Root Growth Mechanism for Single Shell Nanotubes

In the catalytic growth experiments, two situations arise. In the first case, the metal particle, which is not frequently observed, is found to be reduced to one or a few metal atoms, as described above. In the second situation, carbon and metal atoms can condense and form alloy particles during the arc discharge. As these particles are cooled, carbon atoms, dissolved in the particle, segregate onto the surface, because the solubility of the surface decreases with decreasing temperature. As the system is cooled, soot is formed. The sizes of the soot particles are several tens of nm wide (much larger than single-shell nanotube diameters), and are identified by TEM observations as embedded metal clusters surrounded by a coating of a few graphitic layers. Some singularities at the surface structure or atomic compositions may catalyze the formation of single-wall tubes (as described by sea-urchin models [43,44]), thereby providing another mechanism for the growth of single-wall carbon nanotubes. After the formation of the tube nuclei, carbon is supplied from the core of the particle to the root of the tubes, which grow longer maintaining hollow capped tips. Addition of carbon atoms (or dimers) from the gas phase at the tube tips (opposite side) also probably helps the growth.

Many single-shell nanotubes are observed to coexist with catalytic particles and often appear to be sticking out of the particle surfaces, as shown in Fig. 16. One end of the tubule is thus free, the other one being embedded in the particle, which often has a size exceeding the nanotube diameter by well over one order of magnitude.

Classical molecular-dynamics simulations [45] reveal a possible atomistic picture for this root growth mode for single-wall tubes. According to the model, carbon atoms precipitate from the metal particle, migrate to the tube base, and are incorporated into the nanotube network, thereby leading to defect-free growth. The simulation consists of treating the outermost layer of a large metal particle, embedded in a few carbon layers, out of which a capped single-shell nanotube protrudes (Fig. 17).

The calculation shows that the addition of new hexagons at the tube base occurs through a sequence of processes involving a pair of "handles" on the opposite bonds of a heptagon. The heptagon defects are present due to the

Fig. 16. Transmission electron micrograph of single-wall nanotubes growing radially from a Ni-carbide particle (bottom) [38]. The top inset illustrates the hypothetical growth process of single-shell tubes from a metal-carbon alloy particle: (a) segregation of carbon towards the surface, (b) nucleation of single-wall tubes on the particle surface, and (c) growth of these nanotubes [44]

Fig. 16. Transmission electron micrograph of single-wall nanotubes growing radially from a Ni-carbide particle (bottom) [38]. The top inset illustrates the hypothetical growth process of single-shell tubes from a metal-carbon alloy particle: (a) segregation of carbon towards the surface, (b) nucleation of single-wall tubes on the particle surface, and (c) growth of these nanotubes [44]

positive curvature needed to create the carbon protrusion (Fig. 17). These "handles" are formed by adatoms between a pair of nearest-neighboring carbon atoms. Calculations show that the energy of a single handle is a minimum at the point of highest curvature, explaining why these handles are attracted to the tube base region, where the heptagons are located [45]. Figure 18 schematically displays the process of hexagon addition (without creating another defect) when an isolated heptagon or a 5-7 pair (pentagon and heptagon rings connected together) is introduced into the carbon network. An even number of handles leads to the creation of new hexagons at the tube stem, and thus to a defect-free root growth mechanism.

Fig. 17. Schematic wireframe representation of the top (a) and side (b) views of a (11,3) nanotube growing out of a flat all-hexagonal graphene sheet by a root mechanism involving the presence of heptagons at the tube base [45]

Providing an atomistic picture of nanotube nucleation is more difficult [45]. The chemical processes involved in the co-evaporation of carbon and metal in the arc discharge, the solvation of carbon into the metal particle, the condensation of metal-carbide particles into quasi-spherical droplets upon cooling, and the subsequent precipitation of carbon, are extremely complex processes. Simulating all these steps requires a microscopically detailed understanding of the process of arc discharge evaporation which is not presently available. However, the present model does show that protrusions with a diameter small compare to their height can lead to nanotube nucleation, while wider protrusions lead only to strained graphene sheets and no nanotube growth.

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