Slow dynamics of supercooled colloidal fluids: spatial heterogeneities and nonequilibrium density fluctuations

Abstract

The coupled diffusion equations recently proposed by Tokuyama for concentrated hard-sphere suspensions are numerically solved, starting from nonequilibrium initial configurations. The most important feature of those equations is that the self-diffusion coefficient D S ( Φ) becomes zero at the glass transition volume fraction φ g as D S ( Φ)∼ D 0|1− Φ( x , t)/ φ g | γ with γ=2 where Φ( x , t) is the local volume fraction of colloids, D 0 the single-particle diffusion constant, and φ g=( 4 3 ) 3/(7 ln 3−8 ln 2+2) . This dynamic anomaly results from the many-body correlations due to the long-range hydrodynamic interactions. Then, it is shown how small initial disturbances can be enhanced by this anomaly near φ g , leading to long-lived, spatial heterogeneities. Those heterogeneities are responsible for the slow relaxation of nonequilibrium density fluctuations. In fact, the self-intermediate scattering function is shown to obey a two-step relaxation around the β-relaxation time t β ∼|1− φ/ φ g | −1, and also to be well approximated by the Kohlrausch–Williams–Watts function with an exponent β around the α-relaxation time t α ∼|1− φ/ φ g | − η , where η= γ/ β, and φ is the particle volume fraction. Thus, the nonexponential α relaxation is shown to be explained by the existence of long-lived, spatial heterogeneities.