Young’s modulus of single-walled nanotubes

Krishnan, A.; Dujardin, Erik; Ebbesen, Thomas W.; Yianilos, P.N.; Treacy, M.M.J.

doi:10.1103/physrevb.58.14013

Cited by 1,520 publications

(823 citation statements)

References 16 publications

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“…One promising approach is to attach carbon nanotubes to the end of AFM tips (see review [147]). Single wall carbon nanotubes are particularly suited because they have a defined structure and they are extremely stiff; their Young's modulus is %1000 GPa [148][149][150]. In addition they can be chemically activated at the end (e.g.…”

Section: Modificationmentioning

confidence: 99%

Force measurements with the atomic force microscope: Technique, interpretation and applications

Butt

Cappella

Kappl

2005

Surface Science Reports

3,242

2,949

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Section: Modificationmentioning

confidence: 99%

Force measurements with the atomic force microscope: Technique, interpretation and applications

Butt

Cappella

Kappl

2005

Surface Science Reports

3,242

2,949

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“…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%

“…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%

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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“…Due to their low mass density and high Young's modulus [1][2][3][4] , SWNTs offer great promise as ultrahigh frequency NEM resonators with applications in ultrasmall mass and force sensing [5][6][7][8][9][10]. To detect the mechanical vibration of nanotube resonators, various methods have been explored so far [7,[11][12][13].…”

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confidence: 99%

Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators

Zhong

2011

Nano Lett.

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We report the capacitive spring softening effect observed in single-walled carbon nanotube (SWNT) nanoelectromechanical (NEM) resonators. The nanotube resonators adopt dual-gate configuration with both bottom-gate and side-gate capable of tuning the resonance frequency through capacitive coupling. Interestingly, downward resonance frequency shifting is observed with increasing side-gate voltage, which can be attributed to the capacitive softening of spring constant. Furthermore, in-plane vibrational modes exhibit much stronger spring softening effect than out-of-plan modes. Our dual-gate design should enable the differentiation between these two types of vibrational modes, and open up new possibility for nonlinear operation of nanotube resonators.

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Young’s modulus of single-walled nanotubes

Cited by 1,520 publications

References 16 publications

Force measurements with the atomic force microscope: Technique, interpretation and applications

Force measurements with the atomic force microscope: Technique, interpretation and applications

Equivalent-continuum modeling of nano-structured materials

Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators

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