Deformation Of Single-walled Carbon Nanotubes Research Articles

Axial-Strain-Induced Torsion in Single-Walled Carbon Nanotubes

Using classical molecular dynamics and empirical potentials, we show that the axial deformation of single-walled carbon nanotubes is coupled to their torsion. The axial-strain-induced torsion is limited to chiral nanotubes-graphite sheets rolled around an axis that breaks its symmetry. Small strain behavior is consistent with chirality and curvature-induced elastic anisotropy (CCIEA)-carbon nanotube rotation is equal and opposite in tension and compression, and decreases with curvature and chirality. The large-strain compressive response is remarkably different. The coupling progressively decreases, in contrast to the tensile case, and changes its sign at a critical compressive strain. Thereafter, it untwists with increasing axial strain and then rotates in the opposite direction, i.e., the same sense as under tension. This suggests that the response is now dictated by a combination of nonlinear elasticity and CCIEA.

Modifications to the Cauchy–Born rule: Applications in the deformation of single-walled carbon nanotubes

This paper presents a study of the Cauchy–Born (CB) rule as applied to the deformation analysis of single-walled carbon nanotubes (SWNTs) that are modeled as 2-dimensional manifolds. The C–C bond vectors in the SWNT are assumed to deform according to the local deformation gradient as per the CB rule or a modified version thereof. Aspects of the CB rule related to spatial inhomogeneity of the deformation gradient at the atomic scale are investigated in the context of a specific class of extension–twist deformation problems. Analytic expressions are derived for the deformed bond lengths using the standard CB rule as well as modified versions of the standard CB rule. Since the deformation map is conveniently prescribed in this work, it is possible to compare the performance of these deformation rules with the exact solution (i.e. the exact analytic expression for the deformed bond vectors) given directly by the deformation map. This approach provides insights into the CB rule and its possible modifications for use in more complicated deformations where an explicit deformation map is not available. Specifically, it is concluded that in the case of inhomogeneous deformations at the atomic scale for which the CB rule is only approximate (as demonstrated in Section 1 of this paper), the mean value theorem in calculus can be used as a guide to modify the CB rule and construct a more rigorous and accurate atomistic–continuum connection. The deformed bond lengths are used to formulate an enriched continuum hyperelastic strain energy density function based on interatomic potentials (the multi-body Tersoff–Brenner [Tersoff, J., 1988. New empirical approach for the structure and energy of covalent systems. Phys. Rev. B 37, 6991–7000; Brenner, D.W., 1990. Empirical potential for hydrocarbons for use in simulating the chemical vapor deposition of diamond films. Phys. Rev. B 42, 9458–9471] empirical interatomic potential for carbon-carbon bonds is used in this work). The deformation map (and hence the deformation gradient, the bond vectors and the continuum strain energy density) contains certain parameters, some of which are imposed and others determined as a result of energy minimization in the standard variational formulation. Numerical results for kinematic coupling and binding energy per atom are presented in the case of imposed extension and twist deformations on representative chiral, zig-zag and armchair nanotubes using the CB rule and its modifications. These results are compared with the exact solution based on the deformation map which serves as a basis for evaluating the efficacy of these deformation rules. The ideas presented in this paper can also be directly extended to other lattices.

Evaluation of Nonuniform Strain in Carbon Nanotube with Bend Junction

Carbon nanotubes (CNTs) have been attracting attention because of their prominent mechanical and electronic properties. In this study, we investigate the deformation of single-walled carbon nanotubes (SWCNTs) with a bend junction using molecular dynamics in order to analyze strain concentration due to the tube shape (macroscopic effect) and the membered ring shape (microscopic effect). At first, we propose a method for evaluating the local strain at each memberded ring. Then, we analyze the strain concentration at the bend junction due to the both of macroscopic and microscopic effects. The strain concentration caused by the microscopic effect is separated by a rough analysis ; and it is about 1.5 times higher than that caused by the macroscopic effect.

Coupling of Extension and Twist in Single-Walled Carbon Nanotubes

This paper presents a study of the deformation behavior of single-walled carbon nanotubes (SWNTs) subjected to extension and twist. The interatomic force description is provided by the Tersoff-Brenner potential for carbon. The rolling of a flat graphene sheet into a SWNT is first simulated by minimizing the energy per atom, the end result being the configuration of an undeformed SWNT. The Cauchy-Born rule is then used to connect the atomistic and continuum descriptions of the deformation of SWNTs, and leads to a multilength scale mechanics framework for simulating deformation of SWNTs under applied loads. Coupled extension and twist of SWNTs is considered next. As an alternative to the Cauchy-Born rule for coupled extension-twist problems, a direct map is formulated. Analytic expressions are derived for the deformed bond lengths using the Cauchy-Born rule and the direct map for this class of deformations. Numerical results are presented for kinematic coupling, for imposed extension and imposed twist problems, using the Cauchy-Born rule as well as the direct map, for representative chiral, armchair and zig-zag SWNTs. Results from both these approaches are carefully compared.

Simulation of the elastic response and the buckling modes of single-walled carbon nanotubes

The mechanical behavior of carbon nanotube (CNT) is one of the basic problems on the nanotube composite and nano machinery. Molecular dynamics is an effective way of investigating the behavior of nano structures. The compression deformation of single-walled carbon nanotubes (SWCNTs) is simulated, using the Tersoff–Brenner potential to describe the interactions of atoms in CNT. From the MD simulation for some SWCNTs whose diameters range from 0.5 nm to 1.7 nm and length ranges from 7 nm to 19 nm, respectively, we get the Young’s modulus from 1.25 TPa to 1.48 TPa. The Young’s modulus of CNT decreases as the radius of CNT increases. The Young’s modulus of zigzag CNT is higher than that of armchair CNT. The results also show that there are two different buckling modes for SWCNTs. The difference between the buckling behavior in macroscopic scale and that in nano scale is studied.

Effects of temperature and vacancy defects on tensile deformation of single-walled carbon nanotubes

This study adopts the Tersoff–Brenner interaction potential function in a series of molecular dynamic (MD) simulations which investigate the mechanical properties under tensile loading of (10,0) zigzag, (8,3) chiral and (6,6) armchair single-walled carbon nanotubes (SWCNTs) of similar radii. The Young's modulus values of the (10,0), (8,3) and (6,6) nanotubes are determined to be approximately 0.92, 0.95, and 1.03 TPa, respectively. Of these nanotubes, the results reveal that the (6,6) nanotube possesses the best tensile strength and toughness properties under tension. Although it is noted that under small tensions, the mechanical properties such as Young's modulus are essentially insensitive to helicity, under larger plastic deformations, they may be influenced by helicity effects. Finally, the simulations demonstrate that the values of the majority of the considered mechanical properties decrease with increasing temperature and increasing vacancy percentage.

Elastic properties of single-walled carbon nanotubes in transverse directions

The elastic deformation of single-walled carbon nanotubes under hydrostatic pressure has been modeled using the molecular structural mechanics method. The computational results indicate that the radial direction elastic modulus deceases with the increase in tube diameter. The circumferential direction elastic modulus is insensitive to tube diameter, and roughly equal to the axial direction modulus. The hydrostatic pressure for tube buckling also deceases with increasing tube diameter and is in the range of 1.5--11 GPa for single-walled carbon nanotubes with diameters of 0.6--2.0 nm; this prediction is in good agreement with existing experimental results. The tube chirality has minor effect on the radial modulus and buckling strength.

A structural mechanics approach for the analysis of carbon nanotubes

This paper presents a structural mechanics approach to modeling the deformation of carbon nanotubes. Fundamental to the proposed concept is the notion that a carbon nanotube is a geometrical frame-like structure and the primary bonds between two nearest-neighboring atoms act like load-bearing beam members, whereas an individual atom acts as the joint of the related load-bearing beam members. By establishing a linkage between structural mechanics and molecular mechanics, the sectional property parameters of these beam members are obtained. The accuracy and stability of the present method is verified by its application to graphite. Computations of the elastic deformation of single-walled carbon nanotubes reveal that the Young’s moduli of carbon nanotubes vary with the tube diameter and are affected by their helicity. With increasing tube diameter, the Young’s moduli of both armchair and zigzag carbon nanotubes increase monotonically and approach the Young’s modulus of graphite. These findings are in good agreement with the existing theoretical and experimental results.

Structural deformation of single-walled carbon nanotubes and fullerene encapsulation due to magnetized-plasma ion irradiation

Positive and negative bias-voltages are applied to single-walled carbon nanotubes (SWNTs) in magnetized alkali–metal and alkali–fullerene plasmas. When accelerated ions are irradiated to the SWNTs through plasma sheaths, drastic structural deformations such as deflection and tube cutting of the SWNTs are observed to take place. Furthermore, this phenomenon is found to be accompanied by the fullerene encapsulation inside the SWNTs in the case of the positive-bias application in the alkali–fullerene plasma, giving the possibility that various kinds of atoms and molecules can effectively be intercalated by our plasma method.