FEATURE ARTICLE
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
Boris Yakobson, Richard Smalley
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.
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