Page 156 - Carbon Nanotubes

146 R. S. RUOFF and D. C. LORENTS

Fig. 2. Cables of parallel SWNTs that have self-assembled during oxidative cleanup of arc-produced soot
composed of randomly oriented SWNTs imbedded in amorphous carbon. Note the large cable consisting
of several tens of SWNTs, triple and single strand tubes bent without kinks, and another bent cable con-
sisting of 6 to 8 SWNTs.

treatment of such cables will need to account for the and technologically important properties. At this
slippage of individual tubes along one another as they stage, we can infer possible behavior from the known
bend. However, the bending moment induced by in-plane properties of graphite.
transverse force will be less influenced by the tube-tube The in-plane thermal conductivity of pyrolytic
binding and, thus, be more closely determined by the graphite is very high, second only to type 11-a dia-
sum of the individual bending constants. mond, which has the highest measured thermal con-
ductivity of any material[l8]. The c-axis thermal
2.3 Bulk modulus conductivity of graphite is, as one might expect, very
The bulk modulus of an ideal SWNT crystal in the low due to the weakly bound layers which are attracted
plane perpendicular to the axis of the tubes can also to each other only by van der Waals forces. Contri-
be calculated as shown by Tersoff and Ruoff and is butions to a finite in-plane thermal conductivity in
proportional to D”2 for tubes of less than 1.0 nm graphite have been discussed by several authors[7,19].
diameter[l7]. For larger diameters, where tube de- At low temperature (~140 K), the main scattering
formation is important, the bulk modulus becomes mechanism is phonon scattering from the edges of the
independent of D and is quite low. Since modulus is finite crystallites[ 191.
independent of D, close-packed large D tubes will pro- Unlike materials such as mica, extremely large sin-
vide a very low density material without change of the glecrystalgraphite has not been possible to grow. Even
bulk modulus. However, since the modulus is highly in highly oriented pyrolytic graphite (HOPG), the in-
nonlinear, the modulus rapidly increases with increas- plane coherence length is typically <lo00 A and, at
ing pressure. These quantities need to be measured in low temperatures, the phonon free path is controlled
the near future. mainly by boundary scattering; at temperatures above
140 K, phonon-phonon (umklapp processes) dominate
3. THERMAL PROPERTIES [20]. TEM images suggest that defect-free tubes exist
The thermal conductivity and thermal expansion of with lengths exceeding several microns, which is sig-
carbon nanotubes are also fundamentally interesting nificantly longer than the typical crystallite diameter