Carbon Nanotube Based Mass Sensor Research Articles

Axial vibration characteristics of carbon nanotube-based mass sensors containing nanoparticles using nonlocal elasticity theory

Carbon nanotubes (CNTs) are sensitive elements for the fabrication of nanomechanical mass sensors with greatly improved sensitivity. In this paper, the axial vibration behavior of single-walled CNTs based mass sensors was examined by nonlocal elasticity theory and Euler–Bernoulli beam theory. The vibration governing equation of the system was derived by the Hamiltonian principle, and the relationships of frequency equations and responses describing the vibration characteristics were all established. An approximate analytical method and simple expression for calculating the fundamental frequency were provided to obtain the expressions of natural frequencies with explicit physical parameters. In addition, combining with the theoretical analysis and considering the damping environment of the sensor under actual working conditions, LAMMPS molecular dynamics simulations were applied to compare and discuss the influence of various physical factors on the vibration behaviors of mass sensors. And the stable vibration signal generated by the damping was used to identify whether the attached nanoparticles fall off. The data revealed that the increase in tip attached mass and adjustment nonlocal parameters could effectively improve the sensitivity of mass sensors.

Nonlocal Timoshenko modeling effectiveness for carbon nanotube-based mass sensors

Carbon nanotubes (CNTs) have been considered for a wide range of nanotechnology applications due to their unique mechanical, thermal, and electrical properties. One of the most notable nanotechnology applications is the frequency shift-based carbon nanotube mass sensor, which has motivated the development of reliable reduced-order models. As such, this research effort focuses on a carbon nanotube-based mass sensor that utilizes Timoshenko beam theory to extend the usability of these models to short and stout structures. Additionally, Eringen's nonlocal elasticity is considered to account for certain nanoscale phenomena. To the authors' knowledge, this is the first time a CNT-based mass sensor modeled with the nonlocal Timoshenko beam theory with a complex-shaped deposited particle has been studied. Considering Timoshenko beam theory and Eringen's nonlocal theory, the Hamilton's principle is utilized to derive the governing equations of motion, boundary conditions, and continuity conditions accounting for a single deposited nanoparticle. Then, it is shown that the obtained frequency shift of the sensor is dependent on the rotary inertia, shear effects, nonlocal parameter, and particle mass, geometry, and location. The variation of each of these parameters leads to a holistic characterization of the proposed system. The discrepancies and limits of applicability between Timoshenko and Euler-Bernoulli models are deeply explored and discussed, particularly for short and stout structures. It is shown that the Euler-Bernoulli model leads to an overprediction of the frequency shifts compared to Timoshenko beam theory, especially for higher modes. The nonlocal Timoshenko-based model is valuable because short and stout structures were found to be preferred for mass sensing applications, since they lead to a higher sensitivity. Other researchers can utilize these findings for the design, modeling, and analysis of nanoscale sensors and resonators.

Uncertainty analysis and stochastic characterization of carbon nanotube-based mass sensor with multiple deposited nanoparticles

Input uncertainties on the location, mass, and geometry of multiple deposited nanoparticles for carbon nanotube-based mass sensor are investigated. The carbon nanotube (CNT) is modeled as an Euler-Bernoulli beam with end constrained boundary conditions and Eringen’s nonlocal elasticity theory to account for size-dependent phenomena. Additionally, the displacement field of the CNT is broken up into components to the left and right of each deposited particle. Utilizing the Hamilton’s principle and the discretized displacement fields, the nonlocal governing equations of motion, boundary conditions, and continuity conditions at the deposited particle locations are derived. The effects of the particle location, mass, and geometry on the inherent frequency shifts before and after deposition are studied. Following these parametric studies, sensitivity analysis and uncertainty quantification methods are applied for two different nominal configurations of the mass sensor. The importance of the input parameters is deeply discussed, focusing especially on the location effects on the first and second natural frequency shifts. It is shown that increasing the mass and size of the particle increases the overall frequency shift, while varying the location of the particles does not strictly lead to increased frequency shifts. Finally, it is shown that due to the high number of input parameters, there are multiple particle configurations that lead to identical frequency shifts. These findings may be used by other researchers to extend the usability, usefulness, and characterization of mass detection devices.

Haar wavelet method for nonlinear vibration of magneto-thermo-elastic carbon nanotube-based mass sensors conveying pulsating viscous fluid

Haar wavelet method for nonlinear vibration of magneto-thermo-elastic carbon nanotube-based mass sensors conveying pulsating viscous fluid

Thermoelastic modeling and comparative analysis of biomass sensors under rippling deformation and magnetic field

This study is intended for investigating the linear and nonlinear responses of carbon nanotube-based mass sensors in thermal and magnetic environment. For accurate modeling, the carbon nanotube rippling deformation effect is considered and various representations for the thermal expansion are examined and compared to each other. By utilizing Euler-Bernoulli beam theory assumptions and Eringen's nonlocal elasticity theory, the nonlinear reduced-order model is developed on the basis of the extended Hamilton's principle. The results show that the natural and resonant frequencies and frequency shifts of the system are strongly dependent on the magnetic field and thermal expansion representation. The method of multiple scale is used to determine the modulation equation including the von Karman and rippling nonlinearities. The results show a very good agreement between the perturbation solution and the numerical integration results for specific conditions of the forcing, temperature difference, and quality factor. A comparative study between the linear and nonlinear mass sensing approaches is performed to show their limits of applicability. It is demonstrated that the linear approach may result in erroneous detection of the deposited mass. The obtained results indicate that the longitudinal magnetic field enhances the dynamic stability of the carbon nanotube mechanical resonator in the pre-buckling oscillation regime, while the dynamic stability of the nanoscale resonator is decreased in the presence of the magnetic field for the post-buckling configuration. Also, the ripple-based nonlinearity is accompanied by an increase in the mass responsivity of the resonator. On the contrary, mass sensitivity of the carbon nanotube resonator is diminished by considering the von Kármán geometric nonlinearity. This study shows the importance of considering the nonlinear effects on the system's sensitivity from frequency and amplitude sensing techniques.

Nonlinear dynamical responses of forced carbon nanotube-based mass sensors under the influence of thermal loadings

This study presents an analytical solution for the nonlinear forced vibration response of bridged carbon nanotube (CNT)-based mass sensors subjected to different types of thermal loading and external harmonic excitations. The structure undergoes a temperature change through its thickness when considering three different distribution patterns of the temperature, namely uniform, linear, and nonlinear. The CNT is modeled as a nonlocal doubly clamped beam that complies with Euler–Bernoulli beam theory and Eringen’s nonlocal elasticity theory. The von Karman geometric nonlinearity is adopted to account for the mid-plane stretching of end-constrained beams. The extended Hamilton’s principle is used to derive the nonlinear governing equations of motion, boundary conditions, and continuity conditions accounting for the location of the deposited particle. The method of multiple scales (MMS) is employed to perform the nonlinear dynamical analysis of the nanobeam. Analytical expressions of the nonlinear dynamic response of the system exposed to thermal loadings in the case of primary resonance are presented. An important contribution of this work is the provision for closed-form expressions of the resonance frequency and the critical amplitude of the considered system. Simultaneously, validation of the results by MMS is achieved by Galerkin’s procedure and Runge–Kutta method. Then, the effects of the thermal loads and some key parameters on the nonlinear resonance frequency and amplitude shifts are discussed, and some meaningful conclusions are drawn.

Effect of temperature on vibrations and buckling behavior of carbon nanotube-based mass sensors using a new temperature-dependent structural model

In last decade, structural mechanics (SM) approach has been one of the most known and effective tools for the determination of the mechanical properties of carbon nanotubes (CNTs) such as elastic modulus, shear modulus, natural frequency, and critical axial buckling strain. Considering increasing applications of CNTs as resonators at low and high temperatures, a new temperature-dependent structural mechanics model is presented here. The proposed model can be utilized to predict the effect of temperature on the mechanical response of CNTs as functional resonators. Mechanical and geometrical properties of equivalent beam element are correlated to the CNT's coefficient of thermal expansion (CTE). Owing to elaborate series of finite element simulations, the frequency shift of a CNTs-based mass sensor with different attached mass and aspect ratio in temperature range of 0–1600 K is calculated. Afterwards, the critical buckling temperature of CNTs-based mass sensor due to increasing the axial force by changing ambient temperature is obtained. Results show that decreasing the first natural frequency is clearly appeared by attaching a mass more than about 1 zg on the CNTs structure. In other words, CNTs can be used to detect particles with mass above 1 zg. Moreover, it is shown that the variation of CTE versus temperature is a critical parameter that influences the vibration and buckling behavior of CNTs-based mass sensors. Increasing temperature leads to decreasing natural frequency due to rising axial forces along the CNTs axis. As a result, the natural frequency approaches to zero when the temperature rises up to the critical buckling temperature. In addition, increase in temperature over the critical buckling temperature changes the mode shape of CNT vibration to the next mode shape.

Role and significance of thermal loading on the performance of carbon nanotube-based mass sensors

Insights on the sensitivity of carbon nanotube-based mass sensors subject to a uniform thermal environment are provided. The thermal loads are introduced as a means of buckling nonlocal carbon nanotube-based mass sensors in an effort to obtain high frequency shifts before and after the deposition of a nanoparticle on a carbon nanotube (CNT), leading to improved mass detection. In introducing thermal loads, the critical buckling temperature, pre-buckling, and post-buckling behaviors of CNTs with an arbitrary deposited mass are investigated. The CNT is modeled as an Euler-Bernoulli beam and the nonlinear governing equations of motion are derived by virtue of the Hamilton's principle. Eringen's nonlocal theory is employed to account for the interatomic long-range interactions, i.e., the size dependent phenomena occurring at the nano-scale. The proposed model allows for an arbitrarily positioned atomic-mass particle and accounts for the effects of the thermal field and the nonlocal parameter on the pre-buckling and post-buckling dynamics of clamped-clamped nanobeams. It is demonstrated that the temperature change has a remarkable influence on the frequency shift and hence on the sensitivity of the CNT-based mass sensor. The results show that augmenting the temperature in the pre-buckling regime leads to a decrease in the frequency shift, while the temperature rise in the post-buckling configuration has an increasing effect on the sensitivity of the CNT-based mass sensor. Also, it is found that when the temperature exceeds a certain point in the post-buckling region, higher frequency shifts can be obtained compared to the pre-buckling regime. In varying parameters, such as the length, diameter, number of walls (single-walled CNTs or multi-walled CNTs), location of the deposited mass, and nonlocal parameter, greater frequency shifts can be obtained in the post-buckling configurations of the CNT, leading to enhanced sensitivity in the system.

Geometrically nonlinear dynamic behavior on detection sensitivity of carbon nanotube-based mass sensor using finite element method

The principle of mass detection using carbon nanotube (CNT) resonators is based on the detection of the resonant frequency shift due to an attached mass. Although CNT resonators can easily show a nonlinear oscillation behavior, there is a lack of studies on the influence of the design parameters and the nonlinear dynamic behavior on the detection sensitivity of CNT-based mass sensors. In addition, most of the finite element method (FEM) analysis models that are used to predict the resonant frequency shift due to attached masses have been implemented in the linear oscillation regime. In order to enhance the sensing performance of the CNT-based mass sensor, a parametric study of the resonant frequency shift is conducted herein with respect to the attached mass, the electrostatic force, the initial tension and the CNT length, using an FEM-based nonlinear analysis model. The FE model is applied to solve the nonlinear dynamic behavior of CNT resonators using direct time integration and the solution is verified by its comparison to the corresponding analytical solution that had been validated in previous studies. The analysis results of the nonlinear dynamic behavior of the CNT resonator indicate that the CNT length plays a key role in the detection sensitivity, and the amount of electrostatic force determines the linear or nonlinear oscillation behavior of the resonator. It is shown that the detection sensitivity can be improved using the nonlinear oscillation behavior and this improvement is more effective with longer CNTs. This study's results justify the possibility and validity of FEM use for the analysis of the nonlinear behavior of CNT resonators and elucidate the relationship between the design parameters and the nonlinear behavior of the CNT-based mass sensor in enhancing the sensing performance.

Thermal effects on nonlinear vibration of a carbon nanotube-based mass sensor using finite element analysis

In the present study we carried out a dynamic analysis of a CNT-based mass sensor by using a finite element method (FEM)-based nonlinear analysis model of the CNT resonator to elucidate the combined effects of thermal effects and nonlinear oscillation behavior upon the overall mass detection sensitivity. Mass sensors using carbon nanotube (CNT) resonators provide very high sensing performance. Because CNT-based resonators can have high aspect ratios, they can easily exhibit nonlinear oscillation behavior due to large displacements. Also, CNT-based devices may experience high temperatures during their manufacture and operation. These geometrical nonlinearities and temperature changes affect the sensing performance of CNT-based mass sensors. However, it is very hard to find previous literature addressing the detection sensitivity of CNT-based mass sensors including considerations of both these nonlinear behaviors and thermal effects. We modeled the nonlinear equation of motion by using the von Karman nonlinear strain–displacement relation, taking into account the additional axial force associated with the thermal effect. The FEM was employed to solve the nonlinear equation of motion because it can effortlessly handle the more complex geometries and boundary conditions. A doubly clamped CNT resonator actuated by distributed electrostatic force was the configuration subjected to the numerical experiments. Thermal effects upon the fundamental resonance behavior and the shift of resonance frequency due to attached mass, i.e., the mass detection sensitivity, were examined in environments of both high and low (or room) temperature. The fundamental resonance frequency increased with decreasing temperature in the high temperature environment, and increased with increasing temperature in the low temperature environment. The magnitude of the shift in resonance frequency caused by an attached mass represents the sensing performance of a mass sensor, i.e., its mass detection sensitivity, and it can be seen that this shift is affected by the temperature change and the amount of electrostatic force. The thermal effects on the mass detection sensitivity are intensified in the linear oscillation regime and increase with increasing CNT length; this intensification can either improve or worsen the detection sensitivity.

Characterizing the nonlinear behaviour of double walled carbon nanotube based nano mass sensor

This work deals with the evaluation of nonlinear behaviour of a curved double walled carbon nanotube (DWCNT) when used for mass sensing applications. The DWCNT is considered to be doubly clamped at a source and a drain. To judge the nonlinear behaviour, equations of motion have been derived using Euler beam theory and Hamilton principle, considering nonlinear van der Waals interaction nonlinear oscillations of a double walled carbon nanotube excited harmonically near its primary resonance are considered. The nonlinear free vibration of double-walled carbon nanotubes based on the elasticity theory is studied in this paper. Modelling of the weak van der Waals force of attraction between the inner and outer tubes is represented using a spring element. The equation of motion involves four nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the double walled carbon nanotube based mass sensor is analyzed in the context of the time response, Poincare maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass, inner and outer tubes and the geometric imperfections of double walled carbon nanotube.

Modelling the nonlinear behaviour of double walled carbon nanotube based resonator with curvature factors

This paper deals with the nonlinear vibration analysis of a double walled carbon nanotube based mass sensor with curvature factor or waviness, which is doubly clamped at a source and a drain. Nonlinear vibrational behaviour of a double-walled carbon nanotube excited harmonically near its primary resonance is considered. The double walled carbon nanotube is harmonically excited by the addition of an excitation force. The modelling involves stretching of the mid plane and damping as per phenomenon. The equation of motion involves four nonlinear terms for inner and outer tubes of DWCNT due to the curved geometry and the stretching of the central plane due to the boundary conditions. The vibrational behaviour of the double walled carbon nanotube with different surface deviations along its axis is analyzed in the context of the time response, Poincaré maps and Fast Fourier Transformation diagrams. The appearance of instability and chaos in the dynamic response is observed as the curvature factor on double walled carbon nanotube is changed. The phenomenon of Periodic doubling and intermittency are observed as the pathway to chaos. The regions of periodic, sub-harmonic and chaotic behaviour are clearly seen to be dependent on added mass and the curvature factors in the double walled carbon nanotube. Poincaré maps and frequency spectra are used to explicate and to demonstrate the miscellany of the system behaviour. With the increase in the curvature factor system excitations increases and results in an increase of the vibration amplitude with reduction in excitation frequency.

Sub-harmonic Bifurcation Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

Bifurcation behaviors are very important for the design of sensors. Using the sub-harmonic Melnikov method, the sub-harmonic bifurcation of single-walled carbon nanotube based mass sensor is investigated in this paper. The parametric conditions for sub-harmonic bifurcation of this system are obtained. It is presented that when the ratio of the excitation amplitude to the damping coefficient crosses a critical value, sub-harmonic bifurcations of <i>m</i> order (odd) can occur. The stability conditions of the bifurcation solution for the system parameters are also obtained by using the affection-angle transformation and average method. The result can provide some guidance for the design of this class of sensors.

Atomistic Finite Element Modeling and Analysis of pinholes in Double Walled Carbon Nanotube based mass sensor

This paper deals with studying the mass sensing characteristics of defective Double Walled carbon Nanotubes (DWCNT) using atomistic finite element method. Simulations are performed on chiral, zigzag and armchair nanotubes with cantilever and bridged conditions using molecular structure mechanics approach. Carbon nanotubes are widely used in the design of nano sensors, nanoresonators and actuators. In this manuscript the authors have categorized defects like larger vacancies termed as pinhole into two types i.e. 6 missing atoms (A type) and 24(B Type) missing atoms on the outer wall of DWCNT. DWCNTs are modeled considering the weak van der waals force of attraction between the inner and outer tubes as a spring element (COMBIN14). The simulation results indicate that the resonant frequency of defective DWCNT reduces with the increase in chiral angle. The simulation results indicate fundamental frequency reduces with the increase in the number of pinhole defects in DWCNT. The maximum frequency reduction takes place when the defect is located nearer to the fixed end of DWCNT which signifies that position of the defect is an important parameter to judge the mass sensing characteristics of DWCNTs.

Mechanical vibrations of carbon nanotube-based mass sensors: an analytical approach

Purpose – The purpose of this paper is to examine the potential of single-walled carbon nanotubes as mass sensors by developing analytical expressions and then comparing the outcome with structural mechanics corresponding predictions. Design/methodology/approach – The carbon nanotube (CNT) resonators are assumed to be either single or double clamped. Analytical formulas capable of describing the vibrational behavior of such CNT-based nanoresonators with an attached mass at nanotube tip or various intermediate positions are developed by combining the Euler–Bernoulli theory and Krylov–Duncan functions. Findings – The validity and the accuracy of these formulas are examined for a wide range of cases via comparisons with corresponding results arisen by spring- or beam-based structural mechanics predictions. Both structural mechanics approaches utilize three-dimensional nanoscale elements formulated according to the molecular theory. The results indicate that the new sensor equations may be utilized for the estimation of vibration response of CNT-based mass sensors with reasonable accuracy. Originality/value – Simple analytical formulas are proved to approximate the mass sensing ability of CNTs adequately, the fact that may significantly contribute in the effort of developing new sensor devices.

Computational models for large amplitude nonlinear vibrations of electrostatically actuated carbon nanotube-based mass sensors

A comprehensive multiphysics model of a cantilevered carbon nanotube (CNT) including geometric and electrostatic nonlinearities is developed. The continuous model is reduced to a finite degree of freedom system by the Galerkin discretization and solved using the harmonic balance method (HBM) coupled with the asymptotic numerical method (ANM). The influence of higher modes on the nonlinear dynamics of the considered resonator is investigated in order to retain the number of modes which will be used by the HBM+ANM procedure. Several simulations are performed for a specific CNT design in order to obtain a wide range of frequency shifts with respect to the mass and position of an added particle. This model is an intuitive way for designers to develop resonant nanosensors vibrating at large amplitudes for mass detection. Particularly, it is demonstrated that the mass and position of a particle can be determined based on the proposed model reduced to the first bending mode coupled with the analytical expressions of the linear frequency shifts for the second and third modes.

CHAOTIC RESPONSE ANALYSIS OF SINGLE-WALLED CARBON NANOTUBE DUE TO SURFACE DEVIATIONS

Nonlinear vibrational behavior of a single-walled carbon nanotube based mass sensors is considered. The modeling involves stretching of the mid plane and damping. The equation of motion involves two nonlinear terms due to the curved geometry and the stretching of the central plane due to the bridged boundary conditions. The manifestation of instability and chaos in the dynamic response is observed. The regions of periodic, sub-harmonic and chaotic behavior are clearly seen to be dependent on added mass and the surface deviations. Poincaré maps and frequency spectra are used to explicate and demonstrate the miscellany of the system behavior.

Nonlinear Dynamic Analysis of Single-Walled Carbon Nanotube Based Mass Sensor

In previous studies, experimentally measured resonance frequencies of carbon nanotubes have been used along with classical beam theory for straight beams. However, it is found that these carbon nanotubes are not straight, and that they have some significant surface deviation associated with them. This paper deals with the nonlinear vibration analysis of a wavy single-walled carbon nanotube based mass sensor, which is doubly clamped at a source and a drain. Nonlinear oscillations of a single-walled carbon nanotube excited harmonically near its primary resonance are considered. The carbon nanotube is excited by the addition of an excitation force. The modeling is carried out using the elastic continuum beam theory concept, which involves stretching of the central plane and phenomenological damping. This model takes into account the existence of waviness in carbon nanotubes. The equation of motion involves two nonlinear terms due to the curved geometry and the stretching of the central plane. The dynamic response of the carbon nanotube based mass sensor is analyzed in the context of the time response, Poincaré maps, and fast Fourier transformation diagrams. The results show the appearance of instability and chaos in the dynamic response as the mass on carbon nanotube is changed. Period doubling and mechanism of intermittency have been observed as the routes to chaos. The appearance of regions of periodic, subharmonic, and chaotic behavior is observed to be strongly dependent on mass and the geometric imperfections of carbon nanotube. Poincaré maps and frequency spectra are used to elucidate and to illustrate the diversity of the system behavior.

Clamped-Free Single-Walled Carbon Nanotube-Based Mass Sensor Treated as Bernoulli–Euler Beam

AbstractIn this study, we investigate the vibrations of the cantilever single-walled carbon nanotube (SWCNT) with attached bacterium on the tip in view of developing the sensor. This sensor will be able to help to identify the bacterium or virus that may be attached to the SWCNT. Two cases are considered: These are light or heavy bacteria attached to the nanotube. The problem is solved by the exact solution, the finite difference method, and the Bubnov–Galerkin method.

The Effect of Pinhole Defect on Dynamic Characteristics of Single Walled Carbon Nanotube Based Mass Sensors

The Effect of Pinhole Defect on Dynamic Characteristics of Single Walled Carbon Nanotube Based Mass Sensors