Kink formation and motion in carbon nanotubes at high temperatures

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.

Nanomechanics of graphene

The super-high strength of single-layer graphene has attracted great interest. In practice, defects resulting from thermodynamics or introduced by fabrication, naturally or artificially, play a pivotal role in the mechanical behaviors of graphene. More importantly, high strength is just one aspect of the magnificent mechanical properties of graphene: its atomic-thin geometry not only leads to ultra-low bending rigidity, but also brings in many other unique properties of graphene in terms of mechanics in contrast to other carbon allotropes, including fullerenes and carbon nanotubes. The out-of-plane deformation is of a 'soft' nature, which gives rise to rich morphology and is crucial for morphology control. In this review article, we aim to summarize current theoretical advances in describing the mechanics of defects in graphene and the theory to capture the out-of-plane deformation. The structure-mechanical property relationship in graphene, in terms of its elasticity, strength, bending and wrinkling, with or without the influence of imperfections, is presented.

Chirality transitions and transport properties of individual few-walled carbon nanotubes as revealed by in situ TEM probing

Physical properties of carbon nanotubes (CNTs) are closely related to the atomic structure, i.e. the chirality. It is highly desirable to develop a technique to modify their chirality and control the resultant transport properties. Herein, we present an in situ transmission electron microscopy (TEM) probing method to monitor the chirality transition and transport properties of individual few-walled CNTs. The changes of tube structure including the chirality are stimulated by programmed bias pulses and associated Joule heating. The chirality change of each shell is analyzed by nanobeam electron diffraction. Supported by molecular dynamics simulations, a preferred chirality transition path is identified, consistent with the Stone-Wales defect formation and dislocation sliding mechanism. The electronic transport properties are measured along with the structural changes, via fabricating transistors using the individual nanotubes as the suspended channels. Metal-to-semiconductor transitions are observed along with the chirality changes as confirmed by both the electron diffraction and electrical measurements. Apart from providing an alternative route to control the chirality of CNTs, the present work demonstrates the rare possibility of obtaining the dynamic structure-properties relationships at the atomic and molecular levels.

Plastic deformation of tubular crystals by dislocation glide

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.

Precise determination of the threshold diameter for a single-walled carbon nanotube to collapse

Closed-edged bilayer graphene nanoribbons were formed by the spontaneous collapse of large-diameter single-walled carbon nanotubes (SWNTs) grown on gold nanoparticles by chemical vapor deposition. Such bilayer graphene nanoribbons could adopt different stacking configurations, such as AB-stacking or stacking order with any rotation angle, correlated with the chiral angles of their parent rounded SWNTs. On the basis of the electron diffraction characterizations on a good number of collapsed and uncollapsed SWNTs, the threshold diameter for SWNTs to collapse was precisely determined to be 5.1 nm, independent of the chiral angle of the SWNTs. The determination is consistent with that calculated by both classical adaptive intermolecular reactive empirical bond order force field and density functional theory after having taken the stacking effect and thermal fluctuation into account.

Action-derived molecular dynamics simulations for the migration and coalescence of vacancies in graphene and carbon nanotubes

We report the results of action-derived molecular dynamics simulations for the migration and coalescence processes of monovacancies in graphene and carbon nanotubes with different chiralities. In carbon nanotubes, the migration pathways and barriers of a monovacancy depend on the tube chirality, while there is no preferential pathway in graphene due to the lattice symmetry and the absence of the curvature effect. The probable pathway changes from the axial to circumferential direction as the chirality varies from armchair to zigzag. The chirality dependence is attributed to the preferential orientation of the reconstructed bond formed around each vacancy site. It is energetically more favourable for two monovacancies to coalesce into a divacancy via alternative movements rather than simultaneous movements. The energy barriers for coalescence are generally determined by the migration barrier for the monovacancy, although there are some variations due to interactions between two diffusing vacancies. In graphene and armchair nanotubes, two monovacancies prefer to migrate along different zigzag atomic chains rather than a single atomic chain connecting these vacancies. On the other hand, in zigzag tubes, the energy barrier for coalescence increases significantly unless monovacancies lie on the same circumference.

Diffusion and drift of graphene flake on graphite surface

Diffusion and drift of a graphene flake on a graphite surface are analyzed. A potential energy relief of the graphene flake is computed using ab initio and empirical calculations. Based on the analysis of this relief, different mechanisms of diffusion and drift of the graphene flake on the graphite surface are considered. A new mechanism of diffusion and drift of the flake is proposed. According to the proposed mechanism, rotational transition of the flake from commensurate to incommensurate state takes place with subsequent simultaneous rotation and translational motion until a commensurate state is reached again, and so on. Analytic expressions for the diffusion coefficient and mobility of the flake corresponding to different mechanisms are derived in wide ranges of temperatures and sizes of the flake. The molecular dynamics simulations and estimates based on ab initio and empirical calculations demonstrate that the proposed mechanism can be dominant under certain conditions. The influence of structural defects on the diffusion of the flake is examined on the basis of calculations of the potential energy relief and molecular dynamics simulations. The methods of control over the diffusion and drift of graphene components in nanoelectromechanical systems are discussed. The possibility to experimentally determine the barriers to relative motion of graphene layers based on the study of diffusion of a graphene flake is considered. The results obtained can also be applied to polycyclic aromatic molecules on graphene and should be qualitatively valid for a set of commensurate adsorbate-adsorbent systems.

Structural, electronic, optical and vibrational properties of nanoscale carbons and nanowires: a colloquial review

This review addresses the field of nanoscience as viewed through the lens of the scientific career of Peter Eklund, thus with a special focus on nanocarbons and nanowires. Peter brought to his research an intense focus, imagination, tenacity, breadth and ingenuity rarely seen in modern science. His goal was to capture the essential physics of natural phenomena. This attitude also guides our writing: we focus on basic principles, without sacrificing accuracy, while hoping to convey an enthusiasm for the science commensurate with Peter's. The term 'colloquial review' is intended to capture this style of presentation. The diverse phenomena of condensed matter physics involve electrons, phonons and the structures within which excitations reside. The 'nano' regime presents particularly interesting and challenging science. Finite size effects play a key role, exemplified by the discrete electronic and phonon spectra of C(60) and other fullerenes. The beauty of such molecules (as well as nanotubes and graphene) is reflected by the theoretical principles that govern their behavior. As to the challenge, 'nano' requires special care in materials preparation and treatment, since the surface-to-volume ratio is so high; they also often present difficulties of acquiring an experimental signal, since the samples can be quite small. All of the atoms participate in the various phenomena, without any genuinely 'bulk' properties. Peter was a master of overcoming such challenges. The primary activity of Eklund's research was to measure and understand the vibrations of atoms in carbon materials. Raman spectroscopy was very dear to Peter. He published several papers on the theory of phonons (Eklund et al 1995a Carbon 33 959-72, Eklund et al 1995b Thin Solid Films 257 211-32, Eklund et al 1992 J. Phys. Chem. Solids 53 1391-413, Dresselhaus and Eklund 2000 Adv. Phys. 49 705-814) and many more papers on measuring phonons (Pimenta et al 1998b Phys. Rev. B 58 16016-9, Rao et al 1997a Nature 338 257-9, Rao et al 1997b Phys. Rev. B 55 4766-73, Rao et al 1997c Science 275 187-91, Rao et al 1998 Thin Solid Films 331 141-7). His careful sample treatment and detailed Raman analysis contributed greatly to the elucidation of photochemical polymerization of solid C(60) (Rao et al 1993b Science 259 955-7). He developed Raman spectroscopy as a standard tool for gauging the diameter of a single-walled carbon nanotube (Bandow et al 1998 Phys. Rev. Lett. 80 3779-82), distinguishing metallic versus semiconducting single-walled carbon nanotubes, (Pimenta et al 1998a J. Mater. Res. 13 2396-404) and measuring the number of graphene layers in a peeled flake of graphite (Gupta et al 2006 Nano Lett. 6 2667-73). For these and other ground breaking contributions to carbon science he received the Graffin Lecture award from the American Carbon Society in 2005, and the Japan Carbon Prize in 2008. As a material, graphite has come full circle. The 1970s renaissance in the science of graphite intercalation compounds paved the way for a later explosion in nanocarbon research by illuminating many beautiful fundamental phenomena, subsequently rediscovered in other forms of nanocarbon. In 1985, Smalley, Kroto, Curl, Heath and O'Brien discovered carbon cage molecules called fullerenes in the soot ablated from a rotating graphite target (Kroto et al 1985 Nature 318 162-3). At that time, Peter's research was focused mainly on the oxide-based high-temperature superconductors. He switched to fullerene research soon after the discovery that an electric arc can prepare fullerenes in bulk quantities (Haufler et al 1990 J. Phys. Chem. 94 8634-6). Later fullerene research spawned nanotubes, and nanotubes spawned a newly exploding research effort on single-layer graphene. Graphene has hence evolved from an oversimplified model of graphite (Wallace 1947 Phys. Rev. 71 622-34) to a new member of the nanocarbon family exhibiting extraordinary electronic properties. Eklund's career spans this 35-year odyssey.

Direct compressive measurements of individual titanium dioxide nanotubes

The mechanical compressive properties of individual thin-wall and thick-wall TiO(2) nanotubes were directly measured for the first time. Nanotubes with outside diameters of 75 and 110 nm and wall thicknesses of 5 and 15 nm, respectively, were axially compressed inside a 400 keV high-resolution transmission electron microscope (TEM) using a new fully integrated TEM-atomic force microscope (AFM) piezo-driven fixture for continuous recording of the force-displacement curves. Individual nanotubes were directly subjected to compressive loading. We found that the Young's modulus of titanium dioxide nanotubes depended on the diameter and wall thickness of the nanotube and is in the range of 23-44 GPa. The thin-wall nanotubes collapsed at approximately 1.0 to 1.2 microN during axial compression.

Mechanism for superelongation of carbon nanotubes at high temperatures

We report molecular dynamics simulations of the recently discovered superelongation of carbon nanotubes (CNTs) at high temperatures. The nearly simultaneous activation and wide distribution of a large number of defects near the elastic limit play a key role in impeding the formation of localized predominant instability and facilitating large tensile elongation. It suggests new and more complex mechanisms for CNT superelongation in contrast with the previously proposed ideal defect glide and pseudoclimb. Defect interaction and evolution generate multistage necking and kinking and new types of larger defects that dominate the tensile elongation and breaking process. Intricate interplay between CNT sizes and defect nucleation and motion determine the overall deformation pattern.

Dislocation dynamics in multiwalled carbon nanotubes at high temperatures

Dislocation dynamics dictate the mechanical behavior of materials. Dislocations in periodic crystalline materials have been well documented. On the contrary, dislocations in cylindrical carbon nanotubes, particularly in multiwalled carbon nanotubes (MWCNTs), remain almost unexplored. Here we report that a room temperature 1/2<0001> sessile dislocation in a MWCNT becomes highly mobile, as characterized by its glide, climb, and the glide-climb interactions, at temperatures of about 2000 degrees C. The dislocation glide leads to the cross-linking of different shells; dislocation climb creates nanocracks; and the interaction of two 1/2<0001> dislocations creates kinks. We found that dislocation loops act as channels for mass transport. These dislocation dynamics are drastically different from that in conventional periodic crystalline materials due to the cylindrical, highly anisotropic structures of MWCNTs.

In situ observation of quasimelting of diamond and reversible graphite-diamond phase transformations

Because of technique difficulties in achieving the extreme high-pressure and high-temperature (HPHT) simultaneously, direct observation of the structures of carbon at extreme HPHT conditions has not been possible. Banhart and Ajayan discovered remarkably that carbon onions can act as nanoscopic pressure cells to generate high pressures. By heating carbon onions to approximately 700 degrees C and under electron beam irradiation, the graphite-to-diamond transformation was observed in situ by transmission electron microscopy (TEM). However, the highest achievable temperature in a TEM heating holder is less than 1000 degrees C. Here we report that, by using carbon nanotubes as heaters and carbon onions as high-pressure cells, temperatures higher than 2000 degrees C and pressures higher than 40 GPa were achieved simultaneously in carbon onions. At such HPHT conditions and facilitated by electron beam irradiation, the diamond formed in the carbon onion cores frequently changed its shape, size, orientation, and internal structure and moved like a fluid, implying that it was in a quasimelting state. The fluctuation between the solid phase of diamond and the fluid/amorphous phase of diamond-like carbon, and the changes of the shape, size, and orientation of the solid diamond, were attributed to the dynamic crystallization of diamond crystal from the quasimolten state and the dynamic graphite-diamond phase transformations. Our discovery offers unprecedented opportunities to studying the nanostructures of carbon at extreme conditions in situ and at an atomic scale.

Enhanced ductile behavior of tensile-elongated individual double-walled and triple-walled carbon nanotubes at high temperatures

We report exceptional ductile behavior in individual double-walled and triple-walled carbon nanotubes at temperatures above 2000 degrees C, with tensile elongation of 190% and diameter reduction of 90%, during in situ tensile-loading experiments conducted inside a high-resolution transmission electron microscope. Concurrent atomic-scale microstructure observations reveal that the superelongation is attributed to a high temperature creep deformation mechanism mediated by atom or vacancy diffusion, dislocation climb, and kink motion at high temperatures. The superelongation in double-walled and triple-walled carbon nanotubes, the creep deformation mechanism, and dislocation climb in carbon nanotubes are reported here for the first time.

How evaporating carbon nanotubes retain their perfection?

We present a mechanism of high-temperature sublimation of carbon nanotubes that does not destroy their ordered makeup even upon significant loss of mass. The atoms depart to the gas phase from the pentagon-heptagon dislocation cores, while the bond disruption is immediately repaired, and the 5|7 seamlessly propagate through the lattice. This explains a broad class of unsettled phenomena when at high temperature or under radiation the nanotubes do not become amorphous but rather shrink in size nearly flawlessly.