Glass formers display universal non-equilibrium dynamics on the level of single-particle jumps

Glasses are inherently out-of-equilibrium systems evolving slowly toward their equilibrium state in a process called physical aging. During aging, dynamic observables depend on the history of the system, hampering comparative studies of dynamics in different glass formers. Here, we demonstrate how glass formers can be directly compared on the level of single-particle jumps, i.e. the structural relaxation events underlying the α-process. Describing the dynamics in terms of a continuous-time random walk, an analytic prediction for the jump rate is derived. The result is subsequently compared to molecular-dynamics simulations of amorphous silica and a polymer melt as two generic representatives of strong and fragile glass formers, and good agreement is found. Copyright c © EPLA, 2015 When a liquid is cooled to low temperatures and crystallization is avoided (either by a fast cooling rate or due to internal constraints), a glass forms. During cooling, a strong increase in viscosity and relaxation times is observed already in the supercooled regime above the glass transition temperature Tg [1–7]. Based on the temperature dependence of the relaxation times, glass formers are divided into strong and fragile glass formers with strong glass formers displaying Arrhenius and fragile glass formers super-Arrhenius behavior [1]. On cooling through Tg the structural relaxation time, i.e. the time necessary to return to equilibrium after a small perturbation [2], exceeds the time scales accessible in experiments. The glass thus “falls out of equilibrium” rendering it an inherently non-equilibrium system, slowly evolving towards its equilibrium state in a process called “physical aging” [8]. Within the aging regime, dynamic observables depend on the history of the system, i.e. the time since vitrification as well as details of the quenching procedure such as the cooling rate. This history dependence effectively hinders a direct comparison of the non-equilibrium dynamics of different glass formers or glasses with different histories. In numerical simulations the accessible time scales are many orders of magnitude smaller than in real-world experiments (typically about 100 ns). Thus, the relaxation times reach the accessible time scales already in the supercooled regime around Tc, the extrapolated critical temperature of mode coupling theory [1,4,5,7]. Still, nonequilibrium effects can be removed by extensive tempering at these temperatures and relaxation toward equilibrium can be achieved. It has been suggested, however, that this prolonged equilibration dynamics displays the same characteristics as physical aging below Tg [9]. While being restricted to short time scales, numerical simulations offer the benefit that the full microscopic information is available. In this way, computer simulations have played a pivotal role in the understanding of glasses, revealing the presence of increasingly complex dynamics upon cooling, evident in strong spatial correlations [1,3,10,11] and dynamic heterogeneities, i.e. the coexistence of “fast” and “slow” particles [1–3,12–18]. Furthermore, a careful analysis of the single-particle trajectories led to the observation that a facet of dynamic heterogeneities manifests itself in long periods of localized motion interrupted by fast jumps [1,19–22]. Inspired by this observation, glass-forming materials have been studied in terms of the continuous-time random walk (CTRW) [23–27], i.e. a random walk with random time