Analysis of a growing dynamic length scale in a glass-forming binary hard-sphere mixture

Abstract

We examine a length scale that characterizes the spatial extent of heterogeneous dynamics in a glass-forming binary hard-sphere mixture up to the mode-coupling volume fraction phi_c. First, we characterize the system's dynamics. Then, we utilize a new method [Phys. Rev. Lett. 105, 217801 (2010)] to extract and analyze the ensemble independent dynamic susceptibility chi_4(t) and the dynamic correlation length xi(t) for a range of times between the beta and alpha relaxation times. We find that in this time range the dynamic correlation length follows a volume fraction independent curve xi(t) ~ ln(t). For longer times, xi(t) departs from this curve and remains constant up to the largest time at which we can determine the length accurately. In addition to the previously established correlation tau_alpha ~ exp[xi(tau_alpha)] between the alpha relaxation time, tau_alpha, and the dynamic correlation length at this time, xi(tau_alpha), we also find a similar correlation for the diffusion coefficient D ~ exp[xi(tau_alpha)^theta] with theta approximately 0.6. We discuss the relevance of these findings for different theories of the glass transition.

References in corpus (14)

• Probing the equilibrium dynamics of colloidal hard spheres above the mode-coupling glass transition
• Inhomogeneous Mode-Coupling Theory and Growing Dynamic Length in Supercooled Liquids
• Growing length and time scales in glass forming liquids
• Spatial correlations in the dynamics of glassforming liquids: Experimental determination of their temperature dependence
• Spontaneous and induced dynamic fluctuations in glass-formers I: General results and dependence on ensemble and dynamics
• The glass transition of dense fluids of hard and compressible spheres
• Spontaneous and induced dynamic correlations in glass-formers II: Model calculations and comparison to numerical simulations
• Evidence of growing spatial correlations at the glass transition from nonlinear response experiments
• Lengthscale dependence of dynamic four-point susceptibilities in glass formers
• Dynamic heterogeneity in a glass forming fluid: susceptibility, structure factor and correlation length
• Equilibrium equation of state of a hard sphere binary mixture at very large densities using replica exchange Monte-Carlo simulations
• Diverging length scale of the inhomogeneous mode-coupling theory: a numerical investigation
• Direct measurements of the dynamical correlation length indicate its divergence at an athermal glass transition
• Divergent four-point dynamic density correlation function of a glassy colloidal suspension: a diagrammatic approach

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