Ordered Droplet Structures at the Liquid Crystal Surface and Elastic-Capillary Colloidal Interactions

We demonstrate a variety of ordered patterns, including hexagonal structures and chains, formed by colloidal particles (droplets) at the free surface of a nematic liquid crystal (LC). The surface placement introduces a new type of particle interaction as compared to particles entirely in the LC bulk. Namely, director deformations caused by the particles lead to distortions of the interface and thus to capillary attraction. The elastic-capillary coupling is strong enough to remain relevant even at the micron-scale when its buoyancy-capillary counterpart becomes irrelevant.

Figure 1

Two-channel FCPM textures of the vertical cross section of the LC film: (a),(b) a single glycerol droplet at the LC-air interface; (c) a row of droplets that is a part of a hexagonal pattern at the LC-air interface; (d) scheme of forces and interfacial tension vectors at the LC-air interface with a strongly exaggerated meniscus slope; (e) 3D director field in the LC layer. The LC layer (glycerol droplet) is manifested by the high (low) intensity of fluorescent light in parts (a), (c); the contrast is opposite in (b).

Figure 2

Optical microscopy pictures of hexagonal structures at the free surface of the thick nematic layer, $h\approx 60\mu \mathrm{m}$, formed by droplets of different average diameter: (a) $2R\approx 7\mu \mathrm{m}$; (b) $2R\approx 1\mu \mathrm{m}$; (c) arrangement of droplets after the surfactant is added to the nematic layer; (d) droplets separation $r_{eq}$ vs $2R$; the data are compared to the dependence $r_{eq}^{pair}=\gamma ({\sigma }_{\mathrm{L}\mathrm{C}\mathrm{A}}{R}^{2}K/W^2{)}^{1/3}$, where $\gamma =0.43$, $K={10}^{-11}N$, ${\sigma }_{\mathrm{L}\mathrm{C}\mathrm{A}}=3.8\times {10}^{-2}\mathrm{J}/{\mathrm{m}}^2$, $W={10}^{-5}\mathrm{J}/{\mathrm{m}}^2$, see the text; (e) schematic drawing of the director field in the top part of the LC layer.

Figure 3

(a) Optical microscopy textures of glycerol droplets forming chains at the free surface of a thin LC layer, $h\approx (7-10)\mu \mathrm{m}$ and (b) the corresponding director field scheme.