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

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 DS(Φ) becomes zero at the glass transition volume fraction φg as DS(Φ)∼D0|1−Φ(x,t)/φg|γ with γ=2 where Φ(x,t) is the local volume fraction of colloids, D0 the single-particle diffusion constant, and φg=(43)3/(7ln3−8ln2+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 φg, 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 tβ∼|1−φ/φg|−1, and also to be well approximated by the Kohlrausch–Williams–Watts function with an exponent β around the α-relaxation time tα∼|1−φ/φg|−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.