In this article, effect of temperature on elastic properties of single-walled carbon nanotubes is investigated by means of a molecular structural mechanics model in which the primary bonds between two nearest-neighboring atoms are treated as a two-node dimensional Euler—Bernoulli beam. By considering the effect of environmental temperature on force constant values of bond stretching, bond angle bending, and torsional resistance, the corresponding basic parameters of these two-node dimensional Euler—Bernoulli beam elements are obtained under different environmental temperatures, respectively. Nano-scale finite element simulations of the elastic properties of single-walled carbon nanotubes under different environmental temperatures reveal that the elastic modulus of single-walled carbon nanotubes decreases significantly with the increase of temperature. It is noted that the Young's modulus of armchair nanotubes is more sensitive to environmental temperature due to the tube chirality. Finally, the relationship between elastic modulus of zigzag and armchair carbon nanotubes and environmental temperature is given by a simple formula.
Iijima, S. (1991). Helical Microtubes of Graphitic Carbon, Nature, 354: 56-58.
2.
Dresselhaus, M.S., Dresselhaus, G. and Eklund, P.C. (1996). Science of Fullerenes and Carbon Nanotubes, Academic Press, San Diego.
3.
Yakobson, B.I. , Brabec, C.J. and Bernholc, J. (1996). Nanomechanics of Carbon Tubes: Instability Beyond Linear Response, Physical Review Letters, 76: 2511-2514.
4.
Fischer, J.E. (1998). Special Issue on Nanotubes, Appl. Phys. A, 67: 1.
5.
Cohen, M.L. (2001). Nanotubes, Nanoscience, and Nanotechnology, Mater . Sci. Eng., 15: 1-11.
6.
Lau, K.T. , Chong, G., Gao , G.H. et al. (2004). Stretching Process of Single- and Multi-Walled Carbon Nanotubes for Nanocomposite Applications , Carbon, 42: 423-460.
7.
Lau, K.T. and Shi, S.Q. (2002). Failure Mechanisms of Carbon Nanotube/Epoxy Composites Pretreated in Different Temperature Environments , Carbon, 40: 2965-2968.
8.
Treacy, M.M.J. , Ebbesen, T.W. and Gibson, J.M. (1996). Exceptionally High Young's Modulus Observed for Individual Carbon Nanotubes , Nature, 381: 678-680.
9.
Wong, E.W., Sheehan, P.E. and Lieber, C.M. (1997). Nanobeam Mechanics: Elasticity, Strength, and Toughness of Nanorods and Nanotubes, Science, 277:1971-1975.
10.
Krishnan, A. , Dujardinm, E., Ebbesen , T.W., Yianilos, P.N. and Treacy, M.M.J. (1998). Young's Modulus of Single-Walled Nanotubes, Physical Review B, 58(20): 14013-14019.
11.
Yu, M.F. , Lourie, O., Dyer , M.J., Moloni, K., Kelly, T.F. and Ruoff, R.S. (2000). Strength and Breaking Mechanism of Multiwalled Carbon Nanotubes under Tensile Load, Science, 287: 637-640.
12.
Overney, G. , Zhong, W. and Tomanek, D. (1993). Structural Rigidity and Low-Frequency Vibrational Modes of Long Carbon Tubules , Zeitschrift fur Physik D, 27: 93-96.
13.
Iijima, S., Brabec, C., Maiti, A. and Bernholc, J. (1996). Structural Flexibility of Carbon Nanotubes, Journal of Chemical Physics, 104(5): 2089-92.
14.
Lu, J.P. (1997). Elastic Properties of Carbon Nanotubes and Nanoropes, Physical Review Letters, 79: 1297-1300.
15.
Vaccarini, L., Goze, C., Henrard , L., Hernandez, E., Bernier, P. and Rubio, A. (2000). Mechanical and Electronic Properties of Carbon and Boronnitride Nanotubes , Carbon, 38(11-12): 1681-1690.
Li, C.Y. and Chou, T.S.A. (2003). Structural Mechanics Approach for the Analysis of Carbon Nanotubes, International Journal of Solids and Structures , 40: 2487-2499.
19.
Xiao, J.R., Gama, B.A. and Gillespie Jr, J.W. (2005). An Analytical Molecular Structural Mechanics Model for the Mechanical Properties of Carbon Nanotubes , International Journal of Solids and Structures, 42: 3075-3092
20.
Li, X. and Bhushan, B. (2002). A Review of Nanoindentation Continuous Stiffness Measurement Technique and its Applications, Material Characterization , 48: 11-36.
21.
Li, X., Gao, H. and Catherine, J. (2003). Nanoindentation of Silver Nanowires, Nano Letters, 3: 1495-1498.
22.
Li, X., Chang, W.C., Chao, Y.J., Wang, R. and Chang, M. (2004). Nanoscale Structure and Mechanical Characterization of a Natural Nanocomposite Material: The Shell of Red Abalone, Nano Letters, 4: 613-617.
23.
Demczyk, B.G. , Wang, Y.M., Cumings , J., Hetman, M., Han , W., Zettle, A. and Ritchie, R.O. (2002). Direct Mechanical Measurement of the Tensile Strength and Elastic Modulus of Multiwalled Carbon Nanotubes , Material and Science Engineering A, 334: 173-178.
24.
Lau, K.T. (2003). Interfacial Bonding Characteristics of Nanotube/Polymer Composites, Chemical Physics Letters, 370: 399-405.
25.
Jin, Y. and Yuan, F.G. (2002). Elastic Properties of Single-Walled Carbon Nanotubes. Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, 3: 1819-1825.
26.
Goze, C., Vaccarini, L., Henrard, L., Bernier, P., Hernandez, E. and Rubio, A. (1999). Elastic and Mechanical Properties of Carbon Nanotubes , Synthetic Metals, 103: 2500-2501.
27.
Hernandez, E., Goze, C., Bernier , P. and Rubio, A. (1999). Elastic Properties of Single-Wall Nanotubes, Applied Physics A, 68: 287-292.
28.
Popov, V.N. , Van Doren, V.E. and Balkanski , M. (2002). Elastic Properties of Single-Walled Carbon Nanotubes, Physical Review B, 61: 3078-3084
29.
Wang, X.Y. and Wang, X. (2004). Numerical Simulation for Bending Modulus of Carbon Nanotubes and Some Explanations for Experiment, Composites: Part B, 35: 79-864.
30.
Wang, X., Zhang, Y.C., Xia, X.H. and Huang, C.H. (2004). Effective Bending Modulus of Carbon Nanotubes with Rippling Deformation, International Journal of Solids and Structures, 41: 6429-39.
31.
Wang, X., Wang, X.Y. and Xiao, J.A. (2005). Nonlinear Analysis of the Bending Modulus of Carbon Nanotubes with Rippling Deformations, Composite Structures , 69: 315-321.
32.
Wang, X. and Yang, H.K. (2005). Axially Critical Load of Multiwall Carbon Nanotubes under Thermal Environment, Journal of Thermal Stresses, 28: 185-196.
33.
Odegard, G.M. , Gates, T.S., Nicholson , L.M. and Wise, K.E. (2002). Equivalent-Continuum Modeling with Application to Carbon Nanotubes. NASA/TM-211454-1-10.
34.
Chang, T. and Gao, H. (2003). Size-Dependent Elastic Properties of a Single-Walled Carbon Nanotube via a Molecular Mechanics Model, Journal of the Mechanics and Physics of Solids, 51: 1059-1074.
35.
Shenoy, V.B. , Miller, R., Tadmor , E.B., Rodney, D., Phillips, R. and Ortiz, M. (1999). An Adaptive Finite Element Approach to Atomic-Scale Mechanics-The Quasicontinuum Method, Journal of the Mechanics and Physics of Solids, 47: 611-642.
36.
Rudd, R.E. and Broughton, J.Q. (2000). Concurrent Coupling of Length Scales in Solid State Systems. Physica Status Solidi B, 217(1): 251-291.
37.
Chung, P.W. and Namburu, R.R. (2003). On a Formulation for a Multi-Scale Atomistic-Continuum Homogenization Method, International Journal of Solids and Structures, 40: 2563-2588.
38.
Xiao, S.P. and Belytschko, T. (2004). A Bridging Domain Method for Coupling Continuum with Molecular Dynamics, Computer Methods in Applied Mechanics and Engineering, 193: 1645-1669.
39.
Liu, B. , Huang, Y., Jiang , H., Qu , S. and Wang, B. (2004). The Atomic-Scale Finite Element Method, Comput. Methods Appl. Mech. Engrg., 193: 1849-1864
40.
Cornell, W.D. , Cieplak, P., Bayly , C.I., Gould, I.R., Merz, K.M., Ferguson, D.M., Spellmeyer, D.C., Fox , T., Caldwell, J.W. and Kollman, P.A. (1995). A Second Generation Force-Field for the Simulation of Proteins, Nucleic-Acids, and Organic-Molecules , Journal of American Chemical Society , 117: 5179-5197.
41.
Rappe, A.K. , Casewit, C.J., Colwell , K.S., Goddard, W.A. and Skiff, W.M. (1992). UFF, A Full Periodic-Table Force-Field for Molecular Mechanics and Molecular Dynamics Simulations, Journal of American Chemical Society , 114: 10024-10035.
42.
Mayo, L.L., Olafson, B.D. and Goddard III, W.A. (1993). Polyoxymethylene. The Hessian Biased Force Field for Molecular Dynamics Simulations, Journal of Physical Chemistry, 97(42): 10891-10902.
43.
Nicholas, J.B. , Hopfinger, A.J., Trouw , F.R. and Iton, L.E. (1991). Molecular Modeling of Zeolite Structure. 2. Structure and Dynamics of Silica Sodalite and Silicate Force Field, Journal of American Chemical Society, 113: 4792-4797.
44.
Kwon, Y.-K., Berber, S. and Tomanek, D. (2004). Thermal Contraction of Carbon Fullerenes and Nanotubes , Physical Review Letters, 92:01590,1-4.
