Effect of van der Waals forces on axial buckling of a double-walled carbon nanotube

An elastic model is presented to study infinitesimal buckling of a double-walled carbon nanotube under axial compression. A simple formula is derived for the critical axial strain, which clearly indicates the role of the van der Waals forces between the inner and outer tubes characterized by two parameters. In particular, the analysis shows that inserting an inner tube into a single-walled nanotube does not increase the critical axial strain as compared to the single-walled nanotube under otherwise identical conditions, despite the fact that the total critical axial force of the double-walled nanotube could be increased due to an increase in the cross-sectional area.

[1]  Seishi Yamada,et al.  Contributions to understanding the behavior of axially compressed cylinders , 1999 .

[2]  Paul Calvert,et al.  Nanotube composites: A recipe for strength , 1999, Nature.

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

[4]  Nan Yao,et al.  Young’s modulus of single-walled carbon nanotubes , 1998 .

[5]  Phaedon Avouris,et al.  Deformation of carbon nanotubes by surface van der Waals forces , 1998 .

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

[7]  V. Crespi,et al.  Plastic Deformations of Carbon Nanotubes , 1998 .

[8]  Linda S. Schadler,et al.  LOAD TRANSFER IN CARBON NANOTUBE EPOXY COMPOSITES , 1998 .

[9]  J. Bernholc,et al.  Nanomechanics of carbon tubes: Instabilities beyond linear response. , 1996, Physical review letters.

[10]  M. Nardelli,et al.  Brittle and Ductile Behavior in Carbon Nanotubes , 1998 .

[11]  L. Donnell,et al.  Beams, plates and shells , 1976, Finite Element Analysis.

[12]  S. Timoshenko.  Theory of Elastic Stability , 1936 .

[13]  Boris I. Yakobson,et al.  FULLERENE NANOTUBES : C1,000,000 AND BEYOND , 1997 .

[14]  J. Lu,et al.  Elastic Properties of Carbon Nanotubes and Nanoropes , 1997, cond-mat/9704219.

[15]  Charles M. Lieber,et al.  Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes , 1997 .

[16]  R. Superfine,et al.  Bending and buckling of carbon nanotubes under large strain , 1997, Nature.

[17]  L. Girifalco.  Interaction potential for carbon (C60) molecules , 1991 .

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

[19]  L. Girifalco,et al.  Energy of Cohesion, Compressibility, and the Potential Energy Functions of the Graphite System , 1956 .

[20]  J. Bernholc,et al.  Theory of growth and mechanical properties of nanotubes , 1998 .

[21]  M. Nardelli,et al.  MECHANISM OF STRAIN RELEASE IN CARBON NANOTUBES , 1998 .

[22]  Nan Yao,et al.  Radial compression and controlled cutting of carbon nanotubes , 1998 .

[23]  Alexander Chajes,et al.  Principles of Structural Stability Theory , 1974 .

[24]  T. Ebbesen,et al.  Exceptionally high Young's modulus observed for individual carbon nanotubes , 1996, Nature.