Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes Under Tensile Load
Tóm tắt
The tensile strengths of individual multiwalled carbon nanotubes (MWCNTs) were measured with a “nanostressing stage” located within a scanning electron microscope. The tensile-loading experiment was prepared and observed entirely within the microscope and was recorded on video. The MWCNTs broke in the outermost layer (“sword-in-sheath” failure), and the tensile strength of this layer ranged from 11 to 63 gigapascals for the set of 19 MWCNTs that were loaded. Analysis of the stress-strain curves for individual MWCNTs indicated that the Young's modulus
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Tài liệu tham khảo
B. I. Yakobson in Fullerenes—Recent Advances in the Chemistry and Physics of Fullerenes and Related Materials R. S. Ruoff and K. M. Kadish Eds. (Electrochemical Society Pennington NJ 1997) vol. 5 (97–42) pp. 549–560.
. The strain rate in this computer simulation was extremely high.
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Experimental details are available at Science Online at www.sciencemag.org/feature/data/1046083.shl.
The SEM nanostressing stage mainly consists of two parts. One is an x - y sliding stage driven by two linear picomotors with a quadrant piezotube on top; another is a z stage driven by a linear picomotor with a theta stage driven by a rotating picomotor on top. The linear picomotor has a step size of about 30 nm and the rotating picomotor has a step resolution of better than 0.1 mrad. The stage can travel 6 mm in three dimensions and rotates continuously in the θ direction along the x axis. All picomotors were driven with a control pad that can manually set constant velocities for the extension and retraction of the picomotor driving shaft. The piezotube can give subnanometer resolution in three axes with several microns of travel range. Operation of the stage inside the SEM showed smooth travel and no interference with the SEM imaging. The LEO 982 FE-SEM has a stated resolution of 1 nm at an operating voltage of 30 kV. The SEM chamber vacuum was better than 3 × 10 −6 torr with the stage inside. The typical tensile-loading experiment lasts 1 min and the typical tensile-loading strain rate is about 0.3 s −1 according to the recorded video tape.
There are three soft cantilevers in series on the same side of the AFM probe. The nominal lengths L of these three separate silicon spring-beam type cantilevers (the cs12 contact mode AFM probe was supplied by NT-MDT) are 350 300 and 250 μm; all have a nominal width w of 35 μm and a nominal thickness t of 1 μm. The force constant ( K ) of each can be calculated with the formula K = Ewt3/4L3. (Here E is for a silicon single crystal 145 GPa.) We measured L w and t in an SEM and used the measured not the nominal values to calculate K.
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If we use the surface energy (γ) of graphite (∼0.24 J m –2 ) and the OD of this MWCNT (33 nm) the capillary force between MWCNT layers which is equal to 2πODγ is calculated to be ∼50 nN; also with use of the shear strength of graphite (∼0.48 MPa) and the initial contact length between MWCNT layers (∼10 mm) the shear force needed for sliding between nested layers would be ∼50 nN. Because each of these values exceeds the measured upper limit force further study of the energetics and forces involved in pullout is needed.
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This work was partially supported by the Office of Naval Research and the Defense Advanced Research Projects Agency under Navy grant N000014-99-1-0769 by NSF under the New Tools and Methods for Nanotechnology grant NSF-DMR 9871874 and by Zyvex. We thank R. E. Smalley's group at Rice University for the MWCNT samples and the staff at the Materials Science Center at the University of Wisconsin (UW) for their assistance (the NSF Materials Research Science and Engineering at UW provides support for the UW electron microscope facilities). We appreciate use of the Washington University TEM facility overseen by P. Gibbons; and we thank B. Files T. Kowalewski B. Yakobson and R. Carpick for commenting on the manuscript. R.S.R. would like to dedicate this paper to the memory of Herbert S. Gutowsky.