Dynamic heterogeneities above and below the mode-coupling temperature: evidence of a dynamic crossover

We examine dynamic heterogeneities in a model glass-forming fluid, a binary harmonic sphere mixture, above and below the mode-coupling temperature T(c). We calculate the ensemble independent susceptibility χ4(τ(α)) and the dynamic correlation length ξ4(τ(α)) at the α-relaxation time τ(α). We also examine in detail the temperature dependence of τ(α) and the diffusion coefficient D. For higher temperatures, we find that the standard Stokes-Einstein relationship, D∼τ(α)(-1), holds, but at lower temperatures a fractional Stokes-Einstein relationship, D∼τ(α)(-σ) with σ = 0.65, emerges. By examining the relationships between τ(α), D, χ4(τ(α)), and ξ4(τ(α)) we determine that the emergence of the fractional Stokes-Einstein relationship is accompanied by a dynamic crossover from τ(α)∼e(k2ξ4) at higher temperatures to τ(α)∼e(k1ξ4(3/2)) at lower temperatures.