Slow Dynamics and Aging of a Colloidal Hard Sphere Glass

The intermediate scattering function (ISF) is measured for a colloidal hard-sphere glass as functions of the scattering vector and waiting time. For scattering vectors near the structure factor peak, we show that the ISF and the stretching index, defined at the crossover time between the fast and slow processes, depend algebraically on the waiting time. By contrast, the Debye-Waller factor is independent of the waiting time.

Figure 1

(a) The ISF for the waiting times indicated, at the structure factor peak ($qR=3.57$). The left inset shows the ISF for a sample age of 10 h at several values of $qR$ around the structure factor peak. The right inset shows the Percus Yevick structure factor for hard spheres along with the nonergodicity parameter from Eq. (2). These values are also shown as the black lines in the left inset and the main graph. (b) $f(q,{\tau }_{\max };t_w)$ (closed symbols) and $f(q,{\tau }_m)$ (open symbols) as functions of the waiting time for several values of $qR$. ${\tau }_{\max }\sim 4\times {10}^5$ is the upper limit of the time window. Lines are power law fits to the data. The nonergodicity parameters, $f(q,\infty )$, obtained from Eq. (2), are shown as horizontal lines.

Figure 2

(a) The width function [Eq. (3)] as a function of delay time at $qR=3.57$ for the waiting times indicated. Inset: $n(q,\tau )$ [Eq. (4)] in the echo DLS range, where the inflection is observed. The minima are indicated by the filled symbols. (b) The stretching index as a function of the waiting time for several scattering vectors. Inset shows the Percus Yevick structure factor. The prefactors of the power law fit are also represented in this inset. Except where indicated the error bars are smaller than the symbols.

Figure 3

The current correlator [Eq. (5)] as a function of delay time at two $q$ vectors and a range of waiting times. The $qR=2.01$ data have been offset for clarity. Inset: four $q$ vectors at two different waiting times (offset for clarity). Best fitting straight lines are shown.