Structural relaxation, dynamical arrest and aging in soft-sphere liquids

TL;DR

This study combines simulations and NE-SCGLE theory to analyze structural relaxation, aging, and dynamical arrest in soft-sphere liquids after quenches, revealing a crossover from equilibration to aging near the glass transition.

Contribution

It provides a comprehensive analysis of aging and relaxation in soft-sphere liquids using combined simulation and theoretical approaches, highlighting a continuous crossover at the glass transition.

Findings

Sub-linear increase of relaxation time with age after quench.

Identification of an empirical equilibration timescale diverging near the glass transition.

Observation of persistent aging effects inside the glass phase.

Abstract

We investigate the structural relaxation of a soft-sphere liquid quenched isochorically ($\phi=0.7$) and instantaneously to different temperatures $T_f$ above and below the glass transition. For this, we combine extensive Brownian dynamics simulations and theoretical calculations based on the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory. The response of the liquid to a quench generally consists of a sub-linear increase of the $\alpha$-relaxation time with system's age. Approaching the ideal glass-transition temperature from above ($T_f>T^a$) sub-aging appears as a transient process describing a broad equilibration crossover for quenches to nearly arrested states. This allows us to empirically determine an equilibration timescale $t^{eq}(T_f)$ that becomes increasingly longer as $T_f$ approaches $T^a$. For quenches inside the glass ($T_f\leq T^a$) the growth rate of the structural relaxation time becomes progressively larger as $T_f$ decreases and, unlike the equilibration scenario, $\tau_{\alpha}$ remains evolving within the whole observation time-window.These features are consistently found in theory and simulations with remarkable semi-quantitative agreement, and coincide with those revealed in the similar and complementary exercise [Phys. Rev. {\bf 96}, 022608 (2017)] that considered a sequence of quenches with fixed final temperature $T_f=0$ but increasing $\phi$ towards the hard-sphere dynamical arrest volume fraction $\phi^a_{HS}=0.582$. The NE-SCGLE analysis, however, unveils various fundamental aspects of the glass transition, involving the abrupt passage from the ordinary equilibration scenario to the persistent aging effects that are characteristic of glass-forming liquids. The theory also explains that, within the time window of any experimental observation, this can only be observed as a continuous crossover.