Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene

Lier, Gregory Van; Alsenoy, C. Van; Doren, V. Van; Geerlings, Pau̧l

doi:10.1016/s0009-2614(00)00764-8

Cited by 479 publications

(216 citation statements)

References 34 publications

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“…In the above-mentioned experiments, the average Young's modulus varies from 0.81 to 1.25 TPa. By using the empirical lattice dynamics model, Lu 4 22 Compared with the above-noted experimental results and theoretical simulation, it is obvious that our calculation results lie fairly within the effective range.…”

Section: ͑9͒supporting

confidence: 54%

A continuum model for zigzag single-walled carbon nanotubes

Leung

Guo

et al. 2005

Applied Physics Letters

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Section: ͑9͒supporting

confidence: 54%

A continuum model for zigzag single-walled carbon nanotubes

Leung

Guo

et al. 2005

Applied Physics Letters

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“…Many experimental [4][5][6][7][8] and theoretical [9][10][11][12][13][14] studies have been performed on single-and multi-walled carbon nanotubes. In particular, deformation modes and nanotube stiffnesses have been closely examined.…”

Section: Wall Thicknessmentioning

confidence: 99%

“…In many studies, it has been assumed that the nanotube "wall thickness" is merely the interplanar spacing of two or more graphene sheets [5,[8][9][10][11][12][13], which is about 0.34 nm in single-crystal graphite. While this simple idealization appears to have intuitive merit, it does not necessarily reflect the effective thickness that is representative of continuum properties.…”

Section: Wall Thicknessmentioning

confidence: 99%

Equivalent-continuum modeling of nano-structured materials

Odegard

2002

Composites Science and Technology

581

302

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A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the molecular potential energy of a nano-structured material with the strain energy of representative truss and continuum models. As important examples with direct application to the development and characterization of singlewalled carbon nanotubes and the design of nanotube-based structural devices, the modeling technique has been applied to two independent examples: the determination of the effectivecontinuum geometry and bending rigidity of a graphene sheet. A representative volume element of the chemical structure of graphene has been substituted with equivalent-truss and equivalentcontinuum models. As a result, an effective thickness of the continuum model has been determined. The determined effective thickness is significantly larger than the inter-planar spacing of graphite. The effective bending rigidity of the equivalent-continuum model of a graphene sheet was determined by equating the molecular potential energy of the molecular model of a graphene sheet subjected to cylindrical bending (to form a nanotube) with the strain energy of an equivalent-continuum plate subjected to cylindrical bending.

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“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] It has been reported 12 that a mere 1 wt % of CNTs embedded into a polystyrene matrix would lead to significant increases in the overall elastic modulus and strength by approximately 35%-42% and 25%, respectively. In view of such potential applications, there is a strong motivation to understand their structural properties.…”

Section: Introductionmentioning

confidence: 99%

Examining the effects of wall numbers on buckling behavior and mechanical properties of multiwalled carbon nanotubes via molecular dynamics simulations

Zhang

Wang

Tan

2008

Journal of Applied Physics

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Molecular dynamics simulations are performed on multiwalled carbon nanotubes ͑MWCNTs͒ under axial compression to investigate the effects of the number of walls and their van der Waals ͑vdW͒ interaction on the buckling behaviors and mechanical properties ͑Young's modulus and Poisson's ratio͒. The Brenner second-generation reactive empirical bond order and Lennard-Jones 12-6 potential have been adopted to describe the short-range bonding and long-range vdW atomic interaction within the carbon nanotubes, respectively. In the presence of vdW interaction, the buckling strain and Young's modulus of MWCNTs increase as the number of tubes is increased while keeping the outermost tube diameter constant, whereas Poisson's ratio was observed to decrease. On the other hand, when the MWCNTs are formed by progressively adding outer tubes while keeping the innermost tube diameter constant, Young's modulus and buckling strain were observed to decrease, whereas Poisson's ratio increases. The buckling load increases with increasing the number of walls due to the larger cross-sectional areas. Individual tubes of MWCNTs with a relatively large difference between the diameters of the inner and outer tubes buckle one at a time as opposed to simultaneously for MWCNTs with a relatively small difference in diameters.

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Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene

Cited by 479 publications

References 34 publications

A continuum model for zigzag single-walled carbon nanotubes

A continuum model for zigzag single-walled carbon nanotubes

Equivalent-continuum modeling of nano-structured materials

Examining the effects of wall numbers on buckling behavior and mechanical properties of multiwalled carbon nanotubes via molecular dynamics simulations

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