Figure 4

Time-dependent diffusion coefficient.

Results of Monte Carlo simulations for the set of fcc ordered (black points) and disordered (blue points) hard sphere packing at increasing packing ratio φ ranging from 0.33 to 0.74 (top to bottom). Data corresponding to the ordered systems are suitably shifted on the vertical axis for readability (D₀ is the same for all these systems). Red lines are power-law fits and quantify the scaling behavior of D(t) in the anomalous diffusion transient. Fcc ordered hard sphere arrangements at packing ratio less than its maximum value reached at a closed packed geometry, i.e. for φ < 0.74, were obtained by decreasing the diameter α of the spheres and letting their centers lie on the fcc lattice points. The three diffusion regimes are clearly distinguishable for both ordered and disordered systems: free diffusion for t < 10 in simulation units (a time simulation unit correspond to ≈2μs); transient anomalous diffusion when in the case of ordered systems and in case of disordered systems; hindered diffusion in tortuosity limit for t > 10⁵.