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Symmetry-dependent strength of carbon nanotubes

D. Pierson*, a, C. Richardsonb, B. I. Yakobsona

aDepartment of Physics, North Carolina State Univeristy, Box 8202, Raleigh, NC 27606
bRensselaer Polytechnic Institute, Troy, NY 12180

This is an abstract for a presentation given at the
Sixth Foresight Conference on Molecular Nanotechnology.
There will be a link from here to the full article when it is available on the web.


The fact that electronic properties of carbon nanotubes inherently depend on the chiral symmetry of the molecular fiber has been theoretically recognized before their actual discovery [1]. In contrast, the mechanical properties at least in the elastic domain are believed to be independent on the chirality (also called helicity).  The argument behind that is due to the rigorous result that hexagonal two-dimensional crystal (Fig. 1) is isotropic in its elastic behavior, and therefore the specific way of folding a graphene sheet into a tubule of given diameter does not affect its elasticity.  Recently, the dislocation-theory based analysis allowed to derive the energetics of the strength-determining yield process as a function of tube helicity [2,3].  The underlying atomistic mechanism is the rotation of a C-C bond (so called Stone-Wales transformation) (Fig. 2), as has been demonstrated by detailed molecular-dynamic simulations [4].  The dislocation theory predicts the following expression for the SW defect formation:

With a rough estimate of C = 28 eV, this means a significant difference in the activation energies for the nucleation of fracture, and therefore a large difference in apparent strength of corresponding nanoscale structures (or a macroscopic assemblies of such structures, like in composites).  We will present detailed molecular dynamic tests of this effect [5]: a computation of the formation energy for SW defects in nanotubes of different helicity under external tension.  Overall the observed symmetry-dependence (Fig. 3) agrees very well with the dislocation-theory based eqn. (1) above.  Beyond that, this allows to identify the numerical values of the parameters, A, B and C (which in this case are based of course on the Brenner-parameterizaton of the Tersoff type potential used in the simulations).  We find values of these coefficients to be reasonably close to the estimates based on elastic constants (C11) of graphene.  The angular (helicity) dependence is in excellent agreement with the previous topology-symmetry analysis.  We conclude therefore that zigzag type ( = 0) nanotubes should be much more resistant to tension than the armchair type, while all other (chiral) types have a strength resistance somewhere in-between, according to the sinusoidal form of the energy equation (1).  (Fig. 4)


[1]  M. S. Dresselhaus, G. Dresselhaus, and P. C. Eklund Science of Fullerenes and Carbon Nanotubes, Academic Press, San Deigo, 1996
[2]  B. I. Yakobson, in Proceedings of the 191st ECS Meeting, Paris, 1997, edited by R. S. Ruoff and K. M. Kadish (ECS, Pennington, 1997), p. 549
[3]  B. I. Yakobson, Appl. Phys. Lett. 72, 918 (1998)
[4]  M. B. Nardelli, B. I. Yakobson, and J. Bernholc, Phys. Rev. B, 57, 4277 (1998)
[5]  C. Richardson, D. Pierson, B. I. Yakobson (to be published)

*Corresponding Address:
D. Pierson
Department of Physics, North Carolina State Univeristy, Box 8202, Raleigh, NC 27606


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