Aging effects manifested in the potential-energy landscape of a model glass former

Nonlinear susceptibilities and higher-order responses related to physical aging: Wiener-Volterra approach and extended Tool-Narayanaswamy-Moynihan models

Large-amplitude thermal excursions imposed on deeply supercooled liquids modulate the nonlinear time evolution of their structural rearrangements. The consequent aftereffects are treated within a Wiener-Volterra expansion in laboratory time that allows one to calculate the associated physical-aging and thermal response functions. These responses and the corresponding higher-harmonic susceptibilities are illustrated using calculations based on the Tool-Narayanaswamy-Moynihan (TNM) model. The conversion from laboratory to material time is thoroughly discussed. Similarities and differences to field-induced higher-harmonic susceptibilities are illustrated using Lissajous and Cole-Cole plots and discussed in terms of aging nonlinearity parameters. For the Lissajous plots, banana-type shapes emerge, while the Cole-Cole plots display cardioidic and other visually appealing patterns. For application beyond the regime in which conventional single-parameter aging concepts work, the Wiener-Volterra material-time-series is introduced as the central tool. Calculations and analyses within this general framework in conjunction with suitable choices of higher-order memory kernels and employing correspondingly extended TNM models yield at least qualitative agreement with recent large-perturbation physical aging experiments. Implications for differential scanning calorimetry and related methods are discussed. The introduced concepts and analyses provide a solid foundation for a generalized description of nonlinear thermal out-of-equilibrium dynamics of glass forming materials, differing from the nonlinear responses known from rheology and dielectric spectroscopy.

Rejuvenation in Deep Thermal Cycling of a Generic Model Glass: A Study of Per-Particle Energy Distribution

We investigate the effect of low temperature (cryogenic) thermal cycling on a generic model glass and observe signature of rejuvenation in terms of per-particle potential energy distributions. Most importantly, these distributions become broader and its average values successively increase when applying consecutive thermal cycles. We show that linear dimension plays a key role for these effects to become visible, since we do only observe a weak effect for a cubic system of roughly one hundred particle diameter but observe strong changes for a rule-type geometry with the longest length being two thousand particle diameters. A consistent interpretation of this new finding is provided in terms of a competition between relaxation processes, which are inherent to glassy systems, and excitation due to thermal treatment. In line with our previous report (Bruns et al., PRR 3, 013234 (2021)), it is shown that, depending on the parameters of thermal cycling, rejuvenation can be either too weak to be detected or strong enough for a clear observation.

Emergent Fractal Energy Landscape as the Origin of Stress-Accelerated Dynamics in Amorphous Solids

The ageing dynamics in a multiplicity of metastable glasses are investigated at various thermomechanical conditions. By using data analytics to deconvolute the integral effects of environmental factors (e.g., energy level, temperature, stress), and by directly scrutinizing the minimum energy pathways for local excitations, we demonstrate external shear would make the system's energy landscape surprisingly fractal and create an emergent low-barrier mode with highly tortuous pathways, leading to an accelerated relaxation. This finding marks a departure from the classic picture of shear-induced simple bias of energy landscape. The insights and implications of this study are also discussed.

Structural relaxation and crystallization in supercooled water from 170 to 260 K

The origin of water's anomalous properties has been debated for decades. Resolution of the problem is hindered by a lack of experimental data in a crucial region of temperatures, T, and pressures where supercooled water rapidly crystallizes-a region often referred to as "no man's land." A recently developed technique where water is heated and cooled at rates greater than 10⁹ K/s now enables experiments in this region. Here, it is used to investigate the structural relaxation and crystallization of deeply supercooled water for 170 K < T < 260 K. Water's relaxation toward a new equilibrium structure depends on its initial structure with hyperquenched glassy water (HQW) typically relaxing more quickly than low-density amorphous solid water (LDA). For HQW and T > 230 K, simple exponential relaxation kinetics is observed. For HQW at lower temperatures, increasingly nonexponential relaxation is observed, which is consistent with the dynamics expected on a rough potential energy landscape. For LDA, approximately exponential relaxation is observed for T > 230 K and T < 200 K, with nonexponential relaxation only at intermediate temperatures. At all temperatures, water's structure can be reproduced by a linear combination of two, local structural motifs, and we show that a simple model accounts for the complex kinetics within this context. The relaxation time, τ _rel , is always shorter than the crystallization time, τ _xtal For HQW, the ratio, τ _xtal /τ _rel , goes through a minimum at ∼198 K where the ratio is about 60.

Single-parameter aging in a binary Lennard-Jones system

This paper studies physical aging by computer simulations of a 2:1 Kob-Andersen binary Lennard-Jones mixture, a system that is less prone to crystallization than the standard 4:1 composition. Starting from thermal-equilibrium states, the time evolution of the following four quantities is monitored by following up and down jumps in temperature: potential energy, virial, average squared force, and the Laplacian of the potential energy. Despite the fact that significantly larger temperature jumps are studied here than in typical similar experiments, to a good approximation, all four quantities conform to the single-parameter-aging scenario derived and validated for small jumps in experiments [T. Hecksher, N. B. Olsen, and J. C. Dyre, J. Chem. Phys. 142, 241103 (2015)]. As a further confirmation of single-parameter aging with a common material time for the four different quantities monitored, their relaxing parts are found to be almost identical for all temperature jumps.

Active glasses

Active glassy matter has recently emerged as a novel class of non-equilibrium soft matter, combining energy-driven, active particle movement with dense and disordered glass-like behavior. Here we review the state-of-the-art in this field from an experimental, numerical, and theoretical perspective. We consider both non-living and living active glassy systems, and discuss how several hallmarks of glassy dynamics (dynamical slowdown, fragility, dynamical heterogeneity, violation of the Stokes-Einstein relation, and aging) are manifested in such materials. We start by reviewing the recent experimental evidence in this area of research, followed by an overview of the main numerical simulation studies and physical theories of active glassy matter. We conclude by outlining several open questions and possible directions for future work.

Nonlinear response theory for Markov processes. II. Fifth-order response functions

The nonlinear response of stochastic models obeying a master equation is calculated up to fifth order in the external field, thus extending the third-order results obtained earlier [G. Diezemann, Phys. Rev. E 85, 051502 (2012)PLEEE81539-375510.1103/PhysRevE.85.051502]. For sinusoidal fields the 5ω component of the susceptibility is computed for the model of dipole reorientations in an asymmetric double well potential and for a trap model with a Gaussian density of states. For most realizations of the models a hump is found in the higher-order susceptibilities. In particular, for the asymmetric double well potential model there are two characteristic temperature regimes showing the occurrence of such a hump as compared to a single characteristic regime in the case of the third-order response. In the case of the trap model the results strongly depend on the variable coupled to the field. As for the third-order response, the low-frequency limit of the susceptibility plays a crucial role with respect to the occurrence of a hump. The findings are discussed in light of recent experimental results obtained for supercooled liquids. The differences found for the third-order and the fifth-order response indicate that nonlinear response functions might serve as a powerful tool to discriminate among the large number of existing models for glassy relaxation.

Energy landscape-driven non-equilibrium evolution of inherent structure in disordered material

Complex states in glasses can be neatly expressed by the potential energy landscape (PEL). However, because PEL is highly multi-dimensional it is difficult to describe how the system moves around in PEL. Here we demonstrate that it is possible to predict the evolution of macroscopic state in a metallic glass, such as ageing and rejuvenation, through a set of simple equations describing excitations in the PEL. The key to this simplification is the realization that the step of activation from the initial state to the saddle point in PEL and the following step of relaxation to the final state are essentially decoupled. The model shows that the interplay between activation and relaxation in PEL is the key driving force that simultaneously explains both the equilibrium of supercooled liquid and the thermal hysteresis observed in experiments. It further predicts anomalous peaks in truncated thermal scanning, validated by independent molecular dynamics simulation.

Generalized fluctuation-dissipation relation and effective temperature upon heating a deeply supercooled liquid

We show that a generalized fluctuation-dissipation relation applies upon instantaneously increasing the temperature of a deeply supercooled liquid. This has the same two-step shape of the relation found upon cooling the liquid, but with opposite violation, indicating an effective temperature that is lower than bath temperature. We show that the effective temperature exhibits some sensible time dependence and that it retains its connection with the partitioned phase space visited in aging. We underline the potential relevance of our numerical results for experimental studies of the fluctuation-dissipation relation in glassy systems.

Microscopic picture of aging in SiO2

We investigate the aging dynamics of amorphous SiO(2) via molecular dynamics simulations of a quench from a high temperature T(i) to a lower temperature T(f). We obtain a microscopic picture of aging dynamics by analyzing single particle trajectories, identifying jump events when a particle escapes the cage formed by its neighbors, and determining how these jumps depend on the waiting time t(w), the time elapsed since the temperature quench to T(f). We find that the only t(w)-dependent microscopic quantity is the number of jumping particles per unit time, which decreases with age. Similar to previous studies for fragile glass formers, we show here for the strong glass former SiO(2) that neither the distribution of jump lengths nor the distribution of times spent in the cage are t(w) dependent. We conclude that the microscopic aging dynamics is surprisingly similar for fragile and strong glass formers.

How coupled elementary units determine the dynamics of macroscopic glass-forming systems

We investigate the dynamics of a binary mixture Lennard-Jones system of different system sizes with respect to the importance of the properties of the underlying potential energy landscape (PEL). We show that the dynamics of small systems can be very well described within the continuous time random walk formalism, which is determined solely by PEL parameters. Finite size analysis shows that the diffusivity of large and small systems are very similar. This suggests that the PEL parameters of the small system also determine the local dynamics in large systems. The structural relaxation time, however, displays significant finite size effects. Furthermore, using a nonequilibrium configuration of a large system, we find that causal connections exist between nearby regions of the system. These findings can be described by the coupled landscape model for which a macroscopic system is described by a superposition of elementary systems, each described by its PEL. A minimum coupling is introduced which accounts for the finite size behavior. The coupling strength, as the single adjustable parameter, becomes smaller closer to the glass transition.

Nonlinear response theory for Markov processes: simple models for glassy relaxation

The theory of nonlinear response for Markov processes obeying a master equation is formulated in terms of time-dependent perturbation theory for the Green's functions and general expressions for the response functions up to third order in the external field are given. The nonlinear response is calculated for a model of dipole reorientations in an asymmetric double well potential, a standard model in the field of dielectric spectroscopy. The static nonlinear response is finite with the exception of a certain temperature T_{0} determined by the value of the asymmetry. In a narrow temperature range around T_{0}, the modulus of the frequency-dependent cubic response shows a peak at a frequency on the order of the relaxation rate and it vanishes for both low frequencies and high frequencies. At temperatures at which the static response is finite (lower and higher than T_{0}), the modulus is found to decay monotonously from the static limit to zero at high frequencies. In addition, results of calculations for a trap model with a Gaussian density of states are presented. In this case, the cubic response depends on the specific dynamical variable considered and also on the way the external field is coupled to the kinetics of the model. In particular, a set of different dynamical variables that gives rise to identical shapes of the linear susceptibility and only to different temperature dependencies of the relaxation times is considered. It is found that the frequency dependence of the nonlinear response functions, however, strongly depends on the particular choice of the variables. The results are discussed in the context of recent theoretical and experimental findings regarding the nonlinear response of supercooled liquids and glasses.

Memory effects in the relaxation of the Gaussian trap model

We investigate the memory effect in a simple model for glassy relaxation, a trap model with a Gaussian density of states. In this model, thermal equilibrium is reached at all finite temperatures and we therefore can consider jumps from low to high temperatures in addition to the quenches usually considered in aging studies. We show that the evolution of the energy following the Kovacs protocol can approximately be expressed as a difference of two monotonously decaying functions and thus show the existence of a so-called Kovacs hump whenever these functions are not single exponentials. It is well established that the Kovacs effect also occurs in the linear response regime, and we show that most of the gross features do not change dramatically when large temperature jumps are considered. However, there is one distinguishing feature that only exists beyond the linear regime, which we discuss in detail. For the memory experiment with inverted temperatures, i.e., jumping up and then down again, we find a very similar behavior apart from an opposite sign of the hump.