Stochastic qualifier of gel and glass transitions in laponite suspensions

The existence of the important similarities between gelation and glass transition makes it hard to distinguish between the two types of nonergodic states experimentally. Here, we report on a stochastic analysis of the scattered light intensity through a colloidal particles suspension during the gel and glass formation. In this analysis, we exploit the methods developed for complex hierarchical systems, such as turbulence. Using the multiplicative log-normal cascade models, we provide a criterion to distinguish gels from glasses.

Figure 1

(Color online) Intensity of light scattering during the gelation process. Inset: the time series for the $I\left(t+1\right)-I\left(t\right)$. In this paper, we express intensities in terms of the detector count rate in kHz.

Figure 2

(Color online) Continuous deformation of the increments’ PDFs for the data sets (a) just after preparation of sample $\left(t_w=80\text{min}\right)$ in the low viscose phase and (b) during the appearance of viscoelastic phase $\left(t_w=610\text{min}\right)$ (here glass system) for $s=5$, 10, 20, and 40 ms (from top to bottom). Solid curves are the PDFs based on Eq. (3), while dashed curves are the Gaussian PDF. For clarity, the PDFs are shifted in the vertical directions.

Figure 3

(Color online) Scale dependence of ${\lambda }_s^2$ vs log $s$ for ergodic regime, (a) gel samples and (b) glass samples.

Figure 4

(Color online) The local temporal dependence of ${\lambda }_s^2$ for various gel and glass samples in ergodic regime. Here, $t_W$ and $t_{eb}$ are waiting time and ergodic breaking time scales, respectively. The average value of ${\lambda }_s^2$ for glass samples are higher than its value for gel samples. It means that the PDF of light intensity increments has more deviation from Gaussian tails for glass samples.

Figure 5

(Color online) Scale-dependence of the subtracted fitting parameter for nonergodic regime (gel and glass samples), ${\lambda }_s^2-{\lambda }_s^2\left(rot\right)$ of the Castaing parameter versus scale $s$ for different waiting time $t_w$. They show that the values of parameter ${\lambda }_s^2-{\lambda }_s^2\left(rot\right)$ for the gel systems are smaller than those for the glass systems.

Figure 6

(Color online) The ensemble average of $⟨{\lambda }_s^2-{\lambda }_s^2\left(rot\right)⟩$ as a function of Laponite concentration.