Buckling analysis of single walled carbon nanotube on Winkler foundation using nonlocal elasticity theory and DTM

In the present work differential transformation method (DTM) is used to predict the buckling behaviour of single walled carbon nanotube (SWCNT) on Winkler foundation under various boundary conditions. Four different boundary conditions namely clamped–clamped, simply supported, clamped hinged and clamped free are used to study the critical buckling loads. Effects of (i) size of SWCNT (ii) nonlocal parameter and (iii) Winkler elastic modulus on nonlocal critical buckling loads are being investigated and discussed. The DTM is implemented for the nonlocal SWCNT analyses and this yields results with high degree of accuracy. Further, present method can be applied to linear and nonlinear problems.     

Free transverse vibration of an axially loaded non-prismatic single-walled carbon nanotube embedded in a two-parameter elastic medium

The free vibration analysis of a single-walled carbon nanotube (SWCNT) is a requisite analysis for the optimal design of nanolevel devices and systems. However, the natural frequencies of structures from free vibration analysis depend, among other things, on their geometry, boundary conditions, material property and the nature of the surrounding medium. Thus in this paper, a mathematical model is presented for the vibration analysis of a geometrically tapered SWCNT. The SWCNT is idealized as a nonlocal Rayleigh (NLR) beam that is axially loaded and embedded in a deformable surrounding medium. A polynomial power law that defines the range of tapers along the longitudinal axis of the continuum is proposed. The variable coefficient governing differential equation of the tapered SWCNT is solved with the Bubnov–Galerkin method. Numerical values, graphical plots and the Pareto charts of the influence of the parameters in the model on the natural frequency of the NLR beam are presented. The presence of the taper ratio alters the natural frequencies of the SWCNT for the values of the radius of gyration considered. The analysis further shows that the influence of the nonlocal parameter with the Pasternak shear modulus is more profound than with the Winkler modulus at the nanoscale level.     

Nonlinear flow-induced vibration of a SWCNT with a geometrical imperfection

Based on the nonlocal continuum theory, transverse vibration of a single-walled carbon nanotube (SWCNT) conveying fluid with immovable support conditions is investigated. Unlike previous similar studies, the SWCNT is assumed to be not perfectly straight and initially includes a slight geometrical curvature as an imperfection. The SWCNT is assumed to be embedded in a Pasternak-type foundation. Hamilton’s principle is applied to drive an efficient governing equation of motion, which covers stretching, large deformation, and imperfection nonlinearities. The perturbation method of multi scales (MMS) is applied and the nonlinear flow-induced frequency ratio is analytically calculated. The obtained results reveal that the imperfection of the nanotube at high flow velocities makes the model severely nonlinear, especially when considering the nonlocal effects. A noteworthy observation is that the nonlinear flow-induced frequency ratio is decreased as the imperfection of the nanotube increases. Whereas through a parametric study, the effects of the flow velocity, nonlocal parameter, the stiffness of the elastic foundation, and the boundary conditions (BCs) on this frequency reduction are calculated and discussed widely.     

Thermo-mechanical vibration of a single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory

A single-elastic beam model has been developed to analyze the thermal vibration of single-walled carbon nanotubes (SWCNT) based on thermal elasticity mechanics, and nonlocal elasticity theory. The nonlocal elasticity takes into account the effect of small size into the formulation. Further, the SWCNT is assumed to be embedded in an elastic medium. A Winkler-type elastic foundation is employed to model the interaction of the SWCNT and the surrounding elastic medium. Differential quadrature method is being utilized and numerical solutions for thermal-vibration response of SWCNT is obtained. Influence of nonlocal small scale effects, temperature change, Winkler constant and vibration modes of the CNT on the frequency are investigated. The present study shows that for low temperature changes, the difference between local frequency and nonlocal frequency is comparatively high. With embedded CNT, for soft elastic medium and larger scale coefficients (e₀a) the nonlocal frequencies are comparatively lower. The nonlocal model-frequencies are always found smaller than the local model-frequencies at all temperature changes considered.     

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.     

Computational study of the effect of carbon vacancy defects on the Young's modulus of (6, 6) single wall carbon nanotube

Most molecular dynamics (MD) simulations for single wall carbon nanotubes (SWCNT) are based on a perfect molecular material structure. The presence of vacancy defects in SWCNTs could lead to deviations from this perfect structure thus affecting the predicted properties. The present paper investigates the effect of carbon vacancy defects in the molecular structure of SWCNT on the Young's modulus of the SWCNT using MD simulations performed via Accelrys and Materials Studio. The effect of the position of the defects in the nanotube ring and the effect of the number of defects on the Young's modulus are studied. The studies indicate that for an enclosed defect with the same shape in a SWCNT structure, its position did not cause any change in the Young's modulus. However, as the number of defects increased, the predicted Young's modulus was found to decrease. For a 10 ring (6, 6) SWCNT, six vacancy defects (corresponding to a defect percentage of 2.5%) reduced the Young's modulus by 13.7%.     

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.     

Increasing the through-thickness thermal conductivity of carbon fiber polymer-matrix composite by curing pressure increase and filler incorporation

The low through-thickness thermal conductivity limits heat dissipation from continuous carbon fiber polymer-matrix composites. This conductivity is increased by up to 60% by raising the curing pressure from 0.1 to 2.0 MPa and up to 33% by incorporation of a filler (?1.5 vol.%) at the interlaminar interface. The 7-μm-diameter 7-W/m K-thermal-conductivity continuous fiber volume fraction is increased by the curing pressure increase, but is essentially unaffected by filler incorporation. The thermal resistivity is dominated by the lamina resistivity (which is contributed substantially by the intralaminar fiber-fiber interfacial resistivity), with the interlaminar interface thermal resistivity being unexpectedly negligible. The lamina resistivity and intralaminar fiber-fiber interfacial resistivity are decreased by up to 56% by raising the curing pressure and up to 36% by filler incorporation. The curing pressure increase does not affect the effectiveness of 1-mm-long 10-μm-diameter 900-1000-W/m K-thermal-conductivity K-1100 carbon fiber or single-walled carbon nanotube (SWCNT) as fillers for enhancing the conductivity, but hinders the effectiveness of carbon black (CB, low-cost), which is less effective than K-1100 or SWCNT at the higher curing pressure, but is almost as effective as K-1100 and SWCNT at the lower curing pressure. The effectiveness for enhancing the flexural modulus/strength/ductility decreases in the order: SWCNT, CB, K-1100.     

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.     

Formation of single-walled carbon nanotube via the interaction of graphene nanoribbons: ab initio density functional calculations

The interaction of bare graphene nanoribbons (GNRs) was investigated by ab initio density functional theory calculations with both the local density approximation (LDA) and the generalized gradient approximation (GGA). Remarkably, two bare 8-GNRs with zigzag-shaped edges are predicted to form an (8, 8) armchair single-wall carbon nanotube (SWCNT) without any obvious activation barrier. The formation of a (10, 0) zigzag SWCNT from two bare 10-GNRs with armchair-shaped edges has activation barriers of 0.23 and 0.61 eV for using the LDA and the revised PBE exchange correlation functional, respectively. Our results suggest a possible route to control the growth of specific types SWCNT via the interaction of GNRs.     

Poly(phenylene sulphide) and poly(ether ether ketone) composites reinforced with single-walled carbon nanotube buckypaper: II – Mechanical properties,electrical and thermal conductivity

The mechanical properties, electrical and thermal conductivity of single-walled carbon nanotube (SWCNT) buckypaper (BP) embedded in poly(ether ether ketone) (PEEK) or poly(phenylene sulphide) (PPS) matrices were investigated. Dynamic mechanical analysis demonstrated a significant increase in the storage modulus and glass transition temperature of the polymers, indicating strong SWCNT–matrix interfacial adhesion. The composites showed improved stiffness and strength, as revealed by tensile and flexural tests, while their ductility and toughness moderately decreased. Exceptional enhancements in the electrical and thermal conductivity of PPS and PEEK were found. Their Young’s moduli and thermal conductivities were compared with the predictions of theoretical models. This investigation indicates that SWCNT-BPs possess great potential to improve the performance of thermoplastics and satisfy a wide variety of demands in multi-disciplinary technological applications.     

Nonlocal continuum model and molecular dynamics for free vibration of single-walled carbon nanotubes

Free transverse, longitudinal and torsional vibrations of single-walled carbon nanotubes (SWCNTs) are investigated through nonlocal beam model, nonlocal rod model and verified by molecular dynamics (MD) simulations. The nonlocal Timoshenko beam model offers a better prediction of the fundamental frequencies of shorter SWCNTs, such as a (5, 5) SWCNT shorter than 3.5 nm, than local beam models. The nonlocal rod model is employed to study the longitudinal and torsional vibrations of SWCNT and found to enable a good prediction of the MD results for shorter SWCNTs. Nonlocal and local continuum models provide a good agreement with MD results for relatively longer SWCNTs, such as (5, 5) SWCNTs longer than 3.5 nm. The scale parameter in nonlocal beam and rod models is estimated by calibrations from MD results.     

Correlation between Young’s modulus and impregnation quality of epoxy-impregnated SWCNT buckypaper

Carbon nanotube (CNT) sheets, also known as buckypaper, have high potential for structural applications due to their high volume fraction of CNT, the strongest and stiffest materials known. In this work, two different techniques, one based on positive pressure and another based on vacuum infiltration, are utilized to impregnate single-walled carbon nanotube (SWCNT) buckypaper sheets of 50–70 μm in thickness, resulting in a Young’s modulus of up to 15.4 GPa. Scanning electron microscopy demonstrates that the vacuum-based technique results in more effective impregnation of the buckypaper than the positive pressure technique. Thermogravimetry analysis of vacuum-impregnated specimens indicated a void content ranging from 5% to 32%. An advanced Mori–Tanaka-based micromechanics technique is also utilized to predict the effect of SWCNT volume fraction and void content on Young’s modulus of nanocomposites. These calculations suggest a higher void content of around 40% for the vacuum-impregnated composites.     

Effect of ending surface on energy and Young's modulus of an armchair single-walled carbon nanotubes

The energy and Young's modulus as a function of tube length for (10, 10) armchair single-walled carbon nanotubes (SWCNTs) are investigated by using a linear scaling self-consistent-charge density functional tight binding (SCC-DFTB) method. It is found that the formula derived from total energy for a zigzag SWCNT [Physica B404, 3930 (2009)] can be also used to explain these calculated length-dependent properties. Moreover, a transition occurs from fast change of length-dependent properties of the SWCNT to their slow change. This transition corresponds to the SWCNT's length of about 5 nm. The length for the armchair SWCNT is about one half of that of the corresponding Zigzag SWCNTs. In addition, a definition of volume for a short SWCNT is discussed.     

Fluctuation-induced tunneling dominated electrical transport in multi-layered single-walled carbon nanotube films

Low temperature measurements may give some insight into the transport mechanism of single-walled carbon nanotube (SWCNT) films, which could lead to an optimal SWCNT film with designed photoelectric properties. Despite intense research efforts on the low temperature transport in SWCNT films, it is still an open question for the low temperature transport in multi-layered SWCNT films. In this work, the multi-layered SWCNT films were prepared with a layer by layer vacuum filtration. It suggests that the space between different layers of the multi-layered SWCNT can be ignored. For deposition of different-layered SWCNT films using the same total amount of SWCNT suspension, the increase of the layer numbers can reduce the density of the resulting films, which may account for the low temperature transport. The effect of thermal annealing and subsequent nitric acid treatment on the electrical properties of the SWCNT films has also been investigated. At the temperature range of 80-300 K, the transport of the multi-layered SWCNT films can be explained by a fluctuation-induced tunneling model. Our results could build a bridge connecting measured temperature coefficient of resistance and the microscopic tunneling barrier.     

Thermal conductance and thermopower of an individual single-wall carbon nanotube

We have observed experimentally that the thermal conductance of a 2.76-microm-long individual suspended single-wall carbon nanotube (SWCNT) was very close to the calculated ballistic thermal conductance of a 1-nm-diameter SWCNT without showing signatures of phonon-phonon Umklapp scattering for temperatures between 110 and 300 K. Although the observed thermopower of the SWCNT can be attributed to a linear diffusion contribution and a constant phonon drag effect, there could be an additional contact effect.     

Young’s moduli of functionalized single-wall carbon nanotubes under tensile loading

This paper quantitatively investigates the effect of chemical functionalization on the axial Young’s moduli of single-walled carbon nanotubes (SWCNTs) based on molecular mechanics (MM) simulation, in which the COMPASS force field is used to model the interatomic interactions in a nonfunctionalized nanotube or a functionalized nanotube grafted with vinyl groups. We obtain the axial Young’s moduli of both functionalized and nonfunctionalized SWCNTs. The influences of the number and distribution density of the sp³-hybridized carbon atoms and the radius and chirality of the SWCNTs on Young’s moduli are studied. The results indicate that Young’s moduli depend strongly on the chirality of the SWCNTs and the distribution density of the sp³-hybridized carbon atoms. A 37.50% content of sp³-hybridized carbon atoms may degrade Young’s modulus by up to 33.36%. In addition, MM simulations show that the functionalization of SWCNTs results in a decrease of Young’s moduli of the corresponding SWCNT/polyethylene composites.     

Nonlinear free vibration of embedded double-walled carbon nanotubes with layerwise boundary conditions

This paper investigates the large-amplitude free vibration of a double-walled carbon nanotube (DWCNT) surrounded by an elastic medium in the presence of temperature change. Based on continuum mechanics, a nonlocal elastic beam model is employed in which nanotubes are coupled together via the van der Waals (vdW) interlayer interactions. The Pasternak foundation model and a nonlinear vdW model are utilized to describe the surrounding elastic medium effect and the vdW interlayer interactions, respectively. DWCNTs with different boundary conditions are analyzed utilizing the Timoshenko beam theory that considers the shear deformation and rotary inertia effects. The governing equations are derived from Hamilton’s principle; the Galerkin method is utilized to discretize the governing equations. The influences of the nonlocal parameter, spring constant, carbon nanotube aspect ratio, and temperature change on the nonlinear free vibration characteristics of a double-walled carbon nanotube with different boundary conditions are thoroughly investigated. It is deduced that the nonlocal parameter, spring constant, and the aspect ratio play significant roles for the value of the nonlinear frequency. Also, the temperature change and the type of boundary conditions have an effect on the nonlinear frequency.     

Effect of matrix glass transition on reinforcement efficiency of epoxy-matrix composites with single walled carbon nanotubes,multi-walled carbon nanotubes,carbon nanofibers and graphite

This study compares the mechanical and thermal properties of glassy and rubbery epoxy–matrix composites reinforced with 1 and 4 wt.% single-walled carbon nanotubes (SWCNTs), multi-walled carbon nanotubes (MWCNTs), graphite, and carbon nanofibers (CNFs). The tensile modulus of most glassy composites was higher than that of the epoxy and increased with higher filler concentration and 4% graphite/epoxy and 4% SWCNT/epoxy exhibited approximately the same highest tensile modulus. The elongation of glassy composites was significantly lower than that of the epoxy and decreased with increasing filler loading. Most rubbery composites showed a higher tensile modulus and elongation than the epoxy and the modulus increased with rising filler content and 4% SWCNT/epoxy showed the highest tensile modulus and tensile strength. In the rubbery regime, glassy and rubbery composites displayed a higher storage modulus than the corresponding epoxy and 4 wt.% SWCNT/epoxy composites showed a 300% improvement in storage modulus compared to the epoxy.     

Diameters of single-walled CNTs (SWCNTs) and related nanochemistry and nanobiology

We reviewed and examined recent progresses related to the nanochemistry and nanobiology of signal-walled carbon nanotubes (SWCNTs), focusing on the diameters of SWCNTs and how the diameters affect the interactions of SWCNT with protein and DNA, which underlay more complex biological responses. The diameters of SWCNTs are closely related to the electronic structure and surface chemistry of SWCNTs, and subsequently affect the interaction of SWCNTs with membrane, protein, and DNA. The surfaces of SWCNT with smaller diameters are more polar, and these with large diameters are more hydrophobic. The preference of SWCNT to interact with Trp/Phe/Met residues indicates it is possible that SWCNT may interfere with normal protein-protein interactions. SWCNT-DNA interactions often change DNA conformation. Besides the promising future of using SWCNTs as delivering nanomaterial, thermal therapy, and other biological applications, we should thoroughly examine the possible effects of carbon nanotube on interrupting normal protein-protein interaction network and other genetic effects at the cellular level.