Plastic deformation of tubular crystals by dislocation glide

Abstract

Tubular crystals, two-dimensional lattices wrapped into cylindrical topologies, arise in many contexts, including botany and biofilaments, and in physical systems such as carbon nanotubes. The geometrical principles of botanical phyllotaxis, describing the spiral packings on cylinders commonly found in nature, have found application in all these systems. Several recent studies have examined defects in tubular crystals associated with crystalline packings that must accommodate a fixed tube radius. Here, we study the mechanics of tubular crystals with variable tube radius, with dislocations interposed between regions of different phyllotactic packings. Unbinding and separation of dislocation pairs with equal and opposite Burgers vectors allow the growth of one phyllotactic domain at the expense of another. In particular, glide separation of dislocations offers a low-energy mode for plastic deformations of solid tubes in response to external stresses, reconfiguring the lattice step by step. Through theory and simulation, we examine how the tube's radius and helicity affects, and is in turn altered by, the mechanics of dislocation glide. We also discuss how a sufficiently strong bending rigidity can alter or arrest the deformations of tubes with small radii.

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

“…In addition, there are a range of problems involving the self assembly (or packing) of spheres and particles in tubes [30][31][32][34][35][36]. The context of this work is further expanded by the recently demonstrated analogy between line-slip structures and dislocations in the crystalline phase on a cylinder [37].…”

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

“…Subsequently, such forms of "tubular" packing have also been observed in bacteriophage tails, bacterial flagella, and microtubules [3] as well as various material systems (e.g., foams, [4,5] colloids, [6,7] and nanoparticles [8] in templating channels, fullerenes in nanotubes, [9,10] fibrous assemblies of Janus particles, [11] chiral nanoparticles, [12] or DNA [13] ). While the packing of equally sized particles has been studied theoretically and understood in detail, [3,[14][15][16][17] it has proven difficult to a priori predict/control assembly of specific structures in experiment. In addition, there have been no works that would consider tubular packing in mixtures of particles of different sizes.…”

“…Figure 1a illustrates the experimental system in which polymeric beads (density ρ p = 0.9-1.13 g cm −3 depending on the material used) are placed in a cylindrical tube (I.D. While the packing of equally sized particles has been studied theoretically and understood in detail, [3,[14][15][16][17] it has proven difficult to a priori predict/control assembly of specific structures in experiment. 15 mm; length, L = 75 mm) filled with an aqueous solution of agarose (≈0.25 wt%, Calbiochem Omnipur Agarose) and with cesium bromide added to adjust the density of the liquid to above that of the particular beads used (ρ l = 1-1.2 g cm −3 ).…”

Convergence in a disk stacking model on the cylinder

“…A. A pattern that goes from (4,4) to (4,5) and back to (4, 4) via triangle and pentagon pairs. The latter shrink slowly, indicating convergence.…”

“…They appear either as descriptive models [16], minimum of a certain energy [17], minimum of packing density [10], or as stable fixed points of a dynamical system with more or less "soft" interactions between stacked elements [18,23,30]. Interesting exceptions to this focus on lattices occur, among others, in [5] where transitions between lattices due to physical deformation of the cylinder are studied in terms of dislocations. Line slip structures, where a part of a cylindrical lattice is translated along a parastichy, appear in the densest packings of spheres for certain parameter values [21].…”