Coupled systems mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Load transfer and energy absorption in transversely compressed multi-walled carbon nanotubes

  • Chen, Xiaoming (Department of Mechanical Engineering, State University of New York at Binghamton) ;
  • Ke, Changhong (Department of Mechanical Engineering, State University of New York at Binghamton)
  • Received : 2016.05.31
  • Accepted : 2017.05.25
  • Published : 2017.09.25
⟨ Previous Next ⟩

Abstract

We present a simple and easy-to-implement lumped stiffness model to elucidate the load transfer mechanism among all individual tube shells and intertube van der Waals (vdW) interactions in transversely compressed multi-walled carbon nanotubes (CNTs). Our model essentially enables theoretical predictions to be made of the relevant transverse mechanical behaviors of multi-walled tubes based on the transverse stiffness properties of single-walled tubes. We demonstrate the validity and accuracy of our model and theoretical predictions through a quantitative study of the transverse deformability of double- and triple-walled CNTs by utilizing our recently reported nanomechanical measurement data. Using the lumped stiffness model, we further evaluate the contribution of each individual tube shell and intertube vdW interaction to the strain energy absorption in the whole tube. Our results show that the innermost tube shell absorbs more strain energy than any other individual tube shells and intertube vdW interactions. Nanotubes of smaller number of walls and outer diameters are found to possess higher strain energy absorption capacities on both a per-volume and a per-weight basis. The proposed model and findings on the load transfer and the energy absorption in multi-walled CNTs directly contribute to a better understanding of their structural and mechanical properties and applications, and are also useful to study the transverse mechanical properties of other one-dimensional tubular nanostructures (e.g., boron nitride nanotubes).

Keywords

Acknowledgement

Supported by : US Air Force Office

References

  1. Bai, X., Golberg, D., Bando, Y., Zhi, C., Tang, C., Mitome, M. and Kurashima, K. (2007), "Deformationdriven electrical transport of individual boron nitride nanotubes", Nano Lett., 7(3), 632-637. https://doi.org/10.1021/nl062540l
  2. Barboza, A.P.M., Chacham, H. and Neves, B.R.A. (2009), "Universal response of single-wall carbon nanotubes to radial compression", Phys. Rev. Lett., 102(2), 025501. https://doi.org/10.1103/PhysRevLett.102.025501
  3. Barboza, A.P.M., Gomes, A.P., Archanjo, B.S., Araujo, P.T., Jorio, A., Ferlauto, A.S., Mazzoni, M.S.C., Chacham, H. and Neves, B.R.A. (2008), "Deformation induced semiconductor-metal transition in single wall carbon nanotubes probed by electric force microscopy", Phys. Rev. Lett., 100(25), 256804. https://doi.org/10.1103/PhysRevLett.100.256804
  4. Bouilly, D., Cabana, J., Meunier, F., Desjardins-Carriere, M., Lapointe, F., Gagnon, P., Larouche, F.L., Adam, E., Paillet, M. and Martel, R. (2011), "Wall-selective probing of double-walled carbon nanotubes using covalent functionalization RID G-7589-2011", Acs Nano, 5(6), 4927-4934. https://doi.org/10.1021/nn201024u
  5. Cao, G., Tang, Y. and Chen, X. (2005), "Elastic properties of carbon nanotubes in the radial direction", Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanoengineering and Nanosystems, 219(2), 73-88. https://doi.org/10.1243/17403499JNN39
  6. Crespi, V.H., Cohen, M.L. and Rubio, A. (1997), "In situ band gap engineering of carbon nanotubes", Phys. Rev. Lett., 79(11), 2093-2096. https://doi.org/10.1103/PhysRevLett.79.2093
  7. Damnjanovic, M., Milosevic, I., Vukovic, T. and Sredanovic, R. (1999), "Full symmetry, optical activity, and potentials of single-wall and multiwall nanotubes", Phys. Rev. B, 60(4), 2728-2739. https://doi.org/10.1103/PhysRevB.60.2728
  8. Dong, X., Fu, D., Xu, Y., Wei, J., Shi, Y., Chen, P. and Li, L.J. (2008), "Label-free electronic detection of DNA using simple double-walled carbon nanotube resistors", J. Phys. Chem. C, 112(26), 9891-9895. https://doi.org/10.1021/jp7121714
  9. Girifalco, L.A., Hodak, M. and Lee, R.S. (2000), "Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential", Phys. Rev. B, 62(19), 13104-13110. https://doi.org/10.1103/PhysRevB.62.13104
  10. Green, A.A. and Hersam, M.C. (2011), "Properties and application of double-walled carbon nanotubes sorted by outer-wall electronic type", ACS Nano, 5(2), 1459-1467. https://doi.org/10.1021/nn103263b
  11. Hajnayeb, A. and Khadem, S.E. (2015), "An analytical study on the nonlinear vibration of a double walled carbon nanotube", Struct. Eng. Mech., 54(5), 987-998. https://doi.org/10.12989/sem.2015.54.5.987
  12. Hertel, T., Walkup, R.E. and Avouris, P. (1998), "Deformation of carbon nanotubes by surface van der Waals forces", Phys. Rev. B, 58(20), 13870-13873. https://doi.org/10.1103/PhysRevB.58.13870
  13. Jiang, L.Y., Huang, Y., Jiang, H., Ravichandran, G., Gao, H., Hwang, K.C. and Liu, B. (2006), "A cohesive law for carbon nanotube/polymer interfaces based on the van der waals force", J. Mech. Phys. Sol., 54(11), 2436-2452. https://doi.org/10.1016/j.jmps.2006.04.009
  14. Jiang, Y.Y., Zhou, W., Kim, T., Huang, Y. and Zuo, J.M. (2008), "Measurement of radial deformation of single-wall carbon nanotubes induced by intertube van der waals forces", Phys. Rev. B, 77(15), 153405. https://doi.org/10.1103/PhysRevB.77.153405
  15. Kim, Y.H., Chang, K.J. and Louie, S.G. (2001), "Electronic structure of radially deformed BN and BC3 nanotubes", Phys. Rev. B, 63(20), 205408. https://doi.org/10.1103/PhysRevB.63.205408
  16. Kinoshita, Y. and Ohno, N. (2010), "Electronic structures of boron nitride nanotubes subjected to tension, torsion, and flattening: A first-principles DFT study", Phys. Rev. B, 82(8), 085433. https://doi.org/10.1103/PhysRevB.82.085433
  17. Li, C. and Chou, T.W. (2004), "Elastic properties of single-walled carbon nanotubes in transverse directions", Phys. Rev. B, 69(7), 073401. https://doi.org/10.1103/PhysRevB.69.073401
  18. Li, Y., Hatakeyama, R., Oohara, W. and Kaneko, T. (2009), "Formation of p-n junction in double-walled carbon nanotubes based on heteromaterial encapsulation", Appl. Phys. Expr., 2(9), 095005. https://doi.org/10.1143/APEX.2.095005
  19. Liu, J. (2012), "Explicit solutions for a SWCNT collapse", Arch. Appl. Mech., 82(6), 767-776. https://doi.org/10.1007/s00419-011-0589-x
  20. Lu, J.P. (1997), "Elastic properties of carbon nanotubes and nanoropes", Phys. Rev. Lett., 79(7), 1297-1300. https://doi.org/10.1103/PhysRevLett.79.1297
  21. Lu, W.B., Wu, J., Song, J., Hwang, K.C., Jiang, L.Y. and Huang, Y. (2008), "A cohesive law for interfaces between multi-wall carbon nanotubes and polymers due to the van der waals interactions", Comput. Meth. Appl. Mech. Eng., 197(41-42), 3261-3267. https://doi.org/10.1016/j.cma.2007.12.008
  22. Morimoto, T., Kuno, A., Yajima, S., Ishibashi, K., Tsuchiya, K. and Yajima, H. (2012), "Effective energy gap of the double-walled carbon nanotubes with field effect transistors ambipolar characteristics", Appl. Phys. Lett., 100(4), 043107. https://doi.org/10.1063/1.3679639
  23. Muthaswami, L., Zheng, Y., Vajtai, R., Shehkawat, G., Ajayan, P. and Geer, R.E. (2007), "Variation of radial elasticity in multiwalled carbon nanotubes", Nano Lett., 7(12), 3891-3894. https://doi.org/10.1021/nl072002o
  24. Nam, I.W., Souri, H. and Lee, H.K. (2016), "Percolation threshold and piezoresistive response of multi-wall carbon nanotube/cement composites", Smart Struct. Syst., 18(2), 217-231. https://doi.org/10.12989/sss.2016.18.2.217
  25. Palaci, I., Fedrigo, S., Brune, H., Klinke, C., Chen, M. and Riedo, E. (2005), "Radial elasticity of multiwalled carbon nanotubes", Phys. Rev. Lett., 94(17), 175502. https://doi.org/10.1103/PhysRevLett.94.175502
  26. Popescu, A. and Woods, L.M. (2009), "Telescopic hot double wall carbon nanotube for nanolithography", Appl. Phys. Lett., 95(20), 203507. https://doi.org/10.1063/1.3263954
  27. Puttock, M.J. and Thwaite, E.G. (1969), Elastic Compression of Spheres and Cylinders at Point and Line Contact, Commonwealth Scientific and Industrial Research Organization, Melbourne, Australia.
  28. Rakrak, K., Zidour, M., Heireche, H., Bousahla, A.A. and Chemi, A. (2016), "Free vibration analysis of chiral double-walled carbon nanotube using non-local elasticity theory", Adv. Nano Res., 4(1), 31-44. https://doi.org/10.12989/anr.2016.4.1.031
  29. Shen, W., Jiang, B., Han, B.S. and Xie, S. (2000), "Investigation of the radial compression of carbon nanotubes with a scanning probe microscope", Phys. Rev. Lett., 84(16), 3634-3637. https://doi.org/10.1103/PhysRevLett.84.3634
  30. Tang, J., Qin, L.C., Sasaki, T., Yudasaka, M., Matsushita, A. and Iijima, S. (2000), "Compressibility and polygonization of single-walled carbon nanotubes under hydrostatic pressure", Phys. Rev. Lett., 85(9), 1887-1889. https://doi.org/10.1103/PhysRevLett.85.1887
  31. Tang, T., Jagota, A. and Hui, C.Y. (2005), "Adhesion between single-walled carbon nanotubes", J. Appl. Phys., 97(7), 074304. https://doi.org/10.1063/1.1871358
  32. Thostenson, C. (2004), "Nanotube buckling in aligned multi-wall carbon nanotube composites", Carbon, 42(14), 3015-3018. https://doi.org/10.1016/j.carbon.2004.06.012
  33. Wang, H.Y., Zhao, M. and Mao, S.X. (2006), "Radial moduli of individual single-walled carbon nanotubes with and without electric current flow", Appl. Phys. Lett., 89(21), 211906. https://doi.org/10.1063/1.2392825
  34. Xiao, J., Lopatnikov, S., Gama, B. and Gillespie, J. (2006), "Nanomechanics on the deformation of singleand multi-walled carbon nanotubes under radial pressure", Mater. Sci. Eng. a-Struct. Mater. Propert. Microstruct. Process., 416(1-2), 192-204. https://doi.org/10.1016/j.msea.2005.09.105
  35. Yang, Y.H. and Li, W.Z. (2011), "Radial elasticity of single-walled carbon nanotube measured by atomic force microscopy", Appl. Phys. Lett., 98(4), 041901. https://doi.org/10.1063/1.3546170
  36. Yu, M.F., Kowalewski, T. and Ruoff, R.S. (2000), "Investigation of the radial deformability of individual carbon nanotubes under controlled indentation force", Phys. Rev. Lett., 85(7), 1456-1459. https://doi.org/10.1103/PhysRevLett.85.1456
  37. Zhao, H., Min, K. and Aluru, N.R. (2009), "Size and chirality dependent elastic properties of graphene nanoribbons under uniaxial tension", Nano Lett., 9(8), 3012-3015. https://doi.org/10.1021/nl901448z
  38. Zheng, M., Chen, X., Bae, I.T., Ke, C., Park, C., Smith, M.W. and Jordan, K. (2012a), "Radial mechanical properties of single-walled boron nitride nanotubes", Small, 8(1), 116-121. https://doi.org/10.1002/smll.201100946
  39. Zheng, M., Zou, L.F., Wang, H., Park, C. and Ke, C. (2012b), "Engineering radial deformations in singlewalled carbon and boron nitride nanotubes using ultrathin nanomembranes", ACS Nano, 6(2), 1814-1822. https://doi.org/10.1021/nn2048813
  40. Zheng, M., Chen, X., Park, C. and Ke, C. (2012c), "Radial deformability of carbon and boron nitride nanotubes", Proceeding of the 23rd International Congress of Theoretical and Applied Mechanics, Beijing, China, August.
  41. Zheng, M., Zou, L., Wang, H., Park, C. and Ke, C. (2012d), "Quantifying the transverse deformability of double-walled carbon and boron nitride nanotubes using an ultrathin nanomembrane covering scheme", J. Appl. Phys., 12(10), 104318.
  42. Zheng, M., Ke, C., Bae, I.T., Park, C., Smith, M.W. and Jordan, K. (2012e), "Radial elasticity of multiwalled boron nitride nanotubes", Nanotechnol., 23(9), 095703. https://doi.org/10.1088/0957-4484/23/9/095703
  43. Zhou, W., Huang, Y., Liu, B., Wu, J., Hwang, K.C. and Wei, B.Q. (2007), "Adhesion between carbon nanotubes and substrate: Mimicking the gecko foothair", Nano, 2(3), 175-179. https://doi.org/10.1142/S1793292007000490