Page 378 - Fiber Fracture

360 J. Bernholc et al.

of nanotube-related papers being published every year. Several recent books and articles
provide a comprehensive description of the early progress in the field of nanotubes and
an extensive bibliography (Dresselhaus et al., 1996; Bernholc et al., 1997; Ebbesen,
1997; Saito et al., 1998).
This paper focuses mainly on the mechanical properties of carbon nanotubes and
discusses their elastic properties and strain-induced transformations. Only single-walled
nanotubes are discussed, since they can be grown with many fewer defects and are thus
much stronger. It is shown that under suitable conditions some nanotubes can deform
plastically, while others must break in a brittle fashion. A map of brittle vs. ductile
behavior of carbon nanotubes with indices up to (100,100) is presented. The electrical
properties of nanotubes are also affected by strain. We will focus here on quantum
(ballistic) conductance, which is very sensitive to the atomic and electronic structure.
It turns out that some nanotubes can tolerate fairly large deformations without much
change to their ballistic conductance, while others are quite sensitive. Both properties
can be used in applications, provided that nanotubes of the appropriate symmetry can be
reliably prepared or selected.

MECHANICAL PROPERTIES

It is by now well established that carbon nanotubes can be reversibly bent to very
high bending angles with very little damage, if any. Nearly atomic resolution images
show highly bent nanotubes (see Fig. 2a), while molecular dynamics simulations that
used realistic many-body potentials have predicted highly reversible bending (Iijima et
al., 1996) (see Fig. 2b). Indeed, reversible bending has subsequently been observed by
manipulation using an AFM tip (Falvo et al., 1997). Furthermore, it has been shown
that even highly distorted configurations (axial compression, twisting) can be due to
elastic deformations with no atomic defects involved (Chopra et al., 1995; Ruoff and
Lorents, 1995; Yakobson et al., 1996). In analyzing these deformations, one can use
macroscopic continuum mechanics, despite the fact that nanotubes are only -1 nm
wide. For example, the elastic shell model describes very well the various buckling and
twisting modes (Yakobson et al., 1996).

Fig. 2. (a) HREM image of kink structures formed under mechanical duress in nanotubes with diameters of
0.8 nm and 1.2 nm. (b) Atomic structure of a single kink obtained in the computer simulation of bending
of the single-walled tube with a diameter of -1.2 nm. The shading indicates the local strain energy at the
various atoms. From Iijima et al. (1996).