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Equilibration of Concentrated Hard Sphere Fluids

We report a systematic molecular dynamics study of the isochoric equilibration of hard-sphere fluids in their metastable regime close to the glass transition. The thermalization process starts with the system prepared in a non-equilibrium state with the desired final volume fraction ϕ but with a prescribed non-equilibrium static structure factor S_0(k; ϕ). The evolution of the α- relaxation time τα (k) and long-time self-diffusion coefficient DL as a function of the evolution time tw is then monitored for an array of volume fractions. For a given waiting time the plot of τα (k; ϕ, tw) as a function of ϕ exhibits two regimes corresponding to samples that have fully equilibrated within this waiting time (ϕ \leq ϕ(c) (tw)), and to samples for which equilibration is not yet complete (ϕ \geq ϕ(c) (tw)). The crossover volume fraction ϕ(c) (tw) increases with tw but seems to saturate to a value ϕ(a) \equiv ϕ(c) (tw \rightarrow \infty) \approx 0.582. We also find that the waiting time t^(eq)_w(ϕ) required to equilibrate a system grows faster than the corresponding equilibrium relaxation time, t^(eq)(ϕ) \approx 0.27 \times [τα (k; ϕ)]^1.43, and that both characteristic times increase strongly as ϕ approaches ϕ^(a), thus suggesting that the measurement of equilibrium properties at and above ϕ(a) is experimentally impossible.