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
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.
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