Page 154 - Carbon Nanotubes

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

which for a typical 1.0-nm tube is about 75% of the 0.1 [ 101. Using Bacon’s data, @ = 0.025, which may in-
ideal, or about 800 GPa. To calculate K for MWNTs dicate the presence of defects in the whisker. Ideally,
we can, in principle, use the scaling relation given by one would like to know the in-plane yield strength of
eqn (l), where it is assumed that the layered tubes have graphite, or directly know the yield strengths of a va-
a homogeneous cross-section. For MWNTs, however, riety of nanotubes (whose geometries are well known)
an important issue in the utilization of the high so that the intrinsic yield strength of a graphene sheet,
strength of the tubes is connected with the question of whether flat or rolled into a scroll, could be deter-
the binding of the tubes to each other. For ideal mined. This is fundamentally important, and we call
MWNTs, that interact with each other only through attention to Coulson’s statement that “the C-C bond
weak van der Waals forces, the stiffness constant K of in graphite is the strongest bond in nature[ll].” This
the individual tubes cannot be realized by simply at- statement highlights the importance of Bacon’s deter-
taching a load to the outer cylinder of the tube because mination of the yield strength of the scroll structures:
each tube acts independently of its neighbors, so that it is the only available number for estimating the yield
ideal tubes can readily slide within one another. strength of a graphene sheet.
For ideal tubes, calculations[8] support that tubes The yield strengths of defect-free SWNTs may be
can translate with respect to one another with low en- higher than that measured for Bacon’s scroll struc-
ergy barriers. Such tube slippage may have been ob- tures, and measurements on defect-free carbon nano-
served by Ge and Sattler in STM studies of MWNTs[9]. tubes may allow the prediction of the yield strength
To realize the full tensile strength of a MWNT, it may of a single, defect-free graphene sheet. Also, the yield
be necessary to open the tube and secure the load to strengths of MWNTs are subject to the same limita-
each of the individual nanotubes. Capped MWNTs, tions discussed above with respect to tube slippage. All
where only the outer tube is available for contact with the discussion here relates to ideal nanotubes; real car-
a surface, are not likely to have high tensile stiffness bon nanotubes may contain faults of various types
or high yield strength. Because the strength of com- that will influence their properties and require exper-
posite materials fabricated using NTs will depend imental measurements of their mechanical constants.
mainly on the surface contact between the matrix and
the tube walls, it appears that composites made from 2.2 Bending of tubes
small-diameter SWNTs are more likely to utilize the Due to the high in-plane tensile strength of graph-
high strength potential of NTs than those made from ite, we can expect SW and MW nanotubes to have
MWNTs. large bending constants because these depend, for
A milestone measurement in carbon science was small deflections, only on the Young’s modulus. In-
Bacon’s production of graphite whiskers. These were deed, the TEM photos of MWNTs show them to be
grown in a DC arc under conditions near the triple very straight, which indicates that they are very rigid.
point of carbon and had a Young’s modulus of 800 In the few observed examples of sharply bent MWNTs,
GPa and a yield strength of 20 GPa. If we assume that they appear to be buckled on the inner radius of the
these whiskers, which Bacon considered to be a scroll- bend as shown in Fig. 1. Sharp bends can also be pro-
like structure, had no hollow core in the center, then duced in NTs by introducing faults, such as pentagon-
the same-scaling rule, eqn (l), can be used for the yield heptagon pairs as suggested by theorists[ 121, and these
strength of carbon nanotubes. As a practical means are occasionally also seen in TEM photos. On the other
of estimating yield strengths, it is usually assumed that hand, TEM photos of SWNTs show them to be much
the yield strength is proportional to the Youngs mod- more pliable, and high curvature bends without buck-
ulus (Le., Y,,, = @E), where @ ranges from 0.05 to ling are seen in many photos of web material contain-

Fig. la. Low-resolution TEM photograph of a bent MWNT showing kinks along the inner radius of the
bend resulting from bending stress that exceeds the elastic limit of the tube.