Extremely persistent dense active fluids.

We study the dynamics of dense three-dimensional systems of active particles for large persistence times τp at constant average self-propulsion force f. These systems are fluid counterparts of previously investigated extremely persistent systems, which in the large persistence time limit relax only on the time scale of τp. We find that many dynamic properties of the systems we study, such as the mean-squared velocity, the self-intermediate scattering function, and the shear-stress correlation function, become τp-independent in the large persistence time limit. In addition, the large τp limits of many dynamic properties, such as the mean-square velocity and the relaxation times of the scattering function, and the shear-stress correlation function, depend on f as power laws with non-trivial exponents. We conjecture that these systems constitute a new class of extremely persistent active systems.

Scaling of the non-phononic spectrum of two-dimensional glasses.

Low-frequency vibrational harmonic modes of glasses are frequently used to rationalize their universal low-temperature properties. One well studied feature is the excess low-frequency density of states over the Debye model prediction. Here, we examine the system size dependence of the density of states for two-dimensional glasses. For systems of fewer than 100 particles, the density of states scales with the system size as if all the modes were plane-wave-like. However, for systems greater than 100 particles, we find a different system-size scaling of the cumulative density of states below the first transverse sound mode frequency, which can be derived from the assumption that these modes are quasi-localized. Moreover, for systems greater than 100 particles, we find that the cumulative density of states scales with the frequency as a power law with the exponent that leads to the exponent ß = 3.5 for the density of states. For systems whose sizes were investigated, we do not see a size-dependence of exponent ß.

Erratum: Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses [Phys. Rev. Lett. 127, 248001 (2021)].

This corrects the article DOI: 10.1103/PhysRevLett.127.248001.

Microscopic analysis of sound attenuation in low-temperature amorphous solids reveals quantitative importance of non-affine effects.

Sound attenuation in low-temperature amorphous solids originates from their disordered structure. However, its detailed mechanism is still being debated. Here, we analyze sound attenuation starting directly from the microscopic equations of motion. We derive an exact expression for the zero-temperature sound damping coefficient. We verify that the sound damping coefficients calculated from our expression agree very well with results from independent simulations of sound attenuation. Small wavevector analysis of our expression shows that sound attenuation is primarily determined by the non-affine displacements' contribution to the sound wave propagation coefficient coming from the frequency shell of the sound wave. Our expression involves only quantities that pertain to solids' static configurations. It can be used to evaluate the low-temperature sound damping coefficients without directly simulating sound attenuation.

Single-particle fluctuations dominate the long-time dynamic susceptibility in glass-forming liquids.

Liquids near the glass transition exhibit dynamical heterogeneity, i.e., correlated regions in the liquid relax at either a much faster rate or a much slower rate than the average. This collective phenomenon has been characterized by measurements of a dynamic susceptibility χ_{4}(t), which is sometimes interpreted in terms of the size of those relaxing regions and the intensity of the fluctuations. We show that the results of those measurements can be affected not only by the collective fluctuations in the relaxation rate, but also by density fluctuations in the initial state and by single-particle fluctuations. We also show that at very long times the average overlap C(t) probing the similarity between an initial and a final state separated by a time interval t decays as a power law C(t)∼t^{-d/2}. This is much slower than the stretched exponential behavior C(t)∼e^{-(t/τ)^{ß}} previously observed at times within one or two orders of magnitude of the α-relaxation time τ_{α}. We find that for times longer than 10-100τ_{α}, the dynamic susceptibility χ_{4}(t) is dominated by single-particle fluctuations, and that χ_{4}(t)≈C(t)∼t^{-d/2}. Finally, we introduce a method to extract the collective relaxation contribution to the dynamic susceptibility χ_{4}(t) by subtracting the effects of single-particle fluctuations and initial state density fluctuations. We apply this method to numerical simulations of two glass-forming models: a binary hard sphere system and a Kob-Andersen Lennard-Jones system. This allows us to extend the analysis of numerical data to timescales much longer than previously possible, and opens the door for further future progress in the study of dynamic heterogeneities, including the determination of the exchange time.

Low-Frequency Excess Vibrational Modes in Two-Dimensional Glasses.

Glasses possess more low-frequency vibrational modes than predicted by Debye theory. These excess modes are crucial for the understanding of the low temperature thermal and mechanical properties of glasses, which differ from those of crystalline solids. Recent simulational studies suggest that the density of the excess modes scales with their frequency ω as ω^{4} in two and higher dimensions. Here, we present extensive numerical studies of two-dimensional model glass formers over a large range of glass stabilities. We find that the density of the excess modes follows D_{exc}(ω)∼ω^{2} up to around the boson peak, regardless of the glass stability. The stability dependence of the overall scale of D_{exc}(ω) correlates with the stability dependence of low-frequency sound attenuation. However, we also find that, in small systems, where the first sound mode is pushed to higher frequencies, at frequencies below the first sound mode, there are excess modes with a system size independent density of states that scales as ω^{3}.

The Einstein effective temperature can predict the tagged active particle density.

We derive a distribution function for the position of a tagged active particle in a slowly varying in space external potential, in a system of interacting active particles. The tagged particle distribution has the form of the Boltzmann distribution but with an effective temperature that replaces the temperature of the heat bath. We show that the effective temperature that enters the tagged particle distribution is the same as the effective temperature defined through the Einstein relation, i.e., it is equal to the ratio of the self-diffusion and tagged particle mobility coefficients. This result shows that this effective temperature, which is defined through a fluctuation-dissipation ratio, is relevant beyond the linear response regime. We verify our theoretical findings through computer simulations. Our theory fails when an additional large length scale appears in our active system. In the system we simulated, this length scale is associated with long-wavelength density fluctuations that emerge upon approaching motility-induced phase separation.

Active matter: Quantifying the departure from equilibrium.

Active matter systems are driven out of equilibrium at the level of individual constituents. One widely studied class are systems of athermal particles that move under the combined influence of interparticle interactions and self-propulsions, with the latter evolving according to the Ornstein-Uhlenbeck stochastic process. Intuitively, these so-called active Ornstein-Uhlenbeck particle (AOUP) systems are farther from equilibrium for longer self-propulsion persistence times. Quantitatively, this is confirmed by the increasing equal-time velocity correlations (which are trivial in equilibrium) and by the increasing violation of the Einstein relation between the self-diffusion and mobility coefficients. In contrast, the entropy production rate, calculated from the ratio of the probabilities of the position space trajectory and its time-reversed counterpart, has a nonmonotonic dependence on the persistence time. Thus, it does not properly quantify the departure of AOUP systems from equilibrium.

Sound attenuation in finite-temperature stable glasses.

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 Γ 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 wavevectors Γ∼k1.5 for an aging glass, but Γ∼k2 when the glass does not age on the timescale of the calculation. For our most stable glass, we find that Γ∼k2 at small wavevectors, then a crossover to Rayleigh scattering scaling Γ∼k4, 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.

Energy transport in glasses.

The temperature dependence of the thermal conductivity is linked to the nature of the energy transport at a frequency ω, which is quantified by thermal diffusivity d(ω). Here we study d(ω) for a poorly annealed glass and a highly stable glass prepared using the swap Monte Carlo algorithm. To calculate d(ω), 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(ω), 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(ω) ∼ ω-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.

Stability dependence of local structural heterogeneities of stable amorphous solids.

The universal anomalous vibrational and thermal properties of amorphous solids are believed to be related to the local variations of the elasticity. Recently it has been shown that the vibrational properties are sensitive to the glass's stability. Here we study the stability dependence of the local elastic constants of a simulated glass former over a broad range of stabilities, from a poorly annealed glass to a glass whose stability is comparable to laboratory exceptionally stable vapor deposited glasses. We show that with increasing stability the glass becomes more uniform as evidenced by a smaller variance of local elastic constants. We find that, according to the definition of local elastic moduli used in this work, the local elastic moduli are not spatially correlated.

Front-Mediated Melting of Isotropic Ultrastable Glasses.

Ultrastable vapor-deposited glasses display uncommon material properties. Most remarkably, upon heating they are believed to melt via a liquid front that originates at the free surface and propagates over a mesoscopic crossover length, before crossing over to bulk melting. We combine swap Monte Carlo with molecular dynamics simulations to prepare and melt isotropic amorphous films of unprecedendtly high kinetic stability. We are able to directly observe both bulk and front melting, and the crossover between them. We measure the front velocity over a broad range of conditions, and a crossover length scale that grows to nearly 400 particle diameters in the regime accessible to simulations. Our results disentangle the relative roles of kinetic stability and vapor deposition in the physical properties of stable glasses.

Sound attenuation in stable glasses.

Understanding the difference between the universal low-temperature properties of amorphous and crystalline solids requires an explanation for the stronger damping of long-wavelength phonons in amorphous solids. A longstanding sound attenuation scenario, resulting from a combination of experiments, theories, and simulations, leads to a quartic scaling of sound attenuation with the wavevector, which is commonly attributed to the Rayleigh scattering of sound. Modern computer simulations offer conflicting conclusions regarding the validity of this picture. We simulate glasses with an unprecedentedly broad range of stabilities to perform the first microscopic analysis of sound damping in model glass formers across a range of experimentally relevant preparation protocols. We present convincing evidence that quartic scaling is recovered for small wavevectors irrespective of the glass's stability. With increasing stability, the wavevector where the quartic scaling begins increases by approximately a factor of three and the sound attenuation decreases by over an order of magnitude. Our results uncover an intimate connection between glass stability and sound damping.

Glassy dynamics in dense systems of active particles.

Despite the diversity of materials designated as active matter, virtually all active systems undergo a form of dynamic arrest when crowding and activity compete, reminiscent of the dynamic arrest observed in colloidal and molecular fluids undergoing a glass transition. We present a short perspective on recent and ongoing efforts to understand how activity competes with other physical interactions in dense systems. We review recent experimental work on active materials that uncovered both classic signatures of glassy dynamics and intriguing novel phenomena at large density. We discuss a minimal model of self-propelled particles where the competition between interparticle interactions, crowding, and self-propulsion can be studied in great detail. We present more complex models that include some additional, material-specific ingredients. We provide some general perspectives on dense active materials, suggesting directions for future research, in particular, for theoretical work.

Viscoelastic shear stress relaxation in two-dimensional glass-forming liquids.

Translational dynamics of 2D glass-forming fluids is strongly influenced by soft, long-wavelength fluctuations first recognized by D. Mermin and H. Wagner. As a result of these fluctuations, characteristic features of glassy dynamics, such as plateaus in the mean-squared displacement and the self-intermediate scattering function, are absent in two dimensions. In contrast, Mermin-Wagner fluctuations do not influence orientational relaxation, and well-developed plateaus are observed in orientational correlation functions. It has been suggested that, by monitoring translational motion of particles relative to that of their neighbors, one can recover characteristic features of glassy dynamics and thus disentangle the Mermin-Wagner fluctuations from the 2D glass transition. Here we use molecular dynamics simulations to study viscoelastic relaxation in two and three dimensions. We find different behavior of the dynamic modulus below the onset of slow dynamics (determined by the orientational or cage-relative correlation functions) in two and three dimensions. The dynamic modulus for 2D supercooled fluids is more stretched than for 3D supercooled fluids and does not exhibit a plateau, which implies the absence of glassy viscoelastic relaxation. At lower temperatures, the 2D dynamic modulus starts exhibiting an intermediate time plateau and decays similarly to the 2D dynamic modulus. The differences in the glassy behavior of 2D and 3D glass-forming fluids parallel differences in the ordering scenarios in two and three dimensions.

Low-frequency vibrational modes of stable glasses.

Unusual features of the vibrational density of states D(ω) of glasses allow one to rationalize their peculiar low-temperature properties. Simulational studies of D(ω) have been restricted to studying poorly annealed glasses that may not be relevant to experiments. Here we report on D(ω) of zero-temperature glasses with kinetic stabilities ranging from poorly annealed to ultrastable glasses. For all preparations, the low-frequency part of D(ω) splits between extended and quasi-localized modes. Extended modes exhibit a boson peak crossing over to Debye behavior (Dex(ω) ~ ω2) at low-frequency, with a strong correlation between the two regimes. Quasi-localized modes obey Dloc(ω) ~ ω4, irrespective of the stability. The prefactor of this quartic law decreases with increasing stability, and the corresponding modes become more localized and sparser. Our work is the first numerical observation of quasi-localized modes in a regime relevant to experiments, and it establishes a direct connection between glasses' stability and their soft vibrational modes.

Comparison of single particle dynamics at the center and on the surface of equilibrium glassy films.

Glasses prepared by vapor depositing molecules onto a properly prepared substrate can have enhanced kinetic stability when compared with glasses prepared by cooling from the liquid state. The enhanced stability is due to the high mobility of particles at the surface, which allows them to find lower energy configurations than for liquid cooled glasses. Here we use molecular dynamics simulations to examine the temperature dependence of the single particle dynamics in the bulk of the film and at the surface of the film. First, we examine the temperature dependence of the self-intermediate scattering functions for particles in the bulk and at the surface. We then examine the temperature dependence of the probability of the logarithm of single particle displacements for bulk and surface particles. Both bulk and surface particle displacements indicate populations of slow and fast particles, i.e., heterogeneous dynamics. We find that the temperature dependence of the surface dynamics mirrors the bulk despite being several orders of magnitude faster.

Origin of Ultrastability in Vapor-Deposited Glasses.

Glass films created by vapor-depositing molecules onto a substrate can exhibit properties similar to those of ordinary glasses aged for thousands of years. It is believed that enhanced surface mobility is the mechanism that allows vapor deposition to create such exceptional glasses, but it is unclear how this effect is related to the final state of the film. Here we use molecular dynamics simulations to model vapor deposition and an efficient Monte Carlo algorithm to determine the deposition rate needed to create ultrastable glassy films. We obtain a scaling relation that quantitatively captures the efficiency gain of vapor deposition over bulk annealing, and demonstrates that surface relaxation plays the same role in the formation of vapor-deposited glasses as bulk relaxation does in ordinary glass formation.

Self-intermediate scattering function analysis of supercooled water confined in hydrophilic silica nanopores.

We study the temperature dependence of the self-intermediate scattering function for supercooled water confined in hydrophilic silica nanopores. We simulate the simple point charge/extended model of water confined to pores of radii 20 Å, 30 Å, and 40 Å over a temperature range of 210 K to 250 K. First, we examine the temperature dependence of the structure of the water and find that there is layering next to the pore surface for all temperatures and diameters. However, there exists a region in the center of the pore where the density is nearly constant. Using the density profile, we divide confined water into different regions and compare the dynamics of the water molecules that start in these regions. To this end, we examine the mean-squared displacement and the self-intermediate scattering functions for the water hydrogens, which would allow one to connect our results with quasi-elastic neutron scattering experiments. We examine the dependence of the self-intermediate scattering function on the magnitude and direction of the wavevector, as well as the proximity to the silica surface. We also examine the rotational-translational decoupling. We find that the anisotropy of the dynamics and the rotational-translational decoupling is weakly temperature dependent.

Kinetic stability and energetics of simulated glasses createdby constant pressure cooling.

We use computer simulations to study the cooling rate dependence of the stability and energetics of model glasses created at constant pressure conditions and compare the results with glasses formed at constant volume conditions. To examine the stability, we determine the time it takes for a glass cooled and reheated at constant pressure to transform back into a liquid, ttrans, and calculate the stability ratio S=ttrans/τα, where τα is the equilibrium relaxation time of the liquid. We find that, for slow enough cooling rates, cooling and reheating at constant pressure results in a larger stability ratio S than for cooling and reheating at constant volume. We also compare the energetics of glasses obtained by cooling while maintaining constant pressure with those of glasses created by cooling from the same state point while maintaining constant volume. We find that cooling at constant pressure results in glasses with lower average potential energy and average inherent structure energy. We note that in model simulations of the vapor deposition process, glasses are created under constant pressure conditions, and thus they should be compared to glasses obtained by constant pressure cooling.