The recently developed nonequilibrium extension of the self-consistent generalized Langevin equation theory of irreversible relaxation [Ramírez-González and Medina-Noyola, Phys. Rev. E 82, 061503 (2010); Ramírez-González and Medina-Noyola, Phys. Rev. E 82, 061504 (2010)] is applied to the description of the irreversible process of equilibration and aging of a glass-forming soft-sphere liquid that follows a sudden temperature quench, within the constraint that the local mean particle density remains uniform and constant. For these particular conditions, this theory describes the nonequilibrium evolution of the static structure factor $S(k;t)$ and of the dynamic properties, such as the self-intermediate scattering function $F_S(k,\tau ;t)$, where $\tau$ is the correlation delay time and $t$ is the evolution or waiting time after the quench. Specific predictions are presented for the deepest quench (to zero temperature). The predicted evolution of the $\alpha$-relaxation time ${\tau }_{\alpha }\left(t\right)$ as a function of $t$ allows us to define the equilibration time $t^{eq}\left(\varphi \right)$, as the time after which ${\tau }_{\alpha }\left(t\right)$ has attained its equilibrium value ${\tau }_{\alpha }^{eq}\left(\varphi \right)$. It is predicted that both, $t^{eq}\left(\varphi \right)$ and ${\tau }_{\alpha }^{eq}\left(\varphi \right)$, diverge as $\varphi \to {\varphi }^{\left(a\right)}$, where ${\varphi }^{\left(a\right)}$ is the hard-sphere dynamic-arrest volume fraction ${\varphi }^{\left(a\right)}(\approx$$0.582)$, thus suggesting that the measurement of equilibrium properties at and above ${\varphi }^{\left(a\right)}$ is experimentally impossible. The theory also predicts that for fixed finite waiting times $t$, the plot of ${\tau }_{\alpha }(t;\varphi )$ as a function of $\varphi$ exhibits two regimes, corresponding to samples that have fully equilibrated within this waiting time $(\varphi \le {\varphi }^{\left(c\right)}\left(t\right))$, and to samples for which equilibration is not yet complete $(\varphi \ge {\varphi }^{\left(c\right)}\left(t\right))$. The crossover volume fraction ${\varphi }^{\left(c\right)}\left(t\right)$ increases with $t$ but saturates to the value ${\varphi }^{\left(a\right)}$.

• Received 1 December 2012

DOI:https://doi.org/10.1103/PhysRevE.87.052306