Quench, Equilibration, and Subaging in Structural Glasses

In the glassy state, all materials undergo a process of structural recovery as they age towards equilibrium. The resultant increase of relaxation times $t_{\alpha }$ is frequently described with a sublinear power of the wait time $t_w^{\mu }$ with an apparent aging exponent $\mu$. We show with molecular dynamics simulations of a Lennard-Jones glass former at various temperatures that the observed aging exponent can be strongly influenced by crossover effects from the freshly quenched state at short $t_w$ and into the equilibrated state at long $t_w$. The aging behavior on the molecular level is quantitatively reproduced by a coarse-grained continuous time random walk description over the entire range of temperatures and wait times. Our model glass always shows normal aging, $t_{\alpha }\sim t_w$, when the observation time window is no longer affected by crossover effects, in agreement with the well-known trap model of aging.

Figure 1

Dynamic structure factor Eq. (1) from MD simulations of an aging LJ glass at two temperatures (solid lines), with the corresponding CTRW predictions (dashed lines, see text). Wait times are logarithmically spaced from left to right, with initial $t_w=7.5$ and final $t_w=75000$.

Figure 2

Relaxation times vs wait times for four temperatures, $T=0.28$ (black circles), $T=0.33$ (blue squares), $T=0.35$ (red triangles), and $T=0.37$ (green diamonds). Dotted lines show the predictions of the CTRW model (see text); solid line has slope one. Inset: The logarithmic slope, $\mu =\partial \ln (t_{\alpha })/\partial t_w$ taken from the middle of the sigmoid vs temperature.

Figure 3

Instantaneous aging exponent calculated from derivative of the CTRW model curves in Fig. 2. Symbols as in Fig. 2.

Figure 4

Distribution of (wait time independent) persistence times measured with MD simulations at four temperatures. Symbols as in Fig. 2. Solid line shows a power-law fit to the $T=0.28$ distribution.