Using thesensemble to probe glasses formed by cooling and aging

Abstract

From length scale distributions characterizing frozen amorphous domains, we relate the s-ensemble method with standard cooling and aging protocols for forming glass. We show that in a general class of models, where space-time scaling is in harmony with that of experiment, the domain size distributions obtained with the s-ensemble are identical to those obtained through cooling or aging, but the computational effort for applying the s-ensemble is generally many orders of magnitude smaller than that of straightforward numerical simulation of cooling or aging.Through biasing statistics of trajectory space, the socalled "s-ensemble" method, non-equilibrium phase transitions emerge between ergodic liquid-like states and dynamically inactive glass-like states. This class of transitions are found in idealized lattice models [1,2] and in simulations of atomistic models [3][4][5]. In the latter case, it affords a systematic computational means of preparing exceptionally stable glass-states states [6]. This Letter draws the conclusion that the s-ensemble transition coincides with the physical glass transition [7], and the ensemble of its inactive states are those of natural structural glass. Specifically, we derive correspondence between spatial correlations in the s-ensemble glass with those in the glass produced with finite-rate cooling or aging. The correspondence provides a basis for an extraordinarily efficient route for preparing structural glass with molecular simulations.Space-time structure of glass-forming liquids. To begin, it is helpful to consider Figs. 1a and 1b, which render trajectories of a two-dimensional 5 × 10 4 -particle system in a fashion that extends the approach of Ref. [8]. The system is a liquid mixture at a temperature that is 80% below that of the onset temperature, T o [8][9][10][11][12], and the trajectory runs for an observation time t obs ≈ 10 τ . Here, τ stands for the equilibrium structural relaxation time. It is about 10 5 integration steps at this particular temperature, and t obs , being 10 times longer, provides ample opportunity to observe the nature of dynamic heterogeneity in the system.Most motions in glass-forming liquids are irrelevant vibrations, and the amplitudes of most of those vibrations are similar in size to typical enduring displacements [8]. Irrelevant vibrations can be filtered out by focusing on inherent structures [13]. The set of particle positions at time t, {r i (t)}, evolves by molecular dynamics; the inherent structure, {r i (t)}, is the position of the potentialenergy minimum closest to {r i (t)}. The renderings in Fig. 1 refer to [a(r, t)] iso , whereHere, we take ∆t to be 10 3 integration steps, which is roughly the average time to complete an enduring displacement of one atomic diameter [8], and [· · · ] iso indicates iso-configurational averaging, which averages many trajectories of length ∆t, all starting from the same configuration [14]. Particles colored red in Fig. 1a are those for which the iso-configuration averagedr i (∆t) is more than 0.6 σ fromr ...

Glasses and aging: A Statistical Mechanics Perspective

“…Displacements instead refer to dynamical moves in short segments of a trajectory, while defects refer to underlying configurations. The explicit definition of defects has since been used to estimate the role of facilitation in glassy dynamics, to provide a microscopic validation of KCMs [264,265], to explain dynamical heterogeneities in glassy materials, or to compute the dynamical facilitation volume [247].…”

Theory of amorphous ices

“…While this protocol overcomes huge time scales associated with glass transitions [41], the calculations are nevertheless time consuming. As such, we have considered limited system sizes, large enough to exhibit clear signatures of glass transitions but not larger.…”

“…Prior work [29,30] has found that anomalous responses of glass transitions begin to disappear from simulations when system sizes are decreased below 200 particles. With N ≈ 200, the stability of glasses we produce is limited to ne ≈ 6σ = 1.5 nm [41].…”

Non-equivalence of Dynamical Ensembles and Emergent Non-ergodicity

“…This canonical ensemble is also called the s-ensemble [19], the driven, biased or tilted ensemble [13] or Esscher transform [20]. The last ensemble has been used to study glass transition [19,[21][22][23][24][25][26][27][28] or as a numerical tool to evaluate rare event probabilities [29,30]. As indicated by their names, the way one introduces dynamical ensembles is in clear analogy with the way ensembles are defined in equilibrium statistical physics.…”