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 Tc. We calculate the ensemble independent susceptibility χ4(τα) and the dynamic correlation length ξ4(τα) at the α-relaxation time τα. We also examine in detail the temperature dependence of τα and the diffusion coefficient D. For higher temperatures, we find that the standard Stokes-Einstein relationship, [12pt]{minimal}{document}D ~ τ _α ⁻¹{document}D∼τα−1, holds, but at lower temperatures a fractional Stokes-Einstein relationship, [12pt]{minimal}{document}D ~ τ _α -σ{document}D∼τα−σ with σ = 0.65, emerges. By examining the relationships between τα, D, χ4(τα), and ξ4(τα) we determine that the emergence of the fractional Stokes-Einstein relationship is accompanied by a dynamic crossover from [12pt]{minimal}{document}τ _α ~ ek₂ ξ ₄{document}τα∼ek2ξ4 at higher temperatures to [12pt]{minimal}{document}τ _α ~ e^k₁ ξ ₄3/2{document}τα∼ek1ξ43/2 at lower temperatures.