Consideration of mechanical properties of single-walled carbon nanotubes under various loading conditions

In this article, mechanical properties of single-walled carbon nanotubes (SWCNTs) with various radiuses under tensile, compressive and lateral loads are considered. Stress–strain curve, elastic modulus, tensile, compressive and rotational stiffness, buckling behaviour, and critical axial compressive load and pressure of eight different zigzag and armchair SWCNTs are investigated to figure out the effect of radius and chirality on mechanical properties of nanotubes. Using molecular dynamic simulation (MDS) method, it can be explained that SWCNTs have higher Young’s modulus and tensile stiffness than compressive elastic modulus and compressive stiffness. Critical axial force of zigzag SWCNT is independent from the radius, but that of armchair type rises by increasing of radius, also these two types show different buckling modes.     

A Comprehensive Numerical Investigation on the Mechanical Properties of Hetero-Junction Carbon Nanotubes

A set of forty-three hetero-junction CNTs, made of forty-four homogeneous carbon nanotubes of different chiralities and configurations with all possible hetero-connection types, were numerically simulated, based on the finite element method in a commercial finite element software and their Young's and shear moduli, and critical buckling loads were obtained and evaluated under the tensile, torsional and buckling loads with an assumption of linear elastic deformation and also compared with each other. The comparison of the linear elastic behavior of hetero-junction CNTs and their corresponding fundamental tubes revealed that the size, type of the connection, and the bending angle in the structure of hetero-junction CNTs considerably influences the mechanical properties of these hetero-structures. It was also discovered that the Stone-Wales defect leads to lower elastic and torsional strength of hetero-junction CNTs when compared to homogeneous CNTs. However, the buckling strength of the hetero-junction CNTs was found to lie in the range of the buckling strength of their corresponding fundamental tubes. It was also determined that the shear modulus of hetero-junction carbon nanotubes generally tends to be closer to the shear modulus of their wider fundamental tubes while critical buckling loads of these heterostructures seem to be closer to critical buckling loads of their thinner fundamental tubes. The evaluation of the elastic properties of hetero-junction carbon nanotubes showed that among the hetero-junction models, those with armchair-armchair and zigzag-zigzag kinks have the highest elastic modulus while the models with armchair-zigzag connections show the lowest elastic stiffness. The results from torsion tests also revealed the fact that zigzag-zigzag and armchair-zigzag hetero-junction carbon nanotubes have the highest and the lowest shear modulus, respectively. Finally, it was observed that the highest critical buckling loads belong to armchair-armchair hetero-junction carbon nanotubes and the lowest buckling strength was found with the hetero-junction models with armchair-zigzag connection.     

Analysis of Single-Walled Carbon Nanotubes Using a Chemical Bond Element Model

提出了一种纳米尺度的有限元方法,碳纳米管中的碳-碳化学键被模拟为键单元．按照平衡关系,根据有限元理论,作用于每个碳原子上的作用力可以写成键单元的刚度矩阵与每个碳原子位移的乘积．在分子力学的基本假设下,键单元刚度矩阵的每个元素可以写为分子力学中力场常数的函数,这样建立起了宏观力学方法(有限元)与纳米尺度力学方法(分子力学)之间的联系．应用该方法模拟了扶椅型与锯齿型单壁碳纳米管的力学行为从而验证了该方法的有效性．分析结果说明单壁碳纳米管的弹性模量与管厚度的选取直接相关．此外,弹性模量对所选取的分子力学中的力场常数非常敏感,管的弹性模量显示出对半径的尺度依赖性,但是管长度对弹性模量的影响小到可以被忽略．     

Mechanical properties of single- and double-walled carbon nanotubes under hydrostatic pressure

Based on a molecular mechanics coupled with atomistic-based continuum theory, a closed-form formula is presented to examine the elastic properties of single- and double-walled carbon nanotubes subjected to hydrostatic pressure. Following the present model, the effects of the armchair and zigzag CNT structures on the pressure behavior are theoretically investigated. The computational result indicates that the bulk modulus is less sensitive to the chiral structures except for very small tube diameters. Moreover, closed-end nanotubes under hydrostatic pressure exhibit a larger bulking modulus than open ended nanotubes. The cap of the zigzag tubes has a larger effect on the bulk modulus when compared to the armchair tubes, especially in small diameter nanotubes. The predicted strain and the bulk modulus are in good agreement with existing theoretical results. PACS 61.46.+w; 62.20.Dc; 62.20.-x; 62.25.+g     

A study of the size-dependent elastic properties of silicon carbide nanotubes: First-principles calculations

The size dependence of elastic properties in single-walled silicon carbide nanotubes are investigated by first-principles calculations. We found the Young?s modulus of the nanotubes increases with increasing diameter and is inversely proportional to Si–C bond length, whereas the Poisson ratio shows an opposite trend. For small tubes the elastic properties change dramatically with the tube size. While for the tubes with the diameter larger than 8 Å, the difference of these properties is small and almost independent of the size and symmetry. The strength of bonding between Si and C atoms is elucidated by the amount of the charge transfer calculated by the Bader analysis.     

Effect of a rippling mode on resonances of carbon nanotubes

A recent study determined the Young's modulus of carbon nanotubes by measuring resonance frequency and using the modulus-frequency relation resulting from the linear vibration theory. It leads to the report that the Young's modulus decreases sharply, from about 1 to 0.1 TPa with the diameter D increasing from 8 to 40 nanometers, and the investigators attributed this decrease to the emergence of an unusual bending mode during the measurement that corresponds to rippling on the inner arc of the bent nanotubes. The nonlinear analysis presented in this paper that captures the rippling mode suggests that the effective Young's modulus can indeed decrease substantially with increasing diameter, and that the results from the classical linear theory may be invalid in such measurements.     

Electrical conductivity of individual polypyrrole microtube

Conducting microtubes (0.4－0.5μm in outer diameter) made of polypyrrole (PPy) doped with p-toluene sulfonic acid (PTSA) were synthesized by a self-assembly method. We report the electrical conductivity of an individual PPy microtube, on which a pair of platinum micro-leads was fabricated by focused ion beam deposition. The measured room-temperature conductivity of the individual PPy microtube was 0.29S/cm, which is comparable to that of template-synthesized PPy micro/nanotubes. The temperature dependence of conductivity of the individual microtube follows the three-dimensional variable-range hopping (3D VRH) model.     

Piezoresistive effect in single-walled carbon nanotubes

This paper reports on the results of the theoretical investigation of the piezoresistive effect in single-walled carbon nanotubes of two structural modifications: arm-chair type and zig-zag type. The variation in the band gap of semiconducting nanotubes under the influence of the compressive and tensile deformations has been analyzed. The main quantitative characteristic of the piezoresistive effect—the longitudinal component of the elastic conductivity tensor—has been calculated, and its dependence on the diameter of semiconducting nanotubes has been shown. The variants of practical implementation of the effect under study have been proposed.     

A density-functional-theory-based finite element model to study the mechanical properties of zigzag phosphorene nanotubes

In this paper, the density functional theory calculations are used to obtain the elastic properties of zigzag phosphorene nanotubes. Besides, based on the similarity between phosphorene nanotubes and a space-frame structure, a three-dimensional finite element model is proposed in which the atomic bonds are simulated by beam elements. The results of density functional theory are employed to compute the properties of the beam elements. Finally, using the proposed finite element model, the elastic modulus of the zigzag phosphorene nanotubes is computed. It is shown that phosphorene nanotubes with larger radii have larger Young's modulus. Comparing the results of finite element model with those of density functional theory, it is concluded that the proposed model can predict the elastic modulus of phosphorene nanotubes with a good accuracy.     

Molecular dynamic investigation of mechanical properties of armchair and zigzag double-walled carbon nanotubes under various loading conditions

Using molecular dynamic simulation (MDS), effects of chirality and Van der Waals interaction on Young's modulus, elastic compressive modulus, bending, tensile, and compressive stiffness, and critical axial force of double-walled carbon nanotube (DWCNT) and its inner and outer tubes are considered. Achieving the highest safety factor, mechanical properties have been investigated under applied load on both inner and outer tubes simultaneously and on each one of them separately. Results indicate that as a compressive element, DWCNT is more beneficial than single-walled carbon nanotube (SWCNT) since it carries two times higher compression before buckling. Except critical axial pressure and tensile stiffness, in other parameters zigzag DWCNT shows higher amounts than armchair type. Outer tube has lower strength than inner tube; therefore, most reliable design of nanostructures can be attained if the mechanical properties of outer tube taken as the properties of DWCNT.     

单壁碳纳米管力学行为的数字散斑相关法实验研究

通过直接单向拉伸超长单壁碳纳米管束长绳,首次借助高精度数字散斑相关法,并结合显维放大技术,测量了单壁碳纳米管的弹性模量和拉伸强度。试验中观察了单壁碳纳米管束长绳的断裂过程。单壁碳纳米管束长绳通过改进的化学气相沉积技术生成。试验得到单壁碳纳米管的平均杨氏模量为129.0±70.3GPa,平均拉伸强度为1.95±0.56GPa,低于计算值和先前其它文献的试验值。     

Poly(Butylene Terephthalate)/Single Wall Carbon Nanotubes Composite Nanofibers by Electrospinning

Poly(buthylene terephthalate)(PBT)/single wall carbon nanotubes (SWCNTs) composite nanofibers were prepared by electrospinning. The effect of carbon nanotubes on the morphology, crystallization, and mechanical properties of the electrospun composite nanofibers were investigated by SEM, DSC, and tensile testing, respectively. SEM observations indicated that the presence of SWCNTs resulted in finer nanofibers for lower loading; however, a broader distribution, especially for the higher diameter ranges was found for nanofibers with higher amounts of carbon nanotubes. SWCNTs accelerated crystallization and acted as a nucleating agent; the degree of crystallinity increased with increasing content of SWCNTs, followed by a moderate decrease at higher content. Specific tensile strength and modulus of the PBT/SWCNTs composite nanofibers mats were higher than that of neat PBT nanofibers mat. However, the elongation at break of composite nanofibers mats was lower than that of the neat PBT nanofibers mat.     

Reinforcement of Carbon Nanotube/Polydimethylsiloxane True Nanocomposite

Russian Physics Journal - The paper shows that the elastic modulus of carbon nanotubes in a polymer matrix nanocomposite is lower not only than its nominal value, but also the elastic modulus of...     

Optimum degree of functionalization for carbon nanotubes

Covalent functionalizations, especially oxidization and derivative functionalization, significantly improve the surface characteristics of carbon nanotubes, but also bring undesired devastation of sidewalls. This paper presents a theoretic model to investigate double-edge effects of covalent functionalization on carbon nanotubes for the polymer composite application. An optimal degree of functionalization is proposed and calculated based on the trade-off of required load-transfer and induced devastation of nanotube sidewalls. The negative effect on elastic modulus is also calculated. For oxidization-based functionalization of originally defect-free nanotubes, the calculation results indicate that about 10% functionalization degree is suggested to be optimum for the balance of efficient load-transfer and conspicuous devastation from the highly covalent functionalization. The original defects in nanotube surface also reduce the optimum functionalization degree and the reduction is dependent on the original defect concentration. The computational results indicate that nanotube diameter and percentages in the polymer composites show considerably effect on the optimum functionalization degree. Carbon nanotubes with smaller diameter show lower optimum functionalization degree. Increasing percentage of carbon nanotubes in the polymer composites also leads to lower optimum functionalization degree.     

Application of scanning force microscopy in nanotube science

Recent developments in the application of scanning force microscopy in nanotube science are reviewed. The non-destructive character of this technique allows the structural characterisation of (chemically modified) single- and multi-wall nanotubes deposited on substrates for further investigations such as electrical transport measurements. Furthermore, SFM is now an established tool for manipulation of nanotubes, which allows position control and determination of elastic constants such as the Young’s modulus. Finally it is shown that very sharp and stable probes for scanning force microscopy can be made from nanotubes due to their excellent stability and aspect ratio. Received: 17 May 1999 / Accepted: 18 May 1999 / Published online: 29 July 1999     

Reshaping elastic nanotubes via self-assembly of surface-adhesive nanoparticles

Elastic sheets with macroscopic dimensions are easy to deform by bending and stretching. Yet shaping nanometric sheets by mechanical manipulation is hard. Here we show that nanoparticle self-assembly could be used to this end. We demonstrate that spherical nanoparticles adhering to the outer surface of an elastic nanotube can self-assemble into linear structures: rings or helices on stretchable nanotubes, and axial strings on nanotubes with high rigidity to stretching. These self-assembled structures are inextricably linked to a variety of deformed nanotube profiles, which can be controlled by tuning the concentration of nanoparticles, the nanoparticle-nanotube diameter ratio and the elastic properties of the nanotube. Our results open the possibility of designing nanoparticle-laden tubular nanostructures with tailored shapes, for potential applications in materials science and nanomedicine.     

Study of the effect of varying core diameter,shell thickness and strain velocity on the tensile properties of single crystals of Cu–Ag core–shell nanowire using molecular dynamics simulations

Core–shell type nanostructures show exceptional properties due to their unique structure having a central solid core of one type and an outer thin shell of another type which draw immense attention among researchers. In this study, molecular dynamics simulations are carried out on single crystals of copper–silver core–shell nanowires having wire diameter ranging from 9 to 30 nm with varying core diameter, shell thickness, and strain velocity. The tensile properties like yield strength, ultimate tensile strength, and Young’s modulus are studied and correlated by varying one parameter at a time and keeping the other two parameters constant. The results obtained for a fixed wire size and different strain velocities were extrapolated to calculate the tensile properties like yield strength and Young’s modulus at standard strain rate of 1 mm/min. The results show ultra-high tensile properties of copper–silver core–shell nanowires, several times than that of bulk copper and silver. These copper–silver core–shell nanowires can be used as a reinforcing agent in bulk metal matrix for developing ultra-high strength nanocomposites.     

TiO2纳米管的力学和电子学性质

基于密度泛函理论研究了纤铁矿和锐钛矿型TiO₂纳米管的原子结构、稳定性、Young模量以及电子能带结构.计算结果显示：在纳米管直径较小时,锐钛矿型TiO₂纳米管的稳定性要好于纤铁矿型纳米管,随着管径的增大,纤铁矿型纳米管变得比锐钛矿型纳米管要更稳定.纤铁矿型TiO₂纳米管具有比锐钛矿型纳米管更大的Young模量,力学性能比较优异.另外,通过对电子能带结构的研究发现,手性对TiO₂纳米管的电子结构影响较大,纤铁矿（0,n）型和锐钛矿（n,0）型纳米管为间接带隙半导体,而纤铁矿（n,0）型和锐钛矿（0,n）型纳米管却具有直接带隙. 关键词： 2纳米管')" href="#">TiO₂纳米管 Young模量 间接带隙 直接带隙     

Mechanical properties of nanotubes of polyelectrolyte multilayers

The elastic properties of nanotubes fabricated by layer-by-layer (LbL) assembly of polyelectrolytes in the nanopores of polycarbonate track-etched membranes have been investigated by resonant contact Atomic Force Microscopy (AFM), for nanotube diameters in the range of 100 to 200 nm. The elastic modulus of the nanotubes was computed from the resonance frequencies of a cantilever resting on freely suspended LbL nanotubes. An average value of 115 MPa was found in air for Young's modulus of these nanostructures, well below the values reported for dry, flat multilayers, but in the range of values reported for water-swollen flat multilayers. These low values are most probably due to the lower degree of ionic cross-linking of LbL nanotubes and their consequently higher water content in air, resulting from the peculiar mode of growth of nanoconfined polyelectrolyte multilayers.     

Transverse elasticity of multi-walled carbon nanotubes

A discrete shell model is proposed to describe the radial deformation of carbon nanotubes under a hydrostatic pressure and the radial Young's modulus of (single- or multi-walled) nanotubes is obtained. It is found that the radial modulus decreases with increasing tube diameter while increases with increasing number of layers. The computational results agree well with the previous results of SWNTs and indicate that the radial modulus of carbon nanotubes is independent of the Poisson's ratio.