Modifying Nobili-Durand surface energy for conically degenerate anchorings at the interface of liquid crystal colloids

Abstract

We propose a surface energy for conically degenerate anchorings of uniaxial liquid crystal mesogens by modifying tensorial Nobili-Durand surface energy that is usually employed for fixed anchoring orientations with preferred polar angles. By minimizing Landau-de Gennes free energy and the proposed surface energy, we obtain the equilibrium director configuration around a spherical colloid in the uniform nematic liquid crystal. Our calculations show that the proposed surface energy can cause boojum or/and Saturn-ring defect textures depending on the equilibrium conic angle. We also study the interactions between two spherical colloids with the equilibrium conic angle 45 • , where the surface energy provides both boojum and Saturn-ring defects on the surface of particles. We compare the calculated anisotropic colloidal interactions with experimental observations [B. Senyuk et al., Hexadecapolar Colloids, Nat. Comm. 7, 10659, 2016]. In agreement with experiment, our results show two stable angular assemblies in the close particle-particle separations. Also, the long-range elastic interactions are almost consistent with the hexadecapolar elastic distortion.

Transformation between elastic dipoles, quadrupoles, octupoles, and hexadecapoles driven by surfactant self-assembly in nematic emulsion

“…4D ), which is in good agreement with numerical modeling ( Fig. 3A , b or c) ( 17 – 19 , 31 ). A color map of the projection n x of n ( r ) onto the x axis orthogonal to n 0 highlights positive, near-zero, and negative n x [ Figs.…”

“…A color map of the projection n x of n ( r ) onto the x axis orthogonal to n 0 highlights positive, near-zero, and negative n x [ Figs. 3B (b and c) and 4E ] around the droplet and is also consistent with a hexadecapolar n ( r )-configuration ( 17 – 19 , 31 , 32 ). Mapping of n x at some distance from the spherical surface reveals that the tilting of n ( r ) with respect to n 0 in the hexadecapole with mixed anchoring has an opposite sequence as compared to that in the hexadecapole with conic anchoring [compare Fig.…”

“…These textural features and n ( r ) are similar to the ones exhibited by an elastic hexadecapole (fig. S2, E to H) previously found forming around colloidal particles with conically degenerate surface anchoring ( 17 – 19 ). However, the n ( r )-structure and defects in the hexadecapoles with tilted anchoring are different from that in hexadecapoles with mixed anchoring observed here.…”

“…S2A), as in the elastic hexadecapoles with conically degenerate surface anchoring (fig. S2E) studied recently ( 17 – 19 ). These experimentally observed topological transformations of elastic multipoles are caused by tangential-to-homeotropic changes of patchy surface anchoring boundary conditions at the LC-glycerol interface ( Fig.…”

“…Such structures of molecular alignment within or around the droplets can serve as reporters of biological microbes or chemical sensors (4,5) and can drive various forms of reconfigurable elasticity-mediated self-assembly (2,7,(11)(12)(13). In emulsions comprising foreign fluid drops within an aligned nematic host, a variety of defect and structures have been reported, giving origin to particle-induced deformations of the far-field alignment that range from elastic dipoles (2) to quadrupoles (7,16), to hexadecapoles, and to even higher-order multipoles (17)(18)(19). Some of these structures, which typically can be characterized by leading-order elastic multipoles, were found intertransforming in response to applied electric fields or changes of temperature and other experimental conditions (7,18).…”