The Attitude of Variation of Elastic Modules in Single Wall Carbon Nanotubes: Nonlinear Mass-Spring Model

Subject Areas : Engineering

A.R  Golkarian ¹ (Department of Mechanical Engineering, Mashhad branch, Islamic Azad University)
M  Jabbarzadeh ² (Department of Mechanical Engineering, Mashhad branch, Islamic Azad University)

Received: 2012-01-17 Accepted : 2012-03-29 Published : 2012-03-30

Keywords: Carbon nanotubes, Elastic modules, Non-linear spring, Morse potential,

Abstract :

The examination of variation of elastic modules in single wall carbon nanotubes (SWCNTs) is the aim of this paper. Full nonlinear spring-like elements are employed to simulate specific atomic structures in the commercial code ABAQUS. Carbon atoms are attached to each node as a mass point using atomic mass of carbon atoms. The influence of dimensions such as variation of length, diameter, aspect ratio and chirality is explored separately on the variations of young's and shear modules. It is observed that the effect of dimensions after a critical aspect ratio in nanotubes is negligible. Also, the influence of chirality on the elastic modules for same dimensions is observable. The results are compared with experimental results and theoretical data.

References:

[1] Chang T., Gao H., 2003, Size dependent elastic properties of a single-walled carbon nanotube via molecular mechanics, Journal of the Mechanics and Physics of Solids 51: 1059-74.

[2] Nasdala L., Ernst G., 2005, Development of a 4 node finite element for the computation of nano-structured materials, Computational Materials Science 33: 443-58.

[3] Li C., Chou T-W., 2003, A structural mechanics approach for the analysis of carbon nanotubes, International Journal of Solids and Structures 40: 2487–99.

[4] Kalamkarov A.L., Georgiades A.V., Rokkam S.K., Veedu V.P., Ghasemi-Nejhad M.N., 2006, Analytical and numerical techniques to predict carbon nanotubes properties, International Journal of Solids and Structures 43: 6832-54.

[5] Meo M., Rossi M., 2006, Prediction of Young’s modulus of single wall carbon nanotubes by molecular-mechanics based finite element modeling, Composites Science and Technology 66: 1597-605.

[6] Giannopoulos G.I., Kakavas P.A., Anifantis N.K., 2008, Evaluation of the effective mechanical properties of single walled carbon nanotubes using a spring based finite element approach, Computational Materials Science 41: 561-9.

[7] Papanikos P., Nikolopoulos D., 2008, Equivalent beams for carbon nanotubes, Computational Materials Science 43: 345-352.

[8] Hemmasizadeh A., Mahzoon M., 2008, A method for developing the equivalent continuum model of a single layer graphene sheet,Thin Solid Films 516: 7636-40.

[9] Shokrieh M.M., Rafiee R., 2010, Prediction of Young’s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach, Material and Design 31: 790-795.

[10] Georgantzinos S.K., Giannopoulos G.I., 2010, Numerical investigation of elastic mechanical properties of grapheme structures, Material and Design 31: 4646-54.

[11] Georgantzinos S.K., Katsareas D.E., 2011, Graphene characterization: A fully non-linear spring-based finite element prediction, Physica E 43: 1833-39.

[12] Rafiee R., Heidarhaei M., 2012, Investigation of chirality and diameter effects on the Young’s modulus of carbon nanotubes using non-linear potentials, Composite Structure 94: 2460-64.

[13] Koloczek J., Young-Kyun K., 2001, Characterization of spatial correlations in carbon nanotubes-modelling studies, Journal of Alloys and Compounds 28: 222-225.

[14] Rappe A.K., Casemit C.J., 1992, A full periodictable force-field for molecular mechanics and molecular dynamics simulations, Journal of the American Chemical society 114: 10024-35.

[15] Xiao J.R., Gama B.A., An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes, International Journal of Solids and Structures 42: 3075-92.

[16] K. Machida, 1999, Principles of molecular mechanics, Wiley ed., Wiley and Kodansha.

[17] Dresselhaus M.S., Dresselhaus G., Saito R., 1995, Physics of Carbon Nanotubes, Carbon 33(7):883–91.

[18] WenXing B., ChangChun Z., 2004, Simulation of Young’s modulus of single-walled carbon nanotubes by molecular dynamics, Physica B 352: 156-63.

[19] Jin Y., Yuan F.G., 2003, Simulation of elastic properties of single-walled carbon nanotubes, Composites Science and Technology 63: 1507-15.

[20] Gupta S., Dharamvir K., 2005, Elastic moduli of single-walled carbon nanotubes and their ropes, Physical Review B 72: 165428(1-16).

[21] Tserpes K.I., Papanikos P., 2005, Finite element modeling of single-walled carbon nanotubes, Composites Part B: Engineering 36: 468-477.