Experimental Insights into the Nanostructure of the Cores of Topological Defects in Liquid Crystals

The nanoscopic structure of the cores of topological defects in anisotropic condensed matter is an unresolved issue, although a number of theoretical predictions have been reported. In the experimental study reported in this Letter, we template the assembly of amphiphilic molecules from the cores of defects in liquid crystals and thereby provide the first experimental evidence that the cores of singular defects that appear optically to be points (with strength $m=+1$) are nanometer-sized closed-loop, disclination lines. We also analyze this result in the context of a model that describes the influence of amphiphilic assemblies on the free energy and stability of the defects. Overall, our experimental results and theoretical predictions reveal that the cores of defects with opposite strengths (e.g., $m=+1$ vs $m=-1$) differ in ways that profoundly influence processes of molecular self-assembly.

Figure 1

(a) Schematic illustration of a pair of apparent point defects with strength $m=+1$ and $-1$ formed in a capillary filled with nematic LC. The inner surface of the capillary caused perpendicular anchoring of the LC. The dashed line illustrates local ordering of mesogens. (b),(d) Polarized light micrographs of point defects and (c),(e) fluorescence micrographs showing the distribution of amphiphiles [DLPC concentrations are $40\mu \mathrm{M}$ in (b),(c) and $47\mu \mathrm{M}$ in (d),(e); the DLPC is mixed with BODIPY-C5 at 3% mol/mol based on DLPC]. The red arrow in (e) indicates the localization of a molecular assembly of DLPC and BODIPY-C5 at the defect that appears optically to have strength $+1$. The white double-headed arrows indicate the orientations of crossed polarizers. Scale bars, $100\mu \mathrm{m}$.

Figure 2

Structure of a point defect of strength (a) $m=+1$ or (c) $-1$ and a disclination loop of strength (b) $m=+1/2$ or (d) $-1/2$. (e)–(h) Representative TEM images of amphiphilic molecular assemblies templated by defects that appear optically to be points with strength $m=+1$. Red solid and dashed lines in (e) indicate the minor and major radii of the toroidal assembly of amphiphiles, respectively. Scale bars, 20 nm.

Figure 3

Schematic illustration of (a) cross section and (b) toroidal shape of the molecular assembly formed within a nanoscopic loop disclination of strength $+1/2$.

Figure 4

Difference in free energy $\mathrm{\Delta }F$ between a disclination loop of strength $m=+1/2$ (red) or $-1/2$ (blue) and a point defect of strength $m=+1$ (red) or $-1$ (blue) plotted as a function of the radius of the disclination loop $a$ in the absence (solid curve) or presence (dashed curve) of lipid assemblies within the core of the defects.