Lifetime of dynamical heterogeneity in a highly supercooled liquid

We numerically examine dynamical heterogeneity in a highly supercooled three-dimensional liquid via molecular-dynamics simulations. To define the local dynamics, we consider two time intervals, $\tau_\alpha$ and $\tau_{\text{ngp}}$. $\tau_\alpha$ is the $\alpha$ relaxation time, and $\tau_{\text{ngp}}$ is the time at which non-Gaussian parameter of the van Hove self-correlation function is maximized. We determine the lifetimes of the heterogeneous dynamics in these two different time intervals, $\tau_{\text{hetero}}(\tau_\alpha)$ and $\tau_{\text{hetero}}(\tau_{\text{ngp}})$, by calculating the time correlation function of the particle dynamics, i.e., the four-point correlation function. We find that the difference between $\tau_{\text{hetero}}(\tau_\alpha)$ and $\tau_{\text{hetero}}(\tau_{\text{ngp}})$ increases with decreasing temperature. At low temperatures, $\tau_{\text{hetero}}(\tau_\alpha)$ is considerably larger than $\tau_{\alpha}$, while $\tau_{\text{hetero}}(\tau_{\text{ngp}})$ remains comparable to $\tau_{\alpha}$. Thus, the lifetime of the heterogeneous dynamics depends strongly on the time interval.Comment: 4pages, 6figure

Measuring Spatial Distribution of Local Elastic Modulus in Glasses

Glasses exhibit spatially inhomogeneous elastic properties, which can be investigated by measuring their elastic moduli at a local scale. Various methods to evaluate the local elastic modulus have been proposed in the literature. A first possibility is to measure the local stress-local strain curve and to obtain the local elastic modulus from the slope of the curve, or equivalently to use a local fluctuation formula. Another possible route is to assume an affine strain and to use the applied global strain instead of the local strain for the calculation of the local modulus. Most recently a third technique has been introduced, which is easy to be implemented and has the advantage of low computational cost. In this contribution, we compare these three approaches by using the same model glass and reveal the differences among them caused by the non-affine deformations

Elastic Moduli and Vibrational Modes in Jammed Particulate Packings

When we elastically impose a homogeneous, affine deformation on amorphous solids, they also undergo an inhomogeneous, non-affine deformation, which can have a crucial impact on the overall elastic response. To correctly understand the elastic modulus $M$, it is therefore necessary to take into account not only the affine modulus $M_A$, but also the non-affine modulus $M_N$ that arises from the non-affine deformation. In the present work, we study the bulk ($M=K$) and shear ($M=G$) moduli in static jammed particulate packings over a range of packing fractions $\varphi$. One novelty of this work is to elucidate the contribution of each vibrational mode to the non-affine $M_N$ through a modal decomposition of the displacement and force fields. In the vicinity of the (un)jamming transition, $\varphi_{c}$, the vibrational density of states, $g(\omega)$, shows a plateau in the intermediate frequency regime above a characteristic frequency $\omega^\ast$. We illustrate that this unusual feature apparent in $g(\omega)$ is reflected in the behavior of $M_N$: As $\varphi \rightarrow \varphi_c$, where $\omega^\ast \rightarrow 0$, those modes for $\omega < \omega^\ast$ contribute less and less, while contributions from those for $\omega > \omega^\ast$ approach a constant value which results in $M_N$ to approach a critical value $M_{Nc}$, as $M_N-M_{Nc} \sim \omega^\ast$. At $\varphi_c$ itself, the bulk modulus attains a finite value $K_c=K_{Ac}-K_{Nc} > 0$, such that $K_{Nc}$ has a value that remains below $K_{Ac}$. In contrast, for the critical shear modulus $G_c$, $G_{Nc}$ and $G_{Ac}$ approach the same value so that the total value becomes exactly zero, $G_c = G_{Ac}-G_{Nc} =0$. We explore what features of the configurational and vibrational properties cause such the distinction between $K$ and $G$, allowing us to validate analytical expressions for their critical values.Comment: 23 pages, 13 figure

Dynamical heterogeneity in a highly supercooled liquid: Consistent calculations of correlation length, intensity, and lifetime

We have investigated dynamical heterogeneity in a highly supercooled liquid using molecular-dynamics simulations in three dimensions. Dynamical heterogeneity can be characterized by three quantities: correlation length $\xi_4$, intensity $\chi_4$, and lifetime $\tau_{\text{hetero}}$. We evaluated all three quantities consistently from a single order parameter. In a previous study (H. Mizuno and R. Yamamoto, Phys. Rev. E {\bf 82}, 030501(R) (2010)), we examined the lifetime $\tau_{\text{hetero}}(t)$ in two time intervals $t=\tau_\alpha$ and $\tau_{\text{ngp}}$, where $\tau_\alpha$ is the $\alpha$-relaxation time and $\tau_{\text{ngp}}$ is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. In the present study, in addition to the lifetime $\tau_{\text{hetero}}(t)$, we evaluated the correlation length $\xi_4(t)$ and the intensity $\chi_4(t)$ from the same order parameter used for the lifetime $\tau_{\text{hetero}}(t)$. We found that as the temperature decreases, the lifetime $\tau_{\text{hetero}}(t)$ grows dramatically, whereas the correlation length $\xi_4(t)$ and the intensity $\chi_4(t)$ increase slowly compared to $\tau_{\text{hetero}}(t)$ or plateaus. Furthermore, we investigated the lifetime $\tau_{\text{hetero}}(t)$ in more detail. We examined the time-interval dependence of the lifetime $\tau_{\text{hetero}}(t)$ and found that as the time interval $t$ increases, $\tau_{\text{hetero}}(t)$ monotonically becomes longer and plateaus at the relaxation time of the two-point density correlation function. At the large time intervals for which $\tau_{\text{hetero}}(t)$ plateaus, the heterogeneous dynamics migrate in space with a diffusion mechanism, such as the particle density.Comment: 12pages, 13figures, to appear in Physical Review

Elastic heterogeneity, vibrational states, and thermal conductivity across an amorphisation transition

Disordered solids exhibit unusual properties of their vibrational states and thermal conductivities. Recent progresses have well established the concept of "elastic heterogeneity", i.e., disordered materials show spatially inhomogeneous elastic moduli. In this study, by using molecular-dynamics simulations, we gradually introduce "disorder" into a numerical system to control its modulus heterogeneity. The system starts from a perfect crystalline state, progressively transforms into an increasingly disordered crystalline state, and finally undergoes structural amorphisation. We monitor independently the elastic heterogeneity, the vibrational states, and the thermal conductivity across this transition, and show that the heterogeneity in elastic moduli is well correlated to vibrational and thermal anomalies of the disordered system

Acoustic excitations and elastic heterogeneities in disordered solids

In the recent years, much attention has been devoted to the inhomogeneous nature of the mechanical response at the nano-scale in disordered solids. Clearly, the elastic heterogeneities that have been characterized in this context are expected to strongly impact the nature of the sound waves which, in contrast to the case of perfect crystals, cannot be completely rationalized in terms of phonons. Building on previous work on a toy model showing an amorphisation transition [Mizuno H, Mossa S, Barrat JL (2013) EPL {\bf 104}:56001], we investigate the relationship between sound waves and elastic heterogeneities in a unified framework, by continuously interpolating from the perfect crystal, through increasingly defective phases, to fully developed glasses. We provide strong evidence of a direct correlation between sound waves features and the extent of the heterogeneous mechanical response at the nano-scale