A Continuum Shell Model Including van derWaals Interaction for Free Vibrations of Double-Walled Carbon Nanotubes

This paper proposes the free vibration analysis of Double-Walled Carbon NanoTubes(DWCNTs).A continuum elastic three-dimensional shell model is used for natural frequency investigation of simply supported DWCNTs.The 3D shell method is compared with beam analyses to show the applicability limits of 1D beam models.The effect of van der Waals interaction between the two cylinders is shown for different Carbon NanoTube(CNT)lengths and vibration modes.Results give the van der Waals interaction effect in terms of frequency values.In order to apply the 3D shell continuum model,DWCNTs are defined as two concentric isotropic cylinders(with an equivalent thickness and Young modulus)which can be linked by means of the interlaminar continuity conditions or by means of an infinitesimal fictitious layer which represents the van der Waals interaction.

Axisymmetric compressive buckling of multi-walled carbon nanotubes under different boundary conditions

The paper studies the axisymmetric compressive buckling behavior of multi-walled carbon nanotubes （MWNTs） under different boundary conditions based on continuum mechanics model. A buckling condition is derived for determining the critical buckling load and associated buckling mode of MWNTs, and numerical results are worked out for MWNTs with different aspect ratios under fixed and simply supported boundary conditions. It is shown that the critical buckling load of MWNTs is insensitive to boundary conditions, except for nanotubes with smaller radii and very small aspect ratio. The associated buckling modes for different layers of MWNTs are in-phase, and the buckling displacement ratios for different layers are independent of the boundary conditions and the length of MWNTs. Moreover, for simply supported boundary conditions, the critical buckling load is compared with the corresponding one for axial compressive buckling, which indicates that the critical buckling load for axial compressive buckling can be well approximated by the corresponding one for axisymmetric compressive buckling. In particular, for axial compressive buckling of double-walled carbon nanotubes, an analytical expression is given for approximating the critical bucklingload. The present investigation may be of some help in fur- ther understanding the mechanical properties of MWNTs.

INVESTIGATION OF THE DYNAMIC BUCKLING OF DOUBLEWALLED CARBON NANOTUBE SUBJECTED TO AXIAL PERIODIC DISTURBING FORCES

The dynamic response of a double_walled carbon nanotube embedded in elastic medium subjected to periodic disturbing forces is investigated. Investigation of the dynamic buckling of a double_walled carbon nanotube develops continuum model. The effect of the van der Waals forces between two tubes and the surrounding elastic medium for axial dynamic buckling are considered. The buckling model subjected to periodic disturbing forces and the critical axial strain and the critical frequencies are given. It is found that the critical axial strain of the embedded multi_walled carbon nanotube due to the intertube van der Waals forces is lower than that of an embedded single_walled carbon nanotube. The van der Waals forces and the surrounding elastic medium affect region of dynamic instability. The van der Waals forces increase the critical frequencies of a double_walled carbon nanotube. The effect of the surrounding elastic medium for the critical frequencies is small.

NONLINEAR DYNAMIC INSTABILITY OF DOUBLE-WALLED CARBON NANOTUBES UNDER PERIODIC EXCITATION

A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes. Taking the geometric nonlinearity of structure deformation, the effects of van der Waals forces as well as the non- coaxial curvature of each nested tube into account, the nonlinear parametric vibration governing equations are derived. Numerical results indicate that the double-walled nanotube （DWNT） can be considered as a single column when the van der Waals forces are sufficiently strong. The stiffness of medium could substantially reduce the area of the nonlinear dynamic instability region, in particular, the geometric nonlinearity can be out of account when the stiffness is large enough. The area of the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes.

GUIDED CIRCUMFERENTIAL WAVES IN DOUBLE-WALLED CARBON NANOTUBES

A model of guided circumferential waves propagating in double-walled carbon nanotubes is built by the theory of wave propagation in continuum mechanics, while the van der Waals force between the inner and outer nanotube has been taken into account in the model. The dispersion curves of the guided circumferential wave propagation are studied, and some dispersion characteristics are illustrated by comparing with those of single-walled carbon nanotubes. It is found that in double-walled carbon nanotubes, the guided circumferential waves will propagate in more dispersive ways. More interactions between neighboring wave modes may take place. In particular, it has been found that a couple of wave modes may disappear at a certain frequency and that, while a couple of wave modes disappear, another new couple of wave modes are excited at the same wave number.

Theoretical calculations of thermophysical properties of single-wall carbon nanotube bundles

Carbon nanotube bundles are promising thermal interfacial materials due to their excellent thermal and mechanical characteristics. In this study, the phonon dispersion relations and density of states of the single-wall carbon nanotube bundles are calculated by using the force constant model. The calculation results show that the inter-tube interaction leads to a significant frequency raise of the low frequency modes. To verify the applied calculation method, the specific heat of a single single-wall carbon nanotube is calculated first based on the obtained phonon dispersion relations and the results coincide well with the experimental data. Moreover, the specific heat of the bundles is calculated and exhibits a slight reduction at low temperatures in comparison with that of the single tube. The thermal conductivity of the bundles at low temperatures is calculated by using the ballistic transport model. The calculation results indicate that the inter-tube interaction, i.e. van der Waals interaction, hinders heat transfer and cannot be neglected at extremely low temperatures. For （5, 5） bundles, the relative difference of the thermal conductivity caused by ignoring inter-tube effect reaches the maximum value of 26% around 17 K, which indicates the significant inter-tube interaction effect on the thermal conductivity at low temperatures.

Modelling of the Usefulness of Carbon Nanotubes as Antiviral Compounds for Treating Alzheimer Disease

The new generations of nano-devices successfully apply with great promise as drug carriers in the treatment of different diseases. The proposed model aims to determine the pharmacological targets and evaluate the bio-safety of usefulness of carbon nanotube conjugated with two different antiviral compounds, Acetylcholine and Ravastigmine, for treating Alzheimer disease. We also obtain the medicinal model mathematically to evaluate the interaction energy arising from encapsulation of each antiviral compound inside the single-walled carbon nanotube. Acetylcholine is modelled as two-connected spheres, while Ravastigmine has two possible structures which are an ellipsoid and cylinder, all interacting with the interior wall of single-walled carbon nanotubes with variant radii rc . Our calculations show that the single-walled carbon nanotube of radius rc greater than 3.391 Åthat will accept both drugs which are quite closer to the recent findings.

Critical Length of Double-Walled Carbon Nanotubes Based Oscillators

The critical lengths of an oscillator based on double-walled carbon nanotubes(DWCNTs)are studied by energy minimization and molecular dynamics simulation.Van der Waals(vdW)potential energy in DWCNTs is shown to be changed periodically with the lattice matching of the inner and outer tubes by using atomistic models with energy minimization method.If the coincidence length between the inner and outer tubes is long enough,the restoring force cannot drive the DWCNT to slide over the vdW potential barrier to assure the DWCNT acts as an oscillator.The critical coincidence lengths of the oscillators are predicted by a very simple equation and then confirmed with energy minimization method for both the zigzag/zigzag system and the armchair/armchair system.The critical length of the armchair/armchair system is much larger than that of the zigzag/zigzag system.The vdW potential energy fluctuation of the armchair/armchair system is weaker than that of the zigzag/zigzag system.So it is easier to slide over the barrier for the armchair/armchair system.The critical lengths of zigzag/zigzag DWCNTbased oscillator are found increasing along with temperature,by molecular dynamics simulations.

Hard-to-Soft Transition in Radial Buckling of Multi-Concentric Nanocylinders

We investigate the cross-sectional buckling of multi-concentric tubular nanomaterials, which are called multiwalled carbon nanotubes (MWNTs), using an analysis based on thin-shell theory. MWNTs under hydrostatic pressure experience radial buckling. As a result of this, different buckling modes are obtained depending on the inter-tube separation d as well as the number of constituent tubes N and the innermost tube diameter. All of the buckling modes are classified into two deformation phases. In the first phase, which corresponds to an elliptic deformation, the radial stiffness increases rapidly with increasing N. In contrast, the second phase yields wavy, corrugated structures along the circumference for which the radial stiffness declines with increasing N. The hard-to-soft phase transition in radial buckling is a direct consequence of the core-shell structure of MWNTs. Special attention is devoted to how the variation in d affects the critical tube number Nc, which separates the two deformation phases observed in N -walled nanotubes, i.e., the elliptic phase for N Nc. We demonstrate that a larger d tends to result in a smaller Nc, which is attributed to the primary role of the interatomic forces between concentric tubes in the hard-to-soft transition during the radial buckling of MWNTs.

A glance on the effects of temperature on axisymmetric dynamic behavior of multiwall carbon nanotubes

In this paper the effects of temperature on the radial breathing modes （RBMs） and radial wave propaga- tion in multiwall carbon nanotubes （MWCNTs） are inves- tigated using a continuum model of multiple elastic isotropic shells. The van der Waals forces between tubes are simulated as a nonlinear function of interlayer spacing of MWCNTs. The governing equations are solved using a finite element method. A wide range of innermost radius-to-thickness ratio of MWCNTs is considered to enhance the investigation. The presented solution is verified by comparing the results with those reported in the literature. The effects of temperature on the van der Waals interaction coefficient between layers of MWCNTs are examined. It is found that the variation of the van der Waals interaction coefficient at high temperature is sensible. Subsequently, variations of RBM frequencies and radial wave propagation in MWCNTs with temperatures up to 1 600 K are illustrated. It is shown that the thick MWC- NTs are more sensible to temperature than the thin ones.

Nanotube-based heterostructures for electrochemistry: A mini-review on lithium storage, hydrogen evolution and beyond

Nanotube-based mixed-dimensional or one-dimensional heterostructures have attracted great attention recently because of their unique physical properties and therefore potential for novel devices. Their chemical properties, however, were less explored but can be utilized for energy storage and conversion.In this review, we summarize the recent progress of nanotube-based low dimensional materials for electrochemistry, in particular, lithium storage and hydrogen evolution. First, we describe the atomic structure of low-dimensional heterostructures and briefly touch previous work on planar van der Waals heterostructures(2D+2D) in electrochemistry applications. Then we focus this review on the more recently developed nanotube-based, i.e., 1D+2D and 1D + 1D heterostructures, and discuss their various preparation approaches and electrochemical performances. Finally, we outline the challenges and opportunities in this direction and particularly emphasize the possibility of building high-performance electrodes using a single-walled carbon nanotube-based ultra-thin 1D heterostructure, and the importance of understanding the fundamental mechanism at atomic precision.

Dynamic shell buckling behavior of multi-walled carbon nanotubes embedded in an elastic medium

This paper studies the dynamic shell buckling behavior of multi-walled carbon nanotubes(MWNTs) embedded in an elastic medium under step axial load based on continuum mechanics model.It is shown that,for occurrence of dynamic shell buckling of MWNTs or MWNTs embedded in an elastic medium,the buckling stress is higher than the critical buckling stress of the corresponding static shell buckling under otherwise identical conditions.Detailed results are demonstrated for dynamic shell buckling of individual double-walled carbon nanotubes(DWNTs) or DWNTs embedded in an elastic medium.A phenomenon is shown that DWNTs or embedded DWNTs in dynamic shell buckling are prone to axisymmetric buckling rather than non-axisymmetric buckling.Numerical results also indicate that the axial buckling form shifts from the lower buckling mode to the higher buckling mode with increasing buckling stress,but the buckling mode is invariable for a certain domain of buckling stress.Further,an approximate analytic formula is presented for the buckling stress and the associated buckling wavelength for dynamic axisymmetric buckling of embedded DWNTs.The effect of radii is also examined.

DYNAMIC BUCKLING BEHAVIOR OF MULTI-WALLED CARBON NANOTUBES SUBJECTED TO STEP AXIAL LOADING

This paper studies the dynamic buckling behavior of multi-walled carbon nanotubes （MWNTs） subjected to step axial loading. A buckling condition is derived, and numerical results are presented for MWNTs under fixed boundary conditions. It is shown that the critical buckling load of MWNTs is of multi-branches and decreases as the time elongates. The associated buckling modes for different layers of MWNTs can be either in-phase or out of phase, which is related to the branch that the critical buckling load belongs to. For MWNTs with the same innermost tube radius, the critical buckling load is decreased when increasing the layers.

Modeling Frequency- and Temperature-Invariant Dissipative Behaviors of Randomly Entangled Carbon Nanotube Networks under Cyclic Loading

Recent experiments have shown that entangled networks of carbon nanotubes exhibit temperature- and frequency-invariant dissipative behaviors under cyclic loading. We have performed coarse-grained molecular dynamics simulations which show that these intriguing phenomena can be attributed to the unstable attachments/detachments between individual carbon nanotubes induced by van der Waals interactions. We show that this behavior can be described by a triboelastic constitutive model. This study highlights the promise of carbon nanomaterials for energy absorption and dissipation under extreme conditions.

Building blocks for one-dimensional van der Waals heterostructures

We recently demonstrated experimentally the synthesis of one-dimensional(1D)van der Waals(vdW)heterostructure,where single-crystal hexagonal boron nitride or molybdenum disulfide nanotubes seamlessly wrapped a singlewalled carbon nanotube and formed a coaxial hetero-nanotube with the diameter typically being 1–5 nm.1D vdW heterostructures have created large room for fundamental research from synthesis to application,but most directions are still at their initial stages.The materials that can be employed to construct 1D vdW heterostructures are limited to only a few types.In this review,we provide an outlook to the question:what are the building blocks available now and could be available in the future for the fabrication of 1D vdW heterostructures?

范德华力对多壁纳米碳管力学性质的影响

用分子动力学方法模拟了多壁纳米碳管在压缩、弯曲变形下力与变形的关系 .通过与组成多壁碳管的各单壁碳管的比较分析 ,揭示了多壁纳米碳管层间范德华力对碳管力学性质的影响 .采用Tersoff Brenner势描述每一单壁纳米碳管内原子间作用 ,采用Lennard Jones势描述碳管壁间范德华力 .计算结果表明 :多壁纳米碳管的比强度明显高于单壁纳米碳管 .纳米碳管的半径虽然对杨氏模量影响不大 ,但对纳米碳管的曲屈行为影响却相当显著 .

在受轴向周期扰动作用下双壁碳纳米管动力屈曲的研究

对双壁碳纳米管受轴向周期扰动的动力响应进行了研究· 采用连续体模型研究双壁碳纳米管的动力屈曲问题,考虑了壁间vanderWaals力和周围弹性介质对轴向动力屈曲的影响· 给出了受轴向周期扰动的屈曲模型及临界应变和临界频率· 发现双壁碳纳米管由于壁间vanderWaals力的作用较单壁碳纳米管具有较低的临界应变· vanderWaals力和周围弹性介质将影响双壁碳纳米管不稳定区,vanderWaals力使受轴向周期性扰动的双壁碳纳米管的临界频率增大。

双层碳纳米管中的周向导波

考虑双层碳纳米管的层间范德华力,采用连续介质力学的波动理论,建立了双层碳纳米管中周向导波传播模型,研究周向导波的频散现象.通过与单层碳纳米管结果的比较表明,双层碳纳米管中周向导波的传播表现出更为明显的频散特性,出现更多的模态干涉现象,并发现在某些特殊频率处出现成对模态的消失与新启现象.

轴压作用下双层碳纳米管屈曲问题的数值分析

考虑双层碳纳米管层间范德华力和弹性介质的作用,利用弹性梁理论,对轴压作用下弹性介质中碳纳米管屈曲问题进行了数值分析.

双层碳纳米管在扭矩作用下的屈曲

考虑双层碳纳米管层间范德华力的作用,利用连续介质力学的壳体理论,建立了扭矩作用下碳纳米管屈曲问题的双层弹性壳体模型,给出了相应的临界屈曲扭矩,分析了双层碳纳米管层间范德华力对临界屈曲扭矩的影响.