Microscopic picture of aging in SiO2

Advances in the study of supercooled water

In this review, we report recent progress in the field of supercooled water. Due to its uniqueness, water presents numerous anomalies with respect to most simple liquids, showing polyamorphism both in the liquid and in the glassy state. We first describe the thermodynamic scenarios hypothesized for the supercooled region and in particular among them the liquid-liquid critical point scenario that has so far received more experimental evidence. We then review the most recent structural indicators, the two-state model picture of water, and the importance of cooperative effects related to the fact that water is a hydrogen-bonded network liquid. We show throughout the review that water's peculiar properties come into play also when water is in solution, confined, and close to biological molecules. Concerning dynamics, upon mild supercooling water behaves as a fragile glass former following the mode coupling theory, and it turns into a strong glass former upon further cooling. Connections between the slow dynamics and the thermodynamics are discussed. The translational relaxation times of density fluctuations show in fact the fragile-to-strong crossover connected to the thermodynamics arising from the existence of two liquids. When considering also rotations, additional crossovers come to play. Mobility-viscosity decoupling is also discussed in supercooled water and aqueous solutions. Finally, the polyamorphism of glassy water is considered through experimental and simulation results both in bulk and in salty aqueous solutions. Grains and grain boundaries are also discussed.

Continuous-time random-walk approach to supercooled liquids: Self-part of the van Hove function and related quantities

From equilibrium molecular dynamics (MD) simulations of a bead-spring model for short-chain glass-forming polymer melts we calculate several quantities characterizing the single-monomer dynamics near the (extrapolated) critical temperature [Formula: see text] of mode-coupling theory: the mean-square displacement g₀(t), the non-Gaussian parameter [Formula: see text] and the self-part of the van Hove function [Formula: see text] which measures the distribution of monomer displacements r in time t. We also determine these quantities from a continuous-time random walk (CTRW) approach. The CTRW is defined in terms of various probability distributions which we know from previous analysis. Utilizing these distributions the CTRW can be solved numerically and compared to the MD data with no adjustable parameter. The MD results reveal the heterogeneous and non-Gaussian single-particle dynamics of the supercooled melt near [Formula: see text]. In the time window of the early [Formula: see text] relaxation [Formula: see text] is large and [Formula: see text] is broad, reflecting the coexistence of monomer displacements that are much smaller ("slow particles") and much larger ("fast particles") than the average at time t, i.e. than [Formula: see text]. For large r the tail of [Formula: see text] is compatible with an exponential decay, as found for many glassy systems. The CTRW can reproduce the spatiotemporal dependence of [Formula: see text] at a qualitative to semiquantitative level. However, it is not quantitatively accurate in the studied temperature regime, although the agreement with the MD data improves upon cooling. In the early [Formula: see text] regime we also analyze the MD results for [Formula: see text] via the space-time factorization theorem predicted by ideal mode-coupling theory. While we find the factorization to be well satisfied for small r, both above and below [Formula: see text] , deviations occur for larger r comprising the tail of [Formula: see text]. The CTRW analysis suggests that single-particle "hops" are a contributing factor for these deviations.

Anomalous diffusion of water molecules at grain boundaries in ice Ih

Using ab initio and classical molecular dynamics simulations, we study pre-melting phenomena in pristine coincident-site-lattice grain boundaries (GBs) in proton-disordered hexagonal ice Ih at temperatures just below the melting point Tm. Concerning pre-melt-layer thicknesses, the results are consistent with the available experimental estimates for low-disorder impurity-free GBs. With regard to molecular mobility, the simulations provide a key new insight: the translational motion of the water molecules is found to be subdiffusive for time scales from ∼10 ns up to at least 0.1 μs. Moreover, the fact that the anomalous diffusion occurs even at temperatures just below Tm where the bulk supercooled liquid still diffuses normally suggests that it is related to the confinement of the GB pre-melt layers by the surrounding crystalline environment. Furthermore, we show that this behavior can be characterized by continuous-time random walk models in which the waiting-time distributions decay according to power-laws that are very similar to those describing dynamics in glass-forming systems.

Universal scaling in the aging of the strong glass former SiO2

We show that the aging dynamics of a strong glass former displays a strikingly simple scaling behavior, connecting the average dynamics with its fluctuations, namely, the dynamical heterogeneities. We perform molecular dynamics simulations of SiO2 with van Beest-Kramer-van Santen interactions, quenching the system from high to low temperature, and study the evolution of the system as a function of the waiting time tw measured from the instant of the quench. We find that both the aging behavior of the dynamic susceptibility χ4 and the aging behavior of the probability distribution P(fs,r) of the local incoherent intermediate scattering function fs,r can be described by simple scaling forms in terms of the global incoherent intermediate scattering function C. The scaling forms are the same that have been found to describe the aging of several fragile glass formers and that, in the case of P(fs,r), have been also predicted theoretically. A thorough study of the length scales involved highlights the importance of intermediate length scales. We also analyze directly the scaling dependence on particle type and on wavevector q and find that both the average and the fluctuations of the slow aging dynamics are controlled by a unique aging clock, which is not only independent of the wavevector q, but is also the same for O and Si atoms.

Relaxation and physical aging in network glasses: a review

Recent progress in the description of glassy relaxation and aging are reviewed for the wide class of network-forming materials such as GeO2, Ge x Se1-x , silicates (SiO2-Na2O) or borates (B2O3-Li2O), all of which have an important usefulness in domestic, geological or optoelectronic applications. A brief introduction of the glass transition phenomenology is given, together with the salient features that are revealed both from theory and experiments. Standard experimental methods used for the characterization of the slowing down of the dynamics are reviewed. We then discuss the important role played by aspects of network topology and rigidity for the understanding of the relaxation of the glass transition, while also permitting analytical predictions of glass properties from simple and insightful models based on the network structure. We also emphasize the great utility of computer simulations which probe the dynamics at the molecular level, and permit the calculation of various structure-related functions in connection with glassy relaxation and the physics of aging which reveal the non-equilibrium nature of glasses. We discuss the notion of spatial variations of structure which leads to the concept of 'dynamic heterogeneities', and recent results in relation to this important topic for network glasses are also reviewed.

Cooling rate and stress relaxation in silica melts and glasses via microsecond molecular dynamics

We have conducted extremely long molecular dynamics simulations of glasses to microsecond times, which close the gap between experimental and atomistic simulation time scales by two to three orders of magnitude. Static, thermal, and structural properties of silica glass are reported for glass cooling rates down to 5×10(9) K/s and viscoelastic response in silica melts and glasses are studied over nine decades of time. We present results from relaxation of hydrostatic compressive stress in silica and show that time-temperature superposition holds in these systems for temperatures from 3500 to 1000 K.

Dynamics in a tetrahedral network glassformer: vibrations, network rearrangements, and diffusion

We perform molecular dynamics simulation on a tetrahedral network glassformer using a model for viscous SiO2 by Coslovich and Pastore [J. Phys.: Condens. Matter 21, 285107 (2009)]. In this system, Si and O particles form a random network at low temperature T. We attach an ellipsoid to each particle to represent its time-averaged vibration tensor. We then examine the anisotropic vibrations of Si and O, where the ellipsoid orientations are correlated with the network. The ellipsoids exhibit marked vibrational heterogeneity. The configuration changes occur as breakage and reorganization of the network, where only one or two particles undergo large jumps at each rearrangement leading to diffusion. To the time-correlation functions, however, the particles surrounding these largely displaced ones yield significantly T-dependent contributions, resulting in a weak violation of the Stokes-Einstein relation. This crossover is mild in silica due to the small Si-O bond numbers per particle, while it is strong in fragile glassformers with large coordination numbers. On long timescales, jump events tend to occur in the same regions forming marked dynamic heterogeneity. We also calculate the diffusion constants and the viscosity. The diffusion obeys activation dynamics and may be studied by short-time analysis of irreversible jumps.

Renewal events in glass-forming liquids

On cooling toward the glass transition temperature, glass-forming liquids display long periods of localized motion interrupted by fast "jumps" in the single-particle trajectories. Several theoretical models based on these single-particle jumps have been proposed, most prominently the continuous-time random walk (CTRW). The central assumption of the CTRW is that jumps are renewal events, i.e. that the internal clock of a particle can be reset upon a jump. In this paper, I present an easy-to-implement method to test whether jumps detected in a supercooled liquid or glass are renewal events or not. The test was applied to molecular dynamics simulations of a short-chain polymer melt, demonstrating that the jumps can in fact be treated as renewal events. The test further revealed that additional relaxation processes are present which are not accounted for in the CTRW picture, highlighting the limitations of this approach. The notion of renewal events in glass-forming systems could be a very important building block for the interpretation of aging and the glass transition. Furthermore, it could have practical implications for the study of non-equilibrium dynamics in glasses as well as mechanical rejuvenation.

Order parameter for structural heterogeneity in disordered solids

We construct a structural order parameter from the energy equipartition of normal modes of vibration to quantify the structural heterogeneity in disordered solids. The order parameter exhibits strong spatial correlations with low-temperature dynamics and local structural entropy. To characterize the role of particles with the most defective local structures identified by the order parameter, we pin them and measure the system response. It turns out that particles with the largest value of the order parameter are responsible for the quasilocalized low-frequency vibration, instability, softening, and nonaffinity of disordered solids. The order parameter thus crucially links the heterogeneous structure to low-temperature dynamics and mechanical properties of disordered solids.

Continuous-time random-walk approach to supercooled liquids. II. Mean-square displacements in polymer melts

The continuous-time random walk (CTRW) describes the single-particle dynamics as a series of jumps separated by random waiting times. This description is applied to analyze trajectories from molecular dynamics (MD) simulations of a supercooled polymer melt. Based on the algorithm presented by Helfferich et al. [Phys. Rev. E 89, 042603 (2014)], we detect jump events of the monomers. As a function of temperature and chain length, we examine key distributions of the CTRW: the jump-length distribution (JLD), the waiting-time distribution (WTD), and the persistence-time distribution (PTD), i.e., the distribution of waiting times for the first jump. For the equilibrium (polymer) liquid under consideration, we verify that the PTD is determined by the WTD. For the mean-square displacement (MSD) of a monomer, the results for the CTRW model are compared with the underlying MD data. The MD data exhibit two regimes of subdiffusive behavior, one for the early α process and another at later times due to chain connectivity. By contrast, the analytical solution of the CTRW yields diffusive behavior for the MSD at all times. Empirically, we can account for the effect of chain connectivity in Monte Carlo simulations of the CTRW. The results of these simulations are then in good agreement with the MD data in the connectivity-dominated regime, but not in the early α regime where they systematically underestimate the MSD from the MD.

Continuous-time random-walk approach to supercooled liquids. I. Different definitions of particle jumps and their consequences

Single-particle trajectories in supercooled liquids display long periods of localization interrupted by "fast moves." This observation suggests a modeling by a continuous-time random walk (CTRW). We perform molecular dynamics simulations of equilibrated short-chain polymer melts near the critical temperature of mode-coupling theory Tc and extract "moves" from the monomer trajectories. We show that not all moves comply with the conditions of a CTRW. Strong forward-backward correlations are found in the supercooled state. A refinement procedure is suggested to exclude these moves from the analysis. We discuss the repercussions of the refinement on the jump-length and waiting-time distributions as well as on characteristic time scales, such as the average waiting time ("exchange time") and the average time for the first move ("persistence time"). The refinement modifies the temperature (T) dependence of these time scales. For instance, the average waiting time changes from an Arrhenius-type to a Vogel-Fulcher-type T dependence. We discuss this observation in the context of the bifurcation of the α process and (Johari) β process found in many glass-forming materials to occur near Tc. Our analysis lays the foundation for a study of the jump-length and waiting-time distributions, their temperature and chain-length dependencies, and the modeling of the monomer dynamics by a CTRW approach in the companion paper [J. Helfferich et al., Phys. Rev. E 89, 042604 (2014)].

Temperature-dependent defect dynamics in the network glass SiO2

We investigate the long time dynamics of a strong glass former, SiO(2), below the glass transition temperature by averaging single-particle trajectories over time windows which comprise roughly 100 particle oscillations. The structure on this coarse-grained time scale is very well defined in terms of coordination numbers, allowing us to identify ill-coordinated atoms, which are called defects in the following. The most numerous defects are O-O neighbors, whose lifetimes are comparable to the equilibration time at low temperature. On the other hand, SiO and OSi defects are very rare and short lived. The lifetime of defects is found to be strongly temperature dependent, consistent with activated processes. Single-particle jumps give rise to local structural rearrangements. We show that in SiO(2) these structural rearrangements are coupled to the creation or annihilation of defects, giving rise to very strong correlations of jumping atoms and defects.

Distribution of local relaxation events in an aging three-dimensional glass: spatiotemporal correlation and dynamical heterogeneity

We investigate the spatiotemporal distribution of microscopic relaxation events, defined through particle hops, in a model polymer glass using molecular dynamics simulations. We introduce an efficient algorithm to directly identify hops during the simulation, which allows the creation of a map of relaxation events for the whole system. Based on this map, we present density-density correlations between hops and directly extract correlation scales. These scales define collaboratively rearranging groups of particles and their size distributions are presented as a function of temperature and age. Dynamical heterogeneity is spatially resolved as the aggregation of hops into clusters, and we analyze their volume distribution and growth during aging. A direct comparison with the four-point dynamical susceptibility χ(4) reveals the formation of a single dominating cluster prior to the χ(4) peak, which indicates maximally correlated dynamics. An analysis of the fractal dimension of the hop clusters finds slightly noncompact shapes in excellent agreement with independent estimates from four-point correlations.