[Paper Review] On the nature of the glass transition in atomistic models of glass formers

Alexander Hudson, Kranthi K. Mandadapu|arXiv (Cornell University)|Apr 11, 2018

Material Dynamics and PropertiesMaterials Science4 citations

TL;DR

This study investigates the glass transition in atomistic models of glass formers by simulating cooling at constant rates, testing predictions from the East model—a kinetically constrained lattice model with hierarchical relaxation. It finds that the structural relaxation time τ crosses over from super-Arrhenius to Arrhenius behavior at a cooling-rate-dependent Tg, with a peak in the slope of lnτ vs. 1/T near Tg, and observes no spatial correlations in short-time particle displacements below Tg, contradicting expectations from the East model.

ABSTRACT

We study the nature of the glass transition by cooling model atomistic glass formers at constant rate from a temperature above the onset of glassy dynamics to $T=0$. Motivated by the East model, a kinetically constrained lattice model with hierarchical relaxation, we make several predictions about the behavior of the supercooled liquid as it passes through the glass transition. We then compare those predictions to the results of our atomistic simulations. Consistent with our predictions, our results show that the relaxation time $τ$ of the material undergoes a crossover from super-Arrhenius to Arrhenius behavior at a cooling-rate-dependent glass transition temperature $T_ ext{g}$. The slope of $\lnτ$ with respect to inverse temperature exhibits a peak near $T_ ext{g}$ that grows more pronounced with slower cooling, matching our expectations qualitatively. Additionally, the limiting value of this slope at low temperature shows remarkable quantitative agreement with our predictions. Our results also show that the rate of short-time particle displacements deviates from the equilibrium linear scaling around $T_ ext{g}$, asymptotically approaching a different linear scaling. To our surprise, these short-time displacements, the dynamic indicators of the underlying excitations responsible for structural relaxation, show no spatial correlations beyond a few particle diameters, both above and below $T_ ext{g}$. This final result is contrary to our expectation, based on previous results for East model glasses formed by cooling, that inter-excitation correlations should emerge as the liquid vitrifies.

Motivation & Objective

• To investigate the nature of the glass transition in atomistic glass formers using constant-rate cooling simulations.
• To test predictions from the East model regarding relaxation time behavior and spatial correlations of excitations.
• To determine whether short-time particle displacements correlate spatially below Tg, as expected in kinetically constrained models.
• To assess the validity of using particle displacements as indicators of underlying excitations in glass-forming liquids.
• To reconcile discrepancies between atomistic simulation results and the theoretical framework of the East model.

Proposed method

• Simulate cooling of atomistic glass formers from above the onset temperature To to T=0 at constant cooling rates.
• Use a dynamic indicator function to identify particles undergoing non-vibrational, short-time displacements as proxies for excitations.
• Analyze the relaxation time τ(T) and its temperature dependence, particularly the slope of lnτ vs. 1/T.
• Compute spatial correlation functions of displacing particles to detect inter-excitation correlations above and below Tg.
• Compare simulation results with theoretical predictions from the East model, particularly the parabolic scaling of lnτ ∝ (1/T - 1/To)².
• Perform robustness checks by varying the indicator function, distance cutoff, observation time, and spatial distribution function.

Experimental results

Research questions

• RQ1 Does the relaxation time τ of atomistic glass formers exhibit a crossover from super-Arrhenius to Arrhenius behavior at a cooling-rate-dependent Tg, as predicted by the East model?
• RQ2 Does the slope of lnτ versus inverse temperature exhibit a peak near Tg, and does this peak grow more pronounced with slower cooling?
• RQ3 Are short-time particle displacements spatially correlated below Tg, as expected from hierarchical relaxation in kinetically constrained models?
• RQ4 Do the dynamic indicators used for particle displacements faithfully reflect the underlying excitations responsible for structural relaxation?
• RQ5 Can the observed lack of spatial correlations in displacing particles be reconciled with the theoretical framework of the East model?

Key findings

• The relaxation time τ exhibits a clear crossover from super-Arrhenius to Arrhenius behavior at a cooling-rate-dependent glass transition temperature Tg, consistent with East model predictions.
• The slope of lnτ versus 1/T shows a pronounced peak near Tg that increases in magnitude with slower cooling rates, matching qualitative expectations from the East model.
• The limiting value of the slope at low temperatures shows remarkable quantitative agreement with theoretical predictions from the East model.
• Short-time particle displacements deviate from equilibrium linear scaling at Tg and asymptotically approach a different linear scaling, indicating a change in dynamic regime.
• Despite strong out-of-equilibrium conditions below Tg, no spatial correlations are found between displacing particles beyond a few particle diameters, contradicting expectations from the East model.
• Robustness checks using varied definitions of the indicator function, distance cutoffs, and observation times confirm the absence of spatial correlations across all tested conditions.