Slow dynamics of supercooled colloidal fluids: spatial heterogeneities andnonequilibrium density fluctuations

The coupled diffusion equations recently proposed by Tokuyama for concentra ted hard-sphere suspensions are numerically solved, starting from nonequili brium initial configurations. The most important feature of those equations is that the self-diffusion coefficient D-S(Phi) becomes zero at the glass transition volume fraction phi(g) as D-S(Phi)similar to D-0\1-Phi(x,t)/phi( g)\(y) with y = 2 where Phi(x,t) is the local volume fraction of colloids, D-0 the single-particle diffusion constant, and phi(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 smal l initial disturbances can be enhanced by this anomaly near phi(g), leading to long-lived, spatial heterogeneities. Those heterogeneities are responsi ble for the slow relaxation of nonequilibrium density fluctuations. in fact , the self-intermediate scattering function is shown to obey a two-step rel axation around the beta-relaxation time t(beta)similar to\1-phi/phi(g)\(-1) , and also to be well approximated by the Kohlrausch-Williams-Watts functio n with an exponent beta around the alpha-relaxation time t(alpha)similar to \1-phi/phi(g)\(-n), where eta = gamma/beta, and phi is the particle volume fraction. Thus, the nonexponential alpha relaxation is shown to be explaine d by the existence of long-lived, spatial heterogeneities. (C) 1999 Elsevie r Science B.V. All rights reserved.