Vibration signature analysis of single walled carbon nanotube based nanomechanical sensors

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Abstract

In the present paper, the simulation of the mechanical responses of individual carbon nanotubes treated as thin shells with thickness has been done using FEM. The resonant frequencies of the fixed free and the bridged SWCNT have been investigated. This analysis explores the resonant frequency shift of SWCNTs caused by the changes in the size of CNT in terms of length as well as the masses. The results showed the sensitivity of the single walled carbon nanotubes to different masses and different lengths. The results indicate that the mass sensitivity of carbon nanotube nanobalances can reach 10−21 g and the mass sensitivity increases when smaller size nanotube resonators are used in mass sensors. The vibration signature exhibits super-harmonic and sub-harmonic response with different level of mass. In order to explore the suitability of the SWCNT as a mass detector device, the simulation results of the resonant frequency of fixed free SWCNT are compared to the published experimental data. It is shown that the FEM simulation results are in good agreement with the experimental data and hence the current modelling approach is suitable as a coupled-field design tool for the development of SWCNT-based NEMS applications.

Introduction

Resonance-based sensors offer the potential of meeting the high-performance requirement of many sensing applications, including metal deposition monitors, chemical reaction monitors, biomedical sensors, mass detector, etc [1], [2], [3], [4]. These applications employ the characteristic of resonators in frequency shifting due to mass loading. The merit of micromechanical resonators is that miniaturization of their dimensions enhances the mass sensitivity of these sensors [5]. It has been reported that the detectable mass can be as small as several femto grams (fg) by using microsized silicon or silicon nitride cantilevers [6], [7]. If the resonators are scaled down to nanosize, the mass sensitivity of the resulting nanosensors can surely be enhanced. The idea of using individual carbon nanotubes as high sensitivity nanobalances was first proposed by Poncharal et al. [8].

In fact, carbon nanotubes are unique nanostructured materials. The extraordinary mechanical and physical properties in addition to the large aspect ratio and low density have made carbon nanotubes ideal components of nanodevices. A wide range of applications of carbon nanotubes have been reported in the literature, such as atomic force microscopy probe tip [9], nanotweezer [10], nanoactuator [11], nanooscillator [12], etc. Recently, the feasibility of using carbon nanotubes as nanomechanical resonators was examined [13]. It was predicted that the fundamental frequencies of cantilevered or bridged single-walled carbon nanotubes could reach the level of 10 GHz–1.5 THz depending on the nanotubes’ diameter and length. This level of fundamental frequency is much higher than the highest frequency nanomechanical resonator so far fabricated by silicon carbide using optical and electron-beam lithography [14]. To explore the suitability of the single walled carbon nanotubes as a mass detector device for many sensing applications, the FEM simulation results for the resonant frequency are compared to the numerical results obtained by Rayleigh Ritz method for the beams having no nanoparticle and with a nanoparticle at the tip or at various intermediate positions along its length [15]. The use of single walled carbon nanotube as bio sensors has been recently examined by Chowdhury et al. [16] using continuum mechanics approach and equations are derived to detect the mass of biological objects. An atomistic finite element model of SWCNT has been investigated by Sakhaee-Pour et al. [17] to develop a predictive equation to propose a quick tool for estimating the natural frequencies with different boundary conditions and geometrical parameters. Li and Chou [18] developed an equivalent structural beam to mimic interatomic forces of the covalently bonded carbon atoms. Georgantzinos and Anifantis [19] have utilized a spring-mass-based finite element formulation for predicting the vibrational behaviour of single- and multi-walled carbon nanotubes to investigate their sensing characteristics when a nanoparticle is attached to them.

Section snippets

CNT modelling

The principle of mass detection using resonators is based on the fact that the resonant frequency is sensitive to the resonator mass, which includes the self-mass of the resonator and the mass attached on the resonator. The change of the mass attached on the resonator can cause a shift of the resonant frequency. The key issue of mass detection is in quantifying the change in the resonant frequency due to the added mass [20].

Continuum mechanics method has been successfully applied to analyze the

SWCNT mass sensors based on resonant frequency shift

The present study considers the case of a bridged SWCNT with a nano-scale particle attached to its tip. The operation of a SWCNT based mass sensor is based on the fact that mass addition to the tip causes a measurable shift in the resonant frequency of the beam. The minimum detectable mass change of the sensor can be approximated by the formula [16], [22]fres=12πkeqmeq(bridgedSWCNT)where fres is the resonant frequency of the bridged SWCNT and keq and meq the equivalent spring constant and the

Results and discussions

In this paper, the finite element model of the SWCNT has been analyzed with the addition of different masses at its centre. In this analysis the modelling of SWCNTs of cylindrical shapes having small thickness has been carried out.

The model that has been developed for the purpose of analysis is as under

Fixed free SWCNTs and bridged SWCNTs having attached mass at their mid position with the variation in the mass from 10−8 fg 10−2 fg for different lengths (L=6, 8 and 10 nm).

As indicated in Fig. 2,

Conclusions

  • 1.

    The present work has analyzed the modelling of fixed free and bridged SWCNT using a Finite Element Model.

  • 2.

    The simulation results and the trend between the Experimental and FEM simulated results, confirms the validity of the current FE model and indicates its suitability for use in the further investigation of the SWCNT as a mass sensor.

  • 3.

    This analysis explores the resonant frequency shift of SWCNTs caused by the changes in the size of CNT in terms of length as well as the masses.

  • 4.

    The results

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