# Three-dimensional crystals of adaptive knots

@article{Tai2019ThreedimensionalCO, title={Three-dimensional crystals of adaptive knots}, author={Jung-Shen B. Tai and Ivan I. Smalyukh}, journal={Science}, year={2019}, volume={365}, pages={1449 - 1453} }

Knot all that it seems Optical micrograph of a self-assembled lattice of knots in a chiral liquid crystalCREDIT: TAI AND SMALYUKH Although for some, knots are merely a frustration caused by poorly tied shoelaces, interest in knots in physical systems spans many disciplines, including fluid and optical vortices, Skyrmion states, liquid crystals, excitable media, polymers, proteins, DNA, and even chemical molecules. Tai and Smalyukh describe the creation of localized knotted structures in…

## 42 Citations

### Knot your regular crystal of atoms

- PhysicsScience
- 2019

Tai and Smalyukh harness topology to create a fundamentally new type of crystal, built with knots tied in a chiral fluid, which causes all of the molecules to rotate like a corkscrew along a preferred direction, the helical axis.

### Electrically powered motions of toron crystallites in chiral liquid crystals

- PhysicsProceedings of the National Academy of Sciences
- 2020

Significance Topological solitons exhibit particle-like behavior and, similar to colloids, allow one to model out-of-equilibrium processes like crystallization, melting, and defect motions in…

### Knotting matters: orderly molecular entanglements.

- ChemistryChemical Society reviews
- 2022

Entangling strands in a well-ordered manner can produce useful effects, from shoelaces and fishing nets to brown paper packages tied up with strings. At the nanoscale, non-crystalline polymer chains…

### Review: Topology of solitons and singular defects in chiral liquid crystals

- Physics
- 2021

Widely known for their uses in displays and electro-optics, liquid crystals are more than just technological marvels. They vividly reveal the topology and structure of various solitonic and singular…

### Liquid Crystalline Half‐Skyrmions and Their Optical Properties

- PhysicsAnnalen der Physik
- 2022

Liquid crystals have intrigued physicists as a platform that facilitates direct visualization of topological concepts. Here, the theoretical and experimental studies demonstrating that a thin film of…

### Topological carnival: electrically-powered motions of toron crystallites in chiral liquid crystals

- Physics
- 2020

Malleability of metals is an example of how dynamics of defects like dislocations induced by external stresses alters material properties and enables technological applications. However, these…

### Surface anchoring as a control parameter for stabilizing torons, skyrmions, twisted walls, fingers, and their hybrids in chiral nematics.

- PhysicsPhysical review. E
- 2020

This work shows that the strength of perpendicular surface boundary conditions can be used to control the structure and topology of solitonic and other localized field configurations and reveals structural stability diagrams and intertransformation of twisted walls and fingers, torons, and skyrmions and their crystalline organizations upon changing boundary conditions.

### Hopf Solitons in Helical and Conical Backgrounds of Chiral Magnetic Solids.

- PhysicsPhysical review letters
- 2020

Numerically predict magnetic heliknotons, an embodiment of such nonzero-Hopf-index solitons localized in all spatial dimensions while embedded in a helical or conical background of chiral magnets.

### Geometric transformation and three-dimensional hopping of Hopf solitons

- PhysicsNature communications
- 2022

Arising in many branches of physics, Hopf solitons are three-dimensional particle-like field distortions with nontrivial topology described by the Hopf map. Despite their recent discovery in colloids…

### Nematic Order, Plasmonic Switching and Self‐Patterning of Colloidal Gold Bipyramids

- PhysicsAdvanced science
- 2021

Dispersing inorganic colloidal nanoparticles within nematic liquid crystals provides a versatile platform both for forming new soft matter phases and for predefining physical behavior through…

## References

SHOWING 1-10 OF 44 REFERENCES

### Reconfigurable Knots and Links in Chiral Nematic Colloids

- Materials ScienceScience
- 2011

The knotting of microscopic topological defect lines in chiral nematic liquid-crystal colloids are demonstrated by using laser tweezers as a micromanipulation tool, demonstrating how relevant the topology can be for the material engineering of soft matter.

### Mutually tangled colloidal knots and induced defect loops in nematic fields.

- Materials Science, PhysicsNature materials
- 2014

It is demonstrated that bulk and surface defects in nematic fluids can be patterned by tuning the topology of colloidal particles dispersed in them by taking advantage of two-photon photopolymerization techniques to make knot-shaped microparticles.

### Diversity of knot solitons in liquid crystals manifested by linking of preimages in torons and hopfions

- Physics
- 2017

Topological solitons are knots in continuous physical fields classified by non-zero Hopf index values. Despite arising in theories that span many branches of physics, from elementary particles to…

### Topological zoo of free-standing knots in confined chiral nematic fluids.

- PhysicsNature communications
- 2014

This work demonstrates the creation of free-standing knotted and linked disclination loops in the cholesteric ordering fields, which are confined to spherical droplets with homeotropic surface anchoring.

### Ferromagnetic Switching of Knotted Vector Fields in Liquid Crystal Colloids.

- PhysicsPhysical review letters
- 2015

Numerical modeling, implemented through free energy minimization to arrive at a field-dependent three-dimensional M(r), shows a good agreement with experiments and provides insights into the torus knot topology of observed field configurations and the corresponding physical underpinnings.

### Knotted defects in nematic liquid crystals.

- MathematicsPhysical review letters
- 2014

A topological heuristic for the resolution of strand crossings in defect coarsening processes is given which allows us to distinguish topological classes of a given link and to make predictions about defect crossings in nematic liquid crystals.

### Optical generation, templating, and polymerization of three-dimensional arrays of liquid-crystal defects decorated by plasmonic nanoparticles

- Materials Science, Physics
- 2013

Defects in liquid crystals are used to model topological entities ranging from Skyrmions in high-energy physics to early-universe cosmic strings, as well as find practical applications in…

### Triclinic nematic colloidal crystals from competing elastic and electrostatic interactions

- Materials ScienceScience
- 2016

Colloidal pair and many-body interactions are examined and it is shown how triclinic crystals with orientational ordering of the semiconductor nanorods emerge from competing long-range elastic and electrostatic forces.

### Topological transformations of Hopf solitons in chiral ferromagnets and liquid crystals

- PhysicsProceedings of the National Academy of Sciences
- 2018

It is shown that both dielectric and ferromagnetic response of the studied material systems allow for stabilizing a host of topological solitons with different Hopf indices, which promise technological applications in the new breeds of information displays and data storage devices.

### Three-dimensional structure and multistable optical switching of triple-twisted particle-like excitations in anisotropic fluids.

- PhysicsNature materials
- 2010

These localized chiro-elastic particle-like excitations--dubbed 'triple-twist torons'--are generated by vortex laser beams and embed the localized three-dimensional twist into a uniform background.