Erratum: Experimental Measurement of Single-Wall Carbon Nanotube Torsional Properties [Phys. Rev. Lett. 96, 256102 (2006)] (original) (raw)

Torsional Response and Stiffening of Individual Multiwalled Carbon Nanotubes

Physical Review Letters, 2002

We report on the characterization of torsional oscillators which use multi-walled carbon nanotubes as the spring elements. Through atomic-force-microscope force-distance measurements we are able to apply torsional strains to the nanotubes and measure their torsional spring constants and effective shear moduli. We find that the effective shear moduli cover a broad range, with the largest values near the theoretically predicted value. The data also suggest that the nanotubes are stiffened by repeated flexing.

Ab initio calculations of the walls shear strength of carbon nanotubes

2009

The dependence of the energy of interwall interaction in double-walled carbon nanotubes (DWNT) on the relative position of walls has been calculated using the density functional method. This dependence is used to evaluate forces that are necessary for the relative telescopic motion of walls and to calculate the shear strength of DWNT for the relative sliding of walls along the nanotube axis and for their relative rotation about this axis. The possibility of experimental verification of the obtained results is discussed.

Young's modulus of single-walled carbon nanotubes Young's modulus of single-walled carbon nanotubes

We report in detail that unlike other materials, carbon nanotubes are so small that changes in structure can affect the Young's modulus. The variation in modulus is attributed to differences in torsional strain, which is the dominant component of the total strain energy. Torsional strain, and correspondingly Young's modulus, increases significantly with decreasing tube diameter and increases slightly with decreasing tube helicity.

On a thickness free expression for the shear modulus of carbon nanotubes

Journal of Applied Physics, 2016

The thickness of carbon nanotubes is an important issue for the characterization and design of these structures. In this article, thickness free expressions for the shear modulus of single-walled carbon nanotubes have been developed by finite element simulations on the minimum potential energy circle. As a part of this work, some equations have been obtained to define the relation between the thickness and the shear modulus, which are in good agreement with previous studies. Moreover, these expressions are in good agreement with both continuum and quantum mechanics and capable to support "Yakobson's paradox," that the scattering data for the elastic properties of carbon nanotubes are due to the not-well-defined thickness for these structures. Furthermore, these expressions can provide a tool for the prediction of the shear modulus of single-walled carbon nanotubes in regards to any thickness assumption when the experimental investigations are too difficult to realize.

Experimental-Computational Study of Shear Interactions within Double-Walled Carbon Nanotube Bundles

Nano Letters, 2012

The mechanical behavior of carbon nanotube (CNT)-based fibers and nanocomposites depends intimately on the shear interactions between adjacent tubes. We have applied an experimental-computational approach to investigate the shear interactions between adjacent CNTs within individual double-walled nanotube (DWNT) bundles. The force required to pull out an inner bundle of DWNTs from an outer shell of DWNTs was measured using in situ scanning electron microscopy methods. The normalized force per CNT−CNT interaction (1.7 ± 1.0 nN) was found to be considerably higher than molecular mechanics (MM)-based predictions for bare CNTs (0.3 nN). This MM result is similar to the force that results from exposure of newly formed CNT surfaces, indicating that the observed pullout force arises from factors beyond what arise from potential energy effects associated with bare CNTs. Through further theoretical considerations we show that the experimentally measured pullout force may include small contributions from carbonyl functional groups terminating the free ends of the CNTs, corrugation of the CNT−CNT interactions, and polygonization of the nanotubes due to their mutual interactions. In addition, surface functional groups, such as hydroxyl groups, that may exist between the nanotubes are found to play an unimportant role. All of these potential energy effects account for less than half of the ∼1.7 nN force. However, partially pulled-out inner bundles are found not to pull back into the outer shell after the outer shell is broken, suggesting that dissipation is responsible for more than half of the pullout force. The sum of force contributions from potential energy and dissipation effects are found to agree with the experimental pullout force within the experimental error.

Young’s modulus of single-walled nanotubes

Physical Review B, 1998

We estimate the stiffness of single-walled carbon nanotubes by observing their freestanding roomtemperature vibrations in a transmission electron microscope. The nanotube dimensions and vibration amplitude are measured from electron micrographs, and it is assumed that the vibration modes are driven stochastically and are those of a clamped cantilever. Micrographs of 27 nanotubes in the diameter range 1.0-1.5 nm were measured to yield an average Young's modulus of ͗Y ͘ϭ1.25 TPa. This value is consistent with previous measurements for multiwalled nanotubes, and is higher than the currently accepted value of the in-plane modulus of graphite. ͓S0163-1829͑98͒00144-1͔

Mechanical Properties of Carbon Nanotubes

2001

This paper presents an overview of the mechanical properties of carbon nanotubes, starting from the linear elastic parameters, nonlinear elastic instabilities and buckling, and the inelastic relaxation, yield strength and fracture mechanisms. A summary of experimental findings is followed by more detailed discussion of theoretical and computational models for the entire range of the deformation amplitudes. Non-covalent forces (supra-molecular interactions) between the nanotubes and with the substrates are also discussed, due to their significance in potential applications.