The effect of Stone–Wales defect on the tensile behavior and fracture of single-walled carbon nanotubes

The effectiveness of carbon nanotubes as reinforcements in the next generation of composites is designated by their mechanical behavior as standalone units. One of the most commonly present topological defects, whose effect on the mechanical behavior of carbon nanotubes needs to be clarified, is the Stone–Wales (SW) defect. In this paper, the effect of SW defect on the tensile behavior and fracture of armchair, zigzag and chiral single-walled carbon nanotubes (SWCNTs) was studied using an atomistic-based progressive fracture model. The model uses the finite element method for analyzing the structure of SWCNTs and the modified Morse interatomic potential for describing the nonlinear force-field of the C–C bonds. In all cases examined, the SW defect serves as nucleation site for fracture. Its effect on the tensile behavior of the SWCNTs depends solely on nanotube chirality. In armchair SWCNTs, contrary to zigzag ones, a significant reduction in failure stress and failure strain was predicted; ranging from 18% to 25% and from 30% to 41%, respectively. In chiral SWCNTs, the effect of the defect is between those of the armchair and zigzag SWCNTs, depending on chiral angle. The stiffness of the nanotubes was not affected. The nanotube size was found to play a minimal role in the tensile behavior of SW-defected SWCNTs; only in cases of very small nanotube diameters, where the fraction of defect area to the nanotube area is high, was a larger decrease in the failure stress predicted.     

Molecular dynamics (MD) simulations of the dependence of C–C bond lengths and bond angles on the tensile strain in single-wall carbon nanotubes (SWCNT)

Molecular dynamics (MD) simulations of tensile pulling of carbon nanotubes (SWCNTs) (both armchair and zigzag configurations) were conducted using the Brenner potential to investigate the variation of the six carbon–carbon bond lengths and bond angles of the hexagons in single-walled carbon nanotubes (SWCNT) as a function of tensile strain. The correlations between stress–strain, bond lengths and bond angles with strain, and the variation of a parameter in the interaction potential, namely, D_min have been studied. Simulations at higher values of strain were also performed to obtain the values of breaking strain. A sharp change in the stress–strain behavior, C–C bond lengths, and bond angles with strain was observed for strains equals to 0.30 for the armchair and 0.18 for the zigzag SWCNTs. The dependence of bond stretching and breaking strain on the chirality of the nanotubes and the functional form of the empirical potential has been investigated. The results of our investigations suggest that the presence of attenuation functions in empirical potentials may cause problems, if bond distances or strains become larger than the onset point of these functions. The effect of the duration of relaxing/thermostating of the nanotube after every stretch on the value of the breaking strain has also been discussed.     

An Investigation into the Mechanical Behavior of Single-Walled Carbon Nanotubes under Uniaxial Tension Using Molecular Statics and Molecular Dynamics Simulations

This study performs a series of Molecular Dynamics (MD) and Molecular Statics (MS) simulations to investigate the mechanical properties of single-walled carbon nanotubes (SWCNTs) under a uniaxial tensile strain. The simulations focus specifically on the effects of the nanotube helicity, the nanotube diameter and the percentage of vacancy defects on the bond length, bond angle and tensile strength of zigzag and armchair SWCNTs. In this study, a good agreement is observed between the MD and MS simulation results for the stress-strain response of the SWCNTs in both the elastic and the plastic deformation regimes. The MS simulations reveal that in the plastic deformation regime, the tensile strength of the armchair and zigzag SWCNTs increases with an increasing wrapping angle. In addition, it is shown that the tensile strength reduces significantly at larger values of the nanotube diameter. Moreover, it is observed that the tensile strength of both SWCNTs reduces as the percentage of defects within the nanotube structure increases. Finally, it is found that the results obtained from the molecular statics method are relatively insensitive to instabilities in the atomic structure, particularly in the absence of thermal fluctuations, and are in good agreement with the predictions obtained from the molecular dynamics method.     

Mechanical behaviors of carbon nanotubes with randomly located vacancy defects

In this paper, (10, 0) zigzag nanotubes and (6, 6) armchair nanotubes are considered to investigate the effects of randomly distributed vacancy defects on mechanical behaviors of single-walled carbon nanotubes. A spatial Poisson point process is employed to randomly locate vacancy defects on nanotubes. Atomistic simulations indicate that the presence of vacancy defects result in reducing nanotube strength but improving nanotube bending stiffness. In addition, the studies of nanotube torsion indicate that vacancy defects prevent nanotubes from being utilized as torsion springs.     

A progressive fracture model for carbon nanotubes

An atomistic-based progressive fracture model for simulating the mechanical performance of carbon nanotubes by taking into account initial topological and vacancy defects is proposed. The concept of the model is based on the assumption that carbon nanotubes, when loaded, behave like space-frame structures. The finite element method is used to analyze the nanotube structure and the modified Morse interatomic potential to simulate the non-linear force field of the C–C bonds. The model has been applied to defected single-walled zigzag, armchair and chiral nanotubes subjected to axial tension. The defects considered were: 10% weakening of a single bond and one missing atom at the middle of the nanotube. The predicted fracture evolution, failure stresses and failure strains of the nanotubes correlate very well with molecular mechanics simulations from the literature.     

Consideration of critical axial properties of pristine and defected carbon nanotubes under compression

Carbon nanotubes are hexagonally configured carbon atoms in cylindrical structures. Exceptionally high mechanical strength, electrical conductivity, surface area, thermal stability and optical transparency of carbon nanotubes outperformed other known materials in numerous advanced applications. However, their mechanical behaviors under practical loading conditions remain to be demonstrated. This study investigates the critical axial properties of pristine and defected single- and multi-walled carbon nanotubes under axial compression. Molecular dynamics simulation method has been employed to consider the destructive effects of Stone-Wales and atom vacancy defects on mechanical properties of armchair and zigzag carbon nanotubes under compressive loading condition. Armchair carbon nanotube shows higher axial stability than zigzag type. Increase in wall number leads to less susceptibility of multi-walled carbon nanotubes to defects and higher stability of them under axial compression. Atom vacancy defect reveals higher destructive effect than Stone-Wales defect on mechanical properties of carbon nanotubes. Critical axial strain of single-walled carbon nanotube declines by 67% and 26% due to atom vacancy and Stone-Wales defects.     

Mechanical properties of carbon nanotube by molecular dynamics simulation

The mechanical properties of single-walled carbon nanotube (SWCNT) are computed and simulated by using molecular dynamics (MD) in this paper. From the MD simulation for an armchair SWCNT whose diameter is 1.2 nm and length is 4.7 nm, we get that its Young modulus is 3.62 TPa, and tensile strength is 9.6 GPa. It is shown that the Young modulus and tensile strength of armchair SWCNTs are 12 order higher than those of ordinary metal materials. Therefore we can draw a conclusion that carbon nanotubes (CNT) belong to a particular material with excellent mechanical properties.     

Nonlinear failure analysis of carbon nanotubes by using molecular-mechanics based models

Equivalent nonlinear fracture models for pristine and reconstructed one- and two-atom vacancy defected single wall carbon nanotubes are developed by using the molecular mechanics based models where the initial reconstructed nanotube models are obtained by using molecular dynamic simulations and nonlinear characteristic of the covalent bonds are obtained by using the modified Morse potential. As a result of analyses, it is concluded that fractures of all types of nanotubes are brittle, armchair nanotubes are stiffer than zigzag nanotubes and vacancy defects significantly affect the mechanical behavior of nanotubes. In brief, fracture stress and strain values of pristine armchair nanotubes are respectively 30% and 32% larger than those of pristine zigzag nanotubes, and predicted failure stress and strain values of vacancy defected nanotubes are respectively 27% and 52% smaller than those of pristine ones. It is shown that large deformation and nonlinear geometric effects are important on fracture behavior of nanotubes. Comparisons are made with the failure stress and strain results reported in literature that show good agreement with our results.     

Temperature sensing using individual single-walled carbon nanotubes

Molecular dynamics simulations and quantum transport theory are employed to study the temperature-dependent electrical properties of individual (12,0) zigzag and (5,5) armchair carbon nanotubes deposited on silicon substrates. The results demonstrate that the magnitude of the leakage current depends on the length of the nanotube. Furthermore, the leakage current is generated periodically along the length of the nanotube. Finally, the results indicate that given an appropriate value of the applied bias voltage, the induced current varies linearly with the temperature over specific temperature ranges. As a result, the temperature can be inversely derived from the measured current signal. Overall, the results show that the (12,0) zigzag and (5,5) armchair carbon nanotubes are suitable for temperature sensing applications over temperature ranges of 200-420?K and 300-440?K, respectively.     

Supramolecular discrimination of carbon nanotubes according to their helicity

Adsorption of specifically designed and geometrically constrained polyaromatic amphiphiles on single-walled carbon nanotubes (SWNTs) was found to be selective of the nanotube helicity angle. Starting from the same SWNT mixture, photoluminescence and resonant Raman spectroscopies show that a pentacenic-based amphiphile leads to the solubilization of armchair SWNTs and that a quaterrylene-based amphiphile leads to the solubilization of zigzag SWNTs. The results were predicted by the design of the two amphiphiles and are consistent with a supramolecular recognition of the nanotube graphene-type atomic structure by the aromatic part of the molecules through optimized pi-pi-stacking interactions.     

Computational Studies on Mechanical and Thermal Properties of Carbon Nanotube Based Nanostructures

The excellent set of properties of carbon nanotube and carbon nanotube-based nanostructures has been established by various studies. However the claimed property values and trends have not been unanimously agreed upon. Using state of the art molecular dynamics and ab initio methods, we have extensively studied the mechanical, thermal and structural properties of carbon nanotubes and carbon nanotube based nanostructures. Additionally this study aims to address the approaches used in various studies to assess the validity and influence of various definitions used for determining the physical properties as reported in earlier experiments and theoretical calculations. We have come up with equations, which quantitatively address the wide differences in trend and values of nanotube axial modulus available across the literature. Applying a novel bond rearrangement scheme, we have found similar values in twist modulus of zigzag and armchair nanotubes. This opposes the claim of difference that was shown to be valid only at finite limit in our study. We have shown that the contribution of van der Waals energy in a multi-wall nanotube is powerful enough to make it hexagonal in shape but negligible in affecting the axial modulus. These insights will also help in designing micromechanics model of materials made from carbon nanotube or nanotube like structures. In particular, we have calculated the mechanical properties (young modulus, bending modulus and twist modulus) of isolated and bundled nanotubes, single and multi-wall nanotubes and single and multi-wall carbon nanotube based tori. We also report studies on thermal variation of moduli and thermal expansion of nanotubes. The result obtained by first principles calculation based interatomic potential agrees well with the experimental results.     

Vibrational analysis of carbon nanotubes and graphene sheets using molecular structural mechanics approach

In this article, the vibrational properties of two kinds of single-layered graphene sheets and single-wall carbon nanotubes (SWCNT) are studied. The simulations are carried out for two types of zigzag carbon nanotubes (6,0), (12,0), armchair carbon nanotubes (4,4), (6,6) and zigzag and armchair graphene sheets with free-fixed and fixed–fixed end conditions.Fundamental frequency is determined by means of molecular structural mechanics approach. In this approach, carbon nanotubes (CNTs) and grapheme sheets are considered as space frames. By constructing equality between strain energies of each element in structural mechanics and potential energies of each bond, equivalent space frames can be achieved. Carbon atoms are considered as concentrated masses placed in beam joints (bond junctions).Results are presented as diagrams stating fundamental frequencies of nanotubes and graphene sheets with respect to aspect ratios. The results indicate that fundamental frequency decreases as aspect ratio increases. So it is preferred to use nanotubes and graphene sheets with lower aspect ratios for dynamic applications in order to prevent resonance and dynamic damage. Fundamental frequency of nanotubes is larger than that of graphene sheets. The results are in good agreement with results of previous researches.     

Kinetics of the oriented interaction of accelerated particles with carbon nanotubes of armchair and zigzag configurations

Kinetics of the channeling of accelerated particles in single-wall carbon nanotubes (CNTs) of the armchair and zigzag configurations has been theoretically studied, with special attention devoted to the oriented motion of positive ions. Based on first principles, the Fokker-Planck equation for the function of particle distribution with respect to transverse variables is constructed using the stochastic equations of particle motion inside nanotubes. Simple analytical formulas are obtained for the radial and axial distribution of moving particles, their distribution with respect to the transverse energy, and the length of particle dechanneling from armchair and zigzag CNTs.     

Single-walled MoTe(2) nanotubes

The structural, electronic, and mechanical properties of single-walled MoTe(2) nanotubes are investigated using density functional theory. All large-diameter MoTe(2) nanotubes are found to be narrow-gap semiconductors, whereas small-diameter nanotubes are found to be less stable compared to large-diameter nanotubes. Notably, the armchair MoTe(2) nanotubes exhibit an indirect band gap, whereas the zigzag nanotubes exhibit a direct band gap. The band gap decreases with decreasing diameter of the tube or if the tube is under compression or elongation in the axial direction. Young's modulus of MoTe(2) nanotubes is calculated and is found to be dependent on the diameter and chirality of the tubes. The armchair nanotubes are stiffer than the zigzag nanotubes with the same diameter. Compared to the homologous MoTe(2) nanotubes, the MoTe(2) nanotubes are softer due to less strain-energy cost in forming the nanotube structures.     

Effects of boron nitride impurities on the elastic properties of carbon nanotubes

The molecular dynamics method is used in this paper to investigate the effect of boron nitride (BN) impurities on the elastic properties of armchair (5, 5) (10, 10) and zigzag (9, 0) (18, 0) single-walled carbon nanotubes (SWCNTs). The results show the Young's moduli of armchair (5, 5) (10, 10) and zigzag (9, 0) (18, 0) SWCNTs with no impurities to be 948?GPa, 901?GPa and 804?GPa, 860?GPa, respectively. When the armchair SWCNTs are doped with BN, their Young's modulus decreases slightly. However, an increase in the doping ratio beyond a certain point does not cause any further reduction in the modulus, which continues to fluctuate at about 800?GPa and 760?GPa, respectively. The zigzag SWCNTs behave somewhat differently. When they are doped with BN, their Young's moduli drop quickly, and then rise as the doping ratio increases until it reaches 100% (i.e.?boron nitride nanotubes are formed), at which point the Young's moduli of the nanotubes are 780?GPa and 835?GPa, respectively, 97% that of the corresponding pure SWCNTs. The effect of a high ratio of BN on zigzag SWCNTs is thus negligible. The reasons for this phenomenon are analyzed according to the law of electron cloud coupling between two atoms, which comes from the local density approximation (LDA) and is based on density functional theory (DFT).     

Chemisorption of hydrogen molecules on carbon nanotubes: charging effect from first-principles calculations

We report a systematic investigation of the charging effect on hydrogen molecule chemisorption on (3, 3), (5, 5), (5, 0), and (8, 0) carbon nanotubes by first-principles calculations. The influence of injected charge on the chemisorption energy barriers is found to be sensitive to the nanotube diameter and chirality. The calculated results also indicate that electron injection is more effective in lowering the energy barrier for armchair carbon nanotubes while hole injection is more effective for zigzag nanotubes. The origin of these interesting trends and systematics can be understood by a close examination of the underlying electronic structure and the electron transfer between the hydrogen molecules and the nanotubes.     

Noncovalent functionalization of carbon nanotubes with porphyrins: meso-tetraphenylporphine and its transition metal complexes

Noncovalent functionalization of carbon nanotubes with meso-tetraphenylporphine (H2TPP) and its metal(II) complexes NiTPP and CoTPP was studied by means of different experimental techniques and theoretical calculations. As follows from the experimental adsorption curves, free H2TPP ligand exhibits the strongest adsorption of three porphyrins tested, followed by CoTPP and NiTPP. At the highest porphyrin concentrations studied, the adsorption at multi-walled carbon nanotubes was about 2% (by weight) for H2TPP, 1% for CoTPP, and 0.5% for NiTPP. Transmission electron microscopy observations revealed carbon nanotubes with a variable degree of surface coverage with porphyrin molecules. According to scanning electron microscopy, the nanotubes glue together rather than debundle; apparently, a large porphyrin excess resulting in polymolecular adsorption is essential for exfoliation/debundling of the nanotube ropes. The nanotube/porphyrins hybrids were studied by infrared and Raman spectroscopy, as well as by scanning tunneling microscopy. Electronic structure calculations were performed at the B3LYP/LANL2MB theoretical level with the unsubstituted porphine (H2P) and its Co(II) complex, on one hand, and open-end armchair (5,5) (ANT) and zigzag (8,0) (ZNT) SWNT models, on the other hand. The interaction of H2P with ANT was found to be by 3.9 kcal mol(-1) stronger than that of CoP. At the same time, CoP+ZNT complex is more stable by 42.7 kcal mol(-1) as compared to H2P+ZNT According to these calculated results, the free porphyrins interact less selectively with zigzag and armchair (i.e., semiconducting and metallic) nanotubes, whereas the difference becomes very large for the metal porphyrins. HOMO-LUMO structure, electrostatic potential and spin density distribution for the paramagnetic cobalt(II) complexes were analyzed.     

Density functional calculations of response of single-walled armchair carbon nanotubes to axial tension

The response of single-walled armchair carbon nanotubes (SWACNTs) to axial tension was studied using density functional calculations. A new response causing an abrupt change in nanotube structure at specific strains was detected. Atom rearrangement results in a lower energy than expected. The geometry of armchair nanotube plays an important role in the observed response, with the effect of curvature being important. There is a meaningful relationship between rearrangement strain and nanotube diameter. Rearrangement can be explained using the Poisson effect, which increases with the lateral displacement and is inversely proportional to nanotube index number.     

Energetic trends of single-walled carbon nanotube ab initio calculations

Hartree–Fock (HF) calculations for a variety of single-walled carbon nanotube (SWCNT) systems indicate linear relationships between electronic energies and changes in length and circumference for both armchair and zigzag type nanotubes. A simple protocol to predict energies for large SWCNT (C atoms >500) is developed through a set of structural parameters and AM1 optimized geometries from small SWCNTs. The energetic trends shown by the calculations are used to support the theory of SWCNT nucleation from a preformed carbon, or graphene with six 5-member rings, cap.     

Investigating the effect of chirality on structural parameters of chiral single-walled carbon nanotubes by molecular dynamics simulation

The structural parameters of thin single-walled carbon nanotubes (SWCNTs) vs. chiral angle were investigated using molecular dynamics (MD) simulation. A comparison was made between nanotube radius obtained from MD simulation and that obtained from ideal rolling graphene model. Brenner empirical bond order potential was used to describe the interaction between carbon atoms. SWCNTs (n, m) with n + m = 6, 8, 10 and 12 were considered. It was observed that chiral nanotubes have three unequal bond lengths and three unequal bond angles, while for armchair and zigzag SWCNTs there are two unequal parameters.