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 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 α-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 ≤ T^a), the growth rate of the structural relaxation time becomes progressively larger as T_f decreases and, unlike the equilibration scenario, τ_α 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 T_f = 0 but increasing ϕ toward the hard-sphere dynamical arrest volume fraction ϕ_HS ^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.