Elasticity-Mediated Self-Organization and Colloidal Interactions of Solid Spheres with Tangential Anchoring in a Nematic Liquid Crystal

Using laser tweezers, we study colloidal interactions of solid microspheres in the nematic bulk caused by elastic distortions around the particles with tangential surface anchoring. The interactions overcome the Brownian motion when the interparticle separation ${\overrightarrow{\mathbf{r}}}_p$ is less than 3 particle diameters. The particles attract when the angle $\theta$ between ${\overrightarrow{\mathbf{r}}}_p$ and the uniform far-field director ${\widehat{\mathbf{n}}}_0$ is between 0° and $\approx 70°$ and repel when $75°\lesssim \theta \le 90°$. The particles aggregate in chains directed at $\approx 30°$ to ${\widehat{\mathbf{n}}}_0$ and, at higher concentrations, form complex kinetically trapped structures.

Figure 1

Colloidal aggregation in the nematic bulk: (a) FCPM texture of the director distortions around a pair of particles; (b) FCPM image of director distortions in the LC colocalized with the fluorescence signal from particles (green) forming chains at $\theta \approx 30°$ to ${\widehat{\mathbf{n}}}_0$; (c) scheme of the director distortions around the spheres in chains; (d) FCPM vertical cross sections along the $d\mathrm{\text{−}}d$ line in (b) illustrating that the particle chains (green, fluorescence from rhodamine-B) are located in the bulk of LC (gray scale, BTBP); (e) aggregation of spheres leading to kinetically trapped network that reflects anisotropy of the host even at high particle concentration $\approx 5\mathrm{wt}.\%$; (f) scheme of chain orientations. The FCPM polarization is perpendicular to ${\widehat{\mathbf{n}}}_0$ in (a),(b) and along the chain in (d).

Figure 2

Trajectories of particle pairs in the LC: (a) both particles are released from the optical traps at different locations (labeled by pairs of numbers 1 through 8; the trajectories of the two particles released at the same time are marked by the same color); (b) one particle is fixed and the other is released from a semicircle of radius $r_p\approx 7.5\mu \mathrm{m}$ at different $\theta$.

Figure 3

Angular dependence of the center-to-center distance $r_p$ between two particles measured when one trap moves around the other trap along a circle of a radius $r_t$.

Figure 4

Angular dependencies of ${\overrightarrow{\mathbf{F}}}_p$ for two MR particles in the LC: (a) $F_p(\theta )$ measured for $r_p=1.5D$ (triangles), $r_p=1.75D$ (squares), and $r_p=2D$ (circles); (b) the angle $\gamma$ between ${\overrightarrow{\mathbf{F}}}_p(\theta )$ and ${\overrightarrow{\mathbf{r}}}_p$ as a function of $\theta$; (c) vector representation of ${\overrightarrow{\mathbf{F}}}_p$ as determined experimentally for $r_p=1.5D$ and $r_p=2.5D$ and calculated for $r_p\gg D$ using (1).

Figure 5

$F_p$ vs $r_p$ measured for $\theta \approx 30°$. The solid lines are plots of $F_p=148(D/r_p{)}^6\mathrm{pN}$. The inset is the log-log plot of the same data.