Mutually tangled colloidal knots and induced defect loops in nematic fields

Colloidal particles dispersed in liquid crystals induce nematic fields and topological defects that are dictated by the topology of the colloidal particles. However, little is known about such interplay of topologies. It is now shown that knot-shaped microparticles in liquid crystals induce defect lines that get entangled with the colloidal knots, and that such mutually tangled configurations satisfy topological constraints and follow predictions from knot theory. Colloidal dispersions in liquid crystals can serve as asoft-matter toolkit for the self-assembly of composite materials with pre-engineered properties and structures that are highly dependent on particle-induced topological defects 1 , 2 , 3 . Here, we demonstrate that bulk and surface defects in nematic fluids can be patterned by tuning the topology of colloidal particles dispersed in them. In particular, by taking advantage of two-photon photopolymerization techniques to make knot-shaped microparticles, we show that the interplay of the topologies of the knotted particles, the nematic field and the induced defects leads to knotted, linked and other topologically non-trivial field configurations 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 . These structures match theoretical predictions made on the basis of the minimization of the elastic free energy and satisfy topological constraints 4 , 5 . Our approach may find uses in self-assembled topological superstructures of knotted particles linked by nematic fields, in topological scaffolds supporting the decoration of defect networks with nanoparticles 1 , and in modelling other physical systems exhibiting topologically analogous phenomena 12 , 13 , 14 , 15 , 16 .