Plastic deformation of tubular crystals by dislocation glide

Geometric frustration of hard-disk packings on cones

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.

Chiral photonic crystals from sphere packing

Inspired by recent developments in self-assembled chiral nanostructures, we have explored the possibility of using spherical particles packed in cylinders as building blocks for chiral photonic crystals. In particular, we focused on an array of parallel cylinders arranged in a perfect triangular lattice, each containing an identical densest sphere packing structure. Despite the non-chirality of both the spheres and cylinders, the self-assembled system can exhibit chirality due to spontaneous symmetry breaking during the assembly process. We have investigated the circular dichroism effects of the system and have found that, for both perfect electric conductor and dielectric spheres, the system can display dual-polarization photonic band gaps for circularly polarized light at normal incidence along the axis of the helix. We have also examined how the polarization band gap size depends on the dielectric constant of the spheres and the packing fraction of the cylinders. Furthermore, we have explored the effects of non-ideality and found that the polarization gap persists even in the presence of imperfections and heterogeneity. Our study suggests that a cluster formed by spheres self-assembling inside parallel cylinders with appropriate material parameters can be a promising approach to creating chiral photonic crystals.

Shape multistability in flexible tubular crystals through interactions of mobile dislocations

Crystalline sheets rolled up into cylinders occur in diverse biological and synthetic systems, including carbon nanotubes, biofilaments of the cellular cytoskeleton, and packings of colloidal particles. In this work, we show, computationally, that such tubular crystals can be programmed with reconfigurable shapes, due to motions of defects that interrupt the periodicity of the crystalline lattice. By identifying and exploiting stable patterns of these defects, we cause tubular crystals to relax into desired target geometries, a design principle that could guide the creation of versatile colloidal analogues to nanotubes. Our results suggest routes to tunable and switchable material properties in ordered, soft materials on deformable surfaces.

We study avenues to shape multistability and shape morphing in flexible crystalline membranes of cylindrical topology, enabled by glide mobility of dislocations. Using computational modeling, we obtain states of mechanical equilibrium presenting a wide variety of tubular crystal deformation geometries, due to an interplay of effective defect interactions with out-of-tangent-plane deformations that reorient the tube axis. Importantly, this interplay often stabilizes defect configurations quite distinct from those predicted for a two-dimensional crystal confined to the surface of a rigid cylinder. We find that relative and absolute stability of competing states depend strongly on control parameters such as bending rigidity, applied stress, and spontaneous curvature. Using stable dislocation pair arrangements as building blocks, we demonstrate that targeted macroscopic three-dimensional conformations of thin crystalline tubes can be programmed by imposing certain sparse patterns of defects. Our findings reveal a broad design space for controllable and reconfigurable colloidal tube geometries, with potential relevance also to architected carbon nanotubes and microtubules.

Buckling and metastability in membranes with dilation arrays

We study periodic arrays of impurities that create localized regions of expansion, embedded in two-dimensional crystalline membranes. These arrays provide a simple elastic model of shape memory. As the size of each dilational impurity increases (or the relative cost of bending to stretching decreases), it becomes energetically favorable for each of the M impurities to buckle up or down into the third dimension, thus allowing for of order 2^{M} metastable surface configurations corresponding to different impurity "spin" configurations. With both discrete simulations and the nonlinear continuum theory of elastic plates, we explore the buckling of both isolated dilations and dilation arrays at zero temperature, guided by analogies with Ising antiferromagnets. We conjecture ground states for systems with triangular and square impurity superlattices, and comment briefly on the possible behaviors at finite temperatures.

Transitions between phyllotactic lattice states in curved geometries

Phyllotaxis, the regular arrangement of leaves or other lateral organs in plants including pineapples, sunflowers and some cacti, has attracted scientific interest for centuries. More recently there has been interest in phyllotaxis within physical systems, especially for cylindrical geometry. In this letter, we expand from a cylindrical geometry and investigate transitions between phyllotactic states of soft vortex matter confined to a conical frustum. We show that the ground states of this system are consistent with previous results for cylindrical confinement and discuss the resulting defect structures at the transitions. We then eliminate these defects from the system by introducing a density gradient to create a configuration in a single state. The nature of the density gradient limits this approach to a small parameter range on the conical system. We therefore seek a new surface, the horn, for which a defect-free state can be maintained for a larger range of parameters.

Dislocation mechanisms in the plastic deformation of monodisperse wet foams within an expansion-contraction microfluidic geometry

Densely packed wet foam was subjected to gradual expansion and contraction in a wide (1400-1800 μm) microfluidic channel to study localized plastic deformation events within the monodisperse bubble matrix. Dislocation glide, reflection, nucleation, and dipole transformations from extensional and compressive stresses were observed across a range of fluid flow rates and bubble packing densities. Disparate, cyclic reflections occur in two independent regions of the flowing foam, and the mechanisms of dislocation reflection under tension are expanded. The use of an asymmetric channel created a dichotomy in the model crystalline system between straighter, aligned bubble rows and curved, misaligned rows due to the corresponding streamlines within the channel. The resulting gradient in crystalline alignment had numerous effects on dislocation mobility and plastic deformation. 7/7 dipoles were found to rearrange to a more stable configuration aligned with the foam flow before dissociating. Dislocations comprising 5/5 dipoles (resembling the inverse-Stone-Wales defect in carbon nanostructures) were discovered to pass through one another via intermediate ring structures, which most commonly consisted of three dislocation pairs around a triangular-shaped central bubble.

Defect formation dynamics in curved elastic surface crystals

Topological defects shape the material and transport properties of physical systems. Examples range from vortex lines in quantum superfluids, defect-mediated buckling of graphene, and grain boundaries in ferromagnets and colloidal crystals, to domain structures formed in the early universe. The Kibble-Zurek (KZ) mechanism describes the topological defect formation in continuous non-equilibrium phase transitions with a constant finite quench rate. Universal KZ scaling laws have been verified experimentally and numerically for second-order transitions in planar Euclidean geometries, but their validity for non-thermal transitions in curved and topologically nontrivial systems still poses open questions. Here, we use recent experimentally confirmed theory to investigate topological defect formation in curved elastic surface crystals formed by stress-quenching a bilayer material. For both spherical and toroidal crystals, we find that the defect densities follow KZ-type power laws. Moreover, the nucleation sequences agree with recent experimental observations for spherical colloidal crystals. Our results suggest that curved elastic bilayers provide an experimentally accessible macroscopic system to study universal properties of non-thermal phase transitions in non-planar geometries.

Non-Equilibrium Self-Assembly of Monocomponent and Multicomponent Tubular Structures in Rotating Fluids

When suspended in a denser rotating fluid, lighter particles experience a cylindrically symmetric confining potential that drives their crystallization into either monocomponent or unprecedented binary tubular packing. These assemblies form around the fluid's axis of rotation, can be dynamically interconverted (upon accelerating or decelerating the fluid), can exhibit preferred chirality, and can be made permanent by solidifying the fluid. The assembly can be extended to fluids forming multiple concentric interfaces or to systems of bubbles forming both ordered and "gradient" structures within curable polymers.

Simulation and observation of line-slip structures in columnar structures of soft spheres

We present the computed phase diagram of columnar structures of soft spheres under pressure, of which the main feature is the appearance and disappearance of line slips, the shearing of adjacent spirals, as pressure is increased. A comparable experimental observation is made on a column of bubbles under forced drainage, clearly exhibiting the expected line slip.

Corrected Article: Simulation and observation of line-slip structures in columnar structures of soft spheres [Phys. Rev. E 96, 012610 (2017)]

This corrects the article DOI: 10.1103/PhysRevE.96.012610.