Aging of rotational diffusion in colloidal gels and glasses

We study the rotational diffusion of aging Laponite suspensions for a wide range of concentrations using depolarized dynamic light scattering. The measured orientational correlation functions undergo an ergodic to nonergodic transition that is characterized by a concentration-dependent ergodicity-breaking time. We find that the relaxation times associated with rotational degree of freedom as a function of waiting time, when scaled with their ergodicity-breaking time, collapse on two distinct master curves. These master curves are similar to those previously found for the translational dynamics; the two different classes of behavior were attributed to colloidal gels and glasses. Therefore, the aging dynamics of rotational degree of freedom provides another signature of the distinct dynamical behavior of colloidal gels and glasses.

Figure 1

Evolution of polarized (VV) and depolarized (VH) intensity correlation functions (symbols) and their corresponding fits (solid lines) to Eq. (4) (a) for a glass (Laponite 3.2 wt$\%$, pure water) and (b) for a gel (Laponite 1.2 wt$\%$, pure water) measured at a scattering angle of ${90}^{\mathrm{o}}$. The waiting times are shown in the legends. Note that here only the correlations in the ergodic regime of aging are fitted. The ergodicity-breaking times are: $t_{\mathrm{eb}}=340$ min for Laponite 3.2 wt$\%$ and $t_{\mathrm{eb}}=18$ days for Laponite 1.2 wt$\%$.

Figure 2

Evolution of fast (${\tau }_1$) and slow (${\tau }_2$) relaxation times and the stretching exponents $\beta$ of VV and VH correlation functions plotted versus scaled waiting time $t_w/t_{\mathrm{eb}}$ for a glass (Laponite 3 wt$\%$, pure water, $t_{\mathrm{eb}}=450$ min) and a gel (Laponite 1.2 wt$\%$, pure water, $t_{\mathrm{eb}}=26000$ min). The lines show the fits of relaxation times with the general form ${\tau }_i\left(t_w\right)={\tau }_0\exp \left(B\frac{t_w}{t_w^{\infty }-t_w}\right)$ [14].

Figure 3

Short-time translational and rotational diffusion coefficients normalized to their values at $t_w\approx 0$ as a function of scaled aging time $t_w/t_{\mathrm{eb}}$ (a) in a glass of Laponite C $=$ 3 wt$\%$ and (b) in a gel of Laponite C $=$ 1.2 wt$\%$.

Figure 4

The orientational correlation functions defined as $f_{\mathrm{VH}}/f_{\mathrm{VV}}$ at different waiting times in a glass (Laponite 3 wt$\%$, pure water) and a gel (Laponite 1.2 wt$\%$, pure water). The lines show the fits with the sum of single and stretched exponential as in Eq. (4).

Figure 5

The orientational and translational relaxation times versus scaled waiting time measured for a Laponite suspension of (a) $C=3$ wt$\%$ (glass) and (b) $C=1.2$ wt$\%$ (gel).

Figure 6

The evolution of (a) the slow relaxation time normalized to its initial value ${\tau }_2/{\tau }_0$ and (b) the stretching exponent $\beta$ of VH correlations versus scaled waiting time $t_w/t_{\mathrm{eb}}$ for different Laponite samples. The colloid concentrations are shown in the legend. Similar to the translational degree of freedom, the samples can be divided into two groups according to the evolution of the slow relaxation times of VH correlations. In both figures the open symbols correspond to gels, the filled symbols to the glass. In panel (a) the solid and dashed line correspond to the glass and gel lines obtained from growth of relaxation time of translational diffusion.

Figure 7

The short time rotational diffusion coefficients normalized to those of infinitely diluted hard disks of radius $R=15$ nm: $D_0^r$.