CARBON nanotubes1 are expected to have a wide variety of interesting properties. Capillarity in open tubes has already been demonstrated2–5, while predictions regarding their electronic structure6–8 and mechanical strength9 remain to be tested. To examine the properties of these structures, one needs tubes with well defined morphologies, length, thickness and a number of concentric shells; but the normal carbon-arc synthesis10,11 yields a range of tube types. In particular, most calculations have been concerned with single-shell tubes, whereas the carbon-arc synthesis produces almost entirely multi-shell tubes. Here we report the synthesis of abundant single-shell tubes with diameters of about one nanometre. Whereas the multi-shell nanotubes are formed on the carbon cathode, these single-shell tubes grow in the gas phase. Electron diffraction from a single tube allows us to confirm the helical arrangement of carbon hexagons deduced previously for multi-shell tubes1.

Single-shell carbon nanotubes of 1-nm diameter

The use of individual molecules as functional electronic devices was first proposed in the 1970s (ref 1) Since then, molecular electronics2,3 has attracted much interest, particularly because it could lead to conceptually new miniaturization strategies in the electronics and computer industry The realization of single-molecule devices has remained challenging, largely owing to difficulties in achieving electrical contact to individual molecules Recent advances in nanotechnology, however, have resulted in electrical measurements on single molecules4,5,6,7 Here we report the fabrication of a field-effect transistor—a three-terminal switching device—that consists of one semiconducting8,9,10 single-wall carbon nanotube11,12 connected to two metal electrodes By applying a voltage to a gate electrode, the nanotube can be switched from a conducting to an insulating state We have previously reported5 similar behaviour for a metallic single-wall carbon nanotube operated at extremely low temperatures The present device, in contrast, operates at room temperature, thereby meeting an important requirement for potential practical applications Electrical measurements on the nanotube transistor indicate that its operation characteristics can be qualitatively described by the semiclassical band-bending models currently used for traditional semiconductor devices The fabrication of the three-terminal switching device at the level of a single molecule represents an important step towards molecular electronics

Room-temperature transistor based on a single carbon nanotube

The major part of this chapter has already appeared in [1], but because of the length restrictions (in Science), the discussion on why we think this form is given in only brief detail. This chapter goes into more depth to try to answer the questions of why the fullerenes form themselves. This is another example of the very special behavior of carbon. From a chemist’s standpoint, it is carbon’s ability to form multiple bonds that allows it to make these low dimensional forms rather than to produce tetrahedral forms. Carbon can readily accomplish this and it is in the mathematics and physics of the way this universe was put together, that carbon is given this property. One of the consequences of this property is that, if left to its own devices as carbon condenses from the vapor and if the temperature range is just right, above 1000°C, but lower than 1400°C, there is an efficient self-assembly process whose endpoint is C60.

https://science.sciencemag.org/content/sci/273/5274/483.full.pdf

Crystalline Ropes of Metallic Carbon Nanotubes

CARBON nanotubes are predicted to have interesting mechanical properties—in particular, high stiffness and axial strength—as a result of their seamless cylindrical graphitic structure1–5. Their mechanical properties have so far eluded direct measurement, however, because of the very small dimensions of nanotubes. Here we estimate the Young's modulus of isolated nanotubes by measuring, in the transmission electron microscope, the amplitude of their intrinsic thermal vibrations. We find that carbon nanotubes have exceptionally high Young's moduli, in the terapascal (TPa) range. Their high stiffness, coupled with their low density, implies that nanotubes might be useful as nanoscale fibres in strong, lightweight composite materials.

Exceptionally high Young's modulus observed for individual carbon nanotubes

The Young's modulus, strength, and toughness of nanostructures are important to proposed applications ranging from nanocomposites to probe microscopy, yet there is little direct knowledge of these key mechanical properties. Atomic force microscopy was used to determine the mechanical properties of individual, structurally isolated silicon carbide (SiC) nanorods (NRs) and multiwall carbon nanotubes (MWNTs) that were pinned at one end to molybdenum disulfide surfaces. The bending force was measured versus displacement along the unpinned lengths. The MWNTs were about two times as stiff as the SiC NRs. Continued bending of the SiC NRs ultimately led to fracture, whereas the MWNTs exhibited an interesting elastic buckling process. The strengths of the SiC NRs were substantially greater than those found previously for larger SiC structures, and they approach theoretical values. Because of buckling, the ultimate strengths of the stiffer MWNTs were less than those of the SiC NRs, although the MWNTs represent a uniquely tough, energy-absorbing material.

http://science.sciencemag.org/content/sci/277/5334/1971.full.pdf

Nanobeam mechanics: Elasticity, strength, and toughness of nanorods and nanotubes

We have calculated the electronic structure of a fullerene tubule using a first-principles, self-consistent, all-electron Gaussian-orbital based local-density-functional approach. Extending these results to a model containing an electron-lattice interaction, we estimate that the mean-field transition temperature from a Peierls-distorted regime to a high-temperature metallic regime should be well below room temperature. Such fullerene tubules should have the advantages (compared to the other conjugated carbon systems) of a carrier density similar to that of metals and zero band gap at room temperature.

Are fullerene tubules metallic

Using both empirical potentials and first-principles total-energy methods, we have examined the energetics and elastic properties of all possible graphitic tubules with radii less than 9 \AA{}. We find that the strain energy per carbon atom relative to an unstrained graphite sheet varies as 1/${\mathit{R}}^{2}$ (where R is the tubule radius) and is insensitive to other aspects of the lattice structure, indicating that relationships derivable from continuum elastic theory persist well into the small-radius limit. We also predict that this strain energy is much smaller than that in highly symmetric fullerene clusters with similar radii, suggesting a possible thermodynamic preference for tubular structures rather than cage structures. The empirical potentials further predict that the elastic constants along the tubule axis generally soften with decreasing tubule radius, although with a distinct dependence on helical conformation.

Energetics of Nanoscale Graphitic Tubules

Scanning tunneling microscopy (STM) and spectroscopy experiments have been recently reported for individual single-wall carbon nanotubes (SWNT) [1,2], confirming the strongly one-dimensional nature expected for the electron states in these materials [3,4]. The STM experiments give a direct experimental probe of the electron density of states (DOS) near the Fermi level. We have recently shown that semiconducting SWNTs with similar diameters will have similar DOS near the Fermi level, and established an analogous correspondence for metallic nanotubes [5]. We also gave expressions for the positions of the peaks near the Fermi level. Here we derive a universal relationship for the DOS in the vicinity of the Fermi level for SWNTs. This relationship, based on the graphene sheet model, scales out the dependence on the nanotube diameter and otherwise only depends on whether the SWNT belongs to the semiconducting or metallic groups of nanotubes. We compare the predictions of this relationship with the DOS results calculated using first-principles band structure results for SWNTs

Universal Density of States for Carbon Nanotubes

We show how all extended graphitic tubules constructed by rolling up a single graphite sheet can be defined in terms of their helical and rotational symmetries. Specification of these symmetries is practically mandatory in all but the simplest calculations of tubule properties as a function of radius and structure. We also report results of a tight-binding study implemented by using these symmetries. This study shows that independent of their helicity the larger-diameter, moderate-band-gap semiconducting tubules all have band gaps given approximately by ${\mathit{E}}_{\mathit{g}}$=\ensuremath{\Vert}${\mathit{V}}_{0}$\ensuremath{\Vert}(${\mathit{d}}_{0}$/${\mathit{R}}_{\mathit{T}}$), where ${\mathit{R}}_{\mathit{T}}$ is the tubule radius and ${\mathit{V}}_{0}$ is the hopping matrix element between nearest-neighboring 2p orbitals oriented normal to the tubule surface and centered on carbon atoms separated by a distance ${\mathit{d}}_{0}$ along this surface. In addition, we show that all tubules constructed by rolling up the graphite sheet can be labeled in a fashion familiar in the description of helical chain polymers with translational symmetry.

Helical and rotational symmetries of nanoscale graphitic tubules.

As most technologically important metals will form oxides readily, any complete study of adhesion at real metal surfaces must include the metal-oxide interface. The role of this ubiquitous oxide layer cannot be overlooked, as the adhesive properties of the oxide or oxide-metal system can be expected to differ profoundly from the adhesive properties of a bare metal surface. We report on the development of a computational method for molecular-dynamics simulations, which explicitly includes variable charge transfer between anions and cations. This method is found to be capable of describing the elastic properties, surface energies, and surface relaxation of crystalline metal oxides accurately. We discuss in detail results using this method for \ensuremath{\alpha}-alumina and several of its low-index faces.

John W. Mintmire

Papers

Are fullerene tubules metallic

Energetics of Nanoscale Graphitic Tubules

Universal Density of States for Carbon Nanotubes

Helical and rotational symmetries of nanoscale graphitic tubules.

Electrostatic potentials for metal-oxide surfaces and interfaces.