Vibrations of carbon nanotubes and their composites: A review

doi:10.1016/j.compscitech.2006.03.031

Composites Science and Technology

Volume 67, Issue 1, January 2007, Pages 1-28

https://doi.org/10.1016/j.compscitech.2006.03.031 Get rights and content

Abstract

Spurred by the discovery of carbon nanotubes in 1991 and the subsequent nanotechnology revolution, there has been a marked increase in the volume of scientific and engineering literature dealing with various aspects of the vibratory behavior of carbon nanotubes and their composites in the last few years. This paper is an attempt to present a coherent yet concise review of as many of these publications as possible. The major topics covered in this review are modeling and simulation of vibrating nanotubes, studies of nanomechanical resonators and oscillators, the use of vibration measurements to characterize nanotube mechanical properties, nanotube augmentation of dynamic structural properties of composites, vibrations of nanotube-based sensors and actuators, sonication of nanotube-reinforced polymer resins, Raman scattering from nanotubes, and high frequency wave–nanotube interactions. Summaries of both theoretical and experimental studies are included, along with key conclusions and recommendations from these studies.

Introduction

The number of publications on carbon nanotubes (CNTs) and CNT-reinforced composite materials has grown very quickly since CNTs were discovered by Iijima [1] more than a decade ago, as evidenced by several recent review articles on mechanical behavior [2], [3], fabrication [4], [5] and applications [6], [7], [8], [9], [10] of such materials. In 2003 a special issue of this journal was dedicated to modeling and characterization of nanostructured materials [11]. Vibrations of CNTs are of considerable importance in a number of nanomechanical devices such as oscillators, charge detectors, clocks, field emission devices and sensors. In addition, CNT vibrations occur during certain manufacturing processes (e.g., ultrasonication in nanocomposite processing) and as part of some nondestructive evaluation processes (e.g., Raman spectroscopy). Electron microscope observations of vibrating CNTs have also been used to indirectly and nondestructively determine the effective elastic moduli and other aspects of mechanical behavior of the CNTs. Microwave excitation has been found to cause intense heating of CNTs. So there is considerable motivation for studying vibration characteristics of CNTs, and the purpose of this article is to review recent literature which is relevant to all aspects and ramifications of CNT vibrations.

Section snippets

Modeling and simulation of vibrating nanotubes

It is important to have accurate theoretical models for the natural frequencies and mode shapes of carbon nanotubes for several reasons. For example, if the nanotubes are to be used as nanomechanical resonators, the oscillation frequency is a key property of the resonator. In addition, the effective elastic modulus of a nanotube may be indirectly determined from its measured natural frequencies or mode shapes if a sufficiently accurate theoretical model is used. Several recent publications have

Nanomechanical resonators, oscillators and field emission devices

Nanometer-scale high frequency resonators are critical components of many nanoelectromechanical systems (NEMS) such as oscillators, charge detection devices, parametric amplifiers, nanoscale clocks and resonant sensors [51], [52], [53]. For example, Sazanova et al. [52] have developed a nanoelectromechanical oscillator based on the electrostatic actuation and detection of a double-clamped CNT with a gate electrode, as shown in Fig. 9. Zheng et al. [54], [55] have proposed the design of an

Use of vibration measurements to characterize nanotube mechanical properties

Both static and dynamic mechanical test methods have been employed to measure the elastic moduli of CNTs. As an example of static testing, Salvetat et al. [75] loaded nanobeams consisting of SWNT ropes at midspan with the tip of an atomic force microscope while the ends were fixed at the edges of a pore in a porous ultrafiltration membrane. The elastic modulus was found to be on the order of 1 TPa, but the shear modulus was estimated to be only about 1 GPa. Modal vibration response measurements

Nanotube augmentation of dynamic mechanical properties of composites

There are numerous reports in the literature on the use of CNTs to augment mechanical properties of composite materials, and these reports have focused primarily on static strength, stiffness and fracture toughness [2], [3], [12], [13], [84]. By contrast, the number of publications dealing with dynamic mechanical properties of CNT-reinforced composites is much smaller. Dynamic mechanical properties are usually described by the use of complex modulus notation $E^{*} = E^{'} + i E^{″} = E^{'} (1 + i η),$ where E^∗ is the

Vibrations in nanotube-based sensors and actuators

The use of carbon nanotubes as sensors has received considerable attention [112], and in some CNT-based sensors, the CNTs are subjected to vibrations. Raman scattering from CNTs will be discussed in more detail in a later section of this paper, but sensors based on Raman spectroscopy will be discussed here. For example, the Raman frequencies of CNTs depend on pressure and strain [113], [114], so Raman shifts can be the basis of nanoscale pressure or strain transducers. In addition, the Raman

Sonication of nanotubes and nanotube-reinforced polymer resins

One of the major difficulties encountered during processing of carbon nanotube-reinforced or nanoparticle-reinforced polymer composites is the inability to achieve a uniform dispersion of the nanotubes or nanoparticles in the liquid polymer. Nanotubes tend to cluster or agglomerate due to physical entanglements of the tubes, van der Waals forces between the carbon surfaces, and the fact that the surface energy of the nanotube clusters is thought to be less than that of the corresponding

Raman scattering from nanotubes

Raman spectroscopy is a widely used technique in materials science which involves the excitation of a sample with intense monochromatic light (typically laser light) followed by observations of the scattering of the incident radiation [174]. The scattered radiation occurs at frequencies corresponding to different vibrational modes of the molecules in the sample (the Raman spectrum), and which are different from the frequency of the incident radiation. The vibrational spectra of molecules are

Absorption of high frequency waves by nanotubes

Experiments with microwave excitation of carbon nanotubes have yielded several very interesting conclusions related to heating of the nanotubes. This has important applications for processing of nanotube-reinforced polymer composites, since microwave radiation is often used for curing of thermosetting polymer matrix materials in composites [226], [227], [228] and because carbon nanotubes are often grown by using a microwave-enhanced chemical vapor deposition process [229], [230], [231], [232].

Concluding remarks

The knowledge base associated with the vibrations of CNTs and their composites has expanded greatly in recent years, as the number of applications involving dynamic behavior of nanometer-scale systems continues to grow. The explosive growth in the literature on this subject is such that the vast majority of the papers reviewed here were published within the last five years, with most of the publications appearing in physics journals. Developments in the simulation of vibrating CNTs span the

Acknowledgment

The support of National Science Foundation Grant No. CMS-03-19767 for “Development of Instrumentation for Measurement of Microscopic Dynamic Motions in Physical Systems” is gratefully acknowledged.

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ReviewVibrations of carbon nanotubes and their composites: A review

Abstract

Introduction

Section snippets

Modeling and simulation of vibrating nanotubes

Nanomechanical resonators, oscillators and field emission devices

Use of vibration measurements to characterize nanotube mechanical properties

Nanotube augmentation of dynamic mechanical properties of composites

Vibrations in nanotube-based sensors and actuators

Sonication of nanotubes and nanotube-reinforced polymer resins

Raman scattering from nanotubes

Absorption of high frequency waves by nanotubes

Concluding remarks

Acknowledgment

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Formulas for natural frequency and mode shape

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Noncoaxial resonance of an isolated multiwall carbon nanotube

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Vibration problems in engineering

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Compos Sci Technol

Free vibration of multiwall nanotubes

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Applicability and limitations of simplified elastic shell equations for carbon nanotubes

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Oscillations of a thin hollow cylinder: carbon nanotubes

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Structural and equivalent continuum properties of single-walled carbon nanotubes

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Vibrations of carbon nanotubes and their composites: A review

Resonance vibration of amorphous SiO₂ nanowires driven by mechanical or electrical field excitation