Iijima's 1991 discovery of needle-like multilayer graphitic carbon tubules (now multi-walled carbon nanotubes), produced by d.c. arc-discharge evaporation of graphite, left their growth mechanism as an explicitly unresolved issue. He proposed a screw-dislocation-like model in which each tube end exposes spiral growth steps one hexagon high that advance by carbon addition, and he observed concentric atomic steps on the needle surfaces whose helical nature was not confirmed. Later literature established the tube helicities, the pentagon-based closure of the ~19° and ~40° caps, and the turbostratic interlayer stacking of the product, and developed competing growth pictures: inter-shell lip-lip interactions at open edges, quantitative screw-dislocation theory of growth rates, and machine-learning molecular dynamics that disfavors continuous spiral growth under catalytic conditions. The surviving open problem is to determine, with kinetics and energetics, how arc-grown multilayer tubules actually grow: whether the screw-dislocation-like spiral-step mechanism operates under arc conditions, and whether the concentric surface steps are helical spirals or merely concentric terraces.

Background

Multilayer graphitic carbon tubules — known since the early 1990s as multi-walled carbon nanotubes (MWCNTs) — are needles a few to a few tens of nanometres in diameter, built from 2 to about 50 coaxial cylindrical sheets of graphite (each sheet is graphene, a one-atom-thick honeycomb lattice of carbon atoms). Sumio Iijima's 1991 Nature letter reported their production by d.c. arc-discharge evaporation of graphite, the method also used for fullerene synthesis: an electric arc between graphite electrodes in an inert gas vaporizes carbon, which condenses at the negative electrode as the needles. Electron diffraction — the recording, in a transmission electron microscope, of the pattern of electrons scattered by a nanometre-sized object — showed multiple sets of {hk0} spots (reflections indexed on the in-plane hexagonal carbon lattice) whose geometry implied that on each tube the carbon hexagons are arranged helically about the needle axis, with a pitch varying from tube to tube. This helical arrangement is what the field now calls nanotube chirality, specified by a chiral angle; together with diameter it fixes a tube's electronic structure. The tubules ended in curved, polygonal or cone-shaped caps with opening angles of about 19° and 40°, rationalized in the paper by requiring a perfect, continuous hexagonal network to close on itself — later understood as closure by inserting pentagonal rings into the hexagonal network, as in fullerene cages, which yields a quantized family of cone angles. The measured interlayer spacing of 0.34 nm is close to the (002) spacing of bulk graphite, whose sheets stack in the ABAB register; in nanotubes, adjacent shells generally have different chirality and are therefore rotationally disordered, a stacking state called turbostratic. For needle growth the paper proposed a screw-dislocation-like model. In ordinary crystals, a screw dislocation — a line defect that turns the lattice planes into a helicoidal ramp — terminating at a surface exposes a self-perpetuating spiral step, and attachment of atoms along that step lets the surface advance continuously at low supersaturation without new-layer nucleation. The proposed analogue is a cylindrical lattice whose tube end is terminated by spiral steps one hexagon high, so carbon addition at the step edge lengthens the tube; concentric atomic steps observed around the needle surfaces would be the surface trace of such spiral growth if they are helical, but the paper did not confirm this. Competing later pictures include open-end growth stabilized by lip-lip interactions (cooperative bonding between the dangling-bond edges of adjacent coaxial shells, allowing carbon to transfer between shells), growth from closed caps, and — for modern catalytic chemical vapor deposition (CVD, growth from a carbon feedstock gas on a metal catalyst particle) — a quantitative screw-dislocation theory in which any chiral nanotube is regarded as a screw dislocation whose Burgers vector (the lattice displacement produced by one turn of the dislocation) sets the growth rate. The unresolved question is which mechanism actually operates in arc-discharge growth of multilayer tubules, with what kinetics and energetics.

Problem Statement

Determine the mechanism by which needle-like multilayer graphitic carbon tubules grow during d.c. arc-discharge evaporation of graphite — the process that produced the tubules reported by Iijima in Nature in 1991. The paper posed its own growth question as a concrete hypothesis: each coaxial graphitic tube ends in spiral growth steps one hexagon high, analogous to a screw dislocation in a cylindrical lattice, so that carbon addition at the step edge lengthens the tube, and the concentric atomic steps observed around the needle surfaces would be the surface trace of this spiral growth if they are helical. The problem is to establish, with kinetics and energetics under arc-discharge conditions, the answers to two mandatory questions: (1) whether multilayer tubule growth proceeds by these screw-dislocation-like spiral steps, or instead by open-end growth mediated by inter-shell lip-lip interactions, or by growth from closed caps, or some combination of these; and (2) whether the concentric atomic steps on the tubule surfaces are helical spirals or merely concentric terraces. A complete answer to (1) and (2) must specify the atomistic pathway of carbon incorporation, its activation energetics at arc-plasma temperatures and supersaturations, and the resulting step geometry on the tubule surfaces, and must also be consistent with what has since been established about the product — pentagon-based cap closure with quantized cone angles (including the ~19 and ~40 degree caps), turbostratic rather than ABAB interlayer stacking, and generally different chirality of adjacent shells.

References

  1. S. Iijima, 'Helical microtubules of graphitic carbon', Nature 354 (6348), 56-58 (1991). DOI: 10.1038/354056a0, https://doi.org/10.1038/354056a0
  2. M. Liu and J. M. Cowley, 'Structures of the helical carbon nanotubes', Carbon 32 (3), 393-403 (1994). DOI: 10.1016/0008-6223(94)90159-7, https://doi.org/10.1016/0008-6223(94)90159-7
  3. M. Ge and K. Sattler, 'Observation of fullerene cones', Chemical Physics Letters 220 (3-5), 192-196 (1994). DOI: 10.1016/0009-2614(94)00167-7, https://doi.org/10.1016/0009-2614(94)00167-7
  4. A. Krishnan, E. Dujardin, M. M. J. Treacy, J. Hugdahl, S. Lynum and T. W. Ebbesen, 'Graphitic cones and the nucleation of curved carbon surfaces', Nature 388 (6641), 451-454 (1997). DOI: 10.1038/41284, https://doi.org/10.1038/41284
  5. M. Buongiorno Nardelli, C. Brabec, A. Maiti, C. Roland and J. Bernholc, 'Lip-Lip Interactions and the Growth of Multiwalled Carbon Nanotubes', Physical Review Letters 80 (2), 313-316 (1998). DOI: 10.1103/PhysRevLett.80.313, https://doi.org/10.1103/PhysRevLett.80.313
  6. S. Amelinckx, A. Lucas and P. Lambin, 'Electron diffraction and microscopy of nanotubes', Reports on Progress in Physics 62 (11), 1471-1524 (1999). DOI: 10.1088/0034-4885/62/11/201, https://doi.org/10.1088/0034-4885/62/11/201
  7. S. Reich, L. Li and J. Robertson, 'Structure and formation energy of carbon nanotube caps', Physical Review B 72 (16), 165423 (2005). DOI: 10.1103/PhysRevB.72.165423, https://doi.org/10.1103/PhysRevB.72.165423
  8. Z. Xu, X. Bai, Z. L. Wang and E. Wang, 'Multiwall Carbon Nanotubes Made of Monochirality Graphite Shells', Journal of the American Chemical Society 128 (4), 1052-1053 (2006). DOI: 10.1021/ja057303j, https://doi.org/10.1021/ja057303j
  9. C. Jin, K. Suenaga and S. Iijima, 'Direct evidence for lip-lip interactions in multi-walled carbon nanotubes', Nano Research 1 (5), 434-439 (2008). DOI: 10.1007/s12274-008-8045-0, https://doi.org/10.1007/s12274-008-8045-0
  10. F. Ding, A. R. Harutyunyan and B. I. Yakobson, 'Dislocation theory of chirality-controlled nanotube growth', Proceedings of the National Academy of Sciences 106 (8), 2506-2509 (2009). DOI: 10.1073/pnas.0811946106, https://doi.org/10.1073/pnas.0811946106
  11. M. Marchand, C. Journet, D. Guillot, J.-M. Benoit, B. I. Yakobson and S. T. Purcell, 'Growing a Carbon Nanotube Atom by Atom: And Yet It Does Turn', Nano Letters 9 (8), 2961-2966 (2009). DOI: 10.1021/nl901380u, https://doi.org/10.1021/nl901380u
  12. N. Arora and N. N. Sharma, 'Arc discharge synthesis of carbon nanotubes: Comprehensive review', Diamond and Related Materials 50, 135-150 (2014). DOI: 10.1016/j.diamond.2014.10.001, https://doi.org/10.1016/j.diamond.2014.10.001
  13. D. Hedman, B. McLean, C. Bichara, S. Maruyama, J. A. Larsson and F. Ding, 'Dynamics of growing carbon nanotube interfaces probed by machine learning-enabled molecular simulations', Nature Communications 15 (1), 4076 (2024). DOI: 10.1038/s41467-024-47999-7, https://doi.org/10.1038/s41467-024-47999-7