Nanomechanics of carbon nanotubes

Kis, András; Zettl, A.

doi:10.1098/rsta.2007.2174

Cited by 108 publications

(71 citation statements)

References 61 publications

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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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confidence: 99%

Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators

Zhong

2011

Nano Lett.

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“…20 Applying a continuum-mechanical model to such data yields a nanotube Young's modulus of around 1.3 TPa in reasonable agreement with predictions. [21][22][23][24][25][26] Analogous mechanical studies of quasi-two-dimensional (2D) percolated SWCNT networks are much less developed. Mixed-length and mixed-type SWCNTs have been chemically treated, for example, to create strong interfacial adhesion on polydimethylsiloxane (PDMS) substrates, 27 but chemical functionalization can have a significantly adverse effect on intrinsic nanotube properties 28 despite the improved mechanical behavior that chemical grafting can induce.…”

Section: ' Introductionmentioning

confidence: 99%

Structural Stability of Transparent Conducting Films Assembled from Length Purified Single-Wall Carbon Nanotubes

et al. 2011

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ABSTRACT:Single-wall carbon nanotube (SWCNT) films show significant promise for transparent electronics applications that demand mechanical flexibility, but durability remains an outstanding issue. In this work, thin membranes of length purified single-wall carbon nanotubes (SWCNTs) are uniaxially and isotropically compressed by depositing them on prestrained polymer substrates. Upon release of the strain, the topography, microstructure, and conductivity of the films are characterized using a combination of optical/fluorescence microscopy, light scattering, force microscopy, electron microscopy, and impedance spectroscopy. Above a critical surface mass density, films assembled from nanotubes of well-defined length exhibit a strongly nonlinear mechanical response. The measured strain dependence reveals a dramatic softening that occurs through an alignment of the SWCNTs normal to the direction of prestrain, which at small strains is also apparent as an anisotropic increase in sheet resistance along the same direction. At higher strains, the membrane conductivities increase due to a compression-induced restoration of conductive pathways. Our measurements reveal the fundamental mode of elasto-plastic deformation in these films and suggest how it might be suppressed. ' INTRODUCTIONIn the past two decades, single-wall carbon nanotubes (SWCNTs) have received considerable attention due to their outstanding mechanical, optical, and electronic properties, and a vast amount of research has been devoted to the characterization of these attributes 1 and the potential applications they suggest. 2 Promising applications are rapidly emerging in such areas as high performance composites, 3 thermoelectric materials, 4 and conducting polymer composites.5 Thin SWCNT films, in particular, show exceptional promise for applications that require transparent coatings with superior mechanical, electronic, and optical qualities. [6][7][8][9] The natural tendency for SWCNTs to form flexible, transparent networks with high electrical conductivity at remarkably low surface coverage is a direct consequence of the magnitude of the typical SWCNT aspect ratio, 10 suggesting that nanotube length is a critical factor in dictating the physical properties of such membranes.The electronic and optical properties of SWCNTs are determined by their electronic band structure, 1 which is specified by the chiral vector (n, m) characterizing the symmetry of rolling a two-dimensional graphene sheet into a hollow tube of diameter a. All existing synthetic techniques therefore produce raw material that contains a distribution of electronic types, ranging from semiconducting to metallic, as well as a broad range of lengths, from 10 nm up to hundreds of micrometers. Since scalable processes for purifying lab-grade quantities of SWCNTs have only recently been formulated, 11-13 thin films of exemplary purified materials have just now become readily available for fundamental research, pointing toward a number of promising applications. Thin SWCNT membranes have rece...

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“…In this study, we suppose that the carbon nanotube is a conductor. After certain corrections when extracting material properties, the use of continuum mechanics is still justified for such systems [56], and various mechanical models exist [57,58]. We focus here on the efficient simulation of the first three cyclic modes of vibration of a nanotube as sketched in Figure 3 via Algorithm 1.…”

Section: Nanotube Vibrationmentioning

confidence: 99%

Cyclic steady states of nonlinear electro-mechanical devices excited at resonance

Brandstetter

Govindjee

2016

Int. J. Numer. Meth. Engng

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SUMMARYWe present an efficient numerical method to solve for cyclic steady states of nonlinear electro-mechanical devices excited at resonance. Many electro-mechanical systems are designed to operate at resonance, where the ramp-up simulation to steady state is computationally very expensive -especially when low damping is present. The proposed method relies on a Newton-Krylov shooting scheme for the direct calculation of the cyclic steady state, as opposed to a naïve transient time-stepping from zero initial conditions. We use a recently developed high-order Eulerian-Lagrangian finite element method in combination with an energy-preserving dynamic contact algorithm in order to solve the coupled electro-mechanical boundary value problem. The nonlinear coupled equations are evolved by means of an operator split of the mechanical and electrical problem with an explicit as well as implicit approach. The presented benchmark examples include the first three fundamental modes of a vibrating nanotube, as well as a micro-electro-mechanical disk resonator in dynamic steady contact. For the examples discussed, we observe power law computational speed-ups of the form S D 0:6 0:8 , where is the linear damping ratio of the corresponding resonance frequency.

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Nanomechanics of carbon nanotubes

Cited by 108 publications

References 61 publications

Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators

Capacitive Spring Softening in Single-Walled Carbon Nanotube Nanoelectromechanical Resonators

Structural Stability of Transparent Conducting Films Assembled from Length Purified Single-Wall Carbon Nanotubes

Cyclic steady states of nonlinear electro-mechanical devices excited at resonance

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