Yes  No

SEARCH  

• Current Issue
• Past Issues
• On the Bookshelf
• Science in the News

• About
• Subscribe
• Advertise
• Sigma Xi

FEATURE ARTICLE

Fullerene Nanotubes: C_1,000,000 and Beyond

Some unusual new molecules—long, hollow fibers with tantalizing electronic and mechanical properties—have joined diamonds and graphite in the carbon family

Boris Yakobson, Richard Smalley

Originally published in the July-August 1997 issue of American Scientist.

Imagine holding in your hand a wand that is a single molecule. Such a wand would be so thin that it could not be seen under an ordinary microscope; it would be a nanotube, just a few atoms in circumference. But it could be very long. Such a tubule in fact exists in the laboratory today, and it has even been used there as a probe, poking down into the world of molecules. Called the carbon nanotube, it is elongated like a fiber, and yet it is hollow and inherits the perfection of atomic arrangement made famous by its predecessor, the buckyball—the remarkable closed cage of 60 symmetrically arranged carbon atoms that was recognized as a new form of carbon when it was discovered a decade ago. The buckyball's molecular family, the fullerenes, has expanded since that discovery; the nanotube is a new and very useful addition.

Carbon nanotubes are, effectively, buckyball structures played out as long strands rather than spheres. Their length can be millions of times greater than their tiny diameter. Their properties as a new material are remarkable—a fact that was evident almost as soon as they were first spotted in 1991, turning up in the soot and dirt piles that fill chambers where scientists produce fullerenes, large geometric carbon molecules.

A chemist might think of a carbon nanotube as a monoelemental polymer. (Most polymers, such as polyethylene, are carbon chains with other elements attached.) The buckyball is designated C₆₀; a carbon nanotube might be C_1,000,000. In physics terms it can be described as a single crystal in one direction, with a unit cell that keeps on propagating and repeating. This periodic pattern has the symmetry of a helix, not as complex as the double helix responsible for life itself, but possessing a special beauty in its monotonous order—a molecular incarnation of Ravel's Bolero. A mathematician will be delighted by the symmetry and rigor of these structures and how nicely they obey Euler's rule for polyhedra.

Likewise the nanotube has what a civil engineer would recognize as a beam-and-truss construction, a billion times smaller than such structures built to human scale. To satisfy the standard chemical requirements of carbon, every beam ties two carbon atoms by a strong covalent bond, and every atom accommodates exactly three neighbors. A nanotube, no matter how long, must thus ultimately be sealed on the ends to leave no dangling "unhappy" chemical bonds. The strength of these bonds and their clever organization makes nanotubes so highly resistant to tension that (with apologies to high-energy physicists) they could justly be called superstrings. Furthermore, electrons move easily along some carbon tubules, although their minuscule cross section permits electrical conductance only in a quantized fashion.

Several analogies, some of them famous, have been invented by science teachers to help their students and themselves comprehend the smallness of the small, and these can help us imagine nanotubes. One difficult dimension to imagine is the nanometer, a billionth of a meter. One could stare at a chip of graphite as Richard Feynman once stared at a drop of water. After magnifying our chip a billion times, creating a metal-gray rocky landscape about the size of Texas, we might spot a three-foot-diameter pipeline stretching from horizon to horizon. This is the nanotube. Actually, a one-nanometer-wide pipeline occupies almost no space even over a substantial length. In fact, nanotubes sufficient to span the 250,000 miles between the earth to the moon at perigee could be loosely rolled into a ball the size of a poppyseed. Together, the smallness of the nanotubes and the chemical properties of carbon atoms packed along their walls in a honeycomb pattern are responsible for their fascinating and useful qualities.

Growing Nanotubes

Nanotubes owe their discovery to Sumio Iijima of NEC Corporation. Iijima's samples were created by a direct-current arc discharge between carbon electrodes immersed in a noble gas. A similar apparatus had been used by Wolfgang Kratschmer of the Max Planck Institute for Nuclear Physics and Donald Huffman of the University of Arizona to mass-produce fullerenes.

The electric arc was used by Roger Bacon in the early 1960s to make "thick" carbon whiskers, and one can speculate that the nanotube discovery was a matter of looking more closely at the smallest products hidden in the soot. Iijima himself suggests that nanotubes may have been formed in those old experiments, but Bacon lacked the high-power microscope required to see them. Although various fullerenes can be produced by different ways of vaporizing carbon, followed by condensation in tiny clusters, the presence of an electric field in the arc discharge seems to promote the growth of the long tubules. Indeed, the nanotubes form only where the current flows, on the larger negative electrode. The typical rate of deposit is about a millimeter per minute at a current and voltage in the range of 100 amperes and 20 volts respectively, which maintains a high temperature of 2,000-3,000 degrees Celsius.

A year later, quite by chance, Thomas Ebbesen and P. M. Ajayan at NEC found a way to produce nanotubes in higher yields and make them available for studies by different techniques. Subsequently they found a way to purify them. An addition of a small amount of transition-metal powder (cobalt, nickel or iron) favors the growth of so-called single-walled nanotubes, a fact independently noticed by Donald Bethune at IBM Corporation and Iijima.

Metal clearly serves as a catalyst, preventing the growing tubular structure from wrapping around and closing into a smaller fullerene cage. The presence of a catalyst also allows one to lower the temperature. Without such cooling the arc is just too hot a place: Nanotubes coalesce and merge like the foam bubbles in a glass of beer. Condensation of a laser-vaporized carbon-catalyst mixture at a lower temperature (1,200 degrees Celsius in an oven-heated quartz tube) allowed a recent breakthrough at Rice University. Single-walled nanotubes now can be produced in yield proportions of more than 70 percent. Moreover, these nanotubes self-organize into bundles--ropes more than one-tenth of a millimeter long that look very promising for engineering applications. It is in this context, connecting dreams with the strides of progress, that we discuss the properties of nanotubes.

Nanotube Shape and Structure

Nanotubes are giant linear fullerenes. A fullerene, by definition, is a closed, convex cage molecule containing only hexagonal and pentagonal faces. (This definition intentionally leaves out possible heptagons, which are responsible for the concave parts and are treated as defects.) Like any simple polyhedron, a fullerene cage or a nanotube satisfies Euler's theorem (earlier proved by Descartes) relating the number of vertices (here, carbon atoms), edges (covalent bonds), and faces: v - e + f = 2. If the number of pentagons is p, and the other (f - p) faces are all hexagonal, then the doubled number of edges (each edge belongs to two faces) is 5p + 6(f - p), which also equals the tripled number of vertices (each trivalent carbon is shared by three adjacent faces).

A simple accounting then yields p = 12, and therefore a nice, defectless nanotube must have exactly 12 pentagons, the same dozen as in the buckyball! The strict rules of topology impose this family trait on all fullerenes. An even more obvious trait the nanotubes inherit from another ancestor, graphite, is a hexagonal pattern on their walls. Figure 4 illustrates this by showing two possible ways of constructing a nanotube from a precursor form of carbon.

One can start by cutting C₆₀ in half and inserting 10 more carbon atoms in the breach to get a rugby-ball-like C₇₀, then adding another belt to make C₈₀, and repeating this process indefinitely to create a buckytube of unlimited length. Or a nanoscopic tailor might start with a nice big piece of a one-atom-thick sheet of graphite, cut a long strip out of it and roll it up into a cylinder with no stitches left. The tailor has a decision to make, though: whether to choose the strip width parallel to the dense zigzag row of bonds, perpendicular to it, or at some angle θ. The first choice results in a so-called zigzag nanotube, the second an armchair tubule; the third arrangement is chiral and results from turning the sheet at an angle somewhere between the angles of the zigzag (0 degrees) and the armchair (30 degrees). The oriented width is specified by a rollup vector (n,m), which records the number of steps along the a and b directions. Its integer components uniquely define the tubule diameter d and its corkscrew symmetry, called helicity, or chiral angle θ. As follows from elementary geometry and an assumption that the C-C bond has its normal length of 0.14 nanometers,

For example, the integers (9,0) or (5,5) correspond respectively to zigzag (θ = 0 degrees) or armchair (θ = 30 degrees) buckytubes that are roughly 0.7 nanometers in diameter. Adding the terminating caps completes the job. Any such seamless, coherent arrangement of atoms has a certain helicity, and recognition of this, based on observed electron-diffraction patterns, was perhaps even more important in Iijima's discovery than the fact that the nanotubes are thin cylinders.

It is the chemical genius of carbon—the ability to satisfy its four valence electrons by bonding with three neighbors—that makes the above structures possible in graphite and its fullerene relatives. Each of three electrons is assigned to a partner; the fourth is shared by everybody, being delocalized all over the network. These shared electrons, called π electrons, make fullerenes aromatic and allow some nanotubes to conduct electricity.

Although sp ²-carbon (the term for the bonding arrangement just described) is happiest in a flat hexagonal tiling, rolling the sheet up expends relatively little elastic energy, which is generously returned when all the dangling unhappy bonds at the edges are eliminated in a seamless cylinder. Furthermore, carbon doesn't really mind a few pentagons or heptagons (seven edges). Geometrically these insertions allow for a local Gaussian curvature, positive and caplike in the case of a pentagon or negative and saddlelike where a heptagon is involved (Figure 5). With these two elements, all kinds of equilibrium shapes and plumbing become possible in carbon construction, giving rise in the literature to numerous fantasies.

Both the morphology of nanotubes and their helical structure are inherently related to the mechanisms by which they grow. The formation of these nanoscopic stalagmites in most cases requires an open end where carbon atoms arriving from the gas phase can coherently land. The growth of nested multiwall nanotubes can be stabilized by the strained "lip-lip" bonding between the coaxial edges, highly fluctuating and therefore accessible for new atoms. In general, the open end can be maintained either by a high electric field, by the entropy opposing the orderly cap termination or by the presence of a metal catalyst. The last mechanism, in the form of a tiny metal (nickel-cobalt) cluster scooting around the nanotube edge, is apparently responsible for the high-yield growth of (10,10) tubes recently reported by one of the authors' (Smalley's) groups. The alloy cluster anneals all unfavorable structures into hexagons, which in turn welcome the newcomers and promote the continuous growth of a straight cylindrical tower (Figure 6).

Crunchy Molecules

The carbon atoms in diamond are tetrahedrally bonded to their four nearest neighbors, forming the rigid three-dimensional lattice that gives diamond its unparalleled hardness. By contrast, the two-dimensional arrangement of atoms in a graphene (graphite-sheet-like) nanotube wall permits some out-of-plane flexibility. Combined with the strength of the constituent bonds, this promises spectacular mechanical properties.

Of course, common graphite doesn't strike one as a very strong material. Everyone has seen a pencil lead broken by a gentle bending effort. But as Uzi Landman from the Georgia Institute of Technology once put it, "small is different." The minuscule diameter of a nanotube merely leaves no room for the numerous imperfections and microcrevices that make a pencil lead so brittle. As early nanotube studies progressed, several groups reported high-resolution images of greatly distorted tubes with no traces of fracturing. However, it was not always clear whether the deformations were truly elastic or partially caused by embedded defects such as pentagonal or heptagonal rings.

In 1994, at one of the international meetings, Iijima approached Jerzy Bernholc of North Carolina State University with a few beautiful transmission-electron-microscope shots of nanotubes, each showing all the distinct features of a nice elastic bend (Figure 7). Meanwhile, in France, a group led by J. F. Despres reported similar observations. In experiments, applying controllable forces to a tiny nanotube is difficult, and so most of the evidence of the behavior of nanotubes as a material relies on still-life images of the singular victims of mechanical duress during sample preparation. If similar shapes could be simulated on a computer, one could learn about the forces involved and judge whether the deformation is indeed elastic and reversible.

The forces and stresses in molecules (the title of Richard Feynman's at-first-unnoticed and controversial undergraduate thesis, which eventually became the famous Hellman-Feynman theorem) are a subtle problem in quantum mechanics. Although numerical methods have progressed dramatically in this field, a first-principles treatment for a molecule containing thousands of atoms often remains prohibitively expensive. To get around this obstacle, one can resort to a recipe for interatomic forces, F, if such a recipe exists and is well tested, and then simply apply classical mechanics in the form of Newton's familiar second law of motion, F = ma (force equals mass times acceleration), to every one of thousands of atoms, thus computing their motion step by step. This is what classical molecular dynamics does. One of us (Yakobson), together with Charles Brabec of North Carolina State University, has been involved in such modeling.

Our calculations predict the energy cost of deforming a nanotube, and its elastic parameters agree with those known for graphite or found by first-principle theoretical methods. We were surprised, however, to see humps and bumps on the strain-energy curves beyond what Hooke's law would predict: that each displacement would generate a proportional restoring (elastic) force.

This indicated that there must be some abrupt changes in the molecule under mechanical load. Indeed, each singularity in the stress-strain curve appears to correspond to a sudden shape switch of an initially perfect cylinder. All generic modes of mechanical load have been studied this way: bending (Figure 7), torsion (Figure 8) and axial compression (Figure 10). In the simulations the nanotube is seen to snap from one shape to the next, emitting acoustic waves along its walls at every "crunch." These "crunchy molecules" never actually break, but reversibly accommodate to external stress. It became clear that, besides the similarity with the patterns seen in experiments, the observed buckling phenomena resemble the instabilities well known in macroscopic elasticity of the hollow objects, thin shells.

The hollow structure is indeed an outstanding feature of fullerene molecules and of nanotubes in particular. On the other hand, the interest in the elasticity of macroscopic shells and rods dates back to the 18th-century work of Leonhard Euler (whose rule for polyhedra we just discussed above). He discovered the phenomenon of elastic instability: A rod or column compressed axially remains straight until a critical force is reached. It then becomes unstable (undergoes bifurcation, mathematically speaking) and buckles sideways. The behavior of the hollow tubules is more complex, but still predictable with continuum-elasticity methods. In its application to nanotubes, the correspondence between the elastic-shell model and molecular dynamics is remarkable. The laws of continuum mechanics are amazingly robust and allow one to treat even intrinsically discrete objects only a few atoms in diameter.

Superstiff Shells

A synergism of atomistic model and macroscopic structural mechanics was achieved with the proper choice of parameters of the continuum shell: a Young's modulus of elasticity (Y) equal to 5 terapascals (a terapascal is a trillion pascals, a unit of pressure), and an effective thickness (h) of 0.07 nanometers. The small thickness simply reflects the fact that flexing is much easier than stretching for a single graphite sheet. The large modulus is in fact consistent with the standard value for graphite, if one takes into account the normal spacing (c) of 0.34 nanometers between the sheets in a stack: Y(h/c) = 1 terapascal.

The shell model has the benefits of any reductionist approach: Instead of dealing with innumerable interatomic forces, one has a smooth piece of uniform material. The insight helps one to handle larger systems, multiwall tubes or onions, sets of cylinders or spheres nested like a Russian doll. For example, this allowed us to calculate a particular hydrostatic compressibility or bending stiffness of a nanotube containing an arbitrary number of walls. The compressibility appears to depend on nanotube diameter and is a mixture of very rigid in-plane behavior and a relatively gentle coupling between the layers (owing to the weak intermolecular van der Waals forces).

Bending stiffness appears to be very high for the thinnest single- or double-walled nanotubes and can surpass the commonly expected level by a factor of four, although it converges to normal values for the thicker nanotubes containing many walls.

The above can serve as a partial explanation of recent measurements of an exceptional Young's modulus. The elegant approach of the scientists from NEC has enabled the amplitude of the thermal vibrations of a tiny nanotube whisker to be visualized (Figure 9) and measured. The equipartition theorem of statistical mechanics prescribes that the energy of any degree of freedom is determined by the temperature. The vibration amplitude, then, allows one to assess the stiffness of the cantilever and the effective Young's modulus of the nanotube material. In spite of some consonance with the shell model (which agrees in turn with the common graphite data!), the extracted high values, up to 4 terapascals, cannot be easily explained. There must be more fundamental causes on the chemical-bond level, a matter that requires further study. The same technique was recently used by a group at the University of California at Berkeley, who also report a high Young's modulus of 1.2 terapascals for a nanotube made of boron nitride.

The ability of a nanotube to sustain axial force to some level, but then to buckle sideways, suits it well for use as a nanoprobe in a scanning microscope, which studies the response of a sample to carefully controlled disturbance. In the work of the Rice group, a nanotube has been employed as a smart tool whose gentle touch does not damage the sample and allows the probe itself to survive the crash if this happens. At the same time, the tool's slenderness allows it to image sharp topographic details.

Strength and Fracture

Although nanotubes sustain all kinds of twisting and bending, there should be some way to break them. How strong in tension is a carbon nanotube? It is too small to be pulled apart with one's hands. It is too strong to be broken when pulled by tiny "optical tweezers" in the laboratory. The proper instruments for a conclusive test are still to be built, or perhaps experimentalists must wait until nanotubes grow longer in chemists' laboratories. In the meantime, some possible tests are being done with computer modeling.

In molecular-dynamics simulations, nanotubes break only at very high strain, and in a peculiar manner. Elastic stretching simply elongates the hexagons in the tube wall, until at the critical point an atomic disorder suddenly nucleates: One or a few carbon-carbon bonds break almost simultaneously, and the resulting hole in a tube wall becomes a precursor of fracture (Figure 11). The atomic disorder propagates very quickly along the circumference of the tube. The strain, which was quite uniform along the tube before this threshold, now redistributes itself to form a largely distorted and unstable neck between the two quickly relaxing segments of the nanotube.

A further stage of fracture displays an interesting feature: the formation of two or more distinct chains of atoms, ... =C=C=C= ... (= denotes a double bond), spanning the two tube fragments. Their vigorous motion (substantially above the thermal level) results in frequent collisions and touching between the chains, which leads to merging of the chains. Soon only one survives. Remarkably, a further increase of the distance between the tube ends does not break this chain. The tube elongates not by virtue of straining the constituent bonds, but rather by increasing the number of carbon atoms that pop out from both sides into the necklace. In this chain carbon atoms have only two neighbors (sp-hybridization), and the change of local order costs substantial energy.

Although large bond strain, and one-dimensional chains in particular, are not modeled very precisely by classical interatomic forces, this scenario is similar to the monoatomic chain unraveling suggested in field-emission experiments, where the electrostatic force unravels the tube as a knitter would unravel the sleeve of a sweater. Furthermore, the high breaking strain is now corroborated by evidence of local tension of above 300 gigapascals (billions of pascals) in the intact (unbroken) stack of carbon sheets in nested fullerenes or "buckyonions" (Figure 12), which translates into an almost 30-percent strain level. More accurate and expensive simulations are under way, and the theoretical strength of a nanotube will soon be identified.

Why is it so important? Generally, of course, a macroscopic chunk of any material is not nearly as strong as theory predicts. The reason for that is the presence of tiny cracks and their ability to amplify and concentrate stress locally (Figure 13, left). When a load is applied uniformly, these stress concentrators multiply it near the crack tip and pull and break the adjacent chemical bonds apart. The crack grows and propagates, and the material fails when one least expects it.

In a bundle of nanotubes the situation looks much more promising: Each tube is very thin, and the coupling between the tubules is weak. As a result, even if one nanotube breaks, it produces almost no effect on the others (Figure 13, right). The tiny crack is blocked, and the chain reaction of fracture is terminated. There is good reason, then, to expect a macroscopic one-inch-thick rope, where 1014 parallel buckywires are all holding together, to be almost as strong as theory predicts.

Just how strong might it be? The Young's modulus of recently grown ropes (a triangular pack of (10,10) single-wall tubules) can be estimated using those shell parameters mentioned above. It turns out to be close to 630 gigapascals. The breaking strain in simulations varies with temperature and the tube diameter, but experimental evidence (the unbroken graphene shells shown in Figure 12) suggests it could be above one-fifth. (Keep in mind this is a preliminary number, which does seem high.) This means one might expect for such ropes a real-life strength of 130 gigapascals, almost a hundred times stronger than steel but one-sixth its weight. This may be a useful combination.

In a 1978 science-fiction novel called Fountains of Paradise Arthur Clarke described a strong filament or cable being lowered from a geosynchronous satellite and used by the engineers of the future to move things up and down from earth-a space elevator. Let's ignore for a moment the tremendous problems involved-atmospheric turbulence, the Coriolis forces, the ravages of ozone and radiation up there-and think about how strong such a cable should be. It takes freshman college physics to figure that the tension in a cable is proportional to its specific gravity ρ = 1.3, a square of the earth radius R, and a simple integral: ∫(1/r ² - r/R _s ³)dr. The integral spans 22,300 miles all the way from the ground to the synchronous orbit, accumulates a lot and produces a strength requirement of 63 gigapascals. As speculative as it is, the story benchmarks this number. None of the materials now known to humankind get close to such strength. Fullerene cables someday may.

Many more-realistic applications can be imagined for a material even half as strong, thanks to the zillions of electrons fidgeting around the carbon ions. Quantum uncertainty and the Pauli exclusion principle (which enforces separation between electrons) prevent the electrons from getting too close under compression, and because of their attraction to positive charges they resist being pulled apart in tension. Not all the electrons play that hard in this tug-of-war game. Some of them occupy atomic orbitals oriented perpendicular to the plane of hexagons (Figure 4f) and contribute very little to cohesion—so little that they are often called "nonbonding." Instead, they can move along the graphene plane (that is the nanotube wall), carrying their negative charge and contributing to the electric conductivity. This brings the discussion to another peculiar property of nanotubes.

Metal or Semiconductor?

Are nanotubes metallic or semiconducting? This question was addressed at the Naval Research Laboratory and Massachusetts Institute of Technology before the first real tubules were sighted. The answer was "both."

The electrical properties of any material are largely determined by quantum partitions-bands in the energy scale that electrons occupy. Some energy levels correspond to states simply incompatible with the symmetry of the material structure and are not allowed. They create gaps between the energy bands available for the electrons. Lower bands are usually full and leave no room for motion. Higher bands can be partially occupied by electrons, able in this case to accept a little kinetic energy and get going if an electric field happens to push them. This partially occupied area is called a conduction band. The conductivity is found in this band. The nature of the gap is the key to modern electronics. Wide-bandgap semiconductors (such as gallium nitride) make more stable and powerful transistors and can emit the blue color sought today for flat-panel displays; a narrow bandgap (as in mercury cadmium telluride) is good for sensing infrared light for night vision.

In planar graphite there is no bandgap between the empty and full states, but there are only a tiny number of electrons capable of moving along the graphene sheets. Graphite therefore has weak conductivity and is called a semimetal. Figure 14 shows what happens, however, when one rolls it up into a tube. Now the velocity of an electron (actually, a wave-vector k, but never mind) has only one direction available, along the tube, rather than the two directions that were available in the graphene plane. Motion in the perpendicular direction is now around the tube and has to satisfy new periodicity conditions. This reduces the azimuthal freedom of an electron to just a few discrete possibilities, as the family of curves indicates.

The electrons occupy the states below a certain energy called the Fermi level (actually, the picture is somewhat blurred by thermal excitations), which in this case is positioned right at the crossing of the valence and conduction bands. Therefore there is no gap; electrons can move, and our (10,10) nanotube should conduct. How well? For graphite, the low density of such carriers results in poor conductivity. For a parallel bundle of armchair nanotubes, the carrier density is tens of thousand times higher, and the conductivity is like that of a good metal.

Since such analysis depends largely on the corkscrew symmetry of the tube, however, its conductivity varies surprisingly with helicity. Only the armchair (n,n) tubes are truly metallic by symmetry. All other tubes have an energy gap, although it is tiny for those zigzag (n,0) tubes with n a multiple of three. The gap decreases in inverse proportion with diameter, and thus approaches zero for planar graphite. In principle, any one-dimensional metal is prone to so-called Peierls instability, when translational symmetry breaks, as in the hydrocarbon chains in polyacetylene, ... ÷CH÷CH÷CH÷ ... → -CH=CH-CH= ..., and the alternating spacing results in a nonzero gap. Fortunately, in the case of nanotubes, even a little thermal motion is sufficient to smear away this pattern and restore the uniformity, so that conductivity stays high even without enrichment by doping, the addition of another element.

In experiments, attaching contacts to a nanotube takes almost as much dexterity as stretching it mechanically. Reports of successes in connecting devices from the macroworld to "molecular wires" came last year from Belgium, then from Harvard and from NEC, with gradual important progress in probe attachment. The simpler two-probe scheme makes it difficult to separate the resistance of the contacts, including a possible Schottky barrier (an area where current can flow only one way), from the resistance of the nanotube itself. A nanotube is placed on a substrate with prearranged gold pads, and then is either contacted by the cantilever probe tip of a microscope or connected by the metal leads deposited lithographically across the tube (Figure 15) and all the way to the pads. Current is put through the external pair of probes, and the voltage measured on the internal couple tells us about the conductivity. Variations of resistivity with temperature and with external magnetic field (magnetoresistance) were used to reveal the nature of conductance.

In these tests both metallic and nonmetallic nanotubes have been found, illustrating the profound sensitivity of the electrical properties to the geometry of a specific tube. However, none of the nanotubes showed an increase in resistance with temperature, a classic attribute of a metal, obscured probably by the multiwall structure and the possible presence of defects. The synthesis of single-wall armchair nanotubes provided a way out of this uncertainty. Their resistivity grows with heat, as it does for all the metal pieces in our home appliances and electric bulbs.

Quantum Wires

Often the nanoworld plays by different rules. Although the electrical conductance of nanotubes is an important emulation of big-world materials, their small size and perfect structure lead to something utterly novel. They behave like waveguides for electrons, permitting only a few propagating modes—a property more common in fiber-optic communication.

Instead of changing smoothly with applied voltages, for instance, currents in nanotubes increase and decrease in a stepwise fashion, revealing the grainy nature of such quantum wires. This phenomenon was first noticed in bundles of tubes, where it was thought that perhaps a single nanotube was throttling the current. It was then explicitly measured on a seventh-of-a-micron-long section of a 1.4-nanometer-wide armchair tubule. Except for the minuscule size (Figure 16), the setup resembles a field-effect transistor in your computer: The current through the tube depends on the bias voltage between the ends and the potential in the middle of the tube (gate).

A symmetrical and stiff nanotube allows no defects and almost no vibrations (phonons), so nothing scatters an electron as it travels almost freely from end to end. This makes its motion ballistic. It behaves like a "particle in a box," and the box is so tiny that the electron motion is quantized, so only a few energy levels are possible. In addition, the capacitance, C, of this box is so small that adding or removing just one electron is energetically costly, e ²/C being greater than the thermal energy. Overall these factors create visible spacing between the energy levels involved in a conductance event. The electron can only glide smoothly from source to drain if a nice overall slope is in place. This happens only at certain gate voltages that adjust the ladder of energy levels up or down, and is indeed observed as a sequence of sharp peaks in the current.

Similarly, a gradual change in the bias causes a stepwise rather than smooth growth of current, demonstrating again quantum behavior in a nanotube wire. To suppress all thermal noise, studies of such behavior require very low temperatures, from 10 degrees Kelvin down to millikelvins, just above absolute zero. Electrical properties of this nature are also sensitive to the perfection of the tube: Even a minor twist or bend can shift those energy levels and result in a sharp electrical signal in the tiny circuit. If these results predict their real-world behavior, nanotubes may open up fascinating opportunities for the developers of microelectromechanical systems of the future.

The conductivity in molecular wires brings attention again to the way that carbon achieves the itineracy necessary for metallic behavior in an extended lattice. It is the same property that makes benzene aromatic. Here the π electrons are completely itinerant around each carbon ring without at the same time being chemically reactive. No normal metal has that property. Lengths of (n,n) carbon nanotubes will be true molecules that are also true metals, something chemistry has never had before. There have been conducting molecules, but they were never good conductors. When doped they became pretty good conductors but pretty bad molecules, destroyed by contact with air or water. The (10,10) buckytubes are the first in a potentially infinite new class of objects that are great molecules and great metallic conductors.

Applications

Potential applications of carbon nanotubes abound, together forming a highly diversified technology portfolio. The first group includes macro-applications, where armies of nanotube molecules might line up to form a light, strong wire or a composite that could be unbeatable as a material for making lightweight vehicles for space, air and ground. If the costs ever permit, these materials might be used in the elements of bridges, or of tall, earthquake-resistant buildings or towers. Light ammunition and bulletproof vests can be envisaged. All these applications rely on mechanical strength, a property that is essentially straightforward but that requires volume production of the crucial components, defect-free nanotubes of greater length.

The hollow structure of nanotubes, in particular of the single-wall and wider variety, apparently gives them their ability to collapse under compression and then to restore the volume. Such a property is required for a product such as heavy-duty shock absorbers. The outstanding thermal conductivity along the tubes, combined with the relatively low rate of heat transport in the perpendicular direction, may be of interest for microelectronics, where progressing miniaturization demands better heat sinks. Development of some of the next-generation processors for our computers is currently arrested by the simple problem of overheating. Further, the similarity in structure and mechanical properties of carbon- and boron-nitride nanotubes suggests a perfect marriage, where a conducting carbon tubule is coated by an insulating and more stable to oxidation boron-nitride.

On the scale of the very small, we encounter an even broader spectrum of possibilities for the use of single nanotubes. The use of crash-proof nanoprobes in scanning microscopy, already demonstrated, exploits the mechanical resilience and conductivity of carbon nanotubes. Open-ended "nanostraws" could penetrate into a cellular structure for chemical probing or could be used as ultrasmall pipettes to inject molecules into living cells with almost no damage to the latter. The yet-unexplored possibility of excitonic transport through semiconducting nanotubes—where energy would travel without charge flow—may lead to novel probes for near-field optical microscopy.

Nanotubes with a wide range of electrical properties likely will serve in smaller and faster computing machines in the future. A pure-carbon metal-semiconductor heterojunction (based on embedding a pentagon-heptagon pair between nanotube segments of different helicity) has been recently analyzed. At low temperatures, quantum ballistic transport gives us nanotube quantum wires, the core of a "single-electron transistor."

The probable coupling of external mechanical stimuli with conductance gives nanotubes entry into the family of future submicroelectromechanical systems. Indeed, a C₆₀-based electromechanical amplifier has recently been reported. One can anticipate even better performance from a nanotube, prone as it is to mechanical distortions. Sharp, conducting nanotube tips could serve as electron guns, lighting up the phosphor layer on flat-panel displays. Furthermore, a buckyball encapsulated in a nanotube segment of proper diameter glides freely from end to end, trapped weakly in each end-cap by van der Waals forces, and an external voltage could move a charged C₆₀- molecule back and forth. One bit of information read or written into such a two-state trigger gives a computer equipped with a two-dimensional array of such "buckyshuttles" an astonishing RAM capacity .

All these applications face a common problem: how to properly implant a nanotube with desirable properties into a larger device or a circuit. To become practical, furthermore, this has to be done multiply and reproducibly. The issues of multiplicity and batch fabrication arise as soon as experimental feasibility is demonstrated.

Making nanotubes of high quality and in volume is crucial if their properties are to be exploited. Recent breakthroughs are significant, but better ways of nanotube making are needed. They may come as a gradual extension of the current methods, or the solution may lie in processes entirely different and unexpected. To challenge biotechnologists, Rod Ruoff from Washington University once tossed out the idea of breeding new spider species that would spin nanotubes on the cheap. The energetics of carbon bonds and the known methods of synthesis suggest that such a useful arachnid would probably be made of metal and enjoy a very hot climate! But nature sometimes does offer a way; there may be some enzyme on the shelf that would reduce the high-temperature process to the soft chemistry of a fermenter.

Vanguard laboratories around the world seek better solutions, both collaborating and competing with each other. Nature doesn't compete with anybody; it just takes its time and surprises us once and again. Who could expect a beautifully shaped pure-carbon torus (Figure 17) to persistently appear as a spinoff of nanotube growth, looking just like a "crop circle" viewed from the air? The future of nanotube science is full of surprises, some of them peculiar, some with the actual promise to improve our lot.

Acknowledgments

One of the authors (Yakobson) is grateful to the Wright Laboratory Materials Directorate and NASA Ames Center for their support. Work at Rice University was supported by the Office of Naval Research and the National Science Foundation. Both authors thank numerous colleagues for their contributions.

Bibliography

• Banhart, F., and P. M. Ajayan. 1996. Carbon onions as nanoscopic pressure cells for diamond formation. Nature 382:433-435.
• Bethune, D. S., C. H. Kiang, M. S. de Vries, G. Gorman, R. Savoy, J. Vazques and R. Beyers. 1993. Cobalt-catalysed growth of carbon nanotubules with single-atomic-layer walls. Nature 363:605-607.
• Bockrath, M., D. H. Cobden, P. L. McEuen, N. Chopra, A. Zettl, A. Thess and R. E. Smalley. 1997. Single-electron transport in ropes of carbon nanotubes. Science 275:1922-1925.
• Chico, L., V. H. Crespi, L. X. Benedict, S. G. Loui and M. L. Cohen. 1996. Pure carbon nanoscale devices: nanotube heterojunctions. Physical Review Letters 76:971-974.
• Chopra, N. G., L. X. Benedict, V. H. Crespi, M. L. Cohen, S. G. Louie and A. Zettl. 1995. Fully collapsed carbon nanotubes. Nature 377:135-138.
• Clarke, Arthur C. 1979. The Fountains of Paradise. New York: Jovanovich. Dai, H., J. H. Hafner, A. G. Rinzler, D. T. Colbert and R. E. Smalley. 1996.
• Dai, H., J. H. Hafner, A. G. Rinzler, D. T. Colbert and R. E. Smalley. 1996. Nanotubes as nanoprobes in scanning probe microscopy. Nature 384:147-150.
• Dai, H., E. W. Wong and C. M. Lieber. 1996. Probing electrical transport in nanomaterials: Conductivity of individual carbon nanotubes. Science 272:523-526.
• Despres, J. F., E. Daguerre and K. Lafdi. 1995. Flexibility of graphene layers in carbon nanotubes. Carbon 33:87-92.
• Dresselhaus, M. S., G. Dresselhaus and P. C. Eklund. 1996. Science of Fullerenes and Carbon Nanotubes. San Diego: Academic Press.
• Ebbesen, T. W., and P. M. Ajayan. 1992. Large-scale synthesis of carbon nanotubes. Nature 358:220-222.
• Ebbesen, T. W., H. J. Lezec, H. Hiura, J. W. Bennett, H. F. Ghaemi and T. Thio. 1996. Electrical conductivity of individual carbon nanotubes. Nature 382:54-56
• Fischer, J. E., H. Dai, A. Thess, R. Lee, N. M. Hanjani, D. DeHaas and R. E. Smalley. 1997. Metallic resistivity in crystalline ropes of single-wall carbon nanotubes. Physical Review B 55:R4921-4924.
• Haddon, R. C. 1993. Chemistry of the fullerenes: The manifestation of strain in a class of continuous aromatic molecules. Science 261:1545-1550.
• Heer, W. A., W. S. Bacsa, A. Chatelain, T. Geftin, R. Humphrey-Baker, L. Forro and D. Ugarte. 1995. Aligned carbon nanotube films: Production and optical and electronic properties. Science 268:845-847.
• Iijima, S. 1991. Helical microtubules of graphitic carbon. Nature 354:56-58.
• Iijima, S., and T. Ichihashi. 1993. Single-shell carbon nanotubes of 1-nm diameter. Nature 361:603-605.
• Iijima, S., C. J. Brabec, A. Maiti and J. Bernholc. 1996. Structural flexibility of carbon nanotubes. Journal of Chemical Physics 104:2089-92.
• Joachim, C., and J. K. Gimzewski. 1997. An electromechanical amplifier using a single molecule. Chemical Physics Letters 265:353-357.
• Isaacs, J. D., A. C. Vine, H. Bradner and G .E. Bachus. 1966. Satellite elongation into a true sky-hook. Science 151:682-683.
• Kratschmer, W., L. D. Lamb, K. Fostiropoulos and D. R. Huffman. 1990. Solid C₆₀: a new form of carbon. Nature 347:354-358.
• Langer, L., V. Bayot, E. Grivei, J.-P. Issi, J. P. Heremans, C. H. Olk, L. Stockman, C. Van Haesendonck and Y. Bruynseraede. 1996. Quantum transport in a multiwalled carbon nanotube. Physical Review Letters 76:479-482.
• Liu, J., H. Dai, J. H. Hafner, D. T. Colbert, R. E. Smalley, S .J. Tans and C. Dekker. 1997. Fullerene crop circles. Nature 385:781-782.
• Mintmire, J. W., B. I. Dunlap and C. T. White. 1992. Are fullerene tubules metallic? Physical Review Letters 68:631-634.
• Rao, A. M., E. Richter, S. Bandow, B. Chase, P. C. Eklund, K. A. Williams, S. Fang, K. R. Subbaswamy, M. Menon, A. Thess, R. E. Smalley, G. Dresselhaus and M. S. Dresselhaus. 1997. Diameter-selective Raman scattering from vibrational modes in carbon nanotubes. Science 275:187-191.
• Rinzler, A. G., J. H. Hafner, P. Nikolaev, L. Lou, S. G. Kim, D. Tomanek, P. Norlander, D. T. Colbert and R. E. Smalley. 1995. Unraveling nanotubes: field emission from an atomic wire. Science 269:1550-1553.
• Ruoff, R. S., J. Tersoff, D. C. Lorents, S. Subramoney and B. Chan. 1993. Radial deformation of carbon nanotubes by van der Waals forces. Nature 364:514-516.
• Saito, R., M. Fujita, G. Dresselhaus and M.S. Dresselhaus. 1992. Electronic structure of chiral graphene tubules. Applied Physics Letters 60:2204-2206.
• Scuseria, G. E. 1992. Negative curvature and hyperfullerenes. Chemical Physics Letters 195:534-536.
• Tans, S. J., M. H. Devoret, H. Dai, A. Thess, R. E. Smalley, L. J. Geerligs and C. Dekker. 1997. Individual single-wall carbon nanotubes as quantum wires. Nature 386:474-476.
• Terrones, M., N. Grobert, J. Olivares, K. Kordatos, W. K. Hsu, J. P. Zhang, J. P. Hare, H. W. Kroto, K. Prassides, A. K. Cheetham, P. Townsend and D. R. M. Walton. In press. Controlled production of aligned nanotube bundles. Nature. Thess, A., R. Lee, P. Nikolaev, H. Dai, P. Petit, J. Robert, C. Xu, Y. H. Lee, S. G. Kim, A. G. Rinzler, D. T. Colbert, G. Scuseria, D. Tomanek, J. E. Fischer and R .E. Smalley. 1996. Crystalline ropes of metallic nanotubes. Science 273:483-487.
• Treacy, M. M. J., T. W. Ebbesen and J. M. Gibson. 1996. Exceptionally high Youngs modulus observed for individual carbon nanotubes. Nature 381:678-680.
• Yakobson, B. I. 1991. Morphology and rate of fracture in decomposition of solids. Physical Review Letters 67:1590-1593.
• Yakobson, B. I., C. J. Brabec and J. Bernholc. 1996a. Nanomechanics of carbon tubes: Instabilities beyond the linear response. Physical Review Letters 76:2511-2514.
• Yakobson, B. I., C. J. Brabec and J. Bernholc. 1996b. Structural mechanics of carbon nanotubes: From continuum elasticity to atomistic fracture. Journal of Computer-Aided Materials Design 3:173-182.
• Yakobson, B. I., M. P. Campbell, C. J. Brabec and J. Bernholc. In press. Tensile strength, atomistics of fracture, and C-chain unraveling in carbon nanotubes. Computational Materials Science.