arXiv subjects

Hideyuki Mizuno

Publications and source records attributed to Hideyuki Mizuno.

At least 37 records · Page 2Linked to original sources

arXiv2023

Arrhenius temperature dependence of the crystallization time of deeply supercooled liquids

Usually, supercooled liquids and glasses are thermodynamically unstable against crystallization. Classical nucleation theory (CNT) has been used to describe the crystallization dynamics of supercooled liquids. However, recent studies on overcompressed hard spheres show that their crystallization dynamics are intermittent and mediated by avalanche-like rearrangements of particles, which largely differ from the CNT. These observations suggest that the crystallization times of deeply supercooled liquids or glasses cannot be described by the CNT, but this point has not yet been studied in detail. In this paper, we use molecular dynamics simulations to study the crystallization dynamics of soft spheres just after an instantaneous quench. We show that although the equilibrium relaxation time increases in a super-Arrhenius manner with decreasing temperature, the crystallization time shows an Arrhenius temperature dependence at very low temperatures. This is contrary to the conventional formula based on the CNT. Furthermore, the estimated energy barrier for the crystallization is surprisingly small compared to that for the equilibrium dynamics. By comparing the crystallization and aging dynamics quantitatively, we show that a coupling between aging and crystallization is the key for understanding the rapid crystallization of deeply supercooled liquids or glasses.

cond-mat.soft↗

arXiv2023

Non-phononic density of states of two-dimensional glasses revealed by random pinning

The vibrational density of states of glasses is considerably different from that of crystals. In particular, there exist spatially localized vibrational modes in glasses. The density of states of these non-phononic modes has been observed to follow $g(ω) \propto ω^4$, where $ω$ is the frequency. However, in two-dimensional systems, the abundance of phonons makes it difficult to accurately determine this non-phononic density of states because they are strongly coupled to non-phononic modes and yield strong system-size and preparation-protocol dependencies. In this article, we utilize the random pinning method to suppress phonons and disentangle their coupling with non-phononic modes and successfully calculate their density of states as $g(ω) \propto ω^4$. We also study their localization properties and confirm that low-frequency non-phononic modes in pinned systems are truly localized without far-field contributions. We finally discuss the excess density of states over the Debye value that results from the hybridization of phonons and non-phononic modes.

cond-mat.soft↗

arXiv2022

Johari-Goldstein $β$ relaxation in glassy dynamics originates from two-scale energy landscape

Supercooled liquids undergo complicated structural relaxation processes, which have been a long-standing problem in both experimental and theoretical aspects of condensed matter physics. In particular, past experiments universally observed for many types of molecular liquids that relaxation dynamics separated into two distinct processes at low temperatures. One of the possible interpretations is that this separation originates from the two-scale hierarchical topography of the potential energy landscape; however, it has never been verified. Molecular dynamics simulations are a promising approach to tackle this issue, but we must overcome laborious difficulties. First, we must handle a model of molecular liquids that is computationally demanding compared to simple spherical models, which have been intensively studied but show only a slower process: $α$ relaxation. Second, we must reach a sufficiently low-temperature regime where the two processes become well separated. Here, we handle an asymmetric dimer system that exhibits a faster process: Johari-Goldstein $β$ relaxation. Then, we employ the parallel tempering method to access the low-temperature regime. These laborious efforts enable us to investigate the potential energy landscape in detail and unveil the first direct evidence of the topographic hierarchy that induces the $β$ relaxation. We also successfully characterize the microscopic motions of particles during each relaxation process. Finally, we study the predictive power of low-frequency modes for two relaxation processes. Our results establish for the first time a fundamental and comprehensive understanding of experimentally observed relaxation dynamics in supercooled liquids.

cond-mat.soft↗

arXiv2022

Low-Frequency Vibrational States in Ideal Glasses with Random Pinning

Glasses exhibit spatially localized vibrations in the low-frequency regime. These localized modes emerge below the boson peak frequency $ω_\text{BP}$, and their vibrational densities of state follow $g(ω) \propto ω^4$ ($ω$ is frequency). Here, we attempt to address how the localized vibrations behave through the ideal glass transition. To do this, we employ a random pinning method, which enables us to study the thermodynamic glass transition. We find that the localized vibrations survive even in equilibrium glass states. Remarkably, the localized vibrations still maintain the properties of appearance below $ω_\text{BP}$ and $g(ω) \propto ω^4$. Our results provide important insight into the material properties of ideal glasses.

cond-mat.soft↗

arXiv2022

Phonon transport properties of particulate physical gels

Particulate physical gels are sparse, low-density amorphous materials in which clusters of glasses are connected to form a heterogeneous network structure. This structure is characterized by two length scales, $ξ_s$ and $ξ_G$: $ξ_s$ measures the length of heterogeneities in the network structure, and $ξ_G$ is the size of glassy clusters. Accordingly, the vibrational states of such a material also exhibit a multiscale nature with two characteristic frequencies, $ω_\ast$ and $ω_G$, which are associated with $ξ_s$ and $ξ_G$, respectively: (i) phonon-like vibrations in the homogeneous medium at $ω< ω_\ast$, (ii) phonon-like vibrations in the heterogeneous medium at $ω_\ast < ω< ω_G$, and (iii) disordered vibrations in the glassy clusters at $ω> ω_G$. Here, we demonstrate that the multiscale characteristics seen in the static structures and vibrational states also extend to the phonon transport properties. Phonon transport exhibits two distinct crossovers at the frequencies $ω_\ast$ and $ω_G$~(or at wavenumbers of $\sim ξ_s^{-1}$ and $\sim ξ_G^{-1}$). In particular, both transverse and longitudinal phonons cross over between Rayleigh scattering at $ω< ω_\ast$ and diffusive damping at $ω>ω_\ast$. Remarkably, the Ioffe--Regel limit is located at the very low frequency of $ω_\ast$. Thus, phonon transport is localized above $ω_\ast$, even where phonon-like vibrational states persist. This markedly strong scattering behavior is caused by the sparse, porous structure of the gel.

cond-mat.soft↗

arXiv2021

Structural, mechanical, and vibrational properties of particulate physical gels

Our lives are surrounded by a rich assortment of disordered materials. In particular, glasses are well known as dense, amorphous materials, whereas gels exist in low-density, disordered states. Recent progress has provided a significant step forward in understanding the material properties of glasses, such as mechanical, vibrational, and transport properties. In contrast, our understanding of particulate physical gels is still highly limited. Here, using molecular dynamics simulations, we study a simple model of particulate physical gels, the Lennard-Jones (LJ) gels, and provide a comprehensive understanding of their structural, mechanical, and vibrational properties, all of which are markedly different from those of glasses. First, the LJ gels show sparse, heterogeneous structures, and the length scale $ξ_s$ of the structures grows as the density is lowered. Second, the gels are extremely soft, with both shear $G$ and bulk $K$ moduli being orders of magnitude smaller than those of glasses. Third, many low-frequency vibrational modes are excited, which form a characteristic plateau with the onset frequency $ω_\ast$ in the vibrational density of states. Structural, mechanical, and vibrational properties, characterized by $ξ_s$, $G$, $K$, and $ω_\ast$, respectively, show power-law scaling behaviors with the density, which establishes a close relationship between them. Throughout the present work, we reveal that gels are multiscale, solid-state materials: (i) homogeneous elastic bodies at long lengths, (ii) heterogeneous elastic bodies with fractal structures at intermediate lengths, and (iii) amorphous structural bodies at short lengths.

cond-mat.soft↗

arXiv2021

Shear-induced Criticality in Glasses Shares Qualitative Similarities with the Gardner Phase

Although glass phases are found in various soft matter systems ubiquitously, we are still far from a complete understanding of them. The concept of marginal stability predicted by infinite-dimensional mean-field theories is drawing attention as a candidate for universal and distinguishing unique features of glasses. While among theoretical predictions, the non-Debye scaling has indeed been observed universally over various classes of glasses, and the Gardner phase is found only in hard sphere systems if we restrict ourselves to the physical dimensions. In this work, we numerically demonstrate that plastic events observed in two-dimensional Lennard-Jones glasses under quasistatic shear exhibit statistical properties that are qualitatively very similar to the Gardner phase.

cond-mat.dis-nn↗

arXiv2021

Understanding the scaling of boson peak through insensitivity of elastic heterogeneity to bending rigidity in polymer glasses

Amorphous materials exhibit peculiar mechanical and vibrational properties, including non-affine elastic responses and excess vibrational states, i.e., the so-called boson peak. For polymer glasses, these properties are considered to be affected by the bending rigidity of the constituent polymer chains. In our recent work [Tomoshige, et al., Sci. Rep. 9 19514 (2019)], we have revealed simple relationships between the variations of vibrational properties and the global elastic properties: the response of the boson peak scales only with that of the global shear modulus. This observation suggests that the spatial heterogeneity of the local shear modulus distribution is insensitive to changes in the bending rigidity. Here, we demonstrate the insensitivity of elastic heterogeneity by directly measuring the local shear modulus distribution. We also study transverse sound wave propagation, which is also shown to scale only with the global shear modulus. Through these analyses, we conclude that the bending rigidity does not alter the spatial heterogeneity of the local shear modulus distribution, which yields vibrational and acoustic properties that are controlled solely by the global shear modulus of a polymer glass.

cond-mat.soft↗

arXiv2021

Computational simulations of the vibrational properties of glasses

Glasses show vibrational properties that are markedly different to those of crystals which are known as phonons. For example, excess low-frequency modes (the so-called boson peak), vibrational localization, and strong scattering of phonons have been the most discussed topics, and a theoretical understanding of these phenomena is challenging. To address this problem, computational simulations are a powerful tool, which have been employed by many previous works. In this chapter, we describe simulation methods for studying the vibrational properties of glasses (and any solid-state materials). We first present a method for studying vibrational eigenmodes. Since vibrational motions of particles are excited along eigenmodes, the eigenmodes are fundamental to descriptions of vibrational properties. The eigenmodes in glasses are non-phonon modes in general, and some of them are even localized in space. We next present a method of analysing phonon transport, which is also crucial for understanding vibrational properties. Since phonons are not eigenmodes in glasses, they are decomposed into several different, non-phonon eigenmodes. As a result, phonons in glasses are strongly scattered. In addition, we describe how to analyse the elastic response. The elastic response of glasses is also anomalous with respect to that of crystals. Finally, we briefly introduce recent advances that have been achieved by means of large-scale computational simulations.

cond-mat.soft↗

arXiv2020

Instantaneous Normal Modes Reveal Structural Signatures for the Herschel-Bulkley Rheology in Sheared Glasses

The Herschel-Bulkley law, a universal constitutive relation, has been empirically known to be applicable to a vast range of soft materials, including sheared glasses. Although the Herschel- Bulkley law has attracted public attention, its structural origin has remained an open question. In this letter, by means of atomistic simulation of binary Lennard-Jones glasses, we report that the instantaneous normal modes with negative eigenvalues, or so-called imaginary modes, serve as the structural signatures for the Herschel-Bulkley rheology in sheared glasses.

cond-mat.soft↗

arXiv2020

Spatial structure of unstable normal modes in a glass-forming liquid

The phenomenology of glass-forming liquids is often described in terms of their underlying, high-dimensional potential energy surface. In particular, the statistics of stationary points sampled as a function of temperature provides useful insight into the thermodynamics and dynamics of the system. To make contact with the real space physics, however, analysis of the spatial structure of the normal modes is required. In this work, we numerically study the potential energy surface of a glass-forming ternary mixture. Starting from liquid configurations equilibrated over a broad range of temperatures using a swap Monte Carlo method, we locate the nearby stationary points and investigate the spatial architecture and the energetics of the associated unstable modes. Through this spatially-resolved analysis, originally developed to study local minima, we corroborate recent evidence that the nature of the unstable modes changes from delocalized to localized around the mode-coupling temperature. We find that the displacement amplitudes of the delocalized modes have a slowly decaying far field, whereas the localized modes consist of a core with large displacements and a rapidly decaying far field. The fractal dimension of unstable modes around the mobility edge is equal to 1, consistent with the scaling of the participation ratio. Finally, we find that around and below the mode-coupling temperature the unstable modes are localized around structural defects, characterized by a disordered local structure markedly different from the liquid's locally favored structure. These defects are similar to those associated to quasi-localized vibrations in local minima and are good candidates to predict the emergence of localized excitations at low temperature.

cond-mat.stat-mech↗

arXiv2020

Novel elastic instability of amorphous solids in finite spatial dimensions

Recently, progress has been made in the understanding of anomalous vibrational excitations in amorphous solids. In the lowest-frequency region, the vibrational spectrum follows a non-Debye quartic law, which persists up to zero frequency without any frequency gap. This gapless vibrational density of states (vDOS) suggests that glasses are on the verge of instability. This feature of marginal stability is now highlighted as a key concept in the theories of glasses. In particular, the elasticity theory based on marginal stability predicts the gapless vDOS. However, this theory yields a quadratic law and \textit{not} the quartic law. To address this inconsistency, we presented a new type of instability, which is different from the conventional one, and proposed that amorphous solids are marginally stable considering the new instability in the preceding study~[M. Shimada, H. Mizuno, and A. Ikeda, Soft Matter, {\bf 16}, 7279, 2020]. In this study, we further extend and detail the results for these instabilities. By analyzing various examples of disorder, we demonstrate that real glasses in finite spatial dimensions can be marginally stable by the proposed novel instability.

cond-mat.dis-nn↗

arXiv2020

Phase transition in the binary mixture of jammed particles with large size dispersity

It has been well established that particulate systems show the jamming transition and critical scaling behaviors associated with it. However, our knowledge is limited to (nearly) monodisperse systems. Recently, a binary mixture of jammed particles with large size dispersity was studied, and it was suggested that two distinct jammed phases appeared. Here, we conduct a thorough numerical study on this system with a special focus on the statistics of and finite-size effects on the fraction of small particles that participate in the rigid network. We present strong evidence that two distinct jammed phases appear depending on the pressure and composition of two species, which are separated by the first-order phase transition. In one of two phases, only large particles are jammed, whereas both small and large particles are jammed in the other phase. We also describe the phase diagram in the pressure-composition plane, where the first-order phase transition line terminates at a critical point. In addition, we investigate the mechanical properties in terms of the elastic moduli over the phase diagram and find that discontinuous changes in elastic moduli emerge across the phase transition. Remarkably, despite the discontinuities, the elastic moduli in each jammed phase exhibit identical scaling laws to those in the monodisperse systems.

cond-mat.soft↗

arXiv2020

Unified View of Avalanche Criticality in Sheared Glasses

Plastic events in sheared glasses are considered an example of so-called avalanches, whose sizes obey a power-law probability distribution with the avalanche critical exponent $τ$. Although mean-field theory predicts a universal value of this exponent, $τ_{\rm MF}=1.5$, numerical simulations have reported different values depending on the literature. Moreover, in the elastic regime, it has been noted that the critical exponent can be different from that in the steady state, and even criticality itself is a matter of debate. Because these confusingly varying results were reported under different setups, our knowledge of avalanche criticality in sheared glasses is greatly limited. To gain a unified understanding, in this work, we conduct a comprehensive numerical investigation of avalanches in Lennard-Jones glasses under athermal quasistatic shear. In particular, by excluding the ambiguity and arbitrariness that has crept into the conventional measurement schemes, we achieve high-precision measurement and demonstrate that the exponent $τ$ in the steady state follows the mean-field prediction of $τ_{\rm MF}=1.5$. Our results also suggest that there are two qualitatively different avalanche events. This binariness leads to the non-universal behavior of the avalanche size distribution and is likely to be the cause of the varying values of $τ$ reported thus far. To investigate the dependence of criticality and universality on applied shear, we further study the statistics of avalanches in the elastic regime and the ensemble of the first avalanche event in different samples, which provide information about the unperturbed system. We show that while the unperturbed system is indeed off-critical, criticality gradually develops as shear is applied. Moreover, the critical exponent obeys the mean-field prediction $τ_{\rm MF}$ universally, once the system becomes critical.

cond-mat.soft↗

arXiv2020

Sound damping in frictionless granular materials: The interplay between configurational disorder and inelasticity

We numerically investigate sound damping in a model of granular materials in two dimensions. We simulate evolution of standing waves in disordered frictionless disks and analyze their damped oscillations by velocity autocorrelation functions and power spectra. We control the strength of inelastic interactions between the disks in contact to examine the effect of energy dissipation on sound characteristics of disordered systems. Increasing the strength of inelastic interactions, we find that (i) sound softening vanishes and (ii) sound attenuation due to configurational disorder, i.e. the Rayleigh scattering at low frequencies and disorder-induced broadening at high frequencies, is completely dominated by the energy dissipation. Our findings suggest that sound damping in granular media is determined by the interplay between elastic heterogeneities and inelastic interactions.

cond-mat.soft↗

arXiv2020

Structural and mechanical characteristics of sphere packings near the jamming transition: From fully amorphous to quasi-ordered structures

Mechanically stable sphere packings are generated in three-dimensional space using the discrete element method, which span a wide range in structural order, ranging from fully amorphous to quasi-ordered structures, as characterized by the bond orientational order parameter. As the packing pressure, $p$, varies from the marginally rigid limit at the jamming transition ($p \approx 0$) to that of more robust systems ($p \gg 0$), the coordination number, $z$, follows a familiar scaling relation with pressure, namely, $Δz = z - z_c \sim p^{1/2}$, where $z_c = 2d = 6$ ($d=3$ is the spatial dimension). While it has previously been noted that $Δz$ does indeed remain the control parameter for determining the packing properties, here we show how the packing structure plays an influential role on the mechanical properties of the packings. Specifically, we find that the elastic (bulk $K$ and shear $G$) moduli, generically referred to as $M$, become functions of both $Δz$ and the structure, to the extent that $M-M_c \sim Δz$. Here, $M_c$ are values of the elastic moduli at the jamming transition, which depend on the structure of the packings. In particular, the zero shear modulus, $G_c=0$, is a special feature of fully amorphous packings, whereas more ordered packings take larger, positive values, $G_c > 0$.

cond-mat.soft↗

arXiv2020

Intermittent rearrangements accompanying thermal fluctuations distinguish glasses from crystals

It is a persistent problem in condensed matter physics that glasses exhibit vibrational and thermal properties that are markedly different from those of crystals. While recent works have advanced our understanding of vibrational excitations in glasses at the harmonic approximation limit, efforts in understanding finite-temperature anharmonic processes have been limited. It is well known that phonons in crystals couple through phonon-phonon interactions, an extremely efficient mechanism for anharmonic decay that is also important in glasses. Here, however, we show that an additional anharmonic channel of different origin emerges in the case of glasses, which induces intermittent rearrangements of particles. We have found that thermal vibrations in glasses trigger transitions among numerous different local minima of the energy landscape, which, however, are located within the same wide (meta)basin. These processes generate motions that are different from both diffusive and out-of-equilibrium aging dynamics. We suggest that the intermittent rearrangements accompanying thermal fluctuations are crucial features distinguishing glasses from crystals.

cond-mat.soft↗

arXiv2020

Sound damping in glasses: interplay between anharmonicities and elastic heterogeneities

Some facets of the way sound waves travel through glasses are still unclear. Recent works have shown that in the low-temperature harmonic limit a crucial role in controlling sound damping is played by local elastic heterogeneity. Sound waves propagation has been demonstrated to be strongly affected by inhomogeneous mechanical features of the materials, which add to the anharmonic couplings at finite temperatures. We describe the interplay between these two effects by molecular dynamics simulation of a model glass. In particular, we focus on the transverse components of the vibrational excitations in terms of dynamic structure factors, and characterize the temperature dependence of sound attenuation rates in an extended frequency range. We provide a complete picture of all phenomena, in terms encompassing both theory and experiments.

cond-mat.mtrl-sci↗