature dependence of the thermal conductivity of amorphous solids is markedly different from that of their crystalline counterparts, but exhibits universal behaviour. Sound attenuation is believed to be related to this universal behaviour. Recent computer simulations demonstrated that in the harmonic approximation sound attenuation $Gamma$ obeys quartic, Rayleigh scattering scaling for small wavevectors $k$ and quadratic scaling for wavevectors above the Ioffe-Regel limit. However, simulations and experiments do not provide a clear picture of what to expect at finite temperatures where anharmonic effects become relevant. Here we study sound attenuation at finite temperatures for model glasses of various stability, from unstable glasses that exhibit rapid aging to glasses whose stability is equal to those created in laboratory experiments. We find several scaling laws depending on the temperature and stability of the glass. First, we find the large wavevector quadratic scaling to be unchanged at all temperatures. Second, we find that at small wavectors $Gamma sim k^{1.5}$ for an aging glass, but $Gamma sim k^2$ when the glass does not age on the timescale of the calculation. For our most stable glass, we find that $Gamma sim k^2$ at small wavevectors, then a crossover to Rayleigh scattering scaling $Gamma sim k^4$, followed by another crossover to the quadratic scaling at large wavevectors. Our computational observation of this quadratic behavior reconciles simulation, theory and experiment, and will advance the understanding of the temperature dependence of thermal conductivity of glasses.
Unlike crystals, glasses age or devitrify over time to lower their free energy, reflecting their intrinsically non-equilibrium nature. This lack of stability is a serious issue in many industrial applications. Here, we show by numerical simulations that devitrification and ageing of quasi hard-sphere glasses are prevented by suppressing volume-fraction inhomogeneities in the spatial arrangement of the particles. A glass of monodisperse quasi hard-sphere particles, known to devitrify and age with `avalanche-like intermittent dynamics, is subjected to small iterative adjustments to particle sizes to make the local volume fractions spatially uniform. We find that this almost entirely prevents structural relaxation and devitrification even in the presence of crystallites. The homogenisation of local volume fractions leads to a dramatic change in the local mechanical environment of each particle, with a clear homogenisation in the number of load-bearing nearest neighbours each particle has. This indicates that we may stabilise glasses by making them more `mechanically homogeneous. Our finding provides a physical principle for glass stabilisation and opens a novel route to the formation of mechanically stabilised glasses.
We report experiments on hard sphere colloidal glasses that reveal a type of shear banding hitherto unobserved in soft glasses. We present a scenario that relates this to an instability arising from shear-concentration coupling, a mechanism previously thought unimportant in this class of materials. Below a characteristic shear rate $dotgamma_c$ we observe increasingly non-linear velocity profiles and strongly localized flows. We attribute this trend to very slight concentration gradients (likely to evade direct detection) arising in the unstable flow regime. A simple model accounts for both the observed increase of $dotgamma_c$ with concentration, and the fluctuations observed in the flow.
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