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

We investigate the structural relaxation of a soft-sphere liquid quenched isochorically (ϕ = 0.7) and instantaneously to different temperatures Tf 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 α-relaxation time with system's age. Approaching the ideal glass-transition temperature from above (Tf > Ta), 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 teq(Tf) that becomes increasingly longer as Tf approaches Ta. For quenches inside the glass (Tf ≤ Ta), the growth rate of the structural relaxation time becomes progressively larger as Tf decreases and, unlike the equilibration scenario, τα 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 a previous and complementary study [P. Mendoza-Méndez et al., Phys. Rev. 96, 022608 (2017)] that considered a sequence of quenches with fixed final temperature Tf = 0 but increasing ϕ toward the hard-sphere dynamical arrest volume fraction ϕHS a=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.

On a fundamental description of the Kovacs' kinetic signatures in glass-forming systems.

The time-evolution equation for the time-dependent static structure factor of the non-equilibrium self-consistent generalized Langevin equation (NE-SCGLE) theory was used to investigate the kinetics of glass-forming systems under isochoric conditions. The kinetics are studied within the framework of the fictive temperature (TF) of the glassy structure. We solve for the kinetics of TF(t) and the time-dependent structure factor and find that they are different but closely related by a function that depends only on temperature. Furthermore, we are able to solve for the evolution of TF(t) in a set of temperature-jump histories referred to as the Kovacs' signatures. We demonstrate that the NE-SCGLE theory reproduces all the Kovacs' signatures, namely, intrinsic isotherm, asymmetry of approach, and memory effect. In addition, we extend the theory into largely unexplored, deep glassy state, regions that are below the notionally "ideal" glass temperature.

First-principles prediction of multiple stationary states in glass-forming liquids.

In the present work, the Non-Equilibrium Self-Consistent Generalized Langevin Equation (NESCGLE) theory is used to predict the final state of glass-forming liquids subjected to different cooling processes. We show that the NESCGLE theory correctly describes two essential features of the glass transition. Such features are the structural recovery and the dependence of the final state with the cooling rate. We demonstrate that below a particular temperature Tc, the system is unable to equilibrate, independently of the cooling rate. We show that the equilibrium state is only reached for the quasistatic process. Additionally, we show how, from the NESCGLE theory, it is possible to deduce a relaxation model of structural recovery, for which we obtain molecular expressions of the parameters.

Crossover from equilibration to aging: Nonequilibrium theory versus simulations.

Understanding glasses and the glass transition requires comprehending the nature of the crossover from the ergodic (or equilibrium) regime, in which the stationary properties of the system have no history dependence, to the mysterious glass transition region, where the measured properties are nonstationary and depend on the protocol of preparation. In this work we use nonequilibrium molecular dynamics simulations to test the main features of the crossover predicted by the molecular version of the recently developed multicomponent nonequilibrium self-consistent generalized Langevin equation theory. According to this theory, the glass transition involves the abrupt passage from the ordinary pattern of full equilibration to the aging scenario characteristic of glass-forming liquids. The same theory explains that this abrupt transition will always be observed as a blurred crossover due to the unavoidable finiteness of the time window of any experimental observation. We find that within their finite waiting-time window, the simulations confirm the general trends predicted by the theory.