tailieunhanh - Mechanical Properties of Carbon Nanotubes

A related modern example is the snakeboard (see LEWIS,OSTROWSKI,MURRAY &BURDICK [1994]),which shares some of the features of these examples butwhich has a crucial difference as well. This example, likemany of the others, has the sym- metry group SE(2) of Euclidean motions of the plane but, now, the corresponding momentum is not conserved. However, the equation satisfied by the momentum associated with the symmetry is useful for understanding the dynamics of the prob- lem and how group motion can be generated. The nonconservation of momentum occurs even with no forces applied (besides the forces of constraint) and is consis- tent with the conservation of energy for these systems. In. | Mechanical Properties of Carbon Nanotubes Boris I. Yakobson1 and Phaedon Avouris2 1 Center for Nanoscale Science and Technology and Department of Mechanical Engineering and Materials Science Rice University Houston TX 77251-1892 USA biy@ 2 IBM . Watson Research Center Yorktown Heights NY 10598 USA avouris@ Abstract. This paper presents an overview of the mechanical properties of carbon nanotubes starting from the linear elastic parameters nonlinear elastic instabilities and buckling and the inelastic relaxation yield strength and fracture mechanisms. A summary of experimental findings is followed by more detailed discussion of theoretical and computational models for the entire range of the deformation amplitudes. Non-covalent forces supra-molecular interactions between the nanotubes and with the substrates are also discussed due to their significance in potential applications. It is noteworthy that the term resilient was first applied not to nanotubes but to smaller fullerene cages when Whetten et al. studied the high-energy collisions of C60 C70 and C84 bouncing from a solid wall of H-terminated diamond 6 . They observed no fragmentation or any irreversible atomic rearrangement in the bouncing back cages which was somewhat surprising and indicated the ability of fullerenes to sustain great elastic distortion. The very same property of resilience becomes more significant in the case of carbon nanotubes since their elongated shape with the aspect ratio close to a thousand makes the mechanical properties especially interesting and important due to potential structural applications. 1 Mechanical Properties and Mesoscopic Duality of Nanotubes The utility of nanotubes as the strongest or stiffest elements in nanoscale devices or composite materials remains a powerful motivation for the research in this area. While the jury is still out on practical realization of these applications an additional incentive comes from the fundamental materials .