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.

Figure 1

Nonequilibrium evolution of the structure and dynamics of a hard-sphere liquid in the process of its isochoric equilibration at fixed volume fraction $\varphi =0.58$ according to the (MD) nonequilibrium simulations (symbols) and to the NE-SCGLE theory (solid lines). (a) Snapshots of $S(k,t_w)$ as a function of $k$, with a zoom at the main peak in the inset, for the indicated sequence of waiting times. (b) Corresponding snapshots (from left to right) of $F_S(k,\tau ;\varphi ,t_w)$ plotted as a function of the correlation time $\tau$ at fixed $k\sigma =7.1$. Inset: The $\alpha$-relaxation time ${\tau }_{\alpha }(t_w,\varphi )$, scaled as ${\tau }_{\alpha }^{*}(t_w,\varphi )\equiv k^2{D}^0{\tau }_{\alpha }(k\sigma ;t_w,\varphi )$, as a function of the evolution time $t_w$, for this equilibration process. The dark circle is the equilibration point ($t_w^{\mathrm{eq}},{\tau }_{\alpha }^{*\mathrm{eq}}$).

Figure 2

Nonequilibrium molecular dynamics simulations (symbols) and NE-SCGLE theoretical results (solid lines, equilibration; dot-dashed lines, aging processes) for the $\alpha$-relaxation time ${\tau }_{\alpha }^{*}(t_w,\varphi )$, plotted as a function of the evolution time $t_w$ for a sequence of fixed volume fractions. Asterisks represent the equilibration points $\left[(t_w^{\mathrm{eq}}\left(\varphi \right),{\tau }_{\alpha }^{*\mathrm{eq}}\left(\varphi \right)\right]$ and the dashed line passing through them is the power-law fit ${\tau }_{\alpha }^{*\mathrm{eq}}\left(\varphi \right)=2.8\times {\left[t_w^{\mathrm{eq}}\left(\varphi \right)\right]}^{0.96}$.

Figure 3

Same as Fig. 2, but here ${\tau }_{\alpha }^{*}(t_w,\varphi )$ is plotted as a function of $\varphi$ for fixed times $t_w={10}^0,{10}^1,{10}^2,{10}^3,{10}^4$, and ${10}^5$ (from bottom to top; the dashed line corresponds to $t_w=\infty$). In this case, the dark asterisks indicate the (theoretical) $t_w$-dependent volume fraction ${\varphi }_{c.o.}\left(t_w\right)$, which describes the crossover from fully equilibrated to insufficiently equilibrated conditions. Inset: Comparison of the predicted (asterisks) and simulated (circles) results for ${\varphi }_{c.o.}\left(t_w\right)$.

Figure 4

Nonequilibrium evolution of the dimensionless $\alpha$-relaxation time, displayed as ${\tau }_{\alpha }^{*} (k=7.1;t_w)$, corresponding to the equilibration processes at fixed volume fractions: (a) $\varphi =0.55$; (b) $\varphi =0.575$.