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Research Papers: Micro-Nano Tribology

Continuum Modeling and Analysis of the Frictional Interaction Between a CNT and a Substrate During Dragging

[+] Author and Article Information
George G. Adams

Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115adams@coe.neu.edu

Palaniappan Nagappan

Department of Mechanical and Industrial Engineering, Northeastern University, Boston, MA 02115

Nicol E. McGruer

Department of Electrical and Computer Engineering, Center for High-rate Nanomanufacturing, Northeastern University, Boston, MA 02115

J. Tribol 131(3), 032002 (Jun 02, 2009) (6 pages) doi:10.1115/1.3142905 History: Received May 23, 2008; Revised April 30, 2009; Published June 02, 2009

A simple method to determine the frictional interaction between a carbon nanotube (CNT) and a substrate is analyzed for feasibility. In this technique an atomic force microscope (AFM) tip is used to drag a CNT along a substrate. Then the deformed shape of the CNT can be viewed either with the AFM or in a scanning electron microscope. An analysis of the steady-state deformed shape allows the determination of the frictional interactions, which occurred during dragging. It is important to quantify these interactions in a variety of potential applications of nanotechnology. In one such example, a CNT based nanoswitch consists of a CNT bridging over a trench. Actuation of the CNT causes it to stretch and can lead to partial slip at the interface. This slip causes hysteresis, which has been observed in the mechanical actuation of a CNT bridge. In this paper continuum level modeling of the frictional interaction is used to determine the relationship between the steady-state deformed shape of the CNT and the frictional interaction, which occurred between the CNT and substrate during dragging. The model and analysis indicate that this method should be feasible for CNTs with aspect ratios approximately in the 100–250 range.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 1

A CNT being pushed along the surface by the tip of an AFM

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Figure 2

Schematic representation for symmetric loading of a CNT acted upon by a force P¯. The force P¯ is the force component from the AFM acting parallel to the substrate.

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Figure 3

Schematic representation for nonsymmetric loading of a CNT acted upon by a force P¯. The force P¯ is the force component from the AFM acting parallel to the substrate.

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Figure 4

Rotation angle (ψ) versus shear stress (τ¯) and versus dimensionless shear stress (τ)

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Figure 5

Variation in radius of curvature (R) at the load point with shear stress (τ¯) and with dimensionless shear stress (τ)

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Figure 6

Final shape of CNT in symmetric loading for various values of τ (100, 200, 300, 400, 500, and 600)

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Figure 7

Variation in rotation angle ψ(0) with shear stress (τ¯) and with dimensionless shear stress (τ) for nonsymmetric condition for various values of a (0.3, 0.35, 0.4, 0.45, and 0.5)

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Figure 8

Variation in ψ′(0) with shear stress (τ¯) and with dimensionless shear stress (τ) for various values of a (0.3, 0.35, 0.4, and 0.5)

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Figure 9

Rotation angle ψ(1−a) (right end of the beam) versus shear stress (τ¯) and versus dimensionless shear stress (τ) for various values of a (0.3, 0.4, and 0.5)

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Figure 10

Variation in rotation angle (ψ(−a)) with shear stress (τ¯) and with dimensionless shear stress (τ) for various values of a (0.3, 0.35, 0.4, 0.45, and 0.5)

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Figure 11

Deformed shape of nanotube for a=0.4 and for various values of shear stress τ (100, 200, 300, and 400)

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Figure 12

Final shape of nanotube for a=0.3 and for various values of shear stress τ (100, 200, 300, and 400)

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