Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic liquid-crystal colloids into knots and links of arbitrary complexity by using laser tweezers as a micromanipulation tool. All knots and links with up to six crossings, including the Hopf link, the Star of David, and the Borromean rings, are demonstrated, stabilizing colloidal particles into an unusual soft matter. The knots in chiral nematic colloids are classified by the quantized self-linking number, a direct measure of the geometric, or Berry’s, phase. Forming arbitrary microscopic knots and links in chiral nematic colloids is a demonstration of how relevant the topology can be for the material engineering of soft matter.
COBISS.SI-ID: 2336868
The conventional topological description given by the fundamental group of nematic order parameter does not adequately explain the entangled defect line structures that have been observed in nematic colloids. We introduce a new topological invariant, the self-linking number, that enables a complete classification of entangled defect line structures in general nematics, even without particles, and demonstrate our formalism using colloidal dimers, for which entangled structures have been previously observed.We also unveil a simple rewiring scheme for the orthogonal crossing of two 1/2 disclinations, based on a tetrahedral rotation of two relevant disclination segments, that allows us to predict possible nematic braids and calculate their self-linking numbers.
COBISS.SI-ID: 2325604
Many biological processes work with an extremely high energetic efficiency, but at first glance this does not hold for ciliary propulsion, reaching about 1%. We have reexamined the problem at the level of a single cilium and an infinite ciliated surface. We numerically determined the optimal shape of the ciliary beating pattern and showed that the optimal collective stroke is remarkably similar to what is observed in microorganisms. For Paramecium we showed that the experimentally measured hydrodynamic efficiency reaches about 50% of the theoretically possible optimum.
COBISS.SI-ID: 25073447