Bulk and lattice properties for rigid carbon nanotubes materials (original) (raw)
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Computers & Structures, 2013
A new general formulation for the mechanical behavior of Single-Walled Carbon Nanotubes is presented. Carbon atoms are located at the nodes of an hexagonal honeycomb lattice wrapped into a cylinder. They are linked by covalent C − C bonds represented by a truss or spring element, and the three-body interaction among two neighboring covalent bonds is reproduced by a rotational spring. The main advantage of our approach is to allow general load conditions (and any chirality) with no need of specific formulation for each load case, in contrast with previous works [26], [27], [31]. Four load configurations are adopted: tension, compression, bending and torsion of cantivelered SWCNTs. Calculations with our own codes for both AMBER and Morse potential functions have been carried out, aimed to compare their final results. Initial positions of the atoms (nodes) into nanotube cylindrical geometry has been reproduced in great detail by means of a conformal mapping from the planar graphene sheet. Therefore, the effect of initial SWCNTs curvature has been introduced explicitly through a system of initial stresses (prestressed state) which contribute to maintain their circular cross-section. Numerical results and deformed shapes for nanotubes with several diameters and chiralities under each load case are used to obtain their mechanical parameters with the only objective of checking the present formulation with previous works [28], [30], [20], [24]. Also, the significance of the atomistic discrete simulations at the nano-scale size against other continuum models is underlined.
Structural stability and energetics of single-walled carbon nanotubes under uniaxial strain
Physical Review B, 2003
A (10ϫ10) single-walled carbon nanotube consisting of 400 atoms with 20 layers is simulated under tensile loading using our developed O(N) parallel tight-binding molecular-dynamics algorithms. It is observed that the simulated carbon nanotube is able to carry the strain up to 122% of the relaxed tube length in elongation and up to 93% for compression. Young's modulus, tensile strength, and the Poisson ratio are calculated and the values found are 0.311 TPa, 4.92 GPa, and 0.287, respectively. The stress-strain curve is obtained. The elastic limit is observed at a strain rate of 0.09 while the breaking point is at 0.23. The frequency of vibration for the pristine (10ϫ10) carbon nanotube in the radial direction is 4.71ϫ10 3 GHz and it is sensitive to the strain rate.
Molecular Dynamics Simulation of Carbon Nanotubes
2013
Elastic properties of single walled carbon nanotubes (SWCNTs) have been determined using molecular dynamics (MD) simulation. Mechanical properties of three types of SWCNTs viz., armchair, zigzag and chiral nanotubes have been evaluated. From computational results, it can be concluded that the Young"s moduli of SWCNTs decrease with increase in radius of SWCNT and increase with increase in CNT volume fractions (V f ) and aspect ratios (l/d).
Mechanics of Carbon Nanotubes1
CRC Press eBooks, 2007
Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures-including high strength, high stiffness, low density and structural perfection-could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young's modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references.
Elastic moduli of multi-walled carbon nanotubes and the effect of van der Waals forces
Composites Science and Technology, 2003
This paper reports a study of the elastic behavior of multi-walled carbon nanotubes (MWCNTs). The nested individual layers of an MWCNT are treated as single-walled frame-like structures and simulated by the molecular structural mechanics method. The interlayer van der Waals forces are represented by Lennard-Jones potential and simulated by a nonlinear truss rod model. The computational results show that the Young's moduli and shear moduli of MWCNTs are in the ranges of 1.05 AE 0.05 and 0.40 AE 0.05 TPa, respectively. Results indicate that the tube diameter, tube chirality and number of tube layers have some noticeable effects on the elastic properties of MWCNTs. Furthermore, it has been demonstrated that the inner layers of an MWCNT can be effectively deformed only through the direct application of tensile or shear forces, not through van der Waals interactions. #
Applied Mechanics Reviews, 2002
Soon after the discovery of carbon nanotubes, it was realized that the theoretically predicted mechanical properties of these interesting structures-including high strength, high stiffness, low density and structural perfection-could make them ideal for a wealth of technological applications. The experimental verification, and in some cases refutation, of these predictions, along with a number of computer simulation methods applied to their modeling, has led over the past decade to an improved but by no means complete understanding of the mechanics of carbon nanotubes. We review the theoretical predictions and discuss the experimental techniques that are most often used for the challenging tasks of visualizing and manipulating these tiny structures. We also outline the computational approaches that have been taken, including ab initio quantum mechanical simulations, classical molecular dynamics, and continuum models. The development of multiscale and multiphysics models and simulation tools naturally arises as a result of the link between basic scientific research and engineering application; while this issue is still under intensive study, we present here some of the approaches to this topic. Our concentration throughout is on the exploration of mechanical properties such as Young's modulus, bending stiffness, buckling criteria, and tensile and compressive strengths. Finally, we discuss several examples of exciting applications that take advantage of these properties, including nanoropes, filled nanotubes, nanoelectromechanical systems, nanosensors, and nanotube-reinforced polymers. This review article cites 349 references.
Elastic properties of single-wall nanotubes
Applied Physics A-materials Science & Processing, 1999
, BC2N, and C3N4. These studies have been carried out using a total-energy, non-orthogonal, tight-binding parametrisation which is shown to provide results in good agreement both with calculations using higher levels of theory and the available experimental data. Our results predict that of all types of nanotubes considered, carbon nanotubes have the highest Young’s modulus. We have considered tubes of different diameters, ranging from 0.5 to 2 nm, and find that in the limit of large diameters the mechanical properties of nanotubes approach those of the corresponding flat graphene-like sheets.
Mechanical properties of single-walled carbon nanotube bundles as bulk materials
Journal of the Mechanics and Physics of Solids, 2005
Single-walled carbon nanotubes (SWNTs) in crystalline bundles may exhibit a transition in which the cross-sections of tubes turn from perfectly circular to hexagonal, depending upon the tube diameter and externally applied pressure, and this structural instability leads to an abrupt change in the bulk elastic properties of SWNT bundles. This paper presents a hybrid atom/continuum model to study the bulk elastic properties of SWNT bundles, and the predicted characteristics of this structural instability agree well with the experimental observations available in the literature. Linearized bulk elastic properties of SWNT bundles with respect to a stable configuration are transversely isotropic and hence can be characterized by five independent elastic moduli. A complete set of these five moduli is predicted for the first time. It is found that the deformability of tube cross-sections play a dominant role in characterizing the transverse moduli. r
Energetics, structure, mechanical and vibrational properties of single-walled carbon nanotubes
Nanotechnology, 1998
In this paper, we present extensive molecular mechanics and molecular dynamics studies on the energy, structure, mechanical and vibrational properties of single-wall carbon nanotubes. In our study we employed an accurate interaction potential derived from quantum mechanics. We explored the stability domains of circular and collapsed cross section structures of armchair (n, n), zigzag (n, 0), and chiral (2n, n) isolated single-walled carbon nanotubes (SWNTs) up to a circular cross section radius of 170Å. We have found three different stability regions based on circular cross section radius. Below 10Å radius only the circular cross section tubules are stable. Between 10 and 30Å both circular and collapsed forms are possible, however, the circular cross section SWNTs are energetically favorable. Beyond 30Å (crossover radius) the collapsed form becomes favorable for all three types of SWNTs. We report the behavior of the SWNTs with radii close to the crossover radius ((45, 45), (80, 0), (70, 35)) under uniaxial compressive and tensile loads. Using classical thin-plane approximation and variation of strain energy as a function of curvature, we calculated the bending modulus of the SWNTs. The calculated bending moduli are κ (n,n) = 963.44 GPa, κ (n,0) = 911.64 GPa, and κ (2n,n) = 935.48 GPa. We also calculated the interlayer spacing between the opposite sides of the tubes and found d (n,n) = 3.38Å, d (2n,n) = 3.39Å, and d (n,0) = 3.41Å. Using an enthalpy optimization method, we have determined the crystal structure and Young's modulus of (10,10) armchair, (17, 0) zigzag and (12, 6) chiral forms (which have similar diameter as (10,10)). They all pack in a triangular pattern in two dimensions. Calculated lattice parameters are a (10,10) = 16.78Å, a (17,0) = 16.52Å and a (12,6) = 16.52Å. Using the second derivatives of potential we calculated Young's modulus along the tube axis and found Y (10,10) = 640.30 GPa, Y (17,0) = 648.43 GPa, and Y (12, = 673.94 GPa. Using the optimized structures of (10, 10), (12, 6) and (17, 0), we determined the vibrational modes and frequencies.
Carbon nanotubes have caught tremendous attention of the researchers during the last decade due to their excellent mechanical, electrical, optical and thermal properties. The exploitation of these fibers as reinforcing agents in making strong fiber composites has been a primary research topic in the recent investigations on composite materials. Although the theoretical results are rather optimistic, the goal of achieving high strength of the carbon nanotube composites is still not satisfactorily realized. We report here a comparative study of the mechanical properties of single-walled, multi-walled and bundle of single-walled carbon nanotubes. Their mechanical behavior is investigated by molecular dynamics simulation, considering Brenner’s second generation reactive empirical bond order interatomic potential between the carbon atoms making a tube. For a long range interaction, we have defined a weak van der Waals force which acts between different layers of a multi-walled tube or between different tubes of a bundle. Samples of three isolated armchair single-wall carbon nanotubes of different diameters, a multi-wall armchair carbon nanotube and finally a bundle of three armchair single-walled nanotubes of same diameter are taken. Their fracture pattern and buckling behavior are modeled and compared. Significant changes are observed in the mechanical properties of the samples of different types of carbon nanotubes which arise due to the interaction between the shells of a multi-walled tube or the tubes in a bundle.