skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


  • NSF Public Access
  • Search Results
  • Geometrical Frustration and Defect Formation in Growth of Colloidal Nanoparticle Crystals on a Cylinder: Implications for Assembly of Chiral Nanomaterials
Title: Geometrical Frustration and Defect Formation in Growth of Colloidal Nanoparticle Crystals on a Cylinder: Implications for Assembly of Chiral Nanomaterials
Using a combination of experiment and simulation, we study how two-dimensional (2D) crystals of colloidal nanoparticles grow on cylindrical substrates. The cylindrical geometry allows us to examine growth in the absence of Gaussian curvature but in the presence of a closure constraintthe requirement that a crystal loops back onto itself. In some cases, this constraint results in structures that have been observed previously in theory and nonequilibrium packing experiments: chiral crystals and crystals with linear defects known as “line slips”. More generally, though, the structures we see differ from those that have been observed: the line slips are kinked and contain partial vacancies. We show that these structures arise because the cylinder changes how the crystal grows. After a crystal wraps around the cylinder and touches itself, it must grow preferentially along the cylinder axis. As a result, crystals with a chiral line slip tend to trap partial vacancies. Indeed, we find that line slips that are less aligned with the cylinder axis incorporate more partial vacancies on average than the ones that are more aligned. These results show that crystal growth on a cylinder is frustrated by the closure requirement, a finding that may shed some light on the assembly of biological nanosystems such as tobacco mosaic virus and might inform ways to fabricate chiral optical nano materials.  more » « less
Award ID(s):
2011754
PAR ID:
10499991
Author(s) / Creator(s):
; ; ; ;
Publisher / Repository:
American Chemical Society
Date Published:
Journal Name:
ACS Applied Nano Materials
Volume:
4
Issue:
10
ISSN:
2574-0970
Page Range / eLocation ID:
10682 to 10691
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; ; ; (, Soft Matter)
    null (Ed.)
    For organic semiconductor crystals exhibiting anisotropic charge transport along different crystallographic directions, nanoconfinement is a powerful strategy to control crystal orientation by aligning the fast crystallographic growth direction(s) with the unconfined axis(es) of nanoconfining scaffolds. Here, design rules are presented to relate crystal morphology, scaffold geometry, and orientation control in solution-processed small-molecule crystals. Specifically, organic semiconductor triisopropylsilylethynyl pyranthrene needle-like crystals with a dimensionality of n = 1 and perylene platelike crystals with n = 2 were grown from solution within nanoconfining scaffolds comprising cylindrical nanopores with a dimensionality of m = 1, representing one unconfined dimension along the cylinder axis, and those comprising nanopillar arrays with a dimensionality of m = 2. For m = n systems, native crystal growth habits were preserved while the crystal orientation in n = m direction(s) was dictated by the geometry of the scaffold. For n ≠ m systems, on the other hand, orientation control was restricted within a single plane, either parallel or perpendicular to the substrate surface. Intriguingly, control over crystal shape was also observed for perylene crystals grown in cylindrical nanopores ( n > m ). Within the nanopores, crystal growth was restricted along a single direction to form a needle-like morphology. Once growth proceeded above the scaffold surface, the crystals adopted their native growth habit to form asymmetric T-shaped single crystals with concave corners. These findings suggest that nanoporous scaffolds with spatially-varying dimensionalities can be used to grow single crystals of complex shapes. 
    more » « less
  2. ; ; ; ; (, Physical Review E)
    Conical surfaces pose an interesting challenge to crystal growth: A crystal growing on a cone can wrap around and meet itself at different radii. We use a disk-packing algorithm to investigate how this closure constraint can geometrically frustrate the growth of single crystals on cones with small opening angles. By varying the crystal seed orientation and cone angle, we find that—except at special commensurate cone angles—crystals typically form a seam that runs along the axial direction of the cone, while near the tip, a disordered particle packing forms. We show that the onset of disorder results from a finite-size effect that depends strongly on the circumference and not on the seed orientation or cone angle. This finite-size effect occurs also on cylinders, and we present evidence that on both cylinders and cones, the defect density increases exponentially as circumference decreases. We introduce a simple model for particle attachment at the seam that explains the dependence on the circumference. Our findings suggest that the growth of single crystals can become frustrated even very far from the tip when the cone has a small opening angle. These results may provide insights into the observed geometry of conical crystals in biological and materials applications. 
    more » « less
  3. ; ; ; ; ; ; ; ; (, Molecular Systems Design & Engineering)
    Optically-active optoelectronic materials are of great interest for many applications, including chiral sensing and circularly polarized light emission. Traditionally, such applications have been enabled by synthetic strategies to design chiral organic semiconductors and conductors. Here, centrosymmetric tetrathiafulvalene (TTF) crystals are rendered chiral on the mesoscale by crystal twisting. During crystallization from the melt, helicoidal TTF fibers were observed to grow radially outwards from a nucleation centre as spherulites, twisting in concert about the growth direction. Because molecular crystals exhibit orientation-dependent refractive indices, periodic concentric bands associated with continually rotating crystal orientations were observed within the spherulites when imaged between crossed polarizers. Under certain conditions, concomitant crystal twisting and bending was observed, resulting in anomolous crystal optical behavior. X-ray diffraction measurements collected on different spherulite bands indicated no difference in the molecular packing between straight and twisted TTF crystals, as expected for microscopic twisting pitches between 20–200 μm. Mueller matrix imaging, however, revealed preferential absorption and refraction of left- or right-circularly polarized light in twisted crystals depending on the twist sense, either clockwise or counterclockwise, about the growth direction. Furthermore, hole mobilities of 2.0 ± 0.9 × 10 −6 cm 2 V −1 s −1 and 1.9 ± 0.8 × 10 −5 cm 2 V −1 s −1 were measured for straight and twisted TTF crystals deposited on organic field-effect transistor platforms, respectively, demonstrating that crystal twisting does not negatively impact charge transport in these systems. 
    more » « less
  4. ; ; ; (, Optica Publishing Group)
    Modes of a dielectric cylindrical waveguide are characterized by three numbers: azimuthal numberm, radial number,s, and a continuous propagation constantβ.1The azimuthal number determines the field dependence of the azimuthal angleφof the cylindrical coordinate system with the polar axis along the axis of the cylinder in the form of exp (imφ). The radial number characterizes the behavior of the field in the radial direction and in an ideal cylinder is given by a cylindrical Bessel functionJm(κm,sr). Discrete values of the parameterκscharacterizing the radial dependence of the field is determined by Maxwell boundary conditions. The propagation constantβdescribes the propagation of the mode along the axis of the fiber (Z-axis of the cylindrical coordinate system). 
    more » « less
  5. ; ; ; (, physica status solidi (b))
    Boron nitride (BN) has numerous advantageous physical and electrical properties for mechanical and (opto‐)electronic applications, yet growing large single crystals is challenging. The ammonothermal method has demonstrated its suitability for large single‐crystal gallium nitride growth and is investigated for its ability to grow BN. The temperature‐dependent solubility of BN in sodium‐containing supercritical ammonia is previously demonstrated. Herein, the application of a temperature gradient across a baffled autoclave toward the continuous dissolution and crystallization of BN is examined. BN deposits on all wetted surfaces in the lower‐temperature zone, predominantly on the autoclave walls as polycrystalline sheets and to a lesser degree on suspended seeds of cubic BN as oriented, micrometer‐sized, repeated trapezoidal platelet units. Analysis of the grown BN crystals by Raman, X‐ray diffraction, and transmission electron microscopy suggests the growth of sp2‐hybridized BN, predominantly the rhombohedral crystal structure on nitrided NiCr alloy surfaces and rhombohedral and hexagonal crystal structures on the cubic BN seed crystal surfaces. The interfacial relationships between the cBN and the sp2‐hybridized BN phases are examined, where favorable attachment sites are discovered between the dissimilar lattices, further supporting the observed crystal growth. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email