Self-assembly of skyrmion-dressed chiral nematic colloids with tangential anchoring

We describe dipolar nematic colloids comprising mutually bound solid microspheres, three-dimensional skyrmions, and point defects in a molecular alignment field of chiral nematic liquid crystals. Nonlinear optical imaging and numerical modeling based on minimization of Landau–de Gennes free energy reveal that the particle-induced skyrmions resemble torons and hopfions, while matching surface boundary conditions at the interfaces of liquid crystal and colloidal spheres. Laser tweezers and videomicroscopy reveal that the skyrmion-colloidal hybrids exhibit purely repulsive elastic pair interactions in the case of parallel dipoles and an unexpected reversal of interaction forces from repulsive to attractive as the center-to-center distance decreases for antiparallel dipoles. The ensuing elastic self-assembly gives rise to colloidal chains of antiparallel dipoles with particles entangled by skyrmions.

Figure 1

Particles with tangential surface anchoring dispersed in an unwound CNLC. Individual particles [(a), (b)] are released in proximity to each other using laser tweezers and prompted to interact while forming colloidal [(c), (d)] dimers, [(e), (f)] trimers, and [(g), (h), (j), (k)] tetramers. The colloidal configurations and director structures are studied [(a), (c), (e), (g), (i)] between crossed polarizers in POM, [(b), (d), (f), (h)] using bright-field optical microscopy, and [(j), (k)] using 3PEF-PM cross sections such as the one shown for a horizontal plane slightly above the cell midplane. Orientations of crossed polarizers in POM are depicted in (g) and (i). 3PEF-PM polarization is linear in (j), as marked by a white double arrow, and circular in (k). The particle diameter is 7 μm.

Figure 2

3D imaging of n(r) induced by individual particles and dimers formed by two antiparallel elastic dipoles. [(a), (b)] POM and [(d), (e)] bright-field micrographs of two individual elastic dipoles, and [(c), (f)] their self-assembled dimer. Bright-field images [(d)–(f)] indicate that the particles might be located at different depths within the sample. [(g)–(i), (m)–(o)] In-plane and [(j)–(l), (p)–(r)] vertical 3PEF-PM cross sections obtained with [(g)–(l)] linearly and [(m)–(r)] circularly polarized excitation light.

Figure 3

Computer-simulated director configurations induced by colloidal spheres with tangential anchoring. (a) Axially symmetric dipolar n(r) in the cell's vertical cross-section. (b), (c) Computer-simulated 3PEF-PM textures in the same cross section (b) for circularly and (c) linearly polarized probing light. (d)–(g) Computer-simulated n(r) of self-assembled colloidal dimers as depicted (d) in the in-plane $x$-$y$ cross section in the cell midplane and (f), (g) vertical cross sections in two perpendicular planes marked in (d). (e) Computer-simulated 3PEF-PM image for circularly polarized excitation light and n(r) shown in (d); the inset shows the corresponding experimental image. The red (dark gray), green (bright gray), and blue (gray) coloring of cylinders in (a), (d), (f), and (g) indicates director projections along the three coordinate directions $x$, $y$, and $z$, respectively. Regions of defects with reduced scalar order parameter are shaded in red (dark gray). Note that the induced bulk and surface defects of a particle dimer shown in (d) and (f) shift away from vertical axes passing through the particle'scenters.

Figure 4

Colloidal pair interactions. (a), (b) Center-to-center distance vs time dependencies probed by videomicroscopy for antiparallel orientation of elastic dipoles when released by laser tweezers at an initial separation (a) just above and (b) just below the critical distance $r_c$, at which the pair-interaction force changes from repulsive to attractive. (c) Pair-interaction force and (d) potential obtained from data similar to those shown in (a) and (b). (e) Particle center-to-center distance vs time for parallel elastic dipoles released by laser tweezers at the smallest achievable separation. (f) Pair-interaction potential and force (shown in the inset) obtained from data similar to those shown in (e). Insets in (a)–(f) show bright-field optical micrographs taken at initial and final distances of the corresponding dependencies.