Molecular Dynamics Investigation of The Elastic Constants and Moduli of Single Walled Carbon Nanotubes
محورهای موضوعی : Journal of NanoanalysisMohammad Mahdi Zaeri 1 , Saeed Ziaei-Rad 2
1 - Department of Chemistry, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
2 - Department of Chemistry, Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran
کلید واژه: Molecular dynamics simulation, elastic constants, elastic moduli, single walled carbon nanotub,
چکیده مقاله :
Determination of the mechanical properties of carbon nanotubes is an essential step in their applications from macroscopic composites to nano-electro-mechanical systems. In this paper we report the results of a series of molecular dynamics simulations carried out to predict the elastic constants, i.e. the elements of the stiffness tensor, and the elastic moduli, namely the Young’s and shear moduli, of various single walled carbon nanotubes. Poisson’s ratios were also calculated. Three different methods were used to run the simulations: applying a predetermined strain and reading the resulted stress, applying forces and constraints to the end atoms and calculating the moduli by assuming an equivalent continuum tube, and lastly applying a predetermined stress and reading the consequent deformation. In each case, the effect of nanotube chirality and diameter was studied. In addition, loading conditions were altered in each method to study the effect of nonlinearity of interatomic interactions. The result of the three methods are compared, with each other as well as with the literature, and discussed to obtain reasonable concluding remarks.
1. D. Qian, G.J. Wagner, W.K. Liu, M.F. Yu and R.S. Ruoff, Appl. Mech. Rev., 55(6), 495 (2002).
2. E.T. Thostenson, Z. Ren and T.W. Chou, Compos. Sci. Technol., 61(13), 1899 (2001).
3. M.F. Yu, J. Eng. Mater. T. ASME, 126(3), 271 (2004).
4 .D. Srivastava, C. Wei and K. Cho, Appl. Mech. Rev., 56(2), 215 (2003).
5. A. Kis and A. Zettl, Philos. T. Roy. Soc. A, 366(1870), 1591 (2008).
6. L.C. Zhang, J. Mater. Process. Tech., 209(9), 4223 (2009).
7. E.T. Thostenson, C. Li and T.W. Chou, Compos. Sci. Technol., 65(3), 491 (2005).
8. R.S. Ruoff, D. Qian and W.K. Liu, C. R. Phys., 4(9), 993 (2003).
9. A. Maiti, Microelectron. J., 39(2), 208 (2008).
10. F. Li, H.M. Cheng, S. Bai, G. Su and M.S. Dresselhaus, Appl. Phys. Lett., 77(20), 3161 (2000).
11. A. Sears and R.C. Batra, Phys. Rev. B, 69(23), 235406 (2004).
12. J.P. Lu, Phys. Rev. Lett., 79(7), 1297 (1997).
13. H.C. Cheng, Y.L. Liu, Y.C. Hsu and W.H. Chen, Int. J. Solids Struct., 46(7), 1695 (2009).
14. S.C. Chowdhury, B.Z.G. Haque, J.W. Gillespie and D.R. Hartman, Comp. Mater. Sci., 65, 133 (2012).
15. M. Rossi and M. Meo, Compos. Sci. Technol., 69(9), 1394 (2009).
16. J. Geng and T. Chang, Phys. Rev. B, 74(24), 245428 (2006).
17. C.L. Zhang and H.S. Shen, Appl. Phys. Lett., 89(8), 081904 (2006).
18. A.R. Hall, L. An, J. Liu, L. Vicci, M.R. Falvo, R. Superfine and S. Washburn, Phys. Rev. Lett., 96(25), 256102 (2006).
19. A.R. Khoei, E. Ban, P. Banihashemi and M.A. Qomi, Mater. Sci. Eng. C, 31(2), 452 (2011).
20. Y.Y. Zhang, C.M. Wang and Y. Xiang, Carbon, 48(14), 4100 (2010).
21. M.M. Zaeri, S. Ziaei-Rad, A. Vahedi and F. Karimzadeh, Carbon, 48(13), 3916 (2010).
22. C.H. Wong, Comp. Mater. Sci., 49(1), 143 (2010).
23. B. WenXing, Z. ChangChun and C. WanZhao, Physica B, 352(1), 156 (2004).
24. H. Xin, Q. Han and X.H. Yao, Carbon, 45(13), 2486 (2007).
25. J.Y. Hsieh, J.M. Lu, M.Y. Huang and C.C. Hwang, Nanotechnology, 17(15), 3920 (2006).
26. C. Li and T.W. Chou, Int. J. Solids Struct., 40(10), 2487 (2003).
27. C. Li and T.W. Chou, Compos. Sci. Technol., 63(11), 1517 (2003).
28. A.L. Kalamkarov, A.V. Georgiades, S.K. Rokkam, V.P. Veedu and M.N. Ghasemi-Nejhad, Int. J. Solids Struct., 43(22), 6832 (2006).
29. P. Zhang, Y. Huang, P.H. Geubelle, P.A. Klein and K.C. Hwang, Int. J. Solids Struct., 39(13), 3893 (2002).
30. P.M. Agrawal, B.S. Sudalayandi, L.M. Raff and R. Komanduri, Comp. Mater. Sci., 38(2), 271 (2006).
31. Q. Lu and B. Bhattacharya, Nanotechnology, 16(4), 555 (2005).
32. A. Fereidoon, M.G. Ahangari, M.D. Ganji and M. Jahanshahi, Comp. Mater. Sci., 53(1), 377 (2012).
33. X. Chen and G. Cao, Nanotechnology, 17(4), 1004 (2006).
34. T. Chang and H. Gao, J. Mech. Phys. Solids, 51(6), 1059 (2003).
35. Z. Yao, C.C. Zhu, M. Cheng and J. Liu, Comp. Mater. Sci., 22(3), 180 (2001).
36. Y.I. Prylutskyy, S.S. Durov, O.V. Ogloblya, E.V. Buzaneva and P. Scharff, Comp. Mater. Sci., 17(2), 352 (2000).
37. Y. Jin and F.G. Yuan, Compos. Sci. Technol., 63(11), 1507 (2003).
38. K.M. Liew, X.Q. He and C.H. Wong, Acta Mater., 52(9), 2521 (2004).
39. Y. Wang, X.X. Wang, X.G. Ni and H.A. Wu, Comp. Mater. Sci., 32(2), 141 (2005).
40. Z. Wang, M. Devel and B. Dulmet, Surf. Sci., 604(5), 496 (2010).
41. K. Mylvaganam and L.C. Zhang, Carbon, 42(10), 2025 (2004).
42. B. Motevalli, A. Montazeri, R. Tavakoli-Darestani and H. Rafii-Tabar, Physica E, 46, 139 (2012).
43. X. Hao, H. Qiang and Y. Xiaohu, Compos. Sci. Technol., 68(7), 1809 (2008).
44. W.H. Duan, Q. Wang, K.M. Liew and X.Q. He, Carbon, 45(9), 1769 (2007).
45. E.B. Tadmor and R.E. Miller, “Modeling materials: continuum, atomistic and multiscale techniques”, Cambridge University Press, 259 (2011).
46. S. Plimpton, J. Comput. Phys., 117(1), 1 (1995).
47. F. Memarian, A. Fereidoon, S. Khodaei, A.H. Mashhadzadeh and M.D. Ganji, Vacuum, 139, 93 (2017).
48. A. Fereidoon, M. Mostafaei, M.D. Ganji and F. Memarian, Superlattice. Microst., 86, 126 (2015).
49. M.M. Zaeri and S. Ziaei-Rad, AIP Adv., 5(11), 117114 (2015).
50. W.D. Cornell, P. Cieplak, C.I. Bayly, I.R. Gould, K.M. Merz, D.M. Ferguson, D.C. Spellmeyer, T. Fox, J.W. Caldwell and P.A. Kollman, J. Am. Chem. Soc., 117(19), 5179 (1995).
51. W.L. Jorgensen and D.L. Severance, J. Am. Chem. Soc., 112(12), 4768 (1990).
52. M.H. Sadd, “Elasticity: theory, applications and numerics”, 2nd ed., Academic Press, 298 (2009).
