A Brief Review on Research Development on Dynamic Behaviors of Carbon Nanotubes

Mohd Afzan Mohd Anuar1,a and Ahmad Azlan Mat Isa1,b

1Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia

aafzan341@salam.uitm.edu.my, bahmadazlan@salam.uitm.edu.my

Keywords: Carbon nanotubes, dynamic characteristics.

Abstract. Carbon nanotubes (CNTs) are said to be among the most potential materials in

applications of nanodevices, nanocomposites and nanostructure due to their excellent mechanical

and physical attributes. CNTs were first discovered by S. Iijima in 1991 where he has reported in his

article the synthesis of needle-like tubes by using an arc-discharge evaporation. After the immense

discovery, the number of research on CNTs has increased significantly, focusing on their

mechanical characteristics, dynamics properties and applications in nanotechnology. This paper

attempts to present a review of a quite number of publications on CNTs and their dynamic

properties. The main topics covered in this review are the applications of CNTs, their dynamic

characteristics including the modeling and simulation of vibrating CNTs, and finally the vibration

modes of CNTs.

Introduction

Investigation on dynamics characteristics of CNTs recently grow very fast after realizing their

novel potential in vibrational applications such as vibration sensors, nanoelectromechanical

systems (NEMS) and ultrahigh frequency nanoresonators. Due to their excellent mechanical and

physical attributes CNTs have been applied also in the development of nanodevices,

nanocomposites and nanostructure [1]. After the discovery of CNTs by S. Iijima in 1991 [2],

numerous number of research about these materials has been observed especially related

with their mechanical characteristics [3,4], dynamics properties [1,5-9] and applications in

nanotechnology [10-13].

Within a couple of decades since the discovery, the researchers have employed various means of

approaches in comprehending the statics as well as the dynamics properties of these materials such

as continuum models [8,19-20], molecular mechanics approach [17-18], development of spring-

mass based finite element models and simulations [1]. Understanding on the dynamics attributes of

CNTs is essential and as much as possible analytical and laboratory work remains needed to take

full advantage of these distinctive materials. Vibratory characteristics of CNTs remain the main

focus of researchers according to the considerable number of publications on CNTs as explained in

the literature review of this paper.

According to the best of our knowledge and background study, recent investigations on dynamics

behavior of CNTs mostly deal with computational modeling based on finite element analysis and

simulation using established continuum models and molecular or atomistic models. Besides that,

there is limited number of research done on the vibration attributes of CNTs in fluidic environment.

This report attempts to appropriately outline a review of a quite number of publications on

application CNTs and their dynamic properties.

Applications of CNTs

A. Sharma et al. [10] have fabricated CNT/Polymer nanocomposites that can be utilized

as hydrogen separating membrane where a small weight fraction of single-walled CNTs

and multiwalled CNTs was dispersed in polycarbonate matrix separately using benzene. Due to

their good mechanical properties, CNTs also have been used in improving the tensile strength of

glass fibres. Recent investigation has been done to study the effect of CNT morphology and

Advanced Materials Research Vol. 667 (2013) pp 30-34Online available since 2013/Mar/11 at www.scientific.net© (2013) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMR.667.30

All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP,www.ttp.net. (ID: 130.194.20.173, Monash University Library, Clayton, Australia-07/12/14,23:08:13)

dispersion in glass fibre coating to its tensile strength. The researchers concluded that the

application of CNT nanocomposites coating on the surface of glass fibre is an effective

way of improving the mechanical attributes of glass fibres [11].

R. Chowdhury et al. [12] has studied the application of single-walled CNTs as a biological object

mass sensor using continuum mechanics based approach. In this particular research, a general

expression of mass of bio-particles based on the frequency-shift of single-walled CNTs was derived.

Fig. 1 shows the single wall CNTs with an attached mass at the tip of nanotube length. J. Wan et al.

[13] in their article reported the method of preparing cell sensor from composite of cellulose and

CNTs. The composite was used to detect leukemia K562 cells on a gold electrode to perform as an

impedance cell sensor.

Fig. 1, Cantilevered CNTs resonator with an end of mass. (a) Original configuration; (b) mathematical idealized configuration [12].

Based on previous research, it has been found that CNTs has extremely high elastic modulus (on

the order of 1 TPa) [14] and low mass density [5]. Thus, they offer an excellent property to be

utilized as ultra high nanoresonators. J.W. Kang and H.J. Hwang [15] have investigated the

oscillation dynamics of a C60 fullerene encapsulated in a single-walled CNT-resonator via classical

molecular dynamics simulations. Due to its special behavior, the researchers suggested that a CNT-

resonator encapsulating a C60 fullerene has a potential application for programmable multiple-

position devices controlled by the resonance frequency. Besides that, D.J. Palmer [16] in his article

stated that CNT-based nanoresonators serve tunability and sensitivity that suitable for high precision

measurement puposes due to their low mass, few defects and high stiffness.

Dynamics behaviors of CNTs

Knowing the dynamics properties of CNTs is essential due to their wide-range of

potential applications e.g. nanoresonators and sensors, and it is also important in determining

indirectly the mechanical properties of CNTs. Therefore, a significant number of researchers have

worked out to look for the most accurate theoretical models that can represent the dynamics

properties of CNTs such as the natural frequencies and their mode shapes. C.Y. Wang and S.

Adhikari [6] have developed a double shell-Stokes flow model to study the axisymmetric

vibration of single-walled CNTs in water. The study has provided the theoretical explanations

and molecular dynamics simulations that could be a useful guideline and modeling tool to

study further on the dynamic behavior of CNTs in fluid environment.

Advanced Materials Research Vol. 667 31

On the other hand, R. Chowdhury et al. [5] have proposed to apply the molecular mechanics

approach to obtain the natural frequencies of zigzag and armchair single-walled CNTs. They found

that the natural frequencies of CNTs decrease as the increase of their aspect ratios and it shows

comparable trends with previous studies using the similar approach.

Timoshenko beam theory has been adopted by J. Yang et al. [7] to model nonlinear free vibration

of single-walled CNTs. In this study, the vibration of CNTs was investigated based on von Karman

geometric nonlinearity and Eringen’s nonlocal elasticity theory. In other research, S.K.

Georgantzinos and N.K. Anifantis [1] have developed a finite element model of multi-walled CNTs

using a springs and lumped masses based on the atomic microstructure of nanotubes. Nanosprings

were used to simulate the interactions between carbon atoms in the nanotube layer while interlayer

bonds were modeled using van der Waals nanosprings Figure 2 illustrates the vibration modes of

clamped-free multi wall CNTs. Apart from that, the study on vibrational characteristics of CNTs

embedded in elastic medium was also performed based on research by J.Yoon et al [9].

Fig. 2, Vibration modes of clamped-free multi wall CNTs: (a) First mode of bending, (b) Second

mode of bending (c) First mode of twisting (d) First mode of axial [1].

Vibration modes of CNTs

In the study of vibrational characteristics, CNTs possess a few modes of vibration such as

radial breathing mode, transverse mode and longitudinal mode. H.C. Cheng et al. [17] has

utilized a modified molecular structural mechanics (MSM) model to study the effect of diameter-

length aspect ratio, temperature and number of layer of CNTs on the radial breathing mode

(RBM) frequencies and mode shapes. RBM frequencies of armchair encapsulating C60 molecules

has been studied by S. Okada [18] and he found that the RBM frequencies indicate unusual shifts

from the corresponding nanotubes depending on the space between the walls of nanotubes and

C60 molecules. The result also showed that the encapsulation of C60 molecules would cause a

higher frequency shift for (10, 10) nanotube but a lower shift for (11, 11) and (12, 12) nanotubes.

R.F. Gibson [8] in his articles review explained a continuum approach that has been used by

researchers to approximate the theoretical resonance frequency of nanotubes in flexural or

transverse mode. According to Bernoulli-Euler beam theory, transverse motion of elastic beam

could be expressed as

32 Nanosynthesis and Nanodevice

(1)

Where E is the Young’s modulus of material, I is the moment of inertia of beam cross-section about

its neutral axis, A is the cross-sectional area of beam, ρ is the density of beam, x is the distance

along beam, w(x,t) is the transverse deflection and t is the time. In order to determine the inner and

outer transverse motion of double-walled CNTs, J. Yoon et al. [19] have developed a double

Timoshenko beam model. Based on Timoshenko beam theory, the transverse displacement w(x,t)

and slope ϕ(x,t) due to bending of beam is governed by Eq. (2) and (3). Those are:

(2)

(3)

Where K is the shear factor depending on the geometrical of cross-section and p is the

distributed loading per unit length of the beam. Meanwhile, the frequencies of single-walled CNTs

in flexural, torsional, radial breathing and longitudinal modes have been computed based on

classical theory of thin-walled hollow isotropic cylinders by G.D. Mahan [20].

Spring-mass based finite element model developed by S.K. Georgantzinos and N.K. Anifantis [1]

has been applied to determine different modes of vibration of multi wall CNTs including breathing

modes and beam-like modes such as bending, twisting and axial modes as well as their

corresponding natural frequencies. In this research, nanosprings have been used to simulate the

nanotube layers and van der Waals nanosprings were used to model interlayer interactions.

Meanwhile, R. Chowdhury et al. [24] have investigated the effect of heterogeneous end constraints

on low frequency vibration modes of multi wall CNTs. The heterogeneity has been modeled by

clamping different number of layers at one end while the other end was simply supported. The result

shows that different end constraints produce different stiffness, maximum displacement the natural

frequency of multi wall CNTs.

Conclusion

The dynamics characteristics of CNTs are remain an important area to be explored by researchers.

There is still limited number of research conducted experimentally due to a few constraints such as

difficulties of probing method for nanolevel vibrations as well as cost factor. Hence, theoretical

methods such as Euler-Bernoulli beam theory, Timoshenko beam model and spring-mass model

have been utilized and considered as reliable and cheaper in producing outcomes which closely

approach the actual behavior of CNTs.

References

[1] S. K. Georgantzinos, N. K. Anifantis, Vibration analysis of multi-walled carbon

nanotubes using a spring-mass based finite element model, Computational Materials

Science 47 (2009) 168-177.

[2] S. Iijima. Helical microtubes of graphitic carbon. Nature 354 (1991) 56-58.

[3] Mechanical properties of carbon nanotubes: theoretical prediction and experimental

measurements. C. R. Physique 4 (2003) 993-1008.

[4] Z.L. Wang, R.P. Gao, P. Poncharal, W.A. de Heer, Z.R. Dai, Z.W. Pan, Mechanical and

electrostatic properties of carbon nanotubes and nanowires. Materials science and

Engineering C 16 (2001) 3-10.

[5] R. Chowdhury, S. Adhikari, C.Y. Wang, F. Scarpa, A molecular mechanics approach for

the vibration of single-walled carbon nanotubes. Computational Materials Science 48 (2010)

730-735.

Advanced Materials Research Vol. 667 33

[6] C.Y. Wang, C.F. Li, S. Adhikari, Axisymmetric vibration of single-walled carbon nanotubes

in water. Physics Letters A 374 (2010) 2467-2474.

[7] J. Yang, L.L. Ke, S. Kitipornchai, Nonlinear free vibration of single-walled carbon

nanotubes using nonlocal Timoshenko beam theory. Physica E 42 (2010) 1727-1735.

[8] R.F. Gibson, E.O. Ayorinde, Y.F. Wen, Vibrations of carbon nanotubes and their

composites: A review. Composites Science and Technology 67 (2007) 1-28.

[9] J. Yoon, C.Q. Ru, A. Mioduchowski, Vibration of an embedded multiwall carbon nanotube.

Composites Science and Technology 63 (2003) 1533-1542.

[10] A. Sharma, S. Kumar, B. Tripathi, M. Singh, Y.K. Vijay, Aligned CNT/Polymer

nanocomposite membranes for hydrogen separation. International Journal of Hydrogen

Energy 34 (2009) 3977-3982.

[11] N.A. Siddiqui, E.L. Li, M.L. Sham, B.Z. Tang, S.L. Gao, E. Mader, J.K. Kim, Tensile

strength of glass fibres with carbon nanotube–epoxy nanocomposite coating: Effects

of CNT morphology and dispersion state. Composites: Part A 41 (2010) 539-548.

[12] R. Chowdhury, S. Adhikari, J. Mitchell, Vibrating carbon nanotubes based bio-sensors.

Physica E 42 (2009) 104-109.

[13] J. Wan, X. Yan, J. Ding, R. Ren, A simple method for preparing biocompatible composite

of cellulose and carbon nanotubes for the cell sensor. Sensors and Actuators B 146 (2010)

221-225.

[14] J.P. Salvetat, G.A.D. Briggs, J.M. Bonard, R.R. Bacsa, A.J. Kulik, T. Stockli et al., Elastic

and shear moduli of single-walled carbon nanotubes rope. Physical Review Letters 82

(1999) 944-947.

[15] J.W. Kang, H.J. Hwang, Molecular dynamics study on oscillation dynamics of a C60

fullerene encapsulated in a vibrating carbon-nanotube-resonator. Computational Materials

Science 50 (2010) 790-795.

[16] D.J. Palmer, Nanotube resonators play a high note. Nanotoday Volume 1, Issue 3 (August

2006) pg. 9.

[17] H.C. Cheng, Y.L. Liu, C.H. Wu, W.H. Chen, On radial breathing vibration of

carbon nanotubes. Computer Methods in Applied Mechanics and Engineering 199 (2010)

2820-2827.

[18] S.Okada, Radial-breathing mode frequencies for nanotube encapsulating fullerenes.

Chemical Physics Letters 438 (2007) 59-62.

[19] J. Yoon, C.Q. Ru, A. Mioduchowski, Timoshenko beam effects on transverse wave

propagation in carbon nanotubes. Composites B 35 (2004) 87-93.

[20] G.D. Mahan, Oscillations of a thin hollow cylinder: carbon nanotubes. Physics Review B

65 (2002) 235402.

[21] D. Mattia, Y. Gogotsi, Review: Static and dynamic behavior of liquids inside carbon

nanotubes. Microfluid Nanofluid 5 (2008) 289-305.

[22] R.M. Stevens, C.V. Nguyen, M. Meyyappan , Carbon nanotube scanning probe for imaging

in aqueous environment. IEEE Transactions on Nanobioscience 3 (2004) 56-60.

[23] G.A. Ozon, I. Manners, S.F. Bidoz, A. Arsenault, Dream naomachines. Advanced Materials

17 (2005) 3011-3018.

[24] R. Chowdhury, C.Y. Wang S. Adhikari, Low frequency vibration of multiwall

carbon nanotubes with heterogeneous boundaries. Journal of Physics D: Applied Physics 43

(2010) 1-8.

34 Nanosynthesis and Nanodevice

Nanosynthesis and Nanodevice 10.4028/www.scientific.net/AMR.667 A Brief Review on Research Development on Dynamic Behaviors of Carbon Nanotubes 10.4028/www.scientific.net/AMR.667.30

DOI References

[1] S. K. Georgantzinos, N. K. Anifantis, Vibration analysis of multi-walled carbon nanotubes using a spring-

mass based finite element model, Computational Materials Science 47 (2009) 168-177.

http://dx.doi.org/10.1016/j.commatsci.2009.07.006 [8] R.F. Gibson, E.O. Ayorinde, Y.F. Wen, Vibrations of carbon nanotubes and their composites: A review.

Composites Science and Technology 67 (2007) 1-28.

http://dx.doi.org/10.1016/j.compscitech.2006.03.031 [17] H.C. Cheng, Y.L. Liu, C.H. Wu, W.H. Chen, On radial breathing vibration of carbon nanotubes.

Computer Methods in Applied Mechanics and Engineering 199 (2010) 2820-2827.

http://dx.doi.org/10.1016/j.cma.2010.05.003 [23] G.A. Ozon, I. Manners, S.F. Bidoz, A. Arsenault, Dream naomachines. Advanced Materials 17 (2005)

3011-3018.

http://dx.doi.org/10.1002/adma.200501767