Three-dimensional crystals of adaptive knots

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Science  27 Sep 2019:
Vol. 365, Issue 6460, pp. 1449-1453
DOI: 10.1126/science.aay1638

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Knot all that it seems

Optical micrograph of a self-assembled lattice of knots in a chiral liquid crystal


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 cholesteric liquid crystals using electric fields (see the Perspective by Alexander). The knots are topologically distinct from the host medium and diffuse and organize like colloidal particles, forming regular crystalline arrangements.

Science, this issue p. 1449; see also p. 1377


Starting with Gauss and Kelvin, knots in fields were postulated to behave like particles, but experimentally they were found only as transient features or required complex boundary conditions to exist and could not self-assemble into three-dimensional crystals. We introduce energetically stable, micrometer-sized knots in helical fields of chiral liquid crystals. While spatially localized and freely diffusing in all directions, they resemble colloidal particles and atoms, self-assembling into crystalline lattices with open and closed structures. These knots are robust and topologically distinct from the host medium, though they can be morphed and reconfigured by weak stimuli under conditions such as those in displays. A combination of energy-minimizing numerical modeling and optical imaging uncovers the internal structure and topology of individual helical field knots and the various hierarchical crystalline organizations that they form.

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