Novel Defect Structures in a Strongly Confined Liquid-Crystalline Blue Phase

In our numerical study based on a phenomenological description of strongly confined liquid crystalline blue phase I (BP I), we find several novel structures characterized by specific configurations of topological disclination lines. The thickness of the system is of the order of the dimension of the unit cell of the bulk BP I, and the confining surfaces adopts homeotropic anchoring. The structures include an array of double-helix disclination lines accompanied by an orthorhombic lattice of double-twist cylinders, and two parallel arrays of winding disclination lines almost perpendicular to each other.

Figure 1

Various (meta)stable structures of disclination lines. Shaded planes represent confining surfaces. The view directions are along (top) and perpendicular to (bottom) the confining surfaces. The parameters used are $w=0.5$ (for all the figures), $d=10$ (a and e), and $d=14$ (b, c, and d). Here we show a “unit structure”, in which four faces other than the confining surfaces are periodic boundaries. For reference, we also present the structure of the bulk BP I in (f). Note that the distance of the viewpoint from the center of those structures are the same for all the figures, and therefore the dimensions of the figures reflect the actual size of the unit structures.

Figure 2

Plots of the free energy $\mathcal{F}$ as a function of the system thickness $d$ for $w=(\mathrm{a})0.1$, (b) 0.5, and (c) 2.5. The legends in (a) are common for all graphs, and the labels (a)–(e) in the legends correspond to those in Fig. 1. In (c), we also indicate by an arrow the dimension of the unit structure of a bulk BP I (12.60).

Figure 3

(a) Orientation profiles at three given cross sections for the structure in Fig. 1c. The locations of the three cross sections are also shown. The positions of disclinations and axes of double-twist cylinders are indicated by crosses (×) and open circles (○), respectively. (b) Schematic illustration of the arrangement of double-twist cylinders with respect to the disclination lines.