Page 157 - Carbon Nanotubes

Mechanical and thermal properties of carbon nanotubes i 47
present in pyrolytic graphite. Therefore, it is possible posites involving carbon nanotubes and plastic, epoxy,
that the on-axis thermal conductivity of carbon nano- metal, or carbon matrices remain on the horizon at the
tubes could exceed that of type 11-a diamond. time of this review.
Because direct calculation of thermal conductivity The ultimate tensile strength of a uniaxially aligned
is difficult[21], experimental measurements on com- fiber-reinforced composite is given to reasonable ac-
posites with nanotubes aligned in the matrix could be curacy by the rule of mixtures relation:
a first step for addressing the thermal conductivity of
carbon nanotubes. High on-axis thermal conductivi-
ties for CCVD high-temperature treated carbon fibers
have been obtained, but have not reached the in-plane
thermal conductivity of graphite (ref. [3], Fig. 5.1 1, where a, is the composite tensile strength, oF is the
p. 115). We expect that the radial thermal conductiv- ultimate tensile strength of the fibers, uk is the matrix
ity in MWNTs will be very low, perhaps even lower stress at the breaking strain of the fibers, and V, is
than the c-axis thermal conductivity of graphite. the volume fraction of fibers in the composite. This
The thermal expansion of carbon nanotubes will rule holds, provided that
differ in a fundamental way from carbon fibers and
from graphite as well. Ruoff[5] has shown that the ra- 1. The “critical volume fraction” is exceeded,
dial thermal expansion coefficient of MWNTs will be 2. the strength distribution or average strength of the
essentially identical to the on-axis thermal expansion fibers is known,
coefficient, even though the nested nanotubes in a 3. the dispersion of fibers in the matrix is free of
MWNT are separated by distances similar to the in- nonuniformities that are a consequence of the fab-
terplanar separation in graphite and the forces be- rication process and that would give rise to stress-
tween nested tubes are also only van der Waals forces. concentrating effects,
The explanation is simple and based on topology: un- 4. the aspect ratio of the fibers is sufficient for the
like graphene sheets in graphite, the nanotube sheet matrix type,
is wrapped onto itsecf so that radial expansion is gov-
erned entirely by the carbon covalent bonding net- 5. the fiber is bound to the matrix with a high-
work; the van der Waals interaction between nested strength, continuous interface.
cylinders is, therefore, incidental to the radial thermal
expansion. We, therefore, expect that the thermal co- The five factors mentioned above are discussed in de-
efficient of expansion will be isotropic, in a defect-free tail in ref. [23] and we mention only briefly factors 2
SWNT or MWNT. through 4 here, and then discuss factor 5 at some
Stress patterns can develop between fibers and matrix length.
in fiber-matrix composites, as a result of differential The strength distribution of carbon nanotubes, fac-
thermal expansion during composite production. An tor 2, could be estimated by a statistical fit to the in-
isotropic thermal coefficient of expansion for carbon ner and outer diameter of many (typically 100 or more
nanotubes may be advantageous in carbon-carbon nanotubes imaged in TEM micrographs) nanotubes
composites, where stress fields often result when com- in a sample. From such a statistical distribution of
mercial high-temperature treated carbon fibers expand nanotube geometries, a strength distribution can be
(and contract) significantly more radially than longi- calculated from eqns. discussed above. Factor 3 is a
tudinally on heating (and cooling)[22]. The carbon fabrication issue, which does not pose a serious prob-
matrix can have a thermal expansion similar to the in- lem and will be addressed in the future by experiments.
plane thermal expansion of graphite (it is graphitized), TEM micrographs have shown SWNTs with aspect ra-
and undesirable stress-induced fracture can result; this tios exceeding 1000, and a typical number for nano-
problem may disappear with NTs substituted for the tubes would be 100 to 300. In this range of aspect
carbon fibers. However, the very low thermal expan- ratios, the composite strength could approach that of
sion coefficient expected for defect-free nanotubes a composite filled with continuous filaments, whose
may be a problem when bonding to a higher thermal volume fraction is given by eqn (3), factor 4.
expansion matrix, such as may be the case for various Factor 5 is an important issue for future experi-
plastics or epoxies, and may cause undesirable stresses ments, and binding to a nominally smooth hexagonal
to develop. bonding network in a nanotube could be a challenging
endeavor. We suggest preliminary experiments to see if
3.1 Application of carbon nanotubes for high it is possible to convert some or all of the 3-coordinated
strength composite materials C atoms in carbon nanotubes to tetravalent C atoms
It is widely perceived that carbon nanotubes will (e.g., by fluorination or oxidation). By analogy, fluo-
allow construction of composites with extraordinary rinated and oxygenated graphites have been made[24].
strength:weight ratios, due to the inherent strength of However, nanotubes may provide a strong topologi-
the nanotubes. Several “rules of thumb” have been de- cal constraint to chemical functionalization due to the
veloped in the study of fiber/matrix composites. Close graphene sheet being wrapped onto itseu. The planes
inspection of these shows that carbon nanotubes sat- in graphite can “buckle” at a local level, with every
isfy several criteria, but that others remain untested neighboring pair of C atoms projecting up and then
(and therefore unsatisfied to date). High-strength com- down due to conversion to sp3 bonding. Can such