Do Carbon Nanotubes Spin When Bundled?
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Do carbon nanotubes spin when bundled? Young-Kyun Kwon and David Tom´anek Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-1116
Young Hee Lee Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-1116, and Department of Physics and Semiconductor Physics Research Center, Jeonbuk National University, Jeonju 561-756, Korea
Kee Hag Lee Department of Physics and Astronomy, Michigan State University, East Lansing, Michigan 48824-1116, and Department of Chemistry, WonKwang University, Iksan, Chonbuk 570-749, Korea
Susumu Saito Department of Physics, Tokyo Institute of Technology, 1-12-1 Oh-okayama, Meguro-ku, Tokyo 152, Japan (Received 5 February 1998; accepted 15 May 1998)
Using ab initio and parametrized techniques, we determine the equilibrium structure of an ordered “bundle” of (10,10) carbon nanotubes. Because of small intertube interaction and lattice frustration, we predict a very soft libration mode to occur at n ø 12 cm21 . This mode is predicted to disappear above the orientational melting temperature which marks the onset of free tube rotations about their axis. We discuss the effect of the weak intertube coupling and orientational disorder on the electronic structure near the Fermi level.
I. INTRODUCTION
Among carbon-based materials, fullerenes (such as the C60 “buckyball”1 ) and nanotubes2 have received much attention recently due to their high structural stability and interesting electronic properties. Structurally rigid3 and highly conducting4 “ropes” of carbon nanotubes are the molecular counterparts of carbon fibers.5 Perfectly spherical C60 molecules are known to spin freely at room temperature6 when crystallized to a solid.7 One may wonder whether the cylindrical singlewall (10,10) carbon nanotubes,5 the abundant species4,8,9 among single-wall tubes, could also rotate relatively freely when forming well-ordered bundles, the “ropes.”4 13 C nuclear magnetic resonance experiments on solid C60 6 have shown that it is only below T ø 260 K that the free C60 rotation is hindered by the asphericity of the intermolecular potential, due to the discrete atomic positions. In bundles of nanotubes, we expect the barrier for rotation to be even lower due to the frustration introduced by triangular packing of tubes that have a D10h symmetry and due to orientational dislocations caused by local twists along the tube axis. Due to their large moment of inertia, nanotubes are not expected to spin as fast as the C60 molecules. Nevertheless, it is useful to study the soft librational motion of nanotubes and their transition to relatively free tube rotations, marking the onset of orientational disorder in nanotube “ropes.” J. Mater. Res., Vol. 13, No. 9, Sep 1998
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Electronic states involved in the superconducting behavior of the alkali-doped C60 solid derive from this molecule’s degenerate lowest unoccupied t1u molecular orbital10 that ext
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