Atomistic simulations of shearing friction and dynamic adhesion of double-walled carbon nanotubes on Au substrates

Functional gecko-mimetic adhesives have attracted a lot of research interest in recent years. In this paper, the physical adhesion behavior of (5, 5)@(10, 10) double-walled carbon nanotubes (DWCNTs) on an Au substrate is investigated by performing detailed, fully atomistic molecular dynamics (MD) simulations. The effects of adhesion temperature, tube length, and peeling velocity on the binding energy, normal adhesion force, lateral shearing friction, and adhesion time are thoroughly analyzed. The simulation results indicate that the binding energy (per unit length) of the DWCNT–Au adhesive system is −26.7 × 10⁻² eV/Å, which is 7.2% higher than that of single-walled counterparts. The tip-surface adhesion force for a single DWCNT is calculated to be 1.4 nN, and thus the adhesive strength of a DWCNT array is about 1.4 × 10¹–1.4 × 10³ N/cm² (corresponding to an aerial density of 10¹⁰–10¹² tubes/cm²). Two distinctive friction modes, namely (i) sliding friction (by the nanotube wall) and (ii) sticking friction (by the nanotube tip), are elucidated in term of the phase relationship of atomic friction forces. Moreover, the effective Young’s moduli of double- and single-walled CNTs are obtained using MD simulations combined with Euler–Bernoulli beam theory. The calculation results show good agreement with previously reported numerical and experimental results.     

On the estimation of mechanical properties of single-walled carbon nanotubes by using a molecular-mechanics based FE approach

Carbon nanotubes (CNTs) have attracted considerable attention in scientific communities due to their remarkable mechanical, thermal and electrical properties (high stiffness, high strength, resilience, etc.). In particular, mechanical properties of single wall nanotubes (SWNTs) have a Young’s modulus of about 1 TPa if normalized to their diameter showing why they are widely considered as reinforcing elements in advanced low weight composite structures. The determinations of mechanical properties of SWNT are currently investigated both experimentally and theoretically. However, to determine CNTs mechanical properties in a direct experimental way is a challenging and not economical task because of the technical difficulties and the costs involved in the manipulation of nanoscale objects. Due to the handling difficulty, estimation of mechanical properties using computer simulations are being performed by several author with different approaches.     

Numerical algorithms for prediction of mechanical properties of single-walled carbon nanotubes based on molecular mechanics model

The objective of this paper is to develop the numerical algorithms for the prediction of mechanical properties of single-walled carbon nanotubes (SWCNTs). By using the energy method, the analytical expressions are obtained and the five independent variables algorithm is developed for the prediction of the elastic properties of SWCNTs via a molecular mechanics model in which the geometrical relationship of carbon nanotube is introduced. It can be found that due to the introduction of the geometrical approximate conditions some errors may exist in the calculation of mechanical properties of SWCNTs in terms of the five independent variables algorithm. Therefore, two improved algorithms, i.e., eigenvalues modified method (EMM) and eigenvalues and eigenvectors modified method (EEMM) are proposed to analyze the possible errors in the numerical results. It is found that the results obtained by the three kinds of algorithms are almost consistent with one another, but EMM and EEMM are preferred to be used because they have properties similar to those of the finite element method, where the consistent equation works just as the constraint condition to void the singularity of the element stiffness matrix. The computational results also reveal that both the surface Young’s modulus and Poisson’s ratio depend on the diameter of carbon nanotubes, and finally converge to the values of the graphite sheet with an increase in the tube diameter in the inverse trends. For SWCNTs with approximately the same diameters, the surface Young’s modulus is in direct and Poisson’s ratio is in inverse proportion to chiral angles, respectively.     

Buckling of defective single-walled and double-walled carbon nanotubes under axial compression by molecular dynamics simulation

Buckling of defective single-walled and double-walled carbon nanotubes (SWCNTs and DWCNTs, respectively) due to axial compressive loads has been studied by molecular dynamics simulations, and results compared with those of the perfect structures. It is found that single vacancy defect greatly weakens the carrying capacity of SWCNTs and DWCNTs, though it does slight harm to the effective elastic modulus of the tubes. The influence of defects on the buckling properties of nanotubes is related to the density of the defects, and the relative position of defects also plays an important role in buckling of DWCNTs. The van der Waals force among atoms in the inner and the outer tubes of short defective DWCNTs makes the critical buckling strain of DWCNTs greater than that of the inner tube.     

A theoretical investigation of thermal effects on vibrational behaviors of single-walled carbon nanotubes

Thermal effects on the vibrational behaviors and dynamic Young’s modulus of single-walled carbon nanotubes (SWCNTs) are investigated through both constant temperature molecular dynamics (MD) simulation and modified molecular structural mechanics (MMSM) modeling. The MD simulation incorporates a modified Nosé-Hoover thermostat model to control the system temperature. In the MMSM modeling, the covalent and nonbonded interactions between carbon atom pairs are modeled with the second generation force field and the Lennard-Jones potential, respectively, where the covalent bonds are treated as Euler-Bernoulli beam and the temperature-dependent bond length and angle are determined through the Badger’s rule and MD simulation. The results derived from these two approaches are compared with each other and the published theoretical and experimental data. Results show that the dynamic Young’s modulus of the SWCNTs tends to be smaller than the published static one obtained from uniaxial tensile tests, and their natural frequency and dynamic Young’s modulus would decrease with increasing temperature. Moreover, a comparable frequency ratio of the first two flexural modes is achieved by these two approaches. The frequency ratio is highly dependent on their aspect ratio but independent of temperature, and would converge to the literature experimental data (about 6.1-6.2) as the aspect ratio becomes very large.     

Molecular orbital calculations of hydrogen storage in carbon and boron nitride clusters

Hydrogen gas storage ability in carbon and boron nitride (BN) clusters was investigated by molecular orbital calculations. From single point energy calculations, H₂ molecules would enter from hexagonal rings of C₆₀ and B₃₆N₃₆ clusters and octagonal rings of B₂₄N₂₄ cluster because of lower energy barrier. Chemisorption calculation of hydrogen for BN clusters showed that hydrogen bonding with nitrogen atoms was more stable than that with boron atoms. Stability of H₂ molecules in BN clusters seems to be higher than that of carbon clusters.     

A framework for stress computation in single-walled carbon nanotubes under uniaxial tension

A procedure is proposed for computing the stresses in an armchair single-walled carbon nanotube (SWCNT) under uniaxial tension. Computation is based on molecular dynamics simulations and the virial stress theorem. The proposed approach is compared with other methods used in the literature for calculating the stresses in CNTs. The loading is applied under two different boundary conditions and different strain rates and the results are compared. It is shown that the method commonly used in the literature for calculating the stresses in CNTs under estimates the ultimate strength by around 35%. It is shown that the value of the displacement increment used to apply the tensile strain is crucial. A convergence study is done to eliminate the computational error due to large displacement increments.     

Carbene-functionalized single-walled carbon nanotubes and their electrical properties

Pure metallic single-walled carbon nanotubes (m-SWCNTs) are very desirable for many electrode and interconnecting applications. However, the lack of reliable processing techniques to sort m-SWCNTs from the as-synthesized SWCNT samples is an obstacle to these applications. The effects of carbene-based covalent functionalization on the electrical properties of an isolated m-SWCNT, a semiconducting (s)-SWCNT, and a mixture network of both m- and s-SWCNTs are reported. For the first time, a semiconducting-to-metallic SWCNT transition upon dichlorocarbene functionalization is observed. Interestingly, the transition is reversible upon thermal annealing under ambient conditions. The electrical properties of m-SWCNTs remain largely unaffected whereas the on-state conductivity of s-SWCNTs is greatly reduced by this process, in agreement with the relevant theoretical predictions. These findings could pave the way for fabricating large-scale SWCNT-based interconnects and electrodes in full-carbon integrated circuits.     

Investigation of temperature effect on the mechanical properties of single-walled carbon nanotubes

A temperature-related higher-order gradient continuum theory is proposed for predicting the mechanical properties of single-walled carbon nanotubes (SWCNTs) at various temperatures. It is found that the axial elastic moduli of zigzag (21, 0), armchair (12, 12) and chiral (15, 9) SWCNTs with similar radii approach 0.7 TPa when T = 0 K, but decline slightly on different slopes. These results indicate that the temperature effect influences the axial Young moduli of zigzag SWCNTs less than those of the other types. Moreover, the parameters λ₁ and λ₂ corresponding to the uniform longitudinal and circumferential stretches at different temperatures are also examined, and the results show that with an increasing temperature, all SWCNTs are stretched in the longitudinal direction, while in the circumferential direction, only the zigzag SWCNTs are stretched, whereas the others are compressed.     

Molecular dynamics simulation of polarizable carbon nanotubes

This paper is aimed to develop a modified force field for molecular dynamics (MD) simulations of polarizable carbon nanotubes (CNTs). The effects of electrical polarization and the associated electronic degrees of freedom are represented by a network of negative charged shell particles which move relative to the surrounding positively charged carbon atoms in response to an applied electric field. In this setting, the negative and positive charges are exactly balanced so that the total system remains electrically neutral, and the motion of the shell particles relative to their equilibrium positions leads to polarization within the nanotube. Potential applications of the proposed model include simulations of controlled translocation of ions, water and polymers through solid-state CNT membranes.     

Optical properties of single-walled carbon nanotubes functionalized with copolymer poly(3,4-ethylenedioxythiophene-co-pyrene)

Optical properties are reported for composites based on single-walled carbon nanotubes (SWNTs) and copolymer poly(3,4-ethylenedioxythiophene-co-pyrene) (PEDOT-Py) prepared by chemical polymerization of two monomers in the presence of carbon nanotubes. A charge transfer between SWNTs and the PEDOT-Py copolymer was demonstrated by Raman scattering. The increase in the relative intensity of the Raman lines peaked at 440–577 cm⁻¹, which were assigned to the ethylenedioxy ring vibrational modes, indicated a significant hindrance steric in the case of the composites based on the PEDOT-Py copolymer and metallic SWNTs. The increase in the absorbance of IR band peaked at 984 cm⁻¹ occurred simultaneously with the disappearance of the IR band at 1639 cm⁻¹. This finding was a consequence of the formation of new covalent bonds between SWNTs and the thiophene and benzene rings of the repeating units of the PEDOT-Py copolymer. The photoluminescence (PL) quenching process of the PEDOT-Py copolymer was induced by semiconducting SWNTs. The PL quenching of PEDOT-Py copolymer in the presence of SWNTs was demonstrated based on the energy level diagrams of the two constituents of the PEDOT-Py/SWNTs composite material.     

Compressive and tensile properties of Ar filled carbon nano-peapods

In order to investigate the compressive and tensile mechanical properties of the carbon nano-peapods filled with Ar atoms outside, inside, or both outside and inside their C₆₀ fullerenes, the MD (molecular dynamics) method was used to simulate the compression and tension of the carbon peapods. According to the calculated results the effects of the filled pattern and amount of Ar atom on the mechanical properties of the carbon peapods were discussed systematically. It is shown that (1) the Ar filled nano-peapods have better compressive properties than the unfilled one, and the more Ar atoms are filled, the better the compressive properties are, (2) when the same amount of Ar atoms are filled, the carbon peapod with Ar atoms both outside and inside its C₆₀ fullerenes has the best compressive properties and the one with Ar atoms only outside has the worst compressive properties, and (3) the filled pattern and amount of Ar atom seem to have little effect on the tensile properties of the carbon peapods.     

Pressure effects on bond lengths and shape of zigzag single-walled carbon nanotubes

We investigate structural parameters, i.e., bond lengths and bond angles of isolated uncapped zigzag single-wall nanotubes in detail. The bond lengths and bond angles are determined for several radii tubes by using a theoretical procedure based on the helical and rotational symmetry for atom coordinates generation, coupled with Tersoff potential for interaction energy calculations. Results show that the structure of zigzag tubes is governed by two bond lengths. One bond length is found to have a value equal to that of graphite, while the other one is larger. Furthermore, the tube length is found to have significant effect only on larger bond length in zigzag tubes. With the application of the pressure, only the larger bond length compresses, the other one remaining practically constant. At some critical pressure, this bond length becomes equal to constant bond length. This behavior of bond lengths is different from those of armchair tubes. An analysis regarding the cross sectional shape has also been done. At some higher pressure, transition from circular to oval cross section takes place. This transition pressure is found to be equal 2.06 GPa for (20,0) tube. Some comparison with chiral tubes has also been made and important differences on bond length behavior have been observed.     

添加纳米碳管对高密度聚乙烯力学行为和结晶过程的影响

利用熔融法制备了一系列具有不同纳米碳管含量的纳米碳管(Q盯)／高密度聚乙烯(HDPE)复合材料。对其拉伸性能的研究结果表明，添加质量分数分别为2％，5％和10％的纳米碳管使HDPE的拉伸模量分别提高了7．4％，27．0％和28．6％，屈服强度分别提高了3．3％，14．4％和18．5％，但是会降低HDPE的断裂强度和断裂伸长率。同时，对复合材料中HDPE结晶过程的研究表明，纳米碳管可以提高HDPE的开始结晶温度，降低结晶活化能，但是会使HDPE的结晶速率下降，结晶度降低。     

单壁碳纳米管束的排布

流体排布法是实现碳纳米管定向排列的一种简单的方法。采用流体排布法在具有浸润性图案化的基底上成功地对单壁碳纳米管(SWNTs)束进行了水平方向上的排布。将SWNTs悬浮液滴入光刻胶制成的微通道中,在流体剪切力作用下,弯曲的SWNTs在一定程度上会被拉伸并且平行地排列在纳米级宽度的微通道中。将排列好的SWNTs阵列转移到一些不同间距的金电极对上面,制作成碳纳米管场效应晶体管(CNTFET)。CNTFET的电性能测试结果表明,制备的SWNTs束可以制造出不同电极间距同时具有良好电性能的CNTFET。     

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.     

Strengthening and toughening of aluminum by single-walled carbon nanotubes

Effects of single-walled carbon nanotubes (SWNTs) on strengthening and toughening behaviors of aluminum-based composites with grain sizes ranging from nano- to micrometer have been investigated. The strength of composites is enhanced as an increase in SWNT volume and a decrease in grain size. Nanocrystalline composite containing 3.5 vol.% SWNTs exhibits good ductility of ∼5% tensile elongation to failure as well as superior yield stress of ∼600 MPa. However, the strengthening efficiency of SWNTs becomes half of the theoretical prediction for nanocrystalline composites due to the recovery process around the interface. Nanocrystalline composite containing 2.0 vol.% SWNTs shows the fracture toughness of ∼57 MPa mm^1/2, which is five times higher than that of starting aluminum. SWNTs may effectively block the propagation of necks and cracks, providing much improved ductility and toughness.     

Odako growth of dense arrays of single-walled carbon nanotubes attached to carbon surfaces

A novel process is demonstrated whereby dense arrays of single-walled carbon nanotubes (SWNT) are grown directly at the interface of a carbon material or carbon fiber. This growth process combines the concepts of SWNT tip growth and alumina-supported SWNT base growth to yield what we refer to as “odako” growth. In odako growth, an alumina flake detaches from the carbon surface and supports catalytic growth of dense SWNT arrays at the tip, leaving a direct interface between the carbon surface and the dense SWNT arrays. In addition to being a new and novel form of SWNT array growth, this technique provides a route toward future development of many important applications for dense aligned SWNT arrays. Electronic Supplementary Material  Supplementary material is available for this article at and is accessible for authorized users. This article is published with open access at Springerlink.com