Energetics, structure, mechanical and vibrational properties of single-walled carbon nanotubes

In this paper, we present extensive molecular mechanics and molecular dynamics studies on the energy, structure, mechanical and vibrational properties of single-wall carbon nanotubes. In our study we employed an accurate interaction potential derived from quantum mechanics. We explored the stability domains of circular and collapsed cross section structures of armchair (n,n), zigzag(n,0) , and chiral (2n,n) isolated single-walled carbon nanotubes (SWNTs) up to a circular cross section radius of 170 A. We have found three different stability regions based on circular cross section radius. Below 10 A radius only the circular cross section tubules are stable. Between 10 and 30 A both circular and collapsed forms are possible, however, the circular cross section SWNTs are energetically favorable. Beyond 30 A (crossover radius) the collapsed form becomes favorable for all three types of SWNTs. We report the behavior of the SWNTs with radii close to the crossover radius ((45, 45), (80, 0), (70, 35)) under uniaxial compressive and tensile loads. Using classical thin-plane approximation and variation of strain energy as a function of curvature, we calculated the bending modulus of the SWNTs. The calculated bending moduli are [kappa][sub](n,n)=963.44 GPa, [kappa][sub](n,0)=911.64 GPa, and [kappa][sub](2n,n)=935.48 GPa. We also calculated the interlayer spacing between the opposite sides of the tubes and found d[sub](n,n)= 3.38 angstroms, d[sub](2n,n)= 3.39 angstroms, and d[sub](n,0)= 3.41 angstroms. Using an enthalpy optimization method, we have determined the crystal structure and Young's modulus of (10,10) armchair, (17,0) zigzag and (12, 6) chiral forms (which have similar diameter as (10,10)). They all pack in a triangular pattern in two dimensions. Calculated lattice parameters are a[sub](10,10)= 16.78 angstroms, a[sub](17,0)= 16.52 angstroms and a[sub](12,6)= 16.52 angstroms. Using the second derivatives of potential we calculated Young's modulus along the tube axis and found Y[sub](10,10)=640.30 GPa, Y[sub](17,0)=648.43 GPa, and Y[sub](12,6)=673.94 GPa. Using the optimized structures of (10,10), (12,6) and (17,0), we determined the vibrational modes and frequencies. Here, we report the highest in-plane mode, compression mode, breathing mode, shearing mode and relevant cyclop mode frequencies.

[1]  W. Goddard,et al.  Position of K atoms in doped single-walled carbon nanotube crystals , 1998 .

[2]  E. Ay'on-Beato,et al.  Regular black hole in general relativity coupled to nonlinear electrodynamics , 1998, gr-qc/9911046.

[3]  E. Richter,et al.  Theory of Size-Dependent Resonance Raman Scattering from Carbon Nanotubes , 1997 .

[4]  Boris I. Yakobson,et al.  High strain rate fracture and C-chain unraveling in carbon nanotubes , 1997 .

[5]  S. Louie,et al.  Low Energy Properties of (n,n) Carbon Nanotubes , 1997 .

[6]  Stephen Taylor,et al.  Molecular dynamics for very large systems on massively parallel computers: The MPSim program , 1997, J. Comput. Chem..

[7]  A. M. Rao,et al.  Diameter-Selective Raman Scattering from Vibrational Modes in Carbon Nanotubes , 1997, Science.

[8]  D.-H.Lee,et al.  Low Energy Properties of the (n,n) Carbon Nanotubes , 1996, cond-mat/9611073.

[9]  Bobby G. Sumpter,et al.  Dynamics of fluid flow inside carbon nanotubes , 1996 .

[10]  Young Hee Lee,et al.  Crystalline Ropes of Metallic Carbon Nanotubes , 1996, Science.

[11]  Madhu Menon,et al.  Structural and vibrational properties of fullerenes and nanotubes in a nonorthogonal tight‐binding scheme , 1996 .

[12]  A. Maiti,et al.  Structural flexibility of carbon nanotubes , 1996 .

[13]  Satoshi Itoh,et al.  Molecular Dynamics Study of Toroidal and Helically Coiled Forms of Graphitic Carbon , 1996 .

[14]  Steven G. Louie,et al.  Fully collapsed carbon nanotubes , 1995, Nature.

[15]  R. Ruoff,et al.  Structural properties of a carbon-nanotube crystal. , 1994, Physical review letters.

[16]  Benedict,et al.  Hybridization effects and metallicity in small radius carbon nanotubes. , 1994, Physical review letters.

[17]  Rodney S. Ruoff,et al.  Radial deformation of carbon nanotubes by van der Waals forces , 1993, Nature.

[18]  M. S. de Vries,et al.  Cobalt-catalysed growth of carbon nanotubes with single-atomic-layer walls , 1993, Nature.

[19]  T. Ichihashi,et al.  Single-shell carbon nanotubes of 1-nm diameter , 1993, Nature.

[20]  Robertson,et al.  Energetics of nanoscale graphitic tubules. , 1992, Physical review. B, Condensed matter.

[21]  Riichiro Saito,et al.  Electronic structure of chiral graphene tubules , 1992 .

[22]  Sawada,et al.  New one-dimensional conductors: Graphitic microtubules. , 1992, Physical review letters.

[23]  S. Iijima.  Helical microtubules of graphitic carbon , 1991, Nature.

[24]  William A. Goddard,et al.  Prediction of fullerene packing in C60 and C70 crystals , 1991, Nature.