Branching of Colloidal Chains in Capillary-Confined Nematics

We report on the observation of colloidal chain assembly and branching inside capillaries filled with a nematic liquid crystal. Because of the homeotropic anchoring of liquid crystalline molecules on the capillary and colloidal droplet surfaces, the assembly of droplets along the capillary axis is expected, producing a transformation of the nematic director field from an escape-radial to quasiradial configuration. However, the subsequent over time branching of the straight colloidal chains is counterintuitive. By numerical simulations, we demonstrate that chain branching can occur by overcoming an energy barrier and can at least dwell as a metastable configuration. Moreover, manipulation of colloidal chains by electric fields and their gradients demonstrates various regimes of chain behavior in electric fields.

Figure 1

(a) Microscope images of the structure in white light and between cross polarizers. The directions of polarizers are indicated. (b) The tip and the end of a droplet chain showing that the companion defects are positioned under the droplets.

Figure 2

(a) A chain with two close branches. Branching of chains is observed after an equilibration time of $\sim 1\mathrm{week}$. (b) A region of branched chain in white light and between cross polarizers. The directions of polarizers are indicated.

Figure 3

Numerical results. Free energy is determined within $\pm 5\%$ precision. (a) The elastic free energy $F$ of a straight 5 droplet segment as a function of lateral shift of one of the middle droplets. Note that the central droplet (large arrow), upper and lower neighbor droplets (small arrows), and all 4 neighbor defects were shifted at the same time. When the central droplet was shifted, for example, by 4 units, the upper (lower) neighbor defect was shifted by 3 units, the upper (lower) neighbor droplet by two units, and upper (lower) second-neighbor defect by one unit. (b) Dependence of $F$ for a branched 5 droplet configuration on the radial position of off-chain droplet. To satisfy the equal volume requirement, an escaped-radial elastic free energy $F_{\mathrm{esc}}=3\pi Kd$ was added to $F$. (c) Elastic free energy as a function of the chain and off-chain droplet pair shift in radial direction. The distance $d$ between the chain and off-chain droplets was fixed. Analogous to (b), $F_{\mathrm{esc}}$ was added.

Figure 4

(a) Most commonly observed droplet chain behavior in electric field ( $2\mathrm{V}/\mu \mathrm{m}$), which is perpendicular to the plane of observation. The time elapsed from the beginning of field application is indicated in seconds. The front shown by an arrow propagating down the capillary corresponds to the transition from the zero DL regime at earlier time to a DL regime at later time. Note that this transition happens at least 10 times faster than the chain movement in earlier time frames. (b) Cross-sectional view of different regimes of chain motion. Filled circle represents a chain, small circles represent $\pm 1/2$ DLs, and LC director orientation is shown by solid lines. The direction of chain motion is indicated by arrows.