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Mesoscale modeling of mechanics of carbon nanotubes: Self-assembly, self-folding, and fracture

Published online by Cambridge University Press:  03 March 2011

Markus J. Buehler*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, 02139
*
a) Address all correspondence to this author.e-mail: [email protected]
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Abstract

Using concepts of hierarchical multiscale modeling, we report development of a mesoscopic model for single-wall carbon nanotubes with parameters completely derived from full atomistic simulations. The parameters in the mesoscopic model are fit to reproduce elastic, fracture, and adhesion properties of carbon nanotubes, in this article demonstrated for (5,5) carbon nanotubes. The mesoscale model enables modeling of the dynamics of systems with hundreds of ultralong carbon nanotubes over time scales approaching microseconds. We apply our mesoscopic model to study self-assembly processes, including self-folding, bundle formation, as well as the response of bundles of carbon nanotubes to severe mechanical stimulation under compression, bending, and tension. Our results with mesoscale modeling corroborate earlier results, suggesting a novel self-folding mechanism, leading to creation of racket-shaped carbon nanotube structures, provided that the aspect ratio of the carbon nanotube is sufficiently large. We find that the persistence length of the (5,5) carbon nanotube is on the order of a few micrometers in the temperature regime from 300 to 1000 K.

Type
Articles
Copyright
Copyright © Materials Research Society 2006

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References

REFERENCES

1.Iijima, S.: Helical microtubules of graphitic carbon. Nature 354, 56 (1991).CrossRefGoogle Scholar
2.Moulton, S.E., Minett, A.I., Wallace, G.G.: Carbon nanotube based electronic and electrochemical sensors. Sens. Lett. 3, 183 (2005).CrossRefGoogle Scholar
3.Modi, A., Koratkar, N., Lass, E., Wei, B.Q., Ajayan, P.M.: Miniaturized gas ionization sensors using carbon nanotubes. Nature 424, 171 (2003).CrossRefGoogle ScholarPubMed
4.Sazonova, V., Yaish, Y., Ustunel, H., Roundy, D., Arias, T.A., McEuen, P.L.: A tunable carbon nanotube electromechanical oscillator. Nature 431, 284 (2004).CrossRefGoogle ScholarPubMed
5.Jiang, H., Yu, M.F., Liu, B., Huang, Y.: Intrinsic energy loss mechanisms in a cantilevered carbon nanotube beam oscillator. Phys. Rev. Lett. 93, 185501 (2004).CrossRefGoogle Scholar
6.Huang, J.Y., Chen, S., Wang, Z.Q., Kempa, K., Wang, Y.M., Jo, S.H., Chen, G., Dresselhaus, M.S., Ren, Z.F.: Superplastic carbon nanotubes—Conditions have been discovered that allow extensive deformation of rigid single-walled nanotubes. Nature 439, 281 (2006).CrossRefGoogle Scholar
7.Zhang, W.D., Yang, F., Gu, P.Y.: Carbon nanotubes grow to pillars. Nanotechnology 16, 2442 (2005).CrossRefGoogle ScholarPubMed
8.Gao, H., Kong, Y., Cui, D., Ozkan, C.S.: Spontaneous insertion of DNA oligonucleotides into carbon nanotubes. Nano Lett. 3, 471 (2003).CrossRefGoogle Scholar
9.Guo, X., Wang, J.B., Zhang, H.W.: Mechanical properties of single-walled carbon nanotubes based on higher order Cauchy– Born rule. Int. J. Solids Struct. 43, 1276 (2006).CrossRefGoogle Scholar
10.Lu, H., Zhang, L.: Analysis of localized failure of single-wall carbon nanotubes. Comput. Mater. Sci. 35, 432 (2006).CrossRefGoogle Scholar
11.Shi, D.L., Feng, X.Q., Jiang, H.Q., Huang, Y.Y., Hwang, K.C.: Multiscale analysis of fracture of carbon nanotubes embedded in composites. Int. J. Fract. 134, 369 (2005).CrossRefGoogle Scholar
12.Li, C.Y., Ruoff, R.S., Chou, T.W.: Modeling of carbon nanotube clamping in tensile tests. Compos. Sci. Technol. 65, 2407 (2005).CrossRefGoogle Scholar
13.Natsuki, T., Endo, M.: Stress simulation of carbon nanotubes in tension and compression. Carbon 42, 2147 (2004).CrossRefGoogle Scholar
14.Qin, L.C., Zhao, X.L., Hirahara, K., Miyamoto, Y., Ando, Y., Iijima, S.: Materials science—The smallest carbon nanotube. Nature 408, 50 (2000).CrossRefGoogle Scholar
15.Ajayan, P.M., Iijima, S.: Smallest carbon nanotube. Nature 358, 23 (1992).CrossRefGoogle Scholar
16.Yakobson, B.I., Brabec, C.J., Bernholc, J.: Nanomechanics of carbon tubes: Instabilities beyond linear response. Phys. Rev. Lett. 76, 2511 (1996).CrossRefGoogle ScholarPubMed
17.Ozaki, T., Iwasa, Y., Mitani, T.: Stiffness of single-walled carbon nanotubes under large strain. Phys. Rev. Lett. 84, 1712 (2000).CrossRefGoogle ScholarPubMed
18.Dereli, G., Ozdogan, C.: Structural stability and energetics of single-walled carbon nanotubes under uniaxial strain. Phys. Rev. B 67, 035416 (2003).CrossRefGoogle Scholar
19.Ru, C.Q.: Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium. J. Mech. Phys. Solids 49, 1265 (2001).CrossRefGoogle Scholar
20.Ni, B., Sinnott, S.B., Mikulski, P.T., Harrison, J.A.: Compression of carbon nanotubes filled with C-60, CH4, or Ne: Predictions from molecular dynamics simulations. Phys. Rev. Lett. 88, 205505 (2002).CrossRefGoogle ScholarPubMed
21.Hod, O., Rabani, E., Baer, R.: Carbon nanotube closed-ring structures. Phys. Rev. B 67, 195408 (2003).CrossRefGoogle Scholar
22.Hertel, T., Walkup, R.E., Avouris, P.: Deformation of carbon nanotubes by surface van der Waals forces. Phys. Rev. B 58, 13870 (1998).CrossRefGoogle Scholar
23.Ulbricht, H., Moos, G., Hertel, T.: Interaction of C-60 with carbon nanotubes and graphite. Phys. Rev. Lett. 90, 095501 (2003).CrossRefGoogle Scholar
24.Arroyo, M., Belytschko, T.: Continuum-mechanics modeling and simulation of carbon nanotubes. Meccanica 40, 455 (2005).CrossRefGoogle Scholar
25.Jiang, H., Huang, Y., Hwang, K.C.: A finite-temperature continuum theory based on interatomic potentials. J. Eng. Mater. Technol. Trans. ASME 127, 408 (2005).CrossRefGoogle Scholar
26.Zhang, P., Huang, Y., Gao, H., Hwang, K.C.: Fracture nucleation in single-wall carbon nanotubes under tension: A continuum analysis incorporating interatomic potentials. J. Appl. Mech.—Trans. ASME 69, 454 (2002).CrossRefGoogle Scholar
27.Yeak, S.H., Ng, T.Y., Liew, K.M.: Multiscale modeling of carbon nanotubes under axial tension and compression. Phys. Rev. B 72, 165401 (2005).CrossRefGoogle Scholar
28.Lu, Q., Bhattacharya, B.: Effect of randomly occurring Stone– Wales defects on mechanical properties of carbon nanotubes using atomistic simulation. Nanotechnol. 16, 555 (2005).CrossRefGoogle Scholar
29.Pugno, N.M., Ruoff, R.S.: Quantized fracture mechanics. Philos. Mag. 84, 2829 (2004).CrossRefGoogle Scholar
30.Marques, M.A.L., Troiani, H.E., Miki-Yoshida, M., Jose-Yacaman, M., Rubio, A.: On the breaking of carbon nanotubes under tension. Nano Lett. 4, 811 (2004).CrossRefGoogle Scholar
31.Zhou, L.G., Shi, S.Q.: Molecular dynamic simulations on tensile mechanical properties of single-walled carbon nanotubes with and without hydrogen storage. Comput. Mater. Sci. 23, 166 (2002).CrossRefGoogle Scholar
32.Molinero, V., Goddard, W.A.: Microscopic mechanism of water diffusion in glucose glasses. Phys. Rev. Lett. 95, 045701 (2005).CrossRefGoogle ScholarPubMed
33.Lamm, M.H., Chen, T., Glotzer, S.C.: Simulated assembly of nanostructured organic/inorganic networks. Nano Lett. 3, 989 (2003).CrossRefGoogle Scholar
34.Underhill, P.T., Doyle, P.S.: On the coarse-graining of polymers into bead-spring chains. J. Non-Newtonian Fluid Mech. 122, 3 (2004).CrossRefGoogle Scholar
35.Maiti, A., Wescott, J., Kung, P.: Nanotube-polymer composites: Insights from Flory–Huggins theory and mesoscale simulations. Mol. Simul. 31, 143 (2005).CrossRefGoogle Scholar
36.Barber, A.H., Cohen, S.R., Eitan, A., Schadler, L.S., Wagner, H.D.: Fracture transitions at a carbon-nanotube/polymer interface. Adv. Mater. 18, 83 (2006).CrossRefGoogle Scholar
37.Barth, J.V., Costantini, G., Kern, K.: Engineering atomic and molecular nanostructures at surfaces. Nature 437, 671 (2005).CrossRefGoogle ScholarPubMed
38.Zhang, M., Fang, S.L., Zakhidov, A.A., Lee, S.B., Aliev, A.E., Williams, C.D., Atkinson, K.R., Baughman, R.H.: Strong, transparent, multifunctional, carbon nanotube sheets. Science 309, 1215 (2005).CrossRefGoogle ScholarPubMed
39.Huang, Y., Chiang, C.Y., Lee, S.K., Gao, Y., Hu, E.L., De Yoreo, J., Belcher, A.M.: Programmable assembly of nanoarchitectures using genetically engineered viruses. Nano Lett. 5, 1429 (2005).CrossRefGoogle ScholarPubMed
40.Hazani, M., Hennrich, F., Kappes, M., Naaman, R., Peled, D., Sidorov, V., Shvarts, D.: DNA-mediated self-assembly of carbon nanotube-based electronic devices. Chem. Phys. Lett. 391, 389 (2004).CrossRefGoogle Scholar
41.Gu, Q., Cheng, C.D., Gonela, R., Suryanarayanan, S., Anabathula, S., Dai, K., Haynie, D.T.: DNA nanowire fabrication. Nanotechnology 17 R14(2006).CrossRefGoogle Scholar
42.Buehler, M.J., Kong, Y., Gao, H.J.: Self-folding and unfolding of carbon nanotubes. J. Eng. Mater. Technol. 128, 3 (2006).CrossRefGoogle Scholar
43.Buehler, M.J., Kong, Y., Gao, H.J.: Deformation mechanisms of very long single-wall carbon nanotubes subject to compressive loading. J. Eng. Mater. Technol. 126, 245 (2004).CrossRefGoogle Scholar
44.Allen, M.P., Tildesley, D.J.: Computer Simulation of Liquids (Oxford University Press, New York, 1989).Google Scholar
45.Tersoff, J.: Empirical interatomic potentials for carbon, with applications to amorphous carbon. Phys. Rev. Lett. 61, 2879 (1988).CrossRefGoogle ScholarPubMed
46.Stillinger, F., Weber, T.A.: Computer-simulation of local order in condensed phases of silicon. Phys. Rev. B 31, 5262 (1985).CrossRefGoogle ScholarPubMed
47.Stadler, J., Mikulla, R., Trebin, H-R.: IMD: A software package for molecular dynamics studies on parallel computers. Int. J. Mod. Phys. C. 8, 1131 (1997).CrossRefGoogle Scholar
48.Roth, J., Gahler, F., Trebin, H-R.: A molecular dynamics run with 5.180.116.000 particles. Int. J. Mod. Phys. C. 11, 317 (2000).CrossRefGoogle Scholar
49.Tsai, D.H.: Virial theorem and stress calculation in molecular-dynamics. J. Chem. Phys. 70, 1375 (1979).CrossRefGoogle Scholar
50.Yang, H.T., Chen, J.W., Yang, L.F., Dong, J.M.: Oscillations of local density of states in defective carbon nanotubes. Phys. Rev. B 71, 085402 (2005).CrossRefGoogle Scholar
51.Ding, F.: Theoretical study of the stability of defects in single-walled carbon nanotubes as a function of their distance from the nanotube end. Phys. Rev. B 72, 245409 (2005).CrossRefGoogle Scholar
52.Buehler, M.J.: Atomistic and continuum modeling of mechanical properties of collagen: Elasticity, fracture and self-assembly. J. Mater. Res. 21(8), 1947(2006).CrossRefGoogle Scholar
53.Buehler, M.J., Gao, H.: Dynamical fracture instabilities due to local hyperelasticity at crack tips. Nature 439, 307 (2006).CrossRefGoogle ScholarPubMed
54.Buehler, M.J., Abraham, F.F., Gao, H.: Hyperelasticity governs dynamic fracture at a critical length scale. Nature 426, 141 (2003).CrossRefGoogle Scholar
55.Mayo, S.L., Olafson, B.D., Goddard, W.A.: Dreiding—A generic force-field for molecular simulations. J. Phys. Chem. 94, 8897 (1990).CrossRefGoogle Scholar
56.Gao, H.: A theory of local limiting speed in dynamic fracture. J. Mech. Phys. Solids. 44, 1453 (1996).CrossRefGoogle Scholar
57.Plimpton, S.: Fast parallel algorithms for short-range molecular-dynamics. J. Comput. Phys. 117, 1 (1995).CrossRefGoogle Scholar
58.Buehler, M.J., Duin, A.C.T.v., Goddard, W.A.: Multi-paradigm modeling of dynamical crack propagation in silicon using the ReaxFF reactive force field. Phys. Rev. Lett. 96, 095505 (2006).CrossRefGoogle Scholar
59.Duin, A.C.T.v., Dasgupta, S., Lorant, F., Goddard, W.A.: ReaxFF: A reactive force field for hydrocarbons. J. Phys. Chem. A. 105, 9396 (2001).CrossRefGoogle Scholar
60.Nielson, K.D., Duin, A.C.T.v., Oxgaard, J., Deng, W., Goddard, W.A.: Development of the ReaxFF reactive force field for describing transition metal catalyzed reactions, with application to the initial stages of the catalytic formation of carbon nanotubes. J. Phys. Chem. A 109, 49 (2005).CrossRefGoogle Scholar
61.Humphrey, W., Dalke, A., Schulten, K.: VMD: Visual molecular dynamics. J. Mol. Graphics 14, 33 (1996).CrossRefGoogle ScholarPubMed