2008
DOI: 10.1002/adfm.200701105
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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

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 … Show more

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Cited by 50 publications
(25 citation statements)
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“…[ 26 ] Other researchers used different beam models to extract the elastic properties from the resonance frequency of single multiwalled CNTs that were perturbed inside an electric fi eld. [ 27,28 ] Lumped-parameter models of boron nitride nanotubes have also been used to extract nonlinear damping properties. [ 29 ] In addition, nonlinear singlebeam models were employed in the in situ study of CNT ring deformation, providing information on the CNT to substrate adhesion.…”
Section: Introductionmentioning
confidence: 99%
“…[ 26 ] Other researchers used different beam models to extract the elastic properties from the resonance frequency of single multiwalled CNTs that were perturbed inside an electric fi eld. [ 27,28 ] Lumped-parameter models of boron nitride nanotubes have also been used to extract nonlinear damping properties. [ 29 ] In addition, nonlinear singlebeam models were employed in the in situ study of CNT ring deformation, providing information on the CNT to substrate adhesion.…”
Section: Introductionmentioning
confidence: 99%
“…The scheme of investigation followed here is based on the fact that CNTs are anisotropic structures and hence these must have preferential deformation and fracture initiations with respect to the direction of loading. CNTs have high longitudinal tensile elastic modulus (about 1 TPa) and tensile strength (150-200 GPa) [29][30][31][32][33][34]. Strong covalent interactions of in-plane C-C bonds in graphene contribute to such a high stiffness and strength of CNTs.…”
mentioning
confidence: 99%
“…The resonance can be directly observed by SEM. [8,13] Examples of a SWCNT (the inset of Fig. 1b) and a MWCNT (Fig.…”
Section: Resultsmentioning
confidence: 99%
“…For constructing MWCNT resonators, individual MWCNT, which is synthesized through arc-discharge process [25], was picked up from CNT powder using a tungsten probe (P1 in Fig. 1a) and the other end of the CNT was connected to an AFM cantilever using nanomanipulation methods reported previously [12,13], For constructing SWCNT resonators, individual SWCNT, which was grown across microtrenches on the SiO 2 /Si substrate using catalytic chemical vapor deposition method [26], was cut short and picked up by a tungsten probe (P1), then the other end of the SWCNT was connected to a Si NW cantilever. An AC voltage (1-3.5 V) [sometimes together with a DC voltage (0-2 V)] was applied to P3 through a signal generator (Agilent 33220A) to drive the CNT into vibration.…”
Section: Methodsmentioning
confidence: 99%