Atomistic mechanism of physical ageing in glassy materials

Using molecular simulations, we identify microscopic relaxation events of individual particles in ageing structural glasses, and determine the full distribution of relaxation times. We find that the memory of the waiting time tw elapsed since the quench extends only up to the first relaxation event, while the distribution of all subsequent relaxation times (persistence times) follows a power law completely independent of history. Our results are in remarkable agreement with the well known phenomenological trap model of ageing. A continuous time random walk (CTRW) parametrized with the atomistic distributions captures the entire bulk diffusion behavior and explains the apparent scaling of the relaxation dynamics with tw during ageing, as well as observed deviations from perfect scaling. The dynamics of glass forming materials is characterized by slow, spatially heterogeneous and temporally intermittent processes [1–6]. Long periods of caged particle vibrations are interrupted by rapid, localized structural relaxations. Dynamical heterogeneity near the glass transition leads to stretched exponential relaxation of correlation and response functions, as well as subdiffusive, non-Gaussian transport. In the glassy state, configurational degrees of freedom continue to evolve slowly. This phenomenon is called physical ageing [7] and is a defining and universal feature of nonequilibrium glassy dynamics [8]. Structural relaxations become increasingly sluggish with the waiting time tw elapsed since vitrification, and almost all material properties change as a result. Ageing often manifests itself as a simple rescaling of the slow, configurational part of the global correlation functions C(t, tw) = Cvib(t) + Cconf (t/t μ w), where μ is the ageing exponent. This scaling behaviour has been observed in a wide range of disordered materials [1] and is particularly pronounced in polymer glasses [7], colloidal suspensions [9, 10], and physical gels [11]. Recent simulations of structural glasses show that scaling also applies approximately to the distribution of local correlation functions [12] and the distribution of particle displacements (van Hove function) [13], which superimpose when plotted at times of equal mean. Scaling of local correlations can be proved to hold exactly for certain spin glass models whose dynamical action obeys time reparametrization invariance [14]. Despite the apparently universal nature of this phenomenon [15], the physical mechanism behind it remains elusive. In this Letter, we directly observe the atomistic dynamics underlying physical ageing on a single particle level through molecular dynamics simulations of two model systems for atomic and polymeric glasses. We consider both the well-known amorphous 80/20 binary Lennard-Jones mixture [16], as well as a bead-spring model for polymer glasses [17, 18], where particles interact via the LennardJones potential and are coupled together by stiff springs to form chains of length 10. Twenty thousand particles each are simulated in a periodic simulation box. For the polymer (80/20) model, the initial ensemble is equilibrated at T = 1.2 (4.0), and then quenched rapidly to T = 0.25 (0.33) to form a glass. The system is aged at constant pressure for various waiting times tw and then the dynamics are followed as a function of the measurement time t. All results are quoted in Lennard-Jones units. In both models, the effect of ageing can be immediately observed through the one-dimensional mean squared displacement 〈∆x(t, tw)〉 shown in Fig. 1, which exhibits three regimes: a short time vibrational regime precedes a long plateau characterized by “caged” motion, followed by a cage escape or α-relaxation regime. The cage escape time increases with increasing tw, but 〈∆x(t, tw) 〉-curves for different waiting times can be superimposed in the cage escape regime by rescaling time with tw. At long times