Glass Transitions in Quasi-Two-Dimensional Suspensions of Colloidal Ellipsoids

We observed a two-step glass transition in monolayers of colloidal ellipsoids by video microscopy. The glass transition in the rotational degree of freedom was at a lower density than that in the translational degree of freedom. Between the two transitions, ellipsoids formed an orientational glass. Approaching the respective glass transitions, the rotational and translational fastest-moving particles in the supercooled liquid moved cooperatively and formed clusters with power-law size distributions. The mean cluster sizes diverge in power law as they approach the glass transitions. The clusters of translational and rotational fastest-moving ellipsoids formed mainly within pseudonematic domains and around the domain boundaries, respectively.

Figure 1

(a) The self-intermediate scattering function $F_s(q,t)$ at $q_m=2.3\mu {\mathrm{m}}^{-1}$ and (b) the orientational correlation $L_4(t)$ for different area fractions. (c) The exponent $\beta$ of the fitting function $e^{-(t/\tau {)}^{\beta }}$ for the long-time $F_s(q_m,t)$ and $L_4(t)$. (d) The fitted relaxation time $\tau (\varphi )\sim ({\varphi }_c-\varphi {)}^{-\gamma }$. Solid symbols: Different choices of $q$ in $F(q,t)$ for the translational motion. Open symbols: Different choices of $n$ in $L_n(t)$ for the orientational motion.

Figure 2

(a) The non-Gaussian parameters of translational displacements along the long axis [${\alpha }_2^{\parallel }(t)$, solid symbols] and the short axis [${\alpha }_2^{\perp }(t)$, open symbols]. $\varphi =0.70,0.74,0.77,0.81$ as labeled in the figures. (b) The non-Gaussian parameters of rotational displacements.

Figure 3

The spatial distributions of the fastest-moving 8% of the particles (labeled in colors) in translational (a),(c),(e) and rotational (b),(d),(f) motions. Ellipsoids in the same cluster have the same color. (a),(b) The same frame at $\varphi =0.70$ (supercooled liquid); (c),(d) the same frame at $\varphi =0.77$ (orientational glass); (e),(f) the same frame at $\varphi =0.81$ (glass) with $\sim 5500$ particles.

Figure 4

The probability distribution functions for the cluster size of (a) translational and (b) rotational fastest-moving particles. The lines are the best fits of $P(N_c)\sim N_c^{-\mu }$. (c) The fitted exponents ${\mu }^{\theta }$ for rotational motions and ${\mu }^T$ for translational motions. The vertical dotted and dashed lines represent the glass transitions for rotational and translational motions, respectively. (d) The weighted mean cluster size $⟨N_c⟩\sim ({\varphi }_c-\varphi {)}^{-\eta }$, where ${\varphi }_c^{\theta }=0.71$ and ${\varphi }_c^T=0.79$.