Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model

Journal of the Mechanics and Physics of Solids

Volumn 51, Issue 6, 2003, Pages 1059-1074

  Chang, Tienchong ^a   Gao, Huajian ^b  

^a TONGJI UNIVERSITY   (China)

^b MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

Author keywords

Continuum mechanics; Elastic properties; Molecular mechanics; Nanotubes

Indexed keywords

CONTINUUM MECHANICS; CRYSTAL ATOMIC STRUCTURE; ELASTICITY; MOLECULAR DYNAMICS; NUMERICAL ANALYSIS; POISSON DISTRIBUTION;

SINGLE-WALLED CARBON NANOTUBES;

CARBON NANOTUBES;

EID: 0037409356     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(03)00006-1     Document Type: Article

References (55)

1. Abraham F.F., Broughton J.Q., Bernstein N., Kaxiras E. Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture. Europhys. Lett. 44(6):1998;783-787.
2. Allinger N.L. Conformational analysis 130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms. J. Am. Chem. Soc. 99:1977;8127-8134.
3. Arroyo, M., Belytschko, T., 2002. Large deformation atomistic-based continuum analysis of carbon nanotubes. AIAA-2002-1317.
4. Bakowies D., Thiel W. MNDO study of large carbon clusters. J. Am. Chem. Soc. 113:1991;3704-3714.
5. Bernholc J., Brabec C., Nardelli B.M., Maiti A., Roland C., Yakobson B.I. Theory of growth and mechanical properties of nanotubes. Appl. Phys. A. 67:1998;39-46.
6. Brenner D.W. Empirical potential for hydrocarbons for use in simulating the chemical vapor-deposition of diamond films. Phys. Rev. B. 42:1990;9458-9471.
7. Burkert, U., Allinger, N.L., 1982. Molecular Mechanics. ACS Monograph 177. American Chemical Society, Washington, DC.
8. Che J., Cagin T., Goddard W.A. Thermal conductivity of carbon nanotubes. Nanotechnology. 11:2000;65-69.
9. Cohen M.L. Nanotubes, nanoscience, and nanotechnology. Mater. Sci. Eng. 15:2001;1-11.
10. Dresselhaus M.S., Dresselhaus G., Eklund P.C. Science of Fullerenes and Carbon Nanotubes. 1996;Academic Press, San Diego.
11. Falvo M.R., Clary G.J., Taylor R.M., Chi V., Brooks F.P., Washburn S., Superfine R. Bending and buckling of carbon nanotubes under large strain. Nature. 389(6651):1997;582-584.
12. Fischer, J.E. (Guest Editor), 1998. Special Issue on nanotubes. Appl. Phys. A 67, 1.
13. Friesecke G., James R.D. A scheme for the passage from atomic to continuum theory for thin films, nanotubes and nanorods. J. Mech. Phys. Solids. 48(6-7):2000;1519-1540.
14. Govindjee S., Sackman J.L. On the use of continuum mechanics to estimate the properties of nanotubes. Solid State Commun. 110:1999;227-230.
15. Goze C., Vaccarini L., Henrard L., Bernier P., Hernandez E., Rubio A. Elastic and mechanical properties of carbon nanotubes. Synth. Met. 103:1999;2500-2501.
16. Harik V.M. Ranges of applicability for the continuum-beam model in the constitutive analysis of carbon-nanotubes. Solid State Commun. 120:2001;331-335.
17. z composite nanotubes Phys. Rev. Lett. 80:1998;4502-4505.
18. Hernandez E., Goze C., Bernier P., Rubio A. Elastic properties of single-wall nanotubes. Appl. Phys. A. 68:1999;287-292.
19. Iijima S. Helical microtubes of graphitic carbon. Nature. 354:1991;56-58.
20. Jin, Y., Yuan, F.G., 2002. Elastic properties of single-walled carbon nanotubes. AIAA-2002-1430.
21. Knap J., Ortiz M. An analysis of the quasicontinuum method. J. Mech. Phys. Solids. 49(9):2001;1899-1923.
22. Krishnan A., Dujardin E., Ebbesen T.W., Yianilos P.N., Treacy M.M.J. Young's modulus of single-walled nanotubes. Phys. Rev. B. 58(20):1998;14013-14019.
23. Leach, A.R., 1996. Molecular Modelling Principles and Applications, Chapter 3. Addison-Wesley Longman Limited, London, p. 131.
24. Liu W.K., Chen Y.J., Uras R.A., Chang C.T. Generalized multiple scale reproducing kernel particle methods. Comput. Methods Appl. Mech. Eng. 139(1-4):1996;91-157.
25. Liu J.Z., Zheng Q.S., Jiang Q. Effect of a rippling mode on resonances of carbon nanotubes. Phys. Rev. Lett. 86:2001;4843-4846.
26. Lourie O., Wagner H.D. Evaluation of Young's modulus of carbon nanotubes by micro-Raman spectroscopy. J. Mater. Res. 13:1998;2418-2422.
27. Lu J.P. Elastic properties of carbon nanotubes and nanoropes. Phys. Rev. Lett. 79:1997;1297-1300.
28. Molina J.M., Savinsky S.S., Khokhriakov N.V. A tight-binding model for calculations of structures and properties of graphitic nanotubes. J. Chem. Phys. 104:1996;4652-4656.
29. Nardelli M.B., Fattebert J.L., Orlikowski D., Roland C., Zhao Q., Bernholc J. Mechanical properties, defects and electronic behavior of carbon nanotubes. Carbon. 38:2000;1703-1711.
30. Odegard, G.M., Gates, T.S., Nicholson, L.M., Wise, K.E., 2002. Equivalent-continuum modeling with application to carbon nanotubes. NASA/TM-2002-211454.
31. Overney G., Zhong W., Tomanek D. Structural rigidity and low-frequency vibrational modes of long carbon tubules. Z. Phys. D: Atoms Mol. Clusters. 27:1993;93-96.
32. Poncharal P., Wang Z.L., Ugarte D., de Heer W.A. Electrostatic deflections and electromechanical resonances of carbon nanotubes. Science. 283:1999;1513-1516.
33. Popov V.N., Van Doren V.E., Balkanski M. Elastic properties of single-walled carbon nanotubes. Phys. Rev. B. 61:2000;3078-3084.
34. Qian D., Wagner G.J., Liu W.K., Yu M.F., Ruoff R.S. Mechanics of carbon nanotubes. Appl. Mech. Rev. 55(2):2002;495-533.
35. Rao A.M., Richter E.A., Eklund P.C., Bandow S. Raman spectroscopy of pristine and doped single wall carbon nanotubes. Thin Solid Films. 331:1998;141-147.
36. Rappe A.K., Casewit C.J. Molecular Mechanics Across Chemistry. 1997;University Science Books, Sausalito, CA.
37. Ru C.Q. Axially compressed buckling of a doublewalled carbon nanotube embedded in an elastic medium. J. Mech. Phys. Solids. 49(6):2001;1265-1279.
38. Rudd R.E., Broughton J.Q. Concurrent coupling of length scales in solid state systems. Phys. Stat. Sol. B. 217(1):2000;251-291.
39. Salvetat J.P., Bonard J.M., Thomson N.H., Kulik A.J., Forro L., Benoit W., Zuppiroli L. Mechanical properties of carbon nanotubes. Appl. Phys. A. 69:1999;255-260.
40. Sanchez-Portal D., Artacho E., Soler J.M., Rubio A., Ordejon P. Ab-initio structural, elastic, and vibrational properties of carbon nanotubes. Phys. Rev. B. 59:1999;12678.
41. Shenoy V.B., Miller R., Tadmor E.B., Rodney D., Phillips R., Ortiz M. An adaptive finite element approach to atomic-scale mechanics - the quasicontinuum method. J. Mech. Phys. Solids. 47(3):1999;611-642.
42. Sinnott S.B. Chemical functionalization of carbon nanotubes. J. Nanosci. Nanotechnol. 2(2):2002;113-123.
43. Tersoff J. Empirical interatomic potential for carbon, with applications to amorphous-carbon. Phys. Rev. Lett. 61:1988;2872-2879.
44. Tersoff J., Ruoff R.S. Structural properties of a carbon-nanotube crystal. Phys. Rev. Lett. 73:1994;676-679.
45. Thostensona E.T., Ren Z., Chou T.W. Advances in the science and technology of carbon nanotubes and their composites. a review Comput. Sci. Techol. 61:2001;1899-1912.
46. Treacy M.M.J., Ebbesen T.W., Gibson J.M. Exceptionally high Young's modulus observed for individual carbon nanotubes. Nature. 381:1996;678-680.
47. Van Lier G., Van Alsenoy C., Van Doren V., Geerlings P. Ab initio study of the elastic properties of single-walled carbon nanotubes and graphene. Chem. Phys. Lett. 326:2000;181.
48. White C.T., Robertson D.H., Mintmire J.W. Helical and rotational symmetries of nanoscale graphatic tubules. Phys. Rev. B. 47:1993;5485-5488.
49. Wong E.W., Sheehan P.E., Lieber C.M. Nanobeam mechanics. elasticity, strength, and toughness of nanorods and nanotubes Science. 277:1997;1971-1975.
50. Yakobson B.I., Smalley R.E. Fullerene nanotubes. C1000000 and beyond Am. Sci. 85:1997;324-337.
51. Yakobson B.I., Brabec C.J., Bernholc J. Nanomechanics of carbon tubes. instability beyond linear response Phys. Rev. Lett. 76:1996;2511-2514.
52. Yao N., Lordi V. Young's modulus of single-walled carbon nanotubes. J. Appl. Phys. 84:1998;1939-1943.
53. Ye L.H., Liu B.G., Wang D.S. Ab initio molecular dynamics study on small carbon nanotubes. Chinese Phys. Lett. 18:2001;1496-1499. (In which β for (n,0) nanotubes was wrongly typed as π-arccos[(1/4)-(3/4)cos(π/n)] ).
54. Zhang P., Lammert P.E., Crespi V.H. Plastic deformations of carbon nanotubes. Phys. Rev. Lett. 81:1998;5346-5349.
55. Zhang P., Huang Y., Geubelle P.H., Klein P.A., Hwang K.C. The elastic modulus of single-wall carbon nanotubes. a continuum analysis incorporating interatomic potentials Int. J. Solids Struct. 39:2002;3893-3906.