Carbon Nanotube Cantilever Research Articles

Study of the large bending behavior of CNTs using LDTM and nonlocal elasticity theory

The general expressions for vertical deflection, horizontal displacement, and strain energy in a bent cantilevered carbon nanotube (CNT) are derived herein under a uniformly distributed load. This derivation employs nonlocal elasticity theory, crucial for understanding nanoscale mechanics due to size effects, and accounts for the nonlinear relationship between bending curvature and deflection under large bending conditions, a novel contribution. In the limiting cases, our expressions for large bending give the corresponding expressions reported in the literature for small bending. Additionally, we introduce the Laplace-Differential Transformation Method (LDTM) for the first time, providing efficient solutions to explore the influence of parameters like aspect ratio and small-scale factors on CNT bending behavior. Comparison with the analytical method validates the accuracy and efficacy of LDTM, offering a rapid solution for nonlinear equations. Our findings reveal that strain energy deviates more prominently from quadratic behavior in CNTs with high aspect ratios, while small-scale parameters have a pronounced effect on CNTs with smaller aspect ratios. These results will be relevant to designing and applying the nanoscale-sized cantilevered CNTs used in MEMs/NEMs.

Dynamics and Stability of Double-Walled Carbon Nanotube Cantilevers Conveying Fluid in an Elastic Medium

The paper concerns the dynamics and stability of double-walled carbon nanotubes conveying fluid. The equations of motion adopted in the current study to describe the dynamics of such nano-pipes stem from the classical Bernoulli–Euler beam theory. Several additional terms are included in the basic equations in order to take into account the influence of the conveyed fluid, the impact of the surrounding medium and the effect of the van der Waals interaction between the inner and outer single-walled carbon nanotubes constituting a double-walled one. In the present work, the flow-induced vibrations of the considered nano-pipes are studied for different values of the length of the pipe, its inner radius, the characteristics of the ambient medium and the velocity of the fluid flow, which is assumed to be constant. The critical fluid flow velocities are obtained at which such a cantilevered double-walled carbon nanotube embedded in an elastic medium loses stability.

A novel approach of bending behavior of carbon nanotubes by combining the effects of higher-order boundary conditions and coupling through doublet mechanics

This article presents the bending behavior of carbon nanotubes (CNTs) based on doublet mechanics (DM) and Euler–Bernoulli beam theory to analyze how deflection changes with higher-order boundary conditions and the coupling, which have not been previously investigated. The governing equations and associated boundary conditions are obtained using the principle of minimum potential. Numerical solutions show an important effect of higher-order boundary conditions on the deflection of cantilever CNTs, unlike simply supported CNTs. A paradox in which DM shows a stiffening behavior for cantilever CNTs is resolved using higher-order boundary conditions. The coupling significantly effects the bending behavior of armchair CNTs.

Determination of Hamaker constant for CNT and AFM probe configuration inside SEM

Mounting the atomic force microscope (AFM) probe on the gripper of the robotic nanoscale manipulators system enables the combination of the AFM and scanning electron microscope (SEM). The AFM–SEM-based method of determining Hamaker constant for carbon nanotube (CNT) and AFM cantilever in the vacuum condition of SEM, which is completed through a robotic nanoscale manipulators system, is presented for the first time. During Hamaker constant determining experiment, the elastic force is measured utilising integrated AFM–SEM imaging technique through detecting the deflection of AFM cantilever that actually equals van der Waals adhesion force. The van der Waals attraction force between CNT and AFM cantilever is calculated through the modelling of a cylindrical nanotube and a flat gold-coated surface. The experiment results indicate that Hamaker's constant measured are comparable to typical values published by previous researchers, being of the order of 100 zJ, which indicates that the present approach is valid and reliable.

Two-level system as topological actuator for nanomechanical modes

We investigate theoretically the dynamics of two quasidegenerate mechanical modes coupled through an open quantum two-level system. A mean-field approach shows that by engineering the retarded response of the two-level system with a coherent drive, the non-Hermitian mechanical spectrum exhibits an exceptional degeneracy point where the two modes coalesce. We show that this degeneracy can be exploited to manipulate the vectorial polarization of the mechanical oscillations. We find that adiabatically varying the detuning and the intensity of the drive induces a rotation of the mechanical polarization, which enables the topological and chiral actuation of one mode from the other. This topological manifestation of the degeneracy is further supported by quantum-jump Monte Carlo simulations to account for the strong quantum fluctuations due to the spontaneous emission of the two-level system. Our presentation focuses on a promising realization based on flexural modes of a carbon-nanotube cantilever coupled to a single-molecule electric dipole irradiated by a laser.

Measurement of Flexural Rigidity of Multi-Walled Carbon Nanotubes by Dynamic Scanning Electron Microscopy

In this work the flexural rigidity of individual large diameter multi-walled carbon nanotubes (MWCNTs) was investigated. The bending modulus were obtained by detecting the resonance frequencies of mechanically excited cantilevered carbon nanotubes using the so-called dynamic scanning electron microscopy technique, and applying the Euler–Bernoulli beam theory. For the nanotubes studied, we determined a modulus of up to 160 GPa. This agrees with values reported by other authors for MWCNTs produced by catalytic chemical vapor deposition, however, it is 6-8 times smaller than values reported for single and multi-walled carbon nanotubes produced by arc-discharge synthesis. Toxicological studies with carbon nanotubes have been showing that inhaled airborne nanofibers that reach the deep airways of the respiratory system may lead to serious, asbestos-like lung diseases. These studies suggested that their toxicity critically depends on the fiber flexural rigidity, with high rigidity causing cell lesions. To complement the correlation between observed toxicological effects and fiber rigidities, reliable and routinely applicable measurement techniques for the flexural rigidity of nanofibers are required.

Static and Dynamic Analysis of Carbon Nano Tube Cantilever for Nano Electro Mechanical Systems Based Applications

The cantilever is the most basic form of the MEMS and NEMS-based applications. It may include actuators and sensors in multiple domains for the detection of deflections due to change in mass and charge from atomic to sub-atomic levels. The main constraints in the real-time environment for sensing applications are good sensitivity and selectivity along with good response time and wide dynamic range. CNTs (Carbon Nano Tubes) possess excellent electrical characteristics with good mechanical strength like elasticity, flexibility, tensile strength and good thermal conductivity. These properties make use of CNTs in NEMS that gives rise to good sensing platforms. In this paper we propose, design and analysis of CNT based Cantilever structure using FEM to determine the change in deflection due to varying load under static analysis. Similarly from dynamic analysis change in resonance frequency for change in thickness of Cantilever is performed. From the experimental results using COMSOL simulation, it is observed that the CNT based Cantilever deflection sensitivity is 9.85 x 10-8 m under maximum stress of 6.71 x 10-9 N/m2. From the dynamic analysis, resonant frequency occurs at 1.8 x 107 Hz for 10 nm thickness and for 50 nm is 7.5 x 107 Hz respectively.

Carbon nanotube-based nanoelectromechanical resonator as mass biosensor

The use of single walled carbon nanotube-based nanoelectromechanical system (NEMS) resonator to sense the biomolecules’ mass is investigated under the influence of an external ac-field. A single walled carbon nanotube (SWCNT) cantilever has been proposed and studied if the mass is attached at the tip or various intermediate positions. The shift of the resonant frequency and the quality factor have been investigated and show high sensitivity to the attached mass of biomolecule and its position. The proposed SWCNT-based NEMS resonator is a good candidate for sensing and tracing biomolecules’ mass as concentration of acetone in human exhale, resulting in a painless, correct, and simple diabetics’ diagnosis.

Towards radio transceiving in-vivo nano-robots

An implementable model and simulation of an oscillating Carbon Nanotube (CNT) for radio communication in nanorobots is presented. A cylindrical CNT cantilever beam, operating under constant direct current supply, is forced to continuously oscillate by applying a controlled electromagnetic force. Oscillation parameters are computed and simulated, including the maximum tip displacement, the acting electromagnetic force and the dynamic response of the CNT, yielding a frequency of oscillation. We develop a model to predict the oscillation frequency of the cantilever beam based on its properties, including the device geometry. The primary functional component of the system is the electrically chargeable cantilever beam which oscillates due to its electric charge and discharge, where the discharge happens when the cantilever moves closer to the counter electrode. Thus, we provide an implementable design of in-vivo transceiver, suitable for future large-scale applications based on radio communicating nanorobots. A swarm of such nanorobots can be regarded as implementable programmable matter.

Stability analysis of cantilever carbon nanotubes subjected to partially distributed tangential force and viscoelastic foundation

• A size-dependent CNT model is developed based on a partially distributed tangential force and viscoelastic foundation. • The foundation is assumed in three different types, including Kelvin, Maxwell and Standard linear solid models. • The applied force induced by magnetic-fluid flow is considered according to Navier–Stokes equation. • Effects of several parameters on the frequencies and flutter instabilities are studied. Dynamic instability of cantilever carbon nanotubes conveying fluid embedded in viscoelastic foundation under a partially distributed tangential force is investigated based on nonlocal elasticity theory and Euler–Bernouli beam theory. The present study has incorporated the effects of nonlocal parameter, Knudsen number, surface effects and magnetic field. And two main parameters have also considered, namely partially distributed tangential force and foundation. It is assumed that viscoelastic foundation has modeled as Kelvin–Voigt, Maxwell and Standard linear solid types. The size-dependent governing equation of transverse vibration is derived using Hamilton’s variational principle and discretized by the Galerkin truncation method. A detailed parameter study is carried out, indicating the stability behavior of the nanotubes. In the light of numerical results, it is shown that variables considered in nondimensional equations have significant effects on natural frequencies and flutter velocities, especially for the foundation distribution length and model as well as the partially distributed tangential force.

Control of carbon nanotube cantilever vibrator for nano-antenna applications

AbstractThe cantilever vibrator motion system of a carbon nanotube (CNT) is considered the next step in developing cold cathodes for VHF-band nano-antennas. In cases where a nano-antenna is used in...

Non‐coherent detection of digitally phase‐modulated signals with carbon nanotube cantilever vibration

Towards the realisation of reliable communication systems using simple nanoscale transceivers, this Letter presents a method for the non-coherent detection of digitally phase-modulated signals. Without the synchronisation of the phases of the transmitted and received carrier signals, data transmission cannot be reliably achieved. To address this issue, the proposed method is developed using a nanoscale receiver that receives the binary phase-modulated signal through the mechanical vibration of a carbon nanotube cantilever. The present analysis reveals that this receiver has an interesting characteristic: the two decision statistics available in the receiver have a phase difference of π / 2 , which means that at least one of the statistics is fairly reliable regardless of the synchronisation error. Through the selection of the more reliable of the two statistics, the proposed method achieves low error in the estimation of the transmitted data even without carrier phase synchronisation. This Letter presents the derivation of the proposed rule for selecting the statistic and numerical results that demonstrate the effectiveness of the proposed method. This Letter is expected to contribute to the realisation of future communication applications using nanoscale transceivers.

Noise‐enhanced field emission current from a carbon nanotube cantilever

Field emission current is widely used to measure various characteristics of nanoscale. In this Letter, a cantilever of a carbon nanotube is focused and the amplification of the current is discussed. Increasing the voltage which induces the current gives the amplification; however, this method results in the large power consumption. This Letter provides the alternative solution with the use of the surrounding noise. Exploiting the non-linear behaviour of the current and introducing a signal processing of time-averaging, the amplification is observed. The theoretical discussion provides the concrete theory of the amplification: essentially such an effect is obtained by the modulation of the probability density of the noisy voltage. The numerical results demonstrate the effectiveness of the method.

Nonlinear behaviour and mass detection sensitivity of geometrically imperfect cantilevered carbon nanotube resonators

This study analyzes numerically the nonlinear static and dynamic behaviours as well as the mass detection sensitivity of a geometrically imperfect cantilevered carbon nanotube (CNT) resonator. More specifically, a new nonlinear model is developed for the cantilevered CNT nanoresonator, taking into account the effects of the initial curvature and cross-sectional area imperfection; furthermore, the new nonlinear model accounts for nonlinear damping and small-scale effects, employing the Kelvin–Voigt damping model and the modified couple stress-based elasticity theory, respectively. The electrostatic interactions in the CNT nanoresonator are modelled through use of a new electrostatic load model, previously developed by the authors. The nonlinear equation of motion of the geometrically imperfect cantilevered CNT nanoresonator is obtained making use of Hamilton’s principle as well as the inextensibility condition. The electromechanical continuous model of the nanoresonator is reduced into a high-dimensional discretized model employing the Galerkin method. The discretized model, consisting of a set of coupled nonlinear ordinary differential equations, is solved numerically employing a continuation technique. The nonlinear behaviour of the nanoresonator is studied and the effect of different parameters on the static deflection and dynamic response is examined. Furthermore, the mass detection sensitivity of the nanoresonator is examined in detail and methods are proposed for enhancing the detection sensitivity.

Flow-induced and mechanical stability of cantilever carbon nanotubes subjected to an axial compressive load

• Vibration behavior of CNTs based on the modified nonlocal theory was analyzed. • Nonlocal parameter increases flutter and divergence boundaries. • Surface effects increase flutter velocities and natural frequencies. • Flutter instability and bifurcation take place due to fluid flow. • Divergence instability is caused by axial force. In the present study, a modified nonlocal elasticity theory is used for flutter and divergence analyses of the cantilever carbon nanotubes (CNTs) conveying fluid. The CNT is embedded in viscoelastic foundation and is subjected to an axial compressive load acting at the free end. An extreme high-order governing equation as well as higher-order boundary conditions is developed using Hamilton's principle for vibration and stability analysis of the CNT. The numerical solution for flutter and divergence velocities is computed using the extended Galerkin method. The validity of the present analysis is confirmed by comparing with molecular dynamics simulation (MDS) and numerical solutions available in the literature. In the numerical results, the effects of nonlocal parameter, surface effects, viscoelastic foundation and compressive axial load on the stability boundaries of the system are investigated. The results show that the stability boundaries of the CNT are strongly dependent on the small scale coefficient and surface effects.

Analysis of the buckling of carbon nanotube under self-weight: The power series and differential quadrature approaches

ABSTRACTThe buckling of carbon nanotube (CNT) under self-weight and resting on elastic foundations is examined in this article. The system is mathematically modeled as nonlocal Euler-Bernoulli beam. Two different numerical schemes are employed to calculate the values of buckling loads, namely power series method (PSM) and differential quadrature method (DQM). Both methods bring out buckling loads which are very close to each other for considered boundary conditions and for chosen values of nonlocal parameter. The spring constant plays an increasing role on the buckling loads for all boundary conditions while the shear constant decreases the buckling loads of cantilevered CNT.

Single Measurement Determination of Mechanical, Electrical, and Surface Properties of a Single Carbon Nanotube via Force Microscopy

Carbon nanotubes (CNTs) have attracted significant attention due to their remarkable mechanical and electrical properties. Although it is assumed that the most important questions about CNTs have been addressed, the opposite is true. CNTs have high mechanical stiffness and electrical conductivity and, due to their small diameter and size, the measurement of those properties at nanoscale level is challenging. Here, we present a unique method to determine their mechanical and electrical properties by using interactions between vertically aligned multiwall CNTs and a metal-coated tipless atomic force microscope cantilever. We used a force–distance measurement (FDM) method with concurrent monitoring of electrical current. We could identify the number of CNTs in contact with the cantilever, stiffness of each individual CNT, the adhesion force between the cantilever and individual CNTs, and the electrical conductivity of each CNT. The method is also suitable for characterizing other vertically aligned nanostructured materials, such as nanowires. This method addresses the long-standing problem of property determination of materials such as CNTs and nanowires and is an important addition to the toolbox of nanoscale characterization methods.

Nonlinear behaviour of cantilevered carbon nanotube resonators based on a new nonlinear electrostatic load model

The present study examines the nonlinear behaviour of a cantilevered carbon nanotube (CNT) resonator and its mass detection sensitivity, employing a new nonlinear electrostatic load model. More specifically, a 3D finite element model is developed in order to obtain the electrostatic load distribution on cantilevered CNT resonators. A new nonlinear electrostatic load model is then proposed accounting for the end effects due to finite length. Additionally, a new nonlinear size-dependent continuum model is developed for the cantilevered CNT resonator, employing the modified couple stress theory (to account for size-effects) together with the Kelvin-Voigt model (to account for nonlinear damping); the size-dependent model takes into account all sources of nonlinearity, i.e. geometrical and inertial nonlinearities as well as nonlinearities associated with damping, small-scale, and electrostatic load. The nonlinear equation of motion of the cantilevered CNT resonator is obtained based on the new models developed for the CNT resonator and the electrostatic load. The Galerkin method is then applied to the nonlinear equation of motion, resulting in a set of nonlinear ordinary differential equations, consisting of geometrical, inertial, electrical, damping, and size-dependent nonlinear terms. This high-dimensional nonlinear discretized model is solved numerically utilizing the pseudo-arclength continuation technique. The nonlinear static and dynamic responses of the system are examined for various cases, investigating the effect of DC and AC voltages, length-scale parameter, nonlinear damping, and electrostatic load. Moreover, the mass detection sensitivity of the system is examined for possible application of the CNT resonator as a nanosensor.

Flutter instability of cantilevered carbon nanotubes caused by magnetic fluid flow subjected to a longitudinal magnetic field

CNT (Carbon nanotube)-based fluidic systems hold a great potential for emerging medical applications such as drug delivery for cancer therapy. CNTs can be used to deliver anticancer drugs into a target site under a magnetic field guidance. One of the critical issues in designing such systems is how to avoid the vibration induced by the fluid flow, which is undesirable and may even promote the structural instability. The main objective of the present research is to develop a fluid structure interaction (FSI) model to investigate the flutter instability of a cantilevered CNT induced by a magnetic fluid flow under a longitudinal magnetic field. The CNT is assumed to be embedded in a viscoelastic matrix to consider the effect of biological medium around it. To obtain a dynamical model for the system, the Navier–Stokes theory of magnetic-fluid flow is coupled to the Euler–Bernoulli beam model for CNT. The small size effects of the magnetic fluid and CNT are considered through the small scale parameters including Knudsen number (Kn) and the nonlocal parameter. Then, the extended Galerkin's method is applied to solve the FSI governing equations, and to derive the stability diagrams of the system. Results show how the magnetic properties of the fluid flow have an effect on improving the stability of the cantilevered CNT by increasing the flutter velocity.

Energy dissipation of damping cantilevered single-walled carbon nanotube oscillator

The cantilevered carbon nanotube is a traditional model in the design of some precise nano-oscillators. The sensitivity that is denoted by the quality factor defined as the ratio of the energy stored to the energy dissipated by losses in the oscillator is an important index for the nano-oscillators. In this paper, the small mass impacting on the single-walled carbon nanotube is simplified as an impact load and the governing equation of the transverse oscillation for the nanotube is established firstly. Based on the structure-preserving idea, the generalized multi-symplectic formulations of the governing equation are constructed. The oscillation of the damping nanotube under the transverse impact load with different amplitudes is simulated after the small numerical dissipation and the good convergence of the scheme constructed is verified. From the numerical results, the effects of the induced tension and the energy dissipation are investigated. More importantly, the high precision and the feasibility of the numerical approach proposed in this paper for reproducing the energy dissipation in the carbon nanotube oscillator are illustrated, which gives a new way to investigate the properties of the carbon nanotube oscillators.