Topological binding and elastic interactions of microspheres and fibres in a nematic liquid crystal

Abstract

We present a detailed analysis of topological binding and elastic interactions between a long, and micrometer-diameter fiber, and a microsphere in a homogeneously aligned nematic liquid crystal. Both objects are surface treated to produce strong perpendicular anchoring of the nematic liquid crystal. We use the opto-thermal micro-quench of the laser tweezers to produce topological defects with prescribed topological charge, such as pairs of a Saturn ring and an anti-ring, hyperbolic and radial hedgehogs on a fiber, as well as zero-charge loops. We study the entanglement and topological charge interaction between the topological defects of the fiber and sphere and we observe a huge variety of different entanglement topologies and defect-mediated elastic bindings. We explain all observed phenomena with simple topological rule: like topological charges repel each other and opposite topological charges attract. These binding mechanisms not only demonstrate the fascinating topology of nematic colloids, but also open a novel route to the assembly of very complex topological networks of fibers, spheres and other objects for applications in liquid crystal photonics.

Magnetic tweezers for captive disclination loops

“…When the anchoring at the nematic (cholesteric)/air is homeotropic, each droplet must contain, for topological reasons, a defect with the topological charge m = 1: a disclination loop equivalent to a radial hedgehog. Captive disclination loops were also observed on glass fibers with homeotropic anchoring immersed in planar nematic samples [32,33]. In this geometry, disclination loops were generated in a controlled manner by the KibbleZurek mechanism during quenching from the isotropic into the nematic phase.…”

Creation and topological charge switching of defect loops on a long fibre in the nematic liquid crystal

“…Determination of the sign of the topological charge of the loops was described elsewhere [26,46]. Briefly, a small test particle such as micro-sphere, treated for perpen-dicular surface anchoring, is released next to the loop.…”

“…This charge neutral loop is created from the topological soliton, i.e. from the vacuum with no topological charges, and the procedure for creating a charge neutral loop out of a topological soliton is explained in detail elsewhere [26,46]. One should note that this loop is not encircling the fibre along its short axis, but starts and ends on the same side of the fibre.…”

“…These forces are of elastic origin and are also called structural forces. The entanglement of topological objects and defects is usually enforced by heating locally the NLC into the isotropic phase and then rapidly cooling it down, as described in our previous work [46]. Briefly, the nematic liquid crystal in the vicinity of the disclination loop around the fibre and the micro-sphere is locally heated using laser tweezers into the isotropic phase and then quenched back to the nematic phase by switching-off the laser.…”

“…Namely, additional pairs of defects can always be created as long as their total topological charge is kept to zero. This was first demonstrated in a series of experiments with long fibers inserted in the NLC [26,[44][45][46]. Using the laser tweezers one is able to create pairs of oppositely charged topological defects, cut them into smaller entities, merge them into larger entities etc... Long fibre included in nematic nematic liquid crystals has emerged as a perfect setting to prove and observe the basic laws of topology in two dimensions.…”