Novel Defect Structures in Nematic Liquid Crystal Shells

We use double-emulsion drops to experimentally investigate the defect structures of spherical shells of nematic liquid crystals. We uncover a rich scenario of coexisting defect structures dictated by the unavoidable finite thickness of even the thinnest shell and by the thickness variation around the sphere. These structures are characterized by a varying number of disclination lines and pairs of surface point defects on the inner and outer surfaces of the nematic shell. In the limit of very thick shells the defect structure ultimately merges with that of a bulk nematic liquid crystal drop.

Figure 1

Bright field (a)–(c) and cross-polarized (d)–(f) images of a density matched nematic shell. The inner fluid consists of a solution of ${\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{D}}_2\mathrm{O}+\mathrm{PVA}$ (1 wt%), the middle fluid is the liquid crystal, and the outer fluid is ${\mathrm{H}}_2\mathrm{O}+\mathrm{PVA}$ (1 wt%). Drop sizes are $2a=93\mu \mathrm{m}$ and $2R=206\mu \mathrm{m}$. As the microscope focal plane is lowered, the upper (a), (d), intermediate (b),(e), and lower boojums (c),(f) can be identified. (g) Schematic of the director field configuration. (h), (i) are magnifications of the inner drop in (e), (f) after some rotation; this allows better visualization of the defects. The lower pair of boojums cannot be resolved with optical microscopy and thus appears as one.

Figure 2

Displacement of the inner drop driven by the elastic forces of the nematic liquid crystal: (a) $t=0\mathrm{s}$; (b) $t=13\mathrm{s}$; (c) $t=55\mathrm{s}$. $2a=53\mu \mathrm{m}$. $2R=234\mu \mathrm{m}$. (d) Within the experimentally observed range, the motion is uniform along the axis joining the two pair of boojums. (e) A trial texture for the nematic director in the experimental situation depicted in (a)–(c). The graph is a plot of the normalized energy, $E/(KR)$, vs $r/R$.

Figure 3

Three type of thin shells commonly observed, distinguished by the number and type of defects: (a),(b) Four defects, (c),(d) two defects, and (e),(f) three defects. For all shells $2a=103\mu \mathrm{m}$ and $2R=110\mu \mathrm{m}$.

Figure 4

Buoyancy driven motion of the inner drop in a nematic shell with four disclinations. $2a=191\mu \mathrm{m}$ and $2R=204\mu \mathrm{m}$. (a)–(c) are schematic visualizations of the defect motion. The inner drop moves along the direction of gravity, toward the midpoint of the arc connecting $C$ and $C^{\prime }$. The defects are first distributed throughout the shell and migrate in time to the top of the shell, ending in the final configuration shown in Fig. 3a, 3b. (d)–(g) are cross-polarized images showing the time evolution of the defects motion: (d) $t=0$; (e) $t=70\mathrm{s}$; (f) $t=90\mathrm{s}$; (g) $t=110\mathrm{s}$. The plane of focus is always at the top of the double-emulsion drop. At approximately zero time, the other two-defect locations are shown in the cross-polarized images (h),(i). The particular defect configuration allows clear visualization of the disclination lines, as shown in the corresponding magnified images.