A continuum model for zigzag single-walled carbon nanotubes

Leung, A.Y.T.; Guo, Xiang; He, X. Q.; Kitipornchai, S.

doi:10.1063/1.1869543

Cited by 28 publications

(12 citation statements)

References 19 publications

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“…The closed-form expressions for elastic properties of achiral SWCNTs under various loading conditions were presented by Shen and Li 64 via a energy approach. Leung et al 65 obtained Young's modulus for zigzag CNTs by developing an equivalent truss model. These expressions are concise but capable of directly linking material properties at different length scales.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear stick-spiral model for predicting mechanical behavior of single-walled carbon nanotubes

Geng

Chang

2006

Phys. Rev. B

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Based on a molecular mechanics concept, a nonlinear stick-spiral model is developed to investigate the mechanical behavior of single-walled carbon nanotubes ͑SWCNTs͒. The model is capable of predicting not only the initial elastic properties ͑e.g., Young's modulus͒ but also the stress-strain relations of a SWCNT under axial, radial, and torsion conditions. The elastic properties, ultimate stress, and failure strain under various loading conditions are discussed and special attention has been paid to the effects of the tube chirality and tube size. Some unique mechanical behaviors of chiral SWCNTs, such as axial strain-induced torsion, circumferential strain-induced torsion, and shear strain-induced extension are also studied. The predicted results from the present model are in good agreement with existing data, but very little computational cost is needed to yield them.

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Section: Introductionmentioning

confidence: 99%

Nonlinear stick-spiral model for predicting mechanical behavior of single-walled carbon nanotubes

Geng

Chang

2006

Phys. Rev. B

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“…From Table 1, compared with the stiffness parameters given by Li and Chou (2003), Leung et al (2005) and Odegard et al (2002), it can be observed that the stretch stiffness and bending stiffness of beam element are reduced but the torsion stiffness is unchanged. Two truss elements are added to compensating the reduced stiffness.…”

Section: Inter-belt Modelmentioning

confidence: 88%

“…Different kinds of structural models have been developed in the past years, such as the beam model given by Li and Chou (2003) (see Fig. 2), the rod model suggested by Odegard et al (2002), and another rod model given by Leung et al (2005) (see Fig. 3).…”

Section: Structural Mechanics Models Of Carbon Nanotubesmentioning

confidence: 99%

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Phonon dispersion analysis of carbon nanotubes based on inter-belt model and symplectic solution method

Zhang

Zheng

Wang

et al. 2007

International Journal of Solids and Structures

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The objective of the study is to develop a totally new theory and structural mechanics model for phonon dispersion analysis of carbon nanotubes. The fundamental theory and computational algorithm for phonon dispersion analysis of carbon nanotubes are developed based on the symplectic theory and algorithm established in applied mechanics in recent years. Carbon nanotubes are simulated by two kinds of structural mechanics models, i.e. the conventional sub-structure model and the inter-belt model. The variational principle for wave dissipation analysis of periodic structure is given on the basis of the symplectic-mathematical theory. Numerical examples are carried out to demonstrate the validity of the theory and algorithm developed. By the comparison of the results obtained by the two kinds of structural mechanics models, it can be found that the inter-belt model has more advantages than the conventional sub-structure model in the calculation of phonon spectra of nanotubes. As a basic research work, the present study illustrates well the potential of the symplectic-mathematical theory as well as the inter-belt model and is valuable for the further research in computational nanomechanics.

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“…[1][2][3][4][5][6] Their extraordinary strength, unique electrical properties and their ability to conduct heat efficiently have generated considerable interest among both experimentalists and theoreticians. [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] Nanotubes may also be produced by synthesis methods, for instance multi-wall nanotubes (MWNTs) which consist of multiple layers of graphene rolled in on themselves to form a cylindrical tube. There are two models which can be used to describe the structures of multi-wall nanotubes.…”

Section: Introductionmentioning

confidence: 99%

Model of plasmon excitations in a bundle and a two-dimensional array of nanotubes

2008

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We calculate the plasma excitations in a bundle as well as a two-dimensional (2D) periodic array of aligned parallel multishell nanotubes on a substrate. The carbon nanotubes are oriented perpendicular to the substrate. The model we use for the system is an electron gas confined to the surface of an infinitely long cylinder embedded in a background dielectric medium. Electron tunneling between individual tubules is neglected. We include the Coulomb interaction between electrons on the same tubule and on different tubules for the same nanotube and neighboring nanotubes. We present a self-consistent field theory for the dispersion equation for intrasubband and intersubband plasmon excitations. For both the bundle and 2D array of aligned parallel nanotubes, the dispersion relation of the collective modes is determined by a three-dimensional wave vector with components in the direction of the nanotube axes and in the transverse directions. The dispersion equation is solved numerically for a singlewall nanotube 2D array as well as a bundle, and the plasmon excitation energies are obtained as a function of wave vector. The intertube Coulomb interaction couples plasmons with different angular momenta m in individual nanotubes, lifting the ±m degeneracy of the single-nanotube modes. This effect is analyzed numerically as a function of the separation between the tubules. We show that the translational symmetry of the lattice is maintained in the plasmon spectrum for the periodic array, and the plasmon energies have a periodic dependence on the transverse wave vector q ⊥ . For the bundle, the Coulomb interaction between nanotubes gives rise to optical plasmon excitations.

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A continuum model for zigzag single-walled carbon nanotubes

Cited by 28 publications

References 19 publications

Nonlinear stick-spiral model for predicting mechanical behavior of single-walled carbon nanotubes

Nonlinear stick-spiral model for predicting mechanical behavior of single-walled carbon nanotubes

Phonon dispersion analysis of carbon nanotubes based on inter-belt model and symplectic solution method

Model of plasmon excitations in a bundle and a two-dimensional array of nanotubes

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