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The Very-Low Shear Modulus of Multi-Walled Carbon Nanotubes Determined Simultaneously with the Axial Young's Modulus via in situ Experiments

Authors

  • Xian-Long Wei,

    1. Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, (P.R. China)
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  • Yang Liu,

    1. Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, (P.R. China)
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  • Qing Chen,

    Corresponding author
    1. Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, (P.R. China)
    • Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, (P.R. China).
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  • Ming-Sheng Wang,

    1. Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, (P.R. China)
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  • Lian-Mao Peng

    1. Key Laboratory for the Physics and Chemistry of Nanodevices and Department of Electronics, Peking University, Beijing 100871, (P.R. China)
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Errata

This article is corrected by:

  1. Errata: The Very-Low Shear Modulus of Multi-Walled Carbon Nanotubes Determined Simultaneously with the Axial Young's Modulus via in situ Experiments Volume 18, Issue 12, Article first published online: 18 June 2008

  • We thank Prof. Jin Zhang for the CNT samples. This work was supported by the NSF of China (60771005, 60728102, 60571002) and the MOST (2006CB932401).

Abstract

The natural frequencies (f) as a function of the length (L) of single, multi-walled carbon nanotubes (CNTs) are measured using the electric-field-induced resonance method together with the “nanoknife” technique for cutting nanotubes to the desired length. The experimental f-L data for short CNTs are found to be adequately described by the Timoshenko beam model, but not by the widely-used Euler-Bernouilli beam model. The failure of the Euler-Bernouilli beam model is due to its neglect of the significant effect of shear deformation caused by the extremely-anisotropic mechanical properties of CNTs. The axial Young's modulus and radial shear modulus of CNTs are obtained simultaneously through fitting the experimental f-L data with the Timoshenko beam model.

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