Glasslike Arrest in Spinodal Decomposition as a Route to Colloidal Gelation

Colloid-polymer mixtures can undergo spinodal decomposition into colloid-rich and colloid-poor regions. Gelation results when interconnected colloid-rich regions solidify. We show that this occurs when these regions undergo a glass transition, leading to dynamic arrest of the spinodal decomposition. The characteristic length scale of the gel decreases with increasing quench depth, and the nonergodicity parameter exhibits a pronounced dependence on scattering vector. Mode coupling theory gives a good description of the dynamics, provided we use the full static structure as input.

Figure 1

Wave vector dependence of the static structure factor for $U/k_{B}T=2.46$ (dashed line), 2.62 (dashed-dot line), 2.89 (○), 3.06 (△), and 3.85 (◇). The solid line corresponds to the hard-sphere $S(q)$ expected at $\varphi =0.25$. Inset: $U$ dependence of $\Delta S_m$, defined as the difference between the value of $S(q)$ at the nearest-neighbor peak and that at the minimum at $qa\sim 1$. The dotted line denotes the point at which the particle-particle position becomes highly correlated. A sharp peak appears concurrently at low $q$.

Figure 2

Images obtained by CARS microscopy: $U/k_{B}T=2.46$ (top left); $U/k_{B}T=2.89$ (top right); $U/k_{B}T=3.06$ (bottom left); $U/k_{B}T=3.85$ (bottom right). The dotted line between the two upper images denotes the boundary beyond which long-lasting, space-filling structures are observed. The scale bars correspond to $10\mu \mathrm{m}$ and the circles to $\pi /q_c$, where $q_c$ is obtained from the small angle SLS data. Inset: Schematic phase diagram for colloid-polymer mixtures as polymer concentration and colloid volume fraction are varied, where the glass transition line is marked (GL). Points denote the approximate location of our samples.

Figure 3

(a) Dynamic structure factor at the $q$ -value of the nearest-neighbor peak for $U/k_{B}T=2.46$ (dashed line), 2.62 (dashed-dot line), 2.89 (○), 3.06 (△), and 3.85 (◇). To account for the increased viscosity due to the added polymer, the time axis is normalized by the ratio of the viscosity of the polymer solution to that of the solvent, $\eta /{\eta }_0$. (b) Dynamic structure factor for $U/k_{B}T=2.89$ obtained at $qa=1.29$ (□), 1.9 (vertical bars), 2.49 (△), 3.03 (○), 3.52 (▽), 4.07 (solid line), and 4.31 (×). The vertical line denotes the $f(q,t)$ values used to approximate the nonergodicity factor $f_c(q)$.

Figure 4

Wave vector dependence of the nonergodicity factor. The symbols are the measured $f_c(q)$. From bottom to top the data are for $U/k_{B}T=2.89$, 3.06, and 3.85. The solid lines are obtained from the MCT calculation using $S(q)$ as input; experimental $S(q)$ at low and high $q$ were smoothed and joined with a spline fit, while at the highest $q$ we use an asymptotic expression for the numerical solution of the PY equation for the Asakura-Oosawa potential, adjusted to match the data. We use values $\tilde{\varphi }=0.37$, 0.52, and 0.50 respectively; the dashed lines are obtained by neglecting the low angle peak.