skip to main content


Title: Three-dimensional crystals of adaptive knots
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.  more » « less
Award ID(s):
1810513
NSF-PAR ID:
10140862
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Science
Volume:
365
Issue:
6460
ISSN:
0036-8075
Page Range / eLocation ID:
1449 to 1453
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Abstract

    The rational design of nanoscopic DNA tiles has yielded highly ordered crystalline matter in 2D and 3D. The most well‐studied 3D tile is the DNA tensegrity triangle, which is known to self‐assemble into macroscopic crystals. However, contemporary rational design parameters for 3D DNA crystals nearly universally invoke integer numbers of DNA helical turns and Watson–Crick (WC) base pairs. In this study, 24‐bp edges are substituted into a previously 21‐bp (two helical turns of DNA) tensegrity triangle motif to explore whether such unconventional motif can self‐assemble into 3D crystals. The use of noncanonical base pairs in the sticky ends results in a cubic arrangement of tensegrity triangles with exceedingly high symmetry, assembling a lattice from winding helical axes and diamond‐like tessellation patterns. Reverting this motif to sticky ends with Watson–Crick pairs results in a trigonal hexagonal arrangement, replicating this diamond arrangement in a hexagonal context. These results showcase that the authors can generate unexpected, highly complex, pathways for materials design by testing modifications to 3D tiles without prior knowledge of the ensuing symmetry. This study expands the rational design toolbox for DNA nanotechnology; and it further illustrates the existence of yet‐unexplored arrangements of crystalline soft matter.

     
    more » « less
  2. Assembling different shaped particles into ordered microstructures is an open challenge in creating multifunctional particle-based materials and devices. Here, we report the two-dimensional (2D) AC electric field mediated assembly of different shaped colloidal particles into amorphous, liquid crystalline, and crystalline microstructures. Particle shapes investigated include disks, ellipses, squares, and rectangles, which show how systematic variations in anisotropy and corner curvature determine the number and type of resulting microstructures. AC electric fields induce dipolar interactions to control particle positional and orientational order. Microstructural states are determined via particle tracking to compute order parameters, which agree with computer simulations and show how particle packing and dipolar interactions together produce each structure. Results demonstrate how choice of particle shape and field conditions enable kinetically viable routes to assemble nematic, tetratic, and smectic liquid crystal structures as well as crystals with stretched 4- and 6-fold symmetry. Results show it is possible to assemble all corresponding hard particle phases, but also show how dipolar interactions influence and produce additional microstructures. Our findings provide design rules for the assembly of diverse microstructures of different shaped particles in AC electric fields, which could enable scalable and reconfigurable particle-based materials, displays, and printing technologies. 
    more » « less
  3. Abstract

    The successful self‐assembly of tensegrity triangle DNA crystals heralded the ability to programmably construct macroscopic crystalline nanomaterials from rationally‐designed, nanoscale components. This 3D DNA tile owes its “tensegrity” nature to its three rotationally stacked double helices locked together by the tensile winding of a center strand segmented into 7 base pair (bp) inter‐junction regions, corresponding to two‐thirds of a helical turn of DNA. All reported tensegrity triangles to date have employed turn inter‐junction segments, yielding right‐handed, antiparallel, “J1” junctions. Here a minimal DNA triangle motif consisting of 3‐bp inter‐junction segments, or one‐third of a helical turn is reported. It is found that the minimal motif exhibits a reversed morphology with a left‐handed tertiary structure mediated by a locally‐parallel Holliday junction—the “L1” junction. This parallel junction yields a predicted helical groove matching pattern that breaks the pseudosymmetry between tile faces, and the junction morphology further suggests a folding mechanism. A Rule of Thirds by which supramolecular chirality can be programmed through inter‐junction DNA segment length is identified. These results underscore the role that global topological forces play in determining local DNA architecture and ultimately point to an under‐explored class of self‐assembling, chiral nanomaterials for topological processes in biological systems.

     
    more » « less
  4. null (Ed.)
    To design and optimize arrays of vertical-axis wind turbines (VAWTs) for maximal power density and minimal wake losses, a careful consideration of the inherently three-dimensional structure of the wakes of these turbines in real operating conditions is needed. Accordingly, a new volumetric particle-tracking velocimetry method was developed to measure three-dimensional flow fields around full-scale VAWTs in field conditions. Experiments were conducted at the Field Laboratory for Optimized Wind Energy (FLOWE) in Lancaster, CA, using six cameras and artificial snow as tracer particles. Velocity and vorticity measurements were obtained for a 2 kW turbine with five straight blades and a 1 kW turbine with three helical blades, each at two distinct tip-speed ratios and at Reynolds numbers based on the rotor diameter $D$ between $1.26 \times 10^{6}$ and $1.81 \times 10^{6}$ . A tilted wake was observed to be induced by the helical-bladed turbine. By considering the dynamics of vortex lines shed from the rotating blades, the tilted wake was connected to the geometry of the helical blades. Furthermore, the effects of the tilted wake on a streamwise horseshoe vortex induced by the rotation of the turbine were quantified. Lastly, the implications of this dynamics for the recovery of the wake were examined. This study thus establishes a fluid-mechanical connection between the geometric features of a VAWT and the salient three-dimensional flow characteristics of its near-wake region, which can potentially inform both the design of turbines and the arrangement of turbines into highly efficient arrays. 
    more » « less
  5. Abstract

    Homochiral helical self‐organizations provide some of the most fundamental architectures of biological macromolecules and of their co‐assemblies although they were first discovered and elucidated only during the early 1950. Helical synthetic covalent macromolecules started to be discovered soon after and were followed by supramolecular macromolecules and their co‐assemblies few decades later. This perspective will provide a brief historical development of chiral helical self‐organizations in biology and in supramolecular chemistry. Helical covalent and supramolecular macromolecules self‐organize and co‐organize helical supramolecular columns and spherical helices that can generate complex liquid crystals, crystals including Frank‐Kasper phases, and quasicrystals. The design of new functions based on synthetic helical assemblies will also be discussed. Personal events from the life of scientists contributing to these developments are also briefly mentioned.

     
    more » « less