Gels and Glasses in a Single System: Evidence for an Intricate Free-Energy Landscape of Glassy Materials

In the free-energy landscape picture of glassy systems, their slow dynamics is due to a complicated free-energy landscape with many local minima. We show that for a colloidal glassy material multiple paths can be taken through the free-energy landscape. The evolution of the nonergodicity parameter shows two distinct master curves that we identify as gels and glasses. We show that for a range of colloid concentrations, the transition to nonergodicity can occur in either direction (gel or glass), accompanied by “hesitations” between the two. Thus, colloidal gels and glasses are merely global free-energy minima in the same free-energy landscape, and the paths leading to these minima can be complicated.

Figure 1

Intermediate scattering function for increasing waiting times (from left to right) $t_a=1$, 49, 71, 80, 85, 89, 91, 99, 112, 141 days for $C=0.2\mathrm{wt}\%$ (a) and $t_a=7$, 40, 54, 71, 86, 113, 260, 1356 min for $C=3.5\mathrm{wt}\%$ (b). The lines are fits. The insets show the distribution of relaxation times obtained directly from the correlation functions by a constrained regularization method (ALV-NonLin software data analysis) at an early stage of aging and just before ergodicity breaking ($t_a=7$ and 80 days for $C=0.2\mathrm{wt}\%$ and $t_a=7$ and 54 min for $C=3.5\mathrm{wt}\%$).

Figure 2

(a) Evolution of the nonergodicity parameter $f(q,\infty )$ for different samples. The samples can be divided into two groups according to the evolution of nonergodicity parameters. In both figures (and the following ones), the open symbols correspond to gels, the filled symbols correspond to the glass. (b) The ergodicity-breaking time as a function of concentration.

Figure 3

The evolution of short-time translational diffusion normalized to its initial value ($t_a\approx 0$) as a function of $t_a/t_{\mathrm{eb}}$.

Figure 4

(a) The ratio ${\tau }_2/{\tau }_1$ and (b) nonergodicity parameter as a function of scaled aging time $t_a/t_{\mathrm{eb}}$. These samples behave like a glass at the early stages of aging and after $t_a/t_{\mathrm{eb}}\approx 1.2$ they evolve as gels. The full lines show the glassy and dotted lines show the gel line, obtained by averaging over all the samples measured.

Figure 5

(a) Scattered intensity as a function of aging time. We have normalized the intensity to its value at the beginning of aging. (b) The scattered intensity as a function of dimensionless wave vector $qR$ for several Laponite concentrations. To compare the $q$ dependence of different samples, we normalized the data to their value at highest measured $qR=0.38$.