Probing the Equilibrium Dynamics of Colloidal Hard Spheres above the Mode-Coupling Glass Transition

We use dynamic light scattering and computer simulations to study equilibrium dynamics and dynamic heterogeneity in concentrated suspensions of colloidal hard spheres. Our study covers an unprecedented density range and spans seven decades in structural relaxation time, ${\tau }_{\alpha }$, including equilibrium measurements above ${\phi }_c$, the location of the glass transition deduced from fitting our data to mode-coupling theory. Instead of falling out of equilibrium, the system remains ergodic above ${\phi }_c$ and enters a new dynamical regime where ${\tau }_{\alpha }$ increases with a functional form that was not anticipated by previous experiments, while the amplitude of dynamic heterogeneity grows slower than a power law with ${\tau }_{\alpha }$, as found in molecular glass formers close to the glass transition.

Figure 1

Time dependence of the self-intermediate scattering function $F_s(q,t)$ in DLS experiments at $q\sigma =6.5$ for representative volume fractions. Lines are stretched exponential fits to the final decay, yielding relaxation times spanning about 7 decades. Ergodicity is preserved above the (avoided) MCT glass transition at ${\phi }_c\approx 0.59$.

Figure 2

(a) Relaxation time scale ${\tau }_{\alpha }$ for hard spheres in experiments (black circles) and simulations (open triangles), respectively, in units of ${\tau }_0=1\sec$ and ${\tau }_0=7\times {10}^4$ MC steps. The red dashed line is a power law fit, Eq. (1), with ${\phi }_c=0.590$ (vertical dotted line) and $\gamma =2.5\pm 0.1$. The continuous blue line is a fit to DLS data using Eq. (2), with ${\phi }_0=0.637$ and $\delta =2$. The zoom in the inset shows that the MCT singularity is absent. (b) Same data plotted against $1/(1-\phi /{\phi }_c)$. A straight line with slope $\gamma$ is obtained in an MCT regime covering almost 3 decades in ${\tau }_{\alpha }$. (c) Data for $\phi >0.41$ plotted using reduced variables with ${\phi }_0=0.637$ and 0.641 for experiments and simulations, respectively.

Figure 3

Peak of dynamic susceptibilites, Eq. (4), measured in (a) simulations and (b) experiments. In (a) both contributions to ${\chi }_4$ are compared, validating ${\chi }_{\phi }$ as a valuable tool to quantify dynamic heterogeneity in hard spheres. The predicted MCT algrebraic divergence (red dashed line) holds over a small density range. The inset shows that the size of dynamic heterogeneities grows slower than a power law at large ${\tau }_{\alpha }$, as found in molecular glass formers.