Fullerene Nanotubes: C1,000,000 and Beyond
Some unusual new molecules—long, hollow fibers with tantalizing electronic and mechanical properties—have joined diamonds and graphite in the carbon family
Originally published in the July-August 1997 issue of
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 C1,000,000. 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.
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
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.
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
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.
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.
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
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.
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.
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.