Shape-Induced Dispersion of Colloids in Anisotropic Fluids

We experimentally study the behavior of micrometer-sized prolate ellipsoidal particles dispersed in a nematic liquid crystal. The latter is an aqueous solution of rodlike micelles. When embedded into such a solvent, ellipsoids with small enough aspect ratios aggregate to form anisotropic structures oriented at an angle with respect to the local background director (as already observed for spheres). This is, however, no longer the case when the aspect ratio reaches a well-defined value: above that value, the ellipsoids remain well dispersed and apparently do no interact with each other, even over very long periods of time (several months). Therefore, there exists a transition from an aggregated to a nonaggregated state as a function of aspect ratio and for a given particle concentration. This behavior has not been predicted so far and we put forward simple calculations to rationalize our observations.

Figure 1

(a) Aggregation of PS spheres in a lyotropic calamitic nematic phase ($N_C$). The clusters are typical of quadrupole–quadrupole interactions in the case of planar anchoring (see inset). Scale: $25\mu \mathrm{m}$. (b) High-$k$ PS ellipsoids (aspect ratio $k=8.3$) dispersed in the same $N_C$ phase. The ellipsoids remain isolated and are aligned along the background director field $\mathbf{n}$. Scale: $25\mu \mathrm{m}$. Inset: Schematic of the director field distortions around an ellipsoid. (c) Typical structures formed by mixtures of spheres (diameter $2\mu \mathrm{m}$) and high-$k$ ellipsoids. Scale: $5\mu \mathrm{m}$.

Figure 2

Small-$k$ ellipsoids (here, $k=3$) embedded in the $N_C$ phase. Aggregation occurs. Double arrow: Director field orientation. Scale: $25\mu \mathrm{m}$. Inset: Zoomed in view of a typical cluster oriented at an angle with respect to the local director field $\mathbf{n}$. Scale: $5\mu \mathrm{m}$.

Figure 3

(a) Normalized elastic free energy $\tilde{F}$ as a function of aspect ratio $k$. Comparison between the full calculation and the dimensional analysis. (b) Computed contour plots of $\Theta (r,\theta )$ (in radians) for a sphere and an ellipsoid with $k=5$. The far-field director is aligned along the $x$ axis. The color bar is common to both plots. The figures 0.11 locate the contour line for which $\Theta =0.11\mathrm{rad}$ with respect to the $x$ axis. Strong planar anchoring is assumed in all cases.

Figure 4

Pair interaction potential $U(d,\theta )$ as a function of $\theta$ (see scheme in the inset) for a pair of particles with various aspect ratios. The particles are maintained at a fixed surface-to-surface distance $d$ close to contact ($d/R=0.4$). The arrow indicates the shift of the attractive well as $k$ increases.