Aging to Equilibrium Dynamics of SiO$_{2}$ K. Vollmayr-Lee ∗ and J. A. Roman Department of Physics and Astronomy, Bucknell University, Lewisburg, Pennsylvania 17837, USA J. Horbach Institut f¨ ur Materialphysik im Weltraum, Deutsches Zentrum f¨ ur Luft- und Raumfahrt (DLR), Linder H¨ ohe, 51147 K¨ oln, Germany (Dated: May 3, 2010) Molecular dynamics computer simulations are used to study the aging dynamics of SiO 2 (mod- eled by the BKS model). Starting from fully equilibrated configurations at high temperatures T i ∈ { 5000 K , 3760 K } , the system is quenched to lower temperatures T f ∈ { 2500 K, 2750 K, 3000 K, 3250 K } and observed after a waiting time t w . Since the simulation runs are long enough to reach equilibrium at T f , we are able to study the transition from out-of-equilibrium to equilibrium dynam- ics. We present results for the partial structure factors, for the generalized incoherent intermediate scattering function C q ( t w , t w + t ), and for the mean square displacement Δ r $^{2}$( t w , t w + t ). We conclude that there are three different t w regions: (I) At very short waiting times, C q ( t w , t w + t ) decays very fast without forming a plateau. Similarly Δ r $^{2}$( t w , t w + t ) increases without forming a plateau. (II) With increasing t w a plateau develops in C q ( t w , t w + t ) and Δ r $^{2}$( t w , t w + t ). For intermediate waiting times the plateau height is independent of t w and T i . Time superposition applies, i.e. C q = C q ( t/t Cq r ) where t Cq r = t Cq r ( t w ) is a waiting time dependent decay time. Furthermore C q = C ( q, t w , t w + t ) scales as C q = C ( q, z ( t w , t ) where z is a function of t w and t only, i.e. independent of q . (III) At large t w the system reaches equilibrium, i.e. C q ( t w , t w + t ) and Δ r $^{2}$( t w , t w + t ) are independent of t w and T i . For C q ( t w , t w + t ) we find that the time superposition of intermediate waiting times (II) includes the equilibrium curve (III). PACS numbers: 61.20.Lc, 61.20.Ja, 64.70.ph, 02.70.Ns, 61.43.Fs When a glass-forming liquid is quenched from an equilibrium state at a high temperature T$_{i}$ to a non- equilibrium state at a lower temperature T$_{f}$ , “aging pro- cesses” set in. Provided that crystallization plays no role at T$_{f}$ (e.g. due to very low crystal nucleation rates), the transition to a final (metastable) equilibrium state occurs on a time scale that corresponds to the typical equilib- rium relaxation time τ$_{eq}$ of the (supercooled) liquid at T$_{f}$ . The dynamics of the system depends on the wait- ing time t$_{w}$ which is the time elapsed after the tempera- ture quench. If τ$_{eq}$ exceeds the waiting time t$_{w}$ then the system is observed in a transient non-equilibrium state which corresponds to a glass for t$_{w}$ ≪ τ$_{eq}$ . During the aging process, i.e. for t$_{w}$ < τ$_{eq}$ , thermodynamic proper- ties such as volume and energy are changing and time translation invariance does not hold: correlation func- tions at time t$_{w}$ + t and the time origin at t$_{w}$ do depend not only on the time difference t but also on the waiting time t$_{w}$ . Recently this aging process has been investigated ex- tensively with experiments [1–6], theoretically [7–9] and with computer simulations. For a more complete sum- mary of previous results we refer the reader to the ref- erences [10, 11] and references therein. Computer sim- ulation studies most similar to the work presented here $^{∗}$Electronic address: kvollmay@bucknell.edu are on attractive colloidal systems [12–15], on the Kob- Andersen Lennard-Jones (KALJ) mixture [16–25], and silica (SiO$_{2}$) [25–28]. In the case of silica the interpreta- tion of the results is less clear than for the KALJ mixture; e.g. different findings [25, 27] have been reported on the violation of the fluctuation-dissipation regime during ag- ing [7–9]. Thus, it remains open whether silica, as the prototype of a glass-forming system forming a tetrahe- dral network structure, exhibits a different aging dynam- ics than, e.g. the KALJ model, where the structure is similar to that of a closed-packed hard-sphere structure. Recent simulation studies on amorphous silica [25–39] have widely used the BKS potential [40] to model the interactions between the atoms. Although it is a simple pair potential, it reproduces various static and dynamic properties of amorphous silica very well. For BKS sil- ica, the self-diffusion constants D$_{α}$ ( α = Si , O) show two different temperature regimes: At high temperatures, D$_{α}$ decays according to a power law, as predicted by the mode coupling theory (MCT) of the glass transition (note, however, that also other interpretations have been assigned to this high temperature regime). At low tem- perature, D$_{α}$ as well as the shear viscosity η exhibit an Arrhenius behavior with an activation energy of the order of 5 eV, in agreement with experiment (see [30] and refer- ences therein). The temperature at which the crossover between both regimes occurs is at T$_{c}$ ≈ 3300 K, corre- sponding to the critical MCT temperature of BKS silica. Previous studies of the aging dynamics of BKS silica [25– 27] were performed in two steps. First, the system was fully equilibrated at a temperature T$_{i}$ > T$_{c}$ . Then, the I. INTRODUCTION arXiv:1001.0715v2 [cond-mat.dis-nn] 27 Jul 2010