scholarly journals Analysis of Vibration Frequency of Carbon Nanotubes used as Nano-Force Sensors Considering Clamped Boundary Condition

Electronics ◽  
2019 ◽  
Vol 8 (10) ◽  
pp. 1082 ◽  
Author(s):  
Toshiaki Natsuki ◽  
Kairi Urakami
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Medium ◽  
Vibration Frequency ◽  
Small Diameter ◽  
Axial Direction ◽  
Force Sensor ◽  
Beam Model ◽  
Atomic Force ◽  
Buckling Stability ◽  
Euler Bernoulli Beam

Carbon nanotubes (CNTs) can be used as atomic force microscope (AFM) probes since they are ideal tip materials with a small diameter, high aspect ratio, and stiffness. In this study, a model of CNTs clamped in an elastic medium is proposed as nanoscale force sensing AFM probes. The relationship between vibration frequency and axial force of the CNT probe clamped in an elastic medium is analyzed based on the Euler-Bernoulli beam model and the Whitney-Riley model. The clamped length of CNTs, and the elastic modulus of elastic medium affect largely on the vibration and the buckling stability of a CNT AFM probe. The result showed that the sensitivity to vibration increases as the applied loads increase. The critical load in which the vibration frequency decreases rapidly, moving to large ones with decreasing ratio of length to diameter of CNTs. The theoretical investigation on the vibration frequency of CNT loaded in the axial direction would give a useful reference for designing a CNT used as a nano-force sensor.

Buckling Instability of Carbon Nanotube Atomic Force Microscope Probe Clamped in an Elastic Medium

2012 ◽  
Vol 3 (2) ◽  
Author(s):  
Jin-Xing Shi ◽  
Toshiaki Natsuki ◽  
Xiao-Wen Lei ◽  
Qing-Qing Ni
Keyword(s):  
Atomic Force Microscope ◽  
Elastic Medium ◽  
Small Diameter ◽  
Beam Model ◽  
Buckling Mode ◽  
Buckling Instability ◽  
Atomic Force ◽  
Buckling Stability ◽  
Afm Probe ◽  
The Stability

Carbon nanotubes (CNTs) can be used as atomic force microscope (AFM) probes due to their robust mechanical properties, high aspect ratio and small diameter. In this study, a model of CNTs clamped in an elastic medium is proposed as CNT AFM probes. The buckling instability of the CNT probe clamped in elastic medium is analyzed based on the nonlocal Euler–Bernoulli beam model and the Whitney–Riley model. The clamped length of CNTs, and the stiffness of elastic medium affect largely on the stability of CNT AFM probe, especially at high buckling mode. The result shows that the buckling stability of the CNT AFM probe can be largely enhanced by increasing the stiffness of elastic medium. Moreover, the nonlocal effects of buckling instability are investigated and found to be lager for high buckling mode. The theoretical investigation on the buckling stability would give a useful reference for designing CNT as AFM probes.

scholarly journals The Attachment of Carbon Nanotubes to Atomic Force Microscopy Tips Using the Pick-Up Method

2020 ◽  
Vol 10 (16) ◽  
pp. 5575
Author(s):  
Christopher T. Gibson
Keyword(s):  
Carbon Nanotubes ◽  
Data Storage ◽  
Small Diameter ◽  
Chemical Vapor ◽  
High Strength ◽  
Image Resolution ◽  
Contact Mode ◽  
Tapping Mode ◽  
Atomic Force ◽  
Afm Tips

In the last 30 years research has shown that the resolution and reproducibility of data acquired using the atomic force microscope (AFM) can be improved through the development of new imaging modes or by modifying the AFM tip. One method that has been explored since the 1990s is to attach carbon nanotubes (CNT) to AFM tips. CNTs possess a small diameter, high aspect ratio, high strength and demonstrate a high degree of wear resistance. While early indications suggested the widespread use of these types of probes would be routine this has not been the case. A number of methods for CNT attachment have been proposed and explored including chemical vapor deposition (CVD), dielectrophoresis and manual attachment inside a scanning electron microscope (SEM). One of the earliest techniques developed is known as the pick-up method and involves adhering CNTs to AFM tips by simply scanning the AFM tip, in tapping mode, across a CNT-covered surface until a CNT attaches to the AFM tip. In this work we will further investigate how, for example, high force tapping mode imaging can improve the stability and success rate of the pick-up method. We will also discuss methods to determine CNT attachment to AFM probes including changes in AFM image resolution, amplitude versus distance curves and SEM imaging. We demonstrate that the pick-up method can be applied to a range of AFM probes, including contact mode probes with relatively soft spring constants (0.28 N/m). Finally, we demonstrate that the pick-up method can be used to attach CNTs to two AFM tips simultaneously. This is significant as it demonstrates the techniques potential for attaching CNTs to multiple AFM tips which could have applications in AFM-based data storage, devices such as the Snomipede, or making CNT-AFM tips more commercially viable.

scholarly journals Nonlinear Dynamics of Carbon Nanotubes Under Large Electrostatic Force

2015 ◽  
Author(s):  
Tiantian Xu ◽  
Mohammad I. Younis
Keyword(s):  
Nonlinear Dynamics ◽  
Carbon Nanotubes ◽  
Electrostatic Force ◽  
Small Diameter ◽  
Dynamic Responses ◽  
Cylindrical Shape ◽  
Beam Model ◽  
Electrostatic Forces ◽  
Complicated Form ◽  
The Impact

Because of the inherent nonlinearities involving the behavior of CNTs when excited by electrostatic forces, modeling and simulating their behavior is challenging. The complicated form of the electrostatic force describing the interaction of their cylindrical shape, forming upper electrodes, to lower electrodes poises serious computational challenges. This presents an obstacle against applying and using several nonlinear dynamics tools typically used to analyze the behavior of complicated nonlinear systems, such as shooting, continuation, and integrity analysis techniques. This works presents an attempt to resolve this issue. We present an investigation of the nonlinear dynamics of carbon nanotubes when actuated by large electrostatic forces. We study expanding the complicated form of the electrostatic force into enough number of terms of the Taylor series. Then, we utilize this form along with an Euler–Bernoulli beam model to study the static and dynamic behavior of CNTs. The geometric nonlinearity and the nonlinear electrostatic force are considered. An efficient reduced-order model (ROM) based on the Galerkin method is developed and utilized to simulate the static and dynamic responses of the CNTs. Several results are generated demonstrating softening and hardening behavior of the CNTs near their primary and secondary resonances. The effect of DC voltage load and AC voltage load on the nonlinearity has been studied. We also investigated the impact of initial slack level on the natural frequency and the nonlinearity. Small diameter and large initial slacked CNTs has been considered.

On the forced vibration of carbon nanotubes via a non-local Euler—Bernoulli beam model

2010 ◽  
Vol 224 (2) ◽  
pp. 497-503 ◽  
Author(s):  
P Karaoglu ◽  
M Aydogdu
Keyword(s):  
Carbon Nanotubes ◽  
Forced Vibration ◽  
Beam Theory ◽  
Beam Model ◽  
Bernoulli Beam ◽  
Resonance Frequencies ◽  
Non Local ◽  
Euler Bernoulli Beam ◽  
Bernoulli Beam Model ◽  
Walled Cnts

This article studies the forced vibration of the carbon nanotubes (CNTs) using the local and the non-local Euler—Bernoulli beam theory. Amplitude ratios for the local and the non-local Euler—Bernoulli beam models are given for single- and double-walled CNTs. It is found that the non-local models give higher amplitudes when compared with the local Euler—Bernoulli beam models. The non-local Euler—Bernoulli beam model predicts lower resonance frequencies.

scholarly journals Determination of the critical velocity of the fluid flowing in a single-walled carbon nanotubes embedded in a polymer matrix

2019 ◽  
pp. 114-119
Author(s):  
D S Lolov ◽  
Sv V Lilkova-Markova
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Medium ◽  
Polymer Matrix ◽  
Fluid Structure Interaction ◽  
Beam Model ◽  
Flowing Fluid ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Single Walled Carbon ◽  
The Stability

Since 90’s carbonic nanotubes are broadly used in nanophysics, nanobiology and nanomechanics in nanofluidic devices, nanocontainers for gas storage and nanopipes conveying fluid. They have a perfect hollow cylindrical geometry and superior mechanical strength. The flowing fluid can be water, oil, dynamic flow of methane, ethane and ethylene molecules. The problem of the fluid-structure interaction could be considered in the case of nanoscale. However, the experiments at the nanoscale are difficult and expensive. That is why the continuum elastic models have been used to study the fluid-structure interaction. The carbon nanotubes are considered with Euler- and Timoshenko-beam models. In this paper the dynamic stability of a single-walled carbon nanotube is investigated on the basis of the Euler-beam model and with the employment of the Generalized Differential Quadrature Method. The tube under investigation is assumed hinged at its both ends and is embedded in a polymer matrix. To study the influence of the surrounding elastic medium (for example, a polymer) on the stability of the pipe, an elastic base of Pasternak is introduced. A differential equation is presented that describes the transverse vibrations of a nanotube embedded in a polymer matrix. Dimensionless parameters are introduced. The scheme of Chebycheva-Gauss-Lobato is used for sampling. The coefficients are calculated using Lagrange interpolation functions. A system of homogeneous equations is written in the matrix form. The obtained numerical results are for flowing fluids with different densities. In order to study the effect of the surrounding elastic medium (such as polymer) on the stability of the pipe the Pasternak elastic foundation is introduced. The critical velocities of each type of fluid are determined for different stiffnesses of this matrix. A decrease in the critical speed with the increasing mass ratio has been established.

Variational Formulation of Vibrations of Multi-Walled Carbon Nanotubes With Geometric and Physical Nonlinearities

2009 ◽  
Author(s):  
Sarp Adali
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Variational Formulation ◽  
Variational Principles ◽  
Beam Model ◽  
Nonlinear Force ◽  
Multi Walled Carbon Nanotubes ◽  
Geometric Boundary ◽  
Walled Carbon Nanotubes ◽  
Euler Bernoulli Beam

Variational principles are derived for multi-walled carbon nanotubes (CNT) undergoing nonlinear vibrations. Two sources of nonlinearity are considered in the continuum modeling of CNTs with the Euler-Bernoulli beam model describing the dynamics of the CNTs. One source is the geometric nonlinearity which may arise as a result of large deflections. The second source is due to van der Waals forces between the nanotubes which can be modeled as a nonlinear force to improve the accuracy of the physical model. After deriving the applicable variational principle, Hamilton’s principle is given. Natural and geometric boundary conditions are derived using the variational formulation of the problem. Several approximate and computational methods of solution such as Rayleigh-Ritz and finite elements employ the variational formulation of the problem and as such these principles are instrumental in obtaining the solutions of vibration problems under complicated boundary conditions.

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