Strength Of Single-walled Carbon Nanotubes Research Articles

Intrinsic strength and failure behaviors of ultra-small single-walled carbon nanotubes

The intrinsic mechanical strength of single-walled carbon nanotubes (SWNTs) within the diameter range of 0.3–0.8nm has been studied based on ab initio density functional theory calculations. In contrast to predicting “smaller is stronger and more elastic” in nanomaterials, the strength of the SWNTs is significantly reduced when decreasing the tube diameter. The results obtained show that the Young’s modulus E significantly reduced in the ultra-small SWNTs with the diameter less than 0.4nm originates from their very large curvature effect, while it is a constant of about 1.0TPa, and independent of the diameter and chiral index for the large tube. We find that the Poisson’s ratio, ideal strength and ideal strain are dependent on the diameter and chiral index. Furthermore, the relations between E and ideal strength indicate that Griffith’s estimate of brittle fracture could break down in the smallest (2, 2) nanotube, with the breaking strength of 15% of E. Our results provide important insights into intrinsic mechanical behavior of ultra-small SWNTs under their curvature effect.

Effects of Pore-Size Range and Composition of Polysaccharide Gels on Flow Behaviors and Selective Sorting of Single-Walled Carbon Nanotubes

We used gel-column chromatography to show the effects of the pore-size range and chemical composition of porous polysaccharide gels on the flow characteristics and metal/semiconductor (m/s) separation of dispersed single-walled carbon nanotubes (SWCNTs). Comparative studies of the flow behaviors of dispersed SWCNTs in a series of Sephacryl gels with different pore sizes showed that a small pore-size range increased the interaction strength of SWCNTs with gels, leading to rapid flow of thicker metallic (m-)SWCNTs through gel beads, and the selective entrapment of thinner semiconducting (s-)SWCNTs. We also found that the effect of the gel composition was more important than that of the gel porosity on the sorting of SWCNTs. When the amine group in the dextran-based Sephacryl gel was replaced by agarose, e.g., Superdex 200 or Sepharose 2B gel, the interaction with the dispersed SWCNTs was enhanced, resulting in slowing down of both the m- and s- SWCNTs throughout the gel, and obvious deterioration in the selectivity for, and purity of, the s-SWCNTs. In contrast, Sephadex G100 gel, which has one dextran group functionalized by hydrophobic epoxypropane, yielded very weak interactions with SWCNTs, leading to direct drainage of both types of SWCNT, despite its fine pore size, similar to that of Sephacryl S100. We therefore propose that the gel pore size and composition exerted a synergistic effect in governing the m/s sorting of SWCNTs with high selectivity, purity, and efficiency.

An approach to multi-body interactions in a continuum-atomistic context: Application to analysis of tension instability in carbon nanotubes

The tensile strength of single-walled carbon nanotubes (CNT) is examined using a continuum-atomistic (CA) approach. The strength is identified with the onset of the CNT instability in tension. The focus of this study is on the effects of multi-body atomic interactions. Multiscale simulations of nanostructures usually make use of two- and/or three-body interatomic potentials. The three-body potentials describe the changes of angles between the adjacent bonds – bond bending. We propose an alternative and simple way to approximately account for the multi-body interactions. We preserve the pair structure of the potentials and consider the multi-body interaction by splitting the changing bond length into two terms. The first term corresponds to the self-similar deformation of the lattice, which does not lead to bond bending. The second term corresponds to the distortional deformation of the lattice, which does lead to bond bending. Such a split of the bond length is accomplished by means of the spherical–deviatoric decomposition of the Green strain tensor. After the split, the continuum-atomistic potential can be written as a function of two bond lengths corresponding to the bond stretching and bending independently. We apply an example exponential continuum-atomistic potential with the split bond length to the study of tension instability of the armchair and zigzag CNTs. The results of the study are compared with those obtained by Zhang et al. (2004. J. Mech. Phys. Solids 52, 977–998) who studied tension instability of carbon nanotubes by using the Tersoff–Brenner three-body potential, and with recent experimental results on the tensile failure of single walled carbon nanotubes.

Prediction of stiffness and strength of single-walled carbon nanotubes by molecular-mechanics based finite element approach

Molecular-mechanics based finite element approach was used to predict the tensile stiffness and strength of single-walled carbon nanotubes. Different types of nanotubes, such as Arm-Chair, Zig-Zag, and chiral type, were discussed in detail. Nanotube stiffness was predicted to be independent of both the nanotube diameter and the nanotube helicity, but Poisson ratio was dependent of the nanotube diameter. In addition to the stiffness, nanotube strength was also analyzed by molecular-mechanics based finite element approach. Modified Morse potential function was selected to model the breakage of CC chemical bond with the separation energy of 7.7 eV. Nanotube strength was predicted at 77–101 GPa with the fracture strain around 0.3. The nanotube strength was found to be moderately dependent of the nanotube helicity, but independent of the nanotube diameter.

Tensile strength of carbon nanotubes under realistic temperature and strain rate

Strain rate and temperature dependence of the tensile strength of single-walled carbon nanotubes has been investigated with molecular dynamics simulations. The tensile failure or yield strain is found to be strongly dependent on the temperature and strain rate. A transition state theory based predictive model is developed for the tensile failure of nanotubes. Based on the parameters fitted from high-strain rate and temperature dependent molecular dynamics simulations, the model predicts that a defect free $\mu m$ long single-wall nanotub at 300K, stretched with a strain rate of $1%/hour$, fails at about $9 \pm 1%$ tensile strain. This is in good agreement with recent experimental findings.

Tensile strength of single-walled carbon nanotubes with defects under hydrostatic pressure

Elastic properties and tensile strength of single-walled carbon nanotubes, which have topological and coordinated defects, under hydrostatic pressure have been studied by using molecular-dynamics simulations and ab initio electronic structure calculations. The Young's moduli in both the axial direction and the radial direction are determined under different levels of hydrostatic pressure. It is found that the stiffness of the nanotubes changes with the strain in a graded manner. When the strain is larger than 0.10, the tubes become softened. The strength at failure of the tubes is lowered by the existence of the defects.

Tensile strength of single-walled carbon nanotubes directly measured from their macroscopic ropes

20 mm long ropes consisting of soundly aligned single-walled carbon nanotube (SWNT) ropes, synthesized by the catalytic decomposition of hydrocarbons, were employed for direct tensile strength measurements. The average tensile strength of SWNT rope composites is as high as 3.6±0.4 GPa, similar to that of carbon fibers. The tensile strength of SWNT bundles was extrapolated from the strength of the composites to be 2.3±0.2 to 14.2±1.4 GPa after simply taking into account the volume fraction of SWNT bundles in the minicomposite, and the tensile strength of single SWNTs was estimated to be as high as 22.2±2.2 GPa. The excellent mechanical properties of SWNTs will make them an ideal reinforcement agent for high performance composite materials.