Elsevier

Diamond and Related Materials

Volume 18, Issues 2–3, February–March 2009, Pages 438-442
Diamond and Related Materials

Computational investigation of the mechanical properties of nanomaterials

https://doi.org/10.1016/j.diamond.2008.10.041Get rights and content

Abstract

The mechanical responses of carbon nanotubes are examined using classical molecular dynamics simulations. Several different types of nanotubes are considered, including pristine single-walled tubes that are empty, filled with fullerenes to form peapods, filled with other nanotubes to form multi-walled tubes, or chemically functionalized. In addition, the responses of single-walled nanotubes with wall vacancies are considered. The results show how the bending force of filled nanotubes increases relative to the bending force of empty nanotubes and indicates how these increases come about. In addition, the simulations reveal the way in which the magnitude of these increases depend on the type of filling material and, in the case of multi-walled tubes, the number of inner tubes. These simulations further illustrate the way in which the inner nanotubes support higher external loads than the fullerenes in cases when the outer nanotubes are identical. The results also indicate that both the bending and buckling forces depend on temperature and the reasons for this dependence are discussed. Lastly, the simulations demonstrate the way in which the introduction of vacancy defects and covalently bound functional groups to the nanotube walls degrades the nanotubes' mechanical properties.

Introduction

Carbon nanotubes (CNTs) have a unique combination of electrical and mechanical properties such as high conductivity, strength and toughness. These properties make them attractive for use as components in nanoelectromechanical systems (NEMS), where they would be subjected to various types of forces such as compression, bending, tension, and torsion. Additionally, CNTs used as tips of atomic force microscopes (AFM) experience both compression and bending during surface contact and scanning. Consequently, there has been intense interest in qualitatively understanding and quantifying the mechanical responses of CNTs.

For example, Ijima et al. [1] found that atomistic simulations of the responses of nanotubes to bending are comparable to images of bent tubes observed in high resolution electron microscope images. Yakobson et al. [2] used similar simulations to examine the mechanical responses of single-walled carbon nanotubes (SWNTs) under axial compression, bending, and torsion. Their results indicated that nanotubes exhibit great flexibility, and may be severely deformed without breaking any chemical bonds. In addition, Garg and Sinnott [3] predicted that heavy chemical functionalization of CNT walls leads to slightly lower SWNT buckling forces because of the disruption of the nanotube wall lattice by the covalent attachment of the functional groups.

The basic mechanical properties of filled SWNTs have been also investigated by Ni et al. [4] who found that filling CNTs with fullerenes, CH4 or Ne increases the loads at which bucking occurs and decreases the effect of temperature on buckling. Additionally, Danailov et al. [5] predicted that filling SWNTs with Au nanowires increases the maximum bending force and the deflection to buckling. In an analogous study Trotter et al. [6] explored the compressibility of CNTs filled with diamond nanowires, smaller nanotubes, C60, CH4, Ne, n-C4H10, or n-C4H7 molecules. They observed that nanowire-filled CNTs and multi-walled CNTs (MWNTs) exhibit similar mechanical responses and that filling CNTs increases their stiffness during compression. Jeong et al. [7], [8], [9] also investigated the effect of filling CNTs on the tensional, torsional, combined tensional and torsional, and biaxial tensional and torsional properties. They observed that these mechanical properties can be improved by filling CNTs, but the failure criteria are different depending on the deformation modes. Other computational methods besides strictly atomistic simulations have also been applied. For instance, the buckling of single-walled and double-walled nanotubes with molecular mechanics and finite element simulations have been examined by Sears and Batra [10]. In addition, elastic shell model calculations have been used by Wang et al. [11] to investigate the influence of filling nanotubes with other tubes on their response to a combination of bending and axial compression. These studies predict that higher forces are required to deform multi-walled nanotubes relative to single-walled nanotubes.

Here, the mechanical responses of pristine hollow, C60-filled, n-butane-filled, and multi-(dual-, triple- and quadruple-) walled CNTs under bending forces at various temperatures are examined using classical molecular dynamics (MD) simulations. The results are compared to the responses of CNTs with covalently bonded functional groups and wall vacancies. They provide insights into the atomic-scale mechanisms responsible for the differing responses under these various conditions.

Section snippets

Computational details

In the simulations of bending CNTs, the forces and the deflections are calculated using the second generation reactive empirical bond order (REBO) potential [12] for the short-range covalent interactions between carbon atoms, and the Lennard–Jones (LJ) potential for the long-range van der Waals interactions between the CNT wall and the filling materials, including C60, organic molecules, or another CNT wall. These van der Waals interactions may play a critical role in influencing the mechanical

Results and discussion

The predicted force versus deflection of various (10, 10) hollow and filled CNTs during the bending tests are illustrated in Fig. 2. Nanotube deflection, Δx, increases linearly with the bending force in the low force region. Both hollow and filled CNTs undergo buckling with increasing bending force, beyond which they cannot support the external bending force. It is further predicted that the bending force of the (10,10) peapod is larger than that of the (10,10) SWNT in agreement with the MD

Conclusions

The simulations discussed here predict that filling SWNTs increases their maximum deflection during bending. MWNTs are predicted to support higher external loads than SWNTs and peapods because the inner CNTs sustain higher external forces than the fullerenes, and the fullerenes are mobile enough to slightly remove themselves from the point of nanotube collapse during deflection. This mechanical behavior of hollow or filled CNTs is predicted to deteriorate at high temperatures, with a greater

Acknowledgements

The authors acknowledge the support of the National Science Foundation funded Network for Computational Nanotechnology (EEC-0228390). They also acknowledge the University of Florida High-Performance Computing Center for providing computational resources and support that have contributed partially to the research results reported within this paper.

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