Mechanical characterization of single-walled carbon nanotubes: Numerical simulation study

The mechanical behaviour of non-chiral and chiral single-walled carbon nanotubes under tensile and bending loading conditions is investigated. For this purpose, three-dimensional finite element modelling is used in order to evaluate the tensile and bending rigidities and, subsequently, the Young's moduli. It is shown that the evolution of rigidity, tensile and bending, as a function of diameter can be described by a unique function for non-chiral and chiral single-walled nanotubes, i.e. regardless of the index or angles of chirality. A comprehensive study of the influence of the nanotube wall thickness and diameter on the Young's modulus values is also carried out. It is established that the evolution of the Young's modulus as a function of the inverse of the wall thickness follows a quasi-linear trend for nanotubes with diameters larger than 1.085 nm. The current numerical simulation results are compared with data reported in the literature. This work provides a benchmark in relation to ascertaining the mechanical properties of chiral and non-chiral single-walled carbon nanotubes by nanoscale continuum models.     

Highly selective dispersion of single-walled carbon nanotubes using aromatic polymers

Solubilizing and purifying carbon nanotubes remains one of the foremost technological hurdles in their investigation and application. We report a dramatic improvement in the preparation of single-walled carbon nanotube solutions based on the ability of specific aromatic polymers to efficiently disperse certain nanotube species with a high degree of selectivity. Evidence of this is provided by optical absorbance and photoluminescence excitation spectra, which show suspensions corresponding to up to approximately 60% relative concentration of a single species of isolated nanotubes with fluorescence quantum yields of up to 1.5%. Different polymers show the ability to discriminate between nanotube species in terms of either diameter or chiral angle. Modelling suggests that rigid-backbone polymers form ordered molecular structures surrounding the nanotubes with n-fold symmetry determined by the tube diameter.     

Atomic layer deposition on suspended single-walled carbon nanotubes via gas-phase noncovalent functionalization

Alternating exposures of nitrogen dioxide gas and trimethylaluminum vapor are shown to functionalize the surfaces of single-walled carbon nanotubes with a self-limited monolayer. Functionalized nanotube surfaces are susceptible to atomic layer deposition of continuous, radially isotropic material. This allows for the creation of coaxial nanotube structures of multiple materials with precisely controlled diameters. Functionalization involves only weak physical bonding, avoiding covalent modification, which should preserve the unique optical, electrical, and mechanical properties of the nanotubes.     

Static and dynamic properties of single-walled boron nitride nanotubes

This paper reports the study of the static and dynamic properties of single-walled boron nitride nanotubes by using the molecular structural mechanics approach. The stiffness parameters of the boron-nitride bond are based on the DREIDING force field. The effects of tube diameter and chirality are investigated. The computational results show that the Young's modulus and the shear modulus of boron nitride nanotubes increase monotonically with nanotube diameter and reach up to 0.9 TPa and 0.5 TPa, respectively, at large tube diameter. The nanotube chirality has only slight effects on the moduli only when tube diameters are small. The fundamental frequencies of boron nitride nanotubes are found to be dependent not only on the nanotube aspect ratio but also on the tube diameter.     

Self-assembly of single-walled carbon nanotubes into multiwalled carbon nanotubes in water: molecular dynamics simulations

We report discoveries from a series of molecular dynamics simulations that single-walled carbon nanotubes, with different diameters, lengths, and chiralities, can coaxially self-assemble into multiwalled carbon nanotubes in water via spontaneous insertion of smaller tubes into larger ones. The assembly process is tube-size-dependent, and the driving force is primarily the intertube van der Waals interactions. The simulations also suggest that a multiwalled carbon nanotube may be separated into single-walled carbon nanotubes under appropriate solvent conditions. This study suggests possible bottom-up self-assembly routes for the fabrication of novel nanodevices and systems.     

Non-adiabatic phonon dispersion of metallic single-walled carbon nanotubes

Non-adiabatic effects can considerably modify the phonon dispersion of low-dimensional metallic systems. Here, these effects are studied for the case of metallic single-walled carbon nanotubes using a perturbative approach within a density-functional-based non-orthogonal tight-binding model. The adiabatic phonon dispersion was found to have logarithmic Kohn anomalies at the Brillouin zone center and at two mirror points inside the zone. The obtained dynamic corrections to the adiabatic phonon dispersion essentially modify and shift the Kohn anomalies as exemplified in the case of nanotube (8, 5). Large corrections have the longitudinal optical phonon, which gives rise to the so-called G- band in the Raman spectra, and the carbon hexagon breathing phonon. The results obtained for the G- band for all nanotubes in the diameter range from 0.8 to 3.0 nm can be used for assignment of the high-frequency features in the Raman spectra of nanotube samples.     

Elastic Vibration Behaviors Oof Carbon Nanotubes Based on Micropolar Mechanics

The concept of the micropolar theory is employed to investigate vibration behaviors of carbon nanotubes. The constitutive relation has been deduced from the two-dimensional analysis of the microstructure of the carbon nanotube. Van der Waals interactions are simulated by a weak spring model. Hamilton's principle is employed to obtain dynamics equations of the multi-walled carbon nanotube. Numerical examples for both single-walled and double-walled carbon nanotubes are presented and the significant difference in vibration behaviors between them has been distinguished. Numerical results show that fundamental frequencies for the cantilever single-walled carbon nanotube decreases with increase of the aspect ratio of them, and the fundamental frequencies of the double-walled carbon nanotube are lower than those of the single-walled carbon nanotube with the same inner diameter and length. The first four natural frequencies for the double-walled carbon are coaxial.     

The controlled fabrication and geometry tunable optics of gold nanotube arrays

Arrays of vertically aligned gold nanotubes are fabricated over several square centimetres which display a geometry tunable plasmonic extinction peak at visible wavelengths and at normal incidence. The fabrication method gives control over nanotube dimensions with inner core diameters of 15-30 nm, wall thicknesses of 5-15 nm and nanotube lengths of up to 300 nm. It is possible to tune the position of the extinction peak through the wavelength range 600-900 nm by varying the inner core diameter and wall thickness. The experimental data are in agreement with numerical modelling of the optical properties which further reveal highly localized and enhanced electric fields around the nanotubes. The tunable nature of the optical response exhibited by such structures could be important for various label-free sensing applications based on both refractive index sensing and surface-enhanced Raman scattering.     

Optically active single-walled carbon nanotubes

The optical, electrical and mechanical properties of single-walled carbon nanotubes (SWNTs) are largely determined by their structures, and bulk availability of uniform materials is vital for extending their technological applications. Since they were first prepared, much effort has been directed toward selective synthesis and separation of SWNTs with specific structures. As-prepared samples of chiral SWNTs contain equal amounts of left- and right-handed helical structures, but little attention has been paid to the separation of these non-superimposable mirror image forms, known as optical isomers. Here, we show that optically active SWNT samples can be obtained by preferentially extracting either right- or left-handed SWNTs from a commercial sample. Chiral 'gable-type' diporphyrin molecules bind with different affinities to the left- and right-handed helical nanotube isomers to form complexes with unequal stabilities that can be readily separated. Significantly, the diporphyrins can be liberated from the complexes afterwards, to provide optically enriched SWNTs.     

Single-walled carbon nanotubes as excitonic optical wires

Although metallic nanostructures are useful for nanoscale optics, all of their key optical properties are determined by their geometry. This makes it difficult to adjust these properties independently, and can restrict applications. Here we use the absolute intensity of Rayleigh scattering to show that single-walled carbon nanotubes can form ideal optical wires. The spatial distribution of the radiation scattered by the nanotubes is determined by their shape, but the intensity and spectrum of the scattered radiation are determined by exciton dynamics, quantum-dot-like optical resonances and other intrinsic properties. Moreover, the nanotubes display a uniform peak optical conductivity of approximately 8 e(2)/h, which we derive using an exciton model, suggesting universal behaviour similar to that observed in nanotube conductance. We further demonstrate a radiative coupling between two distant nanotubes, with potential applications in metamaterials and optical antennas.     

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.     

Selection of carbon nanotubes with specific chiralities using helical assemblies of flavin mononucleotide

The chirality of single-walled carbon nanotubes affects many of their physical and electronic properties. Current production methods result in nanotubes of mixed chiralities, so facile extraction of specific chiralities of single-walled carbon nanotubes is an important step in their effective utilization. Here we show that the flavin mononucleotide, a common redox cofactor, wraps around single-walled carbon nanotubes in a helical pattern that imparts efficient individualization and chirality selection. The cooperative hydrogen bonding between adjacent flavin moieties results in the formation of a helical ribbon, which organizes around single-walled carbon nanotubes through concentric pi-pi interactions between the flavin mononucleotide and the underlying graphene wall. The strength of the helical flavin mononucleotide assembly is strongly dependent on nanotube chirality. In the presence of a surfactant, the flavin mononucleotide assembly is disrupted and replaced without precipitation by a surfactant micelle. The significantly higher affinity of the flavin mononucleotide assembly for (8,6)-single-walled carbon nanotubes results in an 85% chirality enrichment from a nanotube sample with broad diameter distribution.     

Chirality dependence of carbon single-walled nanotube material properties: axial Young's modulus

The potential use of individual carbon nanotubes as nano devices warrants detailed investigation of their mechanical behavior based on structural and geometrical configurations. The objective of this paper is to unravel the structural and chirality dependence of the axial Young's modulus of a carbon single-walled nanotube by analytical and numerical approaches. In this work, we employ the general homogenization composite shell model developed based on the asymptotic homogenization technique for analytical modeling of single-walled nanotubes. We derive the working formulae for the effective elastic properties of carbon single-walled nanotube of any chirality and predict the structural and chiral dependence of the effective axial Young's modulus of the nanotube. Also, a finite element analysis on the chirality dependence of the axial Young's modulus of the carbon nanotube is reported. The outcomes of our analyses are compared with available experimental and simulation results.     

Harmonic oscillators of carbon nanotube arrays

The harmonic properties of single-walled carbon nanotube (10, 10) arrays in cantilever geometry of lengths, L = 1,000 to 10,000 nm and diameters, D = 15 to 70 nm have been measured recently, and a linear relationship between the first natural frequency and the ratio of array diameter and the square of the span length, D/L2 was postulated. In the present work the authors show that this relationship is highly nonlinear, especially for large values of the ratio, D/L2. In addition, for a given array length, L = 1000 nm, the first natural frequency of the cantilever is shown to vary little with diameters more than 30 nm and to become asymptotic to a value of 22 MHz as it is further increased. The present study is based on earlier work of the authors wherein the flexural stiffness of the single-walled carbon nanotube (CNT) array of hexagonal symmetry and of non-covalent bonding, due to van der Waals interactions, was predicted in terms of the chirality of the nanotubes and the shearing transfer efficiency between nanotubes when subjected to flexural deformation. In addition, predictions are shown to be in agreement with the experimental evidence wherein the flexural modulus of the CNT array decreases with an increase in array diameter.     

Equilibrium and nonequilibrium transport of oxygen in carbon nanotubes

The equilibrium and nonequilibrium transport of O(2) through open-ended, hydrogen-terminated, single-walled carbon nanotubes is examined using classical molecular dynamics simulations. It is found in both cases that the O(2) forms well-defined layers around the nanotube interior and/or exterior, and that molecular transport approaches normal mode-diffusion as the nanotube diameter increases. The interactions between the O(2) and the nantubes are stronger than that among the O(2), and this difference increases as the nanotube diameter decreases.     

Chiral selectivity in the charge-transfer bleaching of single-walled carbon-nanotube spectra

Chiral selective reactivity and redox chemistry of carbon nanotubes are two emerging fields of nanoscience. These areas hold strong promise for producing methods for isolating nanotubes into pure samples of a single electronic type, and for reversible doping of nanotubes for electronics applications. Here, we study the selective reactivity of single-walled carbon nanotubes with organic acceptor molecules. We observe spectral bleaching of the nanotube electronic transitions consistent with an electron-transfer reaction occurring from the nanotubes to the organic acceptors. The reaction kinetics are found to have a strong chiral dependence, with rates being slowest for large-bandgap species and increasing for smaller-bandgap nanotubes. The chiral-dependent kinetics can be tuned to effectively freeze the reacted spectra at a fixed chiral distribution. Such tunable redox chemistry may be important for future applications in reversible non-covalent modification of nanotube electronic properties and in chiral selective separations.     

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.     

Toward the extraction of single species of single-walled carbon nanotubes using fluorene-based polymers

High purity of (7,5) SWNTs (approximately 79% of the semisonducting SWNT ensemble) can be obtained by polymer-assisted extraction from the narrow-diameter distributed SWNTs produced by the catalyst Co-MCM-41. The fluorene-based polymers are able to selectively wrap the single-walled carbon nanotubes (SWNTs) with certain chiral angles or diameters depending on their chemical structures. Poly(9,9-dioctyfluoreny1-2, 7-diyl) and poly[(9,9-dihexylfluorenyl-2,7-diyl)-co-(9,10-anthracene)] selectively wrap SWNTs with high chiral angles (>24.5 degrees). By contrast, poly[9,9-dioctylfluorenyl-2,7-diyl)-co-1,4-benzo-{2,1'-3}-thiadiazole)] preferentially wraps the SWNTs with certain diameter (1.02-1.06 nm).     

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.