Atomistic Modeling of Elasticity and Fracture of a (10, 10) Single Wall Carbon Nanotube
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Atomistic Modeling of Elasticity and Fracture of a (10,10) Single Wall Carbon Nanotube Ryan King1, and Markus J Buehler2 1 Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Mass. Ave, Cambridge, 02139 2 Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, 77 Mass. Ave, Room 1-272, Cambridge, MA, 02139 Corresponding author, electronic address [email protected] ABSTRACT We use the ReaxFF reactive force field to model extreme tensile deformation of a (10,10) armchair carbon nanotube. The ReaxFF force field has been developed based on DFT quantum mechanical calculations without any empirical parameters (Duin et al., 2001). We report an analysis of the stress-strain relationship for the elastic and plastic regime, including a description of the microscopic fracture mechanisms. We find Young’s modulus to be around 1 TPa, close to experimental values. Our modeling yields a fracture tensile strain of approximately 30%, with a maximum tensile stress of approximately 300 GPa. Fracture of the CNT originates from formation of 5-7 Stone-Wales-like defects, leading to formation of micro-cracks. INTRODUCTION Carbon nanotubes (CNTs) constitute a prominent example of nanomaterials, with many potential applications that could take advantage of their unique mechanical, electrical and optical properties [1-6]. A fundamental understanding of the properties of individual CNTs, or assemblies of CNTs in bundles or nanopillars [7], or in conjunction with biological molecules such as DNA [8] may be critical to enable new technologies and to engineer CNT based devices. In particular, the mechanical properties of CNTs are important in many applications. This includes cases in which the primary role of CNTs is not related to their mechanical properties. Nevertheless, a thorough understanding of the mechanical properties is essential to design manufacturing processes or to ensure reliability during operation of devices. The mechanics of carbon nanotubes has been discussed in various articles published over the last decade, both from a continuum and atomistic perspective [9-15]. In a classical article by Yacobsen et al. (1996) [16], the behavior of single, free-standing single wall carbon nanotubes (SWNTs) under compressive loading was investigated using classical, molecular-dynamics (MD) with empirical potentials. The longest tube considered was 6 nm with a diameter of 1 nm. The authors developed a continuum shell model to describe the Figure 1: Initial geometry of the CNT. The plot shows two different views of the undeformed tube.
Figure 2: Stress versus strain plot for the (10,10) single wall CNT, simulation carried out with the ReaxFF reactive force field. The CNT fractures at a critical strain of about 30 %. We
observe an almost perfectly linear regime with a Young’s modulus of E ≈ 1 TPa for tensile strains less than 18%. The black line is a moving average. buckling modes of the CNTs. SWNTs under tensile and compressive loading were studied by Dereli and Ozdoga
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