Mechanical instabilities of individual multiwalled carbon nanotubes under cyclic axial compression

Nano Letters

Volumn 7, Issue 5, 2007, Pages 1149-1154

  Yap, Hsao W ^a,c   Lakes, Roderic S ^b   Carpick, Robert W ^b,c  

^a Wisconsin Electric Machines and Power Electronics Consortium   (United States)

^b UNIVERSITY OF WISCONSIN MADISON   (United States)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMMETRIC SHELL BUCKLING; ELASTIC BUCKLING; POSTBUCKLING;

ASPECT RATIO; ATOMIC FORCE MICROSCOPY; AXIAL COMPRESSION; STIFFNESS;

MULTIWALLED CARBON NANOTUBES (MWCN);

EID: 34249686123     PISSN: 15306984     EISSN: None     Source Type: Journal    
DOI: 10.1021/nl062763b     Document Type: Article

References (36)

1. Iijima, S. Nature 1991, 354, 56.
2. Falvo, M. R.; Clary, G. J.; Taylor, R. M., II; Chi, V.; Brook, F. P., Jr.; Washburn, S.; Superfine, R. Nature 1997, 389, 582.
3. Iijima, S.; Brabec, C.; Maiti, A.; Bernholc, J. J. Chem. Phys. 1996, 104, 2089.
4. Timoshenko, S. P. Theory of Elastic Stability; Mc-Graw Hill Book Co.: New York, 1961.
5. Yamaki, N. Elastic Stability of Circular Cylindrical Shells; North-Holland Series in Applied Mathematics and Mechanics, 27; North Holland: Amsterdam, 1984.
6. Pantano, A.; Boyce, M. C.; Parks, D. M. J. Eng. Mater. Technol. 2004, 126, 279.
7. Yakobson, B. I.; Brabec, C. J.; Bernholc, J. Phys. Rev. Lett. 1996, 76, 2511.
8. Zhang, C.-L.; Shen, H.-S. Carbon 2006, 44, 2608.
9. Garg, A.; Han, J.; Sinnott, S. B. Phys. Rev. Lett. 1998, 81, 2260.
10. Lakes, R. S.; Lee, T.; Bersie, A.; Wang, Y. C. Nature 2001, 410, 565.
11. Jaglinski, T.; Kochmann, D.; Stone, D. S.; Lakes, R. S. Science 2007, 375, 620.
12. Kuzumaki, T.; Mitsuda, Y. Jpn. J. Appl. Phys. 2006, 45, 364.
13. Lee, S. I.; Howell, S. W.; Raman, A.; Reifenberger, R.; Nguyen, C. V.; Meyyappan, M. Nanotechnology 2004, 15, 416.
14. Poggi, M. A.; Boyles, J. S.; Bottomley, L. A.; McFarland, A. W.; Colton, J. S.; Nguyen, C. V.; Stevens, R. M.; Lillehei, P. T. Nano Lett. 2004, 4, 1009.
15. Kaplan-Ashiri, I.; Cohen, S. R.; Gartsman, K.; Ivanovskaya, V.; Heine, T.; Seifert, G.; Wiesel, I.; Wagner, H. D.; Tenne, R. Proc. Nat. Acad. Sci. U.S.A. 2006, 103, 523.
16. Waters, J. F.; Guduru, P. R.; Jouzi, M.; Xu, J. M.; Hanlon, T.; Suresh, S. Appl. Phys. Lett. 2005, 87, 103109.
17. Sader, J. E.; Chon, J. W. M.; Mulvaney, P. Rev. Sci. Instrum. 1999, 70, 3967.
18. Lixin, D.; Arai, F.; Fukuda, T. IEEE Int. Conf. Robotics Automation, Pt. 2 2002, 1477.
19. Yap, H. Y.; Ramaker, B.; Sumant, A. V.; Carpick, R. W. Diamond Relat. Mater. 2006, 15, 1622.
20. The diameters of the 16 MWCNT/CNFs are determined by TEM to range from 60 to 110 nm (average of 86 nm) and wall thicknesses range from 25 to 35 nm (average 31 nm). The aspect ratio ranges from 18 to 45 (average 35).
21. The force is obtained by multiplying the cantilever deflection signal (volts) with the sensitivity (nm/V) and the normal stiffness of the cantilever (N/m). The latter is obtained by the Sader method (ref 15) and the former by pressing the tip onto a clean and stiff surface prior to sample loading. The MWCNT displacement is obtained by subtracting the cantilever displacement from the sample displacement during loading (after optical interference is taken into account). The percentage error in the force calibration is ∼9% (∼3% from the sensitivity measurements, ∼5% from the quality factor measurements, and ∼1% for the measurements of the other parameters in the Sader method).
22. The unloading curve has been translated down by 30 nm for clarity. A total of three out of five AFM - MWCNTs exhibited this behavior.
23. Lake, M. S.; Georgiadis, N. NASA Tech. Memo. 1990, 1, 4174.
24. Yu, M.-F.; Lourie, O.; Dyer, M. J.; Moloni, K.; Kelly, T. F.; Ruoff, R. S. Science 2000, 287, 637.
25. Wong, E. W.; Sheehan, P. E.; Lieber, C. M. Science 1997, 277, 1971.
26. The sample is displaced normal to the plane of the inclined cantilever, namely at 11° from vertical, using the "x-rotate option" of the Nanoscope controller, to minimize translation of the tip relative to the MWCNT/F, and to reduce transverse forces acting on the MWCNT. See also. Cannara, R. J.; Brukman M. J.; Carpick, R. W. Rev. Sci. Instrum. 2005, 76, 53706-1. Optical interference causes the spurious effect where the trace and retrace curves are not aligned prior to contact.
27. Wang, L.; Hu, H.; Guo, W. Act. Mech. Sol. Sin. 2005, 18, 123.
28. Yap, H. W.; Lakes, R. S.; Carpick, R. W. In preparation.
29. Ru, C. Q. Phys. Rev. B 2000, 62, 9973.
30. Ru, C. Q. J. Appl Phys. 2001, 89, 3426.
31. Cumings, J.; Zettl, A. Science 2000, 289, 602.
32. The lengths of these MWCNT/Fs exhibiting shell buckling vary from 1100 to 1900 nm (average 1437 nm) and the normal stiffnesses from 2.40 to 14.84 N/m (8.48 N/m). The critical buckling strains range from 0.47 to 3.20% (average 1.68%) and critical buckling loads from 91 to 220 nN (average 139 nN).
33. Wang, C. Y.; Ru, C. Q.; Mioduchowski, A. J. Appl. Mech. 2004, 71, 622.
34. Tu, Z.-C.; Ou-Yang, Z.-C. Phys. Rev. B 2002, 65, 233407.
35. Song, J. H.; Wang, X. D.; Reido, E.; Wang, Z. L. Nano Lett. 2005, 5, 1954.
36. Chang, T.; Hou, J.; Guo. X. Appl. Phys. Lett. 2006, 88, 211906.