Nematic-Smectic Transition under Confinement in Liquid Crystalline Colloidal Shells

We carry out the first study of smectic liquid crystalline colloidal shells and investigate how their complex internal structure depends on the director configuration in the nematic phase, preceding the smectic phase on cooling. Differences in the free energy cost of director bend and splay give an initial skewed distribution of topological defects in the nematic phase. In the smectic phase, the topological and geometrical constraints of the spherical shell imposed on the developing 1D quasi-long-range order create a conflict that triggers a series of buckling instabilities. Two different characteristic defect patterns arise, one driven by the curvature of the shell, the other by the strong nonuniformities in the director field in the vicinity of the topological defects.

Figure 1

Geometry of the liquid crystal (LC) shell and the water/glycerol ($w+g$) inner phase.

Figure 2

$N$-SmA transition in a planar-aligned shell ($R\approx 100\mu \mathrm{m}$, $\overline{h}\approx 4\mu \mathrm{m}$). In (a)–(h) the focus is on the thin shell side, where the defects are concentrated, thus the initial signs of the transition (e)–(g)—starting on the thick side—are blurry. In (i) the focus is on the thick side. Drawings (b) and (c) sketch $\mathbf{n}(\mathbf{r})$ corresponding to (a) on the thin and thick sides, respectively.

Figure 3

Planar-aligned shell ($R\approx 350\mu \mathrm{m}$, $\overline{h}\approx 10\mu \mathrm{m}$) in its nematic phase (a) and during the very initial stage of the $N$-SmA transition (b-f). The focus is on the thicker side of the shell, where the transition starts.

Figure 4

(a) Smectic layering in a curved shell poses problems for retaining the smectic layer thickness, which can be solved by dislocations (upper path) or layer buckling (lower path). (b) Sketch of how the effective layer distance along a cut can increase from $a_0$ at the inside to $a_1>a_0$ at the outside through a gradually increasing layer undulation.

Figure 5

$N$-SmA transition in a planar-aligned shell ($R\approx 100\mu \mathrm{m}$, $\overline{h}\approx 3\mu \mathrm{m}$), followed until steady state. Drawings (c) and (f) sketch $\mathbf{n}(\mathbf{r})$ for states (b) and (e). The focus is initially on the thin defect-rich shell side; thus, the first signs of the transition—starting on the thick side—are blurry (b). In (h) and (i) (no analyzer) the focus is on the thick shell side.