The influence of mechanical deformation on the electrical properties of single wall carbon nanotubes

Recent experimental studies and atomistic simulations have shown that carbon nanotubes (CNTs) display strong interplay between the mechanical deformation and electrical properties. We have developed a simple and accurate method to determine atom positions in a uniformly deformed CNT via a continuum analysis based on the interatomic potential. A shift vector is introduced to ensure the equilibrium of atoms. Such an approach, involving only three variables for the entire CNT, agrees very well with the molecular mechanics calculations. We then study the effect of mechanical deformation on the band gap change of single wall CNTs under tension, torsion, and combined tension/torsion via the k-space tight-binding method. Prior studies without this shift vector lead to significant overestimation of the band gap change. It is established that the conducting CNTs may easily become semi-conducting ones subject to mechanical deformation, but the semi-conducting CNTs never become conducting ones upon deformation.     

Quantum field induced strains in nanostructures and prospects for optical actuation

We develop the mechanics theory of a phenomenon in which strain is induced in nanoscale structures in the absence of applied stress, due solely to the presence of quantum mechanical confinement of charge carriers. The direct effect of strain on electronic structure has been widely studied in recent years, but the “reverse coupling” effect that we investigate, which is only appreciable in the smallest structures, has been largely ignored even though its effects are present in first principles atomistic calculations. We develop a simple effective mass approach that can be used to model this universal physical phenomenon allowing a transparent scheme to identify its occurrence. We relate quantum field induced strain to acoustic polarons and identify the presence of this effect in density functional theory calculations of strain and quantum confinement in free-standing Si and GaAs quantum dots. Finally, we discuss the use of this quantum confinement induced strain as a mechanism for universal optical actuation in nanowire structures in the context of recent experimental results on carbon nanotubes.     

Mechanics of deformation of single- and multi-wall carbon nanotubes

An effective continuum/finite element (FE) approach for modeling the structure and the deformation of single- and multi-wall carbon nanotubes (CNTs) is presented. Individual tubes are modeled using shell elements, where a specific pairing of elastic properties and mechanical thickness of the tube wall is identified to enable successful modeling with shell theory. The incorporation and role of an initial internal distributed stress through the thickness of the wall, due to the cylindrical nature of the tube, are discussed. The effects of van der Waals forces, crucial in multi-wall nanotubes and in tube/tube or tube/substrate interactions, are simulated by the construction of special interaction elements.The success of this new CNT modeling approach is verified by first comparing simulations of deformation of single-wall nanotubes with molecular dynamics results available in the literature. Simulations of final deformed configurations, as well strain energy histories, are in excellent agreement with the atomistic models for various deformations. The approach was then applied to the bending of multi-wall carbon nanotubes (MWNTs), and the deformed configurations were compared to corresponding high-resolution images from experiments. The proposed approach successfully predicts the experimentally observed wavelengths and shapes of the wrinkles that develop in bent MWNTs, a complex phenomenon dominated by inter-layer interactions. Presented results demonstrate that the proposed FE technique could provide a valuable tool for studying the mechanical behavior of MWNTs as single entities, as well as their effectiveness as load-bearing entities in nanocomposite materials.     

Deformation of metallic single-walled carbon nanotubes in electric field based on elastic theory

The electromechanical properties of metallic single-walled carbon nanotubes (SWCNTs) in the electric field are demonstrated with a column shell model in this paper.A hemisphere model is introduced to determine the charge distribution and the local electric field in SWCNTs.By treating the SWCNT as an elastic column shell,the analytical solutions of the charged SWCNT’s axial strain and the radial strain are obtained.SWCNTs with a larger aspect ratio show greater deformation.The greatest radial deformation appears at the end of the tube.The significant axial strain can be induced in CNTs with a large length (around 100 nm) even though the applied electric field is not strong enough.When SWCNTs are fixed at both ends,the radius of SWCNTs becomes small along the axial position.     

Study of dynamic stability of the double-walled carbon nanotube under axial loading embedded in an elastic medium by the energy method

In this paper, the dynamic stability of single- and double-walled carbon nanotubes (SWCNT and DWCNT) under dynamic axial loading is investigated using the continuum mechanics model and the minimum total energy method. The natural frequencies of the SWCNT and the critical dynamic axial load of the SWCNT and DWCNT are obtained using the Rayleigh-Ritz method. The effects of the elastic medium and the van der Waals forces between the two layers in the DWCNT are taken into account using the Winkler model and Lennard-Jones theory, respectively. The effect of the small length scale is also considered using the Eringen Model. The critical dynamic axial load is increased by inserting an inner carbon nanotube (CNT) into an isolated CNT embedded in an elastic medium.     

压电体中考虑表面效应时开裂孔洞的断裂特征

研究了反平面机械载荷和面内电载荷作用下压电体中考虑表面效应时孔边双裂纹问题的断裂特征。基于Gurtin-Murdoch表面理论模型，通过构造映射函数，利用复势电弹理论获得了应力场和电位移场的闭合解答。给出了裂纹尖端应力强度因子、电位移场强因子和能量释放率的解析解。讨论了开裂孔洞几何参数和施加力电载荷对电弹场强因子和能量释放率的影响。     

典型纳尺度结构的热振动

热振动是一定温度下纳尺度结构的固有运动,对其动力学行为有着重要的影响.当空间进入纳米尺度,结构呈现离散性,量子效应、边界效应、范德华力等变得不可忽略,纳尺度结构在热噪声随机激励下的动力学行为表现出众多异乎寻常的特性.以碳纳米管和石墨烯为代表的纳尺度碳材料具有优良的力学、电学和化学性质.在此介绍多种针对纳尺度结构热振动问题的研究方法、及碳纳米管和石墨烯的低温热振动、碳纳米管的非线性热振动研究进展.     

Multiscale computations for carbon nanotubes based on a hybrid QM/QC (quantum mechanical and quasicontinuum) approach

An effective multiscale computing scheme based on QM/QC (quantum mechanics/quasicontinuum) is applied for simulation of Carbon nanotubes (CNTS) mechanics. First, quasicontinuum simulation of deformations of curved crystalline structures is conducted to examine the fully nonlocal behavior of CNTs with the aid of high-order interpolation functions and the “cluster” concept, which facilitates accurate energy approximation for crystals. Next, a multiscale computing approach based on QM/QC hybridization is devised, and applied for simulation of CNT mechanics. The bonding configuration changes, e.g. bond breaking or creation, near defect sites are correctly represented with the QM/QC hybrid model. For studying electronic properties coupled with the mechanical deformation of CNTs, the change of the electrical properties from an initial semiconductor into metal under mechanical bending is investigated. Single-walled CNTs having various types of defects and subjected to uniaxial tension are considered for fracture. The theoretical strength of the CNTs in the presence of each defect is computed based on the QM/QC hybrid scheme, wherein the defect neighborhood is modeled as a QM zone for a first-principle-based calculation using density functional theory (DFT), and the remaining area as a QC zone. This multiscale computing approach greatly improves the accuracy in the prediction of the failure strains of CNTs over a purely molecular mechanical or quasicontinuum method.     

Closed form solution for two unequal collinear semi-permeable straight cracks in a piezoelectric media

The problem of two unequal collinear straight cracks weakening a poled transversely isotropic piezoelectric ceramic is addressed under semi-permeable electric boundary conditions on the crack faces. The plate has been subjected to combined in-plane normal(to the faces of the cracks) mechanical and electric loads. Problem is formulated employing Stroh formalism and solved using complex variable technique. The elastic field, electric field and energy release rate are obtained in closed analytic form. A case study is presented for poled PZT-5H cracked plate to study the effect of prescribed mechanical load, electric load, inter-crack distance and crack lengths on crack arrest parameters stress intensity factor (SIF), electric displacement intensity factor (EDIF) and mechanical and total energy release rates (ERR). Moreover a comparative study is done of impermeable and semi-permeable crack face boundary conditions on SIF, EDIF and ERR, and results obtained is presented graphically. It is observed that the effect of dielectric medium in the crack gap cannot be ignored.     

Thermal effects on interfacial stress transfer characteristics of carbon nanotubes/polymer composites

The paper presents an analytical method to investigate thermal effects on interfacial stress transfer characteristics of single/multi-walled carbon nanotubes/polymer composites system under thermal loading by means of thermoelastic theory and conventional fiber pullout models. In example calculations, the mechanical properties and the thermal expansion coefficients of carbon nanotubes and polymer matrix are, respectively, treated as the functions of temperature change. Numerical examples show that the interfacial shear stress transfer behavior can be described and affected by several parameters such as the temperature field, volume fraction of CNT, and numbers of wall layer and the outermost radius of carbon nanotubes. From the results carried out it is found that mismatch of thermal expansion coefficients between the carbon nanotubes and polymer matrix may be more important in governing interfacial stress transfer characteristics of carbon nanotubes/polymer composite system.     

An analytical molecular structural mechanics model for the mechanical properties of carbon nanotubes

An analytical molecular structural mechanics model for the prediction of mechanical properties of defect-free carbon nanotubes is developed by incorporating the modified Morse potential with an analytical molecular structural model. The developed model is capable of predicting Young’s moduli, Poisson’s ratios and stress–strain relationships of carbon nanotubes under tension and torsion loading conditions. Results on the mechanical properties of single-walled carbon nanotubes show that Young’s moduli of carbon nanotubes are sensitive to the tube diameter and the helicity. Young’s moduli of both armchair and zigzag carbon nanotubes increase monotonically and approach Young’s modulus of graphite when the tube diameter is increased. The nonlinear stress–strain relationships for defect-free nanotubes have been predicted, which gives a good approximation on the ultimate strength and strain to failure of nanotubes. Armchair nanotubes exhibit higher tensile strength than zigzag nanotubes but their torsion strengths are identical based on the present study. The present theoretical investigation provides a very simple approach to predict the mechanical properties of carbon nanotubes.     

A dielectrophoretic study of the carbon nanotube chaining process and its dependence on the local electric fields

The chaining process of a system of interacting carbon nanotubes (CNTs) under an alternating current electric field is investigated at two regions of different electric field characteristics. For the region of uniform electric field (far from the electrodes), a two-dimensional multiparticle approach based on the dielectrophoretic (DEP) theory and classical mechanics is proposed to investigate the CNT rotational and translation motion. For this scenario, CNT rotation and alignment along the electric field direction occurs first, followed by the translation and chaining processes which were found to be highly dependent on the CNT-to-CNT initial configuration. On the other hand, the presence of high electric field gradients governs the CNT chaining at regions near the electrodes. DEP forces caused by such gradients were computed by finite element analysis and compared to the magnitude of the CNT-to-CNT interacting forces at zones of uniform electric fields. A critical distance of CNT-to-CNT separation was estimated, which determines if a CNT is attracted towards the electrode or if it is attracted by other CNTs away from the electrodes. Experimental evidence of CNTs dynamic motion under electric fields is presented to support the predicted trends.     

Dynamic and buckling analysis of polymer hybrid composite beam with variable thickness

This work deals with a study of the dynamic and buckling analysis of polymer hybrid composite(PHC) beam. The beam has variable thickness and is reinforced by carbon nanotubes(CNTs) and nanoclay(NC) simultaneously. The governing equations are derived based on the first shear deformation theory(FSDT). A three-phase HalpinTsai approach is used to predict the mechanical properties of the PHC. We focus our attention on the effect of the simultaneous addition of NC and CNT on the vibration and buckling analysis of the PHC beam with variable thickness. Also a comparison study is done on the sensation of three impressive parameters including CNT, NC weight fractions, and the shape factor of fillers on the mechanical properties of PHC beams,as well as fundamental frequencies of free vibrations and critical buckling load. The results show that the increase of shape factor value, NC, and CNT weight fractions leads to considerable reinforcement in mechanical properties as well as increase of the dimensionless fundamental frequency and buckling load. The variation of CNT weight fraction on elastic modulus is more sensitive rather than shear modulus but the effect of NC weight fraction on elastic and shear moduli is fairly the same. The shape factor values more than the medium level do not affect the mechanical properties.     

低维碳和氮化硼材料的物理力学研究进展

碳纳米管、石墨烯和六方氮化硼等低维材料具有优异的力学和电学性质,已经引起广泛的科学兴趣。然而由电荷、分子轨道、电子结构和自旋态构成的低维材料的局域场与力学变形、机械运动和物理化学环境等外场间往往存在强烈耦合,这导致低维材料会呈现出新颖独特的物理力学性能。论文对近年来碳纳米管、石墨烯和六方氮化硼等低维材料的力学性能、力电耦合与器件原理、表面和界面结构性能调控、层间相互作用、能量耗散和摩擦等物理力学方面的研究进展进行了简要综述,并讨论了利用低维材料多场耦合特性和结构性能关联发展新型功能器件的方法和途径,以及纳米力学和纳尺度物理力学的前沿和发展趋势。     

An elastic model for bioinspired design of carbon nanotube bundles

Collagen fibers provide a good example of making strong micro-or mesoscale fibers from nanoscale tropocollagen molecules through a staggered and crosslinked organization in a bottom-up manner.Mimicking the architectural features of collagen fibers has been shown to be a promising approach to develop carbon nanotube(CNT)fibers of high performance.In the present work,an elastic model is developed to describe the load transfer and failure propagation within the bioinspired CNT bundles,and to establish the relations of the mechanical properties of the bundles with a number of geometrical and physical parameters such as the CNT aspect ratio and longitudinal gap,interface cross-link density,and the functionalizationinduced degradation in CNTs,etc.With the model,the stress distributions along the CNT-CNT interface as well as in every individual CNT are well captured,and the failure propagation along the interface and its effects on the mechanical properties of the CNT bundles are predicted.The work may provide useful guidelines for the design of novel CNT fibers in practice.     

Computer simulation of mechanical properties of carbon nanostructures

The aim of the present paper is the theoretical investigation of the mechanical properties of carbon nanostructures of graphene and single-wall carbon nanotubes by using nanoscopic and macroscopic approaches. The nanoobject structures in free and deformed states were considered and the corresponding energies were computed in the framework of quantum mechanics methods by using the original software package of semi-empirical programsNDDO/sp-spd (developed in the Institute of Applied Mechanics, Russian Academy of Sciences) in parallel computations. The nanostructural deformations were prescribed in the approximation of the mechano-chemical deformation coordinate. The deformation forces were described by the energy gradients in selected coordinates of microscopic deformations. The mechanical characteristics of nanoobjects such as Young’s modulus, rigidity coefficients, works done in deformation, critical stresses, and relative elongations in fracture were calculated in the framework of the macroscopic linear theory of elasticity; the deformation forces determined by quantum mechanical calculations were used in the corresponding relations. It was found that the mechanical characteristics of single-wall carbon nanotubes (CNT) depend on their diameter and chirality, and the deformation properties of a graphene sheet are asymmetric with respect to two normal extension modes directed along the “zigzag” and “armchair” on the sheet edges. The calculated mechanical characteristics are in good agreement with the experimental data known fromthe literature, in both the values and the deformation asymmetrywith respect to different deformation modes.     

Dynamic response of a cracked piezoelectric ceramic under arbitrary electro-mechanical impact

The dynamic response of a cracked piezoelectric ceramic under in-plane electric and anti-plane mechanical impact is investigated by the integral transform method. The electric and mechanical loads are assumed to be arbitrary functions of time. It is shown that the dynamic crack-tip stress and electric displacement fields still have a square-root singularity. Numerical computations for the dynamic stress intensity factor show that the electric load has a significant influence on the dynamic response of stress field. On the other hand, the dynamic response of the electric field is determined solely by the applied electric field. The electric field will promote or retard the propagation of the crack depending on the time elapsed since the application of the external electro-mechanical loads.     

A single degree of freedom ‘lollipop’ model for carbon nanotube bundle formation

Current carbon nanotube (CNT) synthesis methods include the production of ordered, free-standing vertically aligned arrays, the properties of which are partially governed by interactions between adjacent tubes. Using material parameters determined by atomistic methods, here we represent individual CNTs by a simple single degree of freedom ‘lollipop’ model to investigate the formation, mechanics, and self-organization of CNT bundles driven by weak van der Waals interactions. The computationally efficient simple single degree of freedom model enables us to study arrays consisting of hundreds of thousands of nanotubes. The effects of nanotube parameters such as aspect ratio, bending stiffness, and surface energy, on formation and bundle size, as well as the intentional manipulation of bundle pattern formation, are investigated. We report studies with both single wall carbon nanotubes (SWCNTs) and double wall carbon nanotubes (DWCNTs) with varying aspect ratios (that is, varying height). We calculate the local density distributions of the nanotube bundles and show that there exists a maximum attainable bundle density regardless of an increase in surface energy for nanotubes with given spacing and stiffness. In addition to applications to CNTs, our model can also be applied to other types of nanotube arrays (e.g. protein nanotubes, polymer nanofilaments).     

Energy density theory formulation and interpretation of cracking behavior for piezoelectric ceramics

Any attempt made to separate energy into electrical and mechanical parts may lead to inconsistencies as they do not necessarily decouple. This is illustrated by application of the energy density function in the linear theory of piezoelasticity. By assuming that a critical energy density function prevails at the onset of crack initiation, it is possible to establish the relative size of an inner and outer damage zone around the crack tip; they correspond to the ligaments at failure caused by pure electric field and pure mechanical load. On physical grounds, the relative size of these zones must depend on the relative magnitude of the mechanical and electrical load. Hence, they can vary in size depending on the electromechanical material and damage resistance properties. Numerical results are obtained for the PZT-4, PZT-5H, and P-7 piezoelectric ceramics. These two ligaments for the two damage zones may coincide for appropriate values of the applied electrical field and mechanical load.Explicit expression of the energy density factor S is derived showing the mixed mode electromechanical coupling effects. The factor S can increase or decrease depending on the direction of the applied electric field with reference to the poling direction. This is in contrast to the result obtained from the energy release rate quantity, which remains unchanged for electric field in the direction of poling or against it.     

单壁碳纳米管屈曲的原子/连续介质混合模型

用数学和力学研究所，上海 200072)//力学学报.--2004,36(6).--744～748 提供了一种运用原子/连续介质混合(hybrid atomic/continuum,HAC)方法解决纳米力学问题的思路. 通过在连续介质力学模型中引入利用分子力学方法获得物性参数，建立了预测单壁碳纳米管临界屈曲参数的HAC模型. 结果表明, HAC模型具有与连续介质力学模型可比拟的简洁性, 同时可表征纳米管微观结构特征对屈曲参数的影响. 计算结果表明，Zigzag纳米管的抗屈曲性能优于Armchair纳米管. 基于Tersoff-Brenner作用势的分子动力学结果证实了这一结论.