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This manuscript investigates the influence of surface deviations, i.e. curvature in double walled carbon nanotube based nano sensors. A number of papers have been published regarding the sensing characteristics of carbon nanotubes particularly single walled carbon nanotubes. The effect of waviness or curvature has been considered and modeled in single walled carbon nanotubes when used as mass or other types of sensors but very little information is available regarding the deviations in double walled carbon nanotubes and the use of such tubes as sensors. It has been found from the experimental images that double walled carbon nanotubes are not straight and that they have a significant amount of surface deviation associated with them. It is also observed that CNTs do not possess the same wavy thickness throughout their length. Hence a constant curvature or radius model may give uniform thickness in terms of curvature throughout the length which may lead to some what inaccurate results. To model the actual curvature ratio a half sine wave model has been selected which better represents the non-uniform thickness. In this paper resonant frequency of double walled carbon nanotubes (DWCNT) with deviations along it is axis and different boundary conditions namely cantilever and bridged have been investigated. The nonlinear equations of motion of the double-walled carbon nanotubes are derived by using Euler beam theory and Hamilton principle, with considering the nonlinear van der Waals forces. The sensitivity of the apparently deviated double walled carbon nanotubes, different masses (attached to the end of outer tube tip on DWCNT and center outer tube tip of the bridged DWCNT) and different lengths has been explored and presented. The dynamic response of sensors has been explained using orbit plot. The system is seen to be exhibiting an onset of periodic and quasi periodic behavior with the change in the surface deviations. The presented results clearly suggest that change in the stiffness associated with the backed out modulus leads to a frequency shift which is considered as a measure of change in mass. The results obtained have been validated with the published experimental literature as well as shell model and are found in good agreement.

This paper studies nonlinear forced vibration of multi-layered graphene sheets (MLGSs). Emphasis is placed on the anti-phase large-amplitude vibration which has the potential to overcome the van der Waals (vdW) interaction between layers for mechanical exfoliation of MLGSs. In contrast to the existing linear analyses, this paper derives a nonlinear explicit expression for analysis of large-amplitude vibration because the nonlinear term in Taylor expansion of vdW force function cannot be ignored when amplitude of vibration is large. Based on the vdW explicit formulation, a nonlinear continuum model is developed for the vibrations of MLGSs subjected to out of plane harmonic excitation in spectral neighborhood of lower resonances. The corresponding amplitude–frequency relationships are discussed comprehensively. The influence of externally excited loads on forced vibration behavior of MLGSs is also investigated. The theoretical model presented is expected to help analyze separation of MLGSs into a few- or even single-layered graphene sheets.

Radioactive Xe and Kr released from nuclear reactors and spent nuclear fuel reprocessing plants can be converted in to useful ones after the radioactive decay. The adsorption techniques employing porous materials are a cost effective solution for the capture of these volatile radionuclides compared to expensive cryogenic distillation process. Among various porous materials, metal-organic frameworks (MOFs) show excellent storage and separation properties. In this paper, we investigate the Xe and Kr adsorption properties of recently reported SBMOF-2 using van der Waals corrected density functional theory. In particular, SBMOF-2 has two types of pores with distinct linker groups along pore channels. Our studies show that Xe is preferred over Kr in both the pore channels, which are in complete agreement with experimental observations. The adsorption energies obtained for SBMOF-2 is comparable to other efficient MOFs reported in the literature for Xe/Kr separation. The two pore channels show slightly different binding energies depending on their linker groups and pore characteristics. The impact of central metal atom on adsorption properties is evaluated. A new SBMOF-2(Mg) with magnesium as central metal atom shows Xe/Kr adsorption behavior similar to the experimentally studied SBMOF-2(Ca). Next, we have investigated the effect of polarizable groups in the pore channels where linker hydrogen atoms are substituted with halogen atoms. There is a significant increase in the adsorption energy of noble gases in the halogenated pore channels. Due to the presence of halogen atoms, electron charge density redistribution takes place in the MOF network leading to permanent dipoles. Accordingly, the adsorption energies increase with the polarizability of halogen atoms. The ab initio calculations performed in this study suggest that Xe/Kr separation properties of MOFs depend upon many competing interactions, which originate from their structural and chemical properties.

Aluminene, one of the group III elemental monolayers, is predicted to be stable in the honeycomb configuration with metallic characteristics. In this paper, we consider aluminene-based heterostructures, investigating their stability, structural and electronic properties. The results based on density functional theory find that the interaction between aluminene and BN or graphene monolayers is weak, and is dominated by the van der Waals forces. The electronic structures calculated using the HSE06 functional show aluminene/graphene and aluminene/BN bilayers to be metallic. Likewise, graphene/aluminene/graphene trilayers are predicted to be metallic. However, BN/aluminene/BN trilayers are predicted to be semiconducting in nature with finite gaps. The results suggest that the interaction of Al atoms with N atoms facilitates the opening up of the gap in trilayer heterostructures, unlike the graphene/BN heterostructures, where inequivalence of the carbon lattice leads to the bandgap. The stacking-dependence of the electronic structure is affirmed by the electron tunneling characteristics calculated for the trilayer heterostructures. The predicted relationship between topology and electronic structure can, therefore, be exploited to tailor the electronic properties of aluminene-based heterostructures.

This paper investigates the inter-molecular interactions during tensile loading in ultrahigh molecular weight polyethylene (UHWMPE) single crystals at the atomistic scale. Molecular dynamics (MD) simulations of velocity controlled chain pullout are employed to study inter-molecular load transfer mechanisms. The transfer of tensile load is governed by van der Waals forces that dominate the inter-molecular shear interactions. The tensile stress build up occurs over a length of approximately 40c, where c is the lattice constant along the chain axis. Atomistic MD models incorporate the influence of surrounding neighboring atoms. Therefore, a nonlocal shear lag continuum model is developed for the first time to bridge length scales by extending the classical shear lag model of stress transfer in composites. The nonlocal model predictions correlate better with the MD results compared to the classical shear lag formulation. Combining the MD and shear lag model results, a bilinear mode II cohesive traction-separation behavior is identified to describe the inter-molecular interactions of the continuum with interface stiffness (2.38 GPa/nm), peak traction (0.14 GPa) and mode II fracture toughness (17 mJ/m2).

Rubber materials are characterized by a variety of inelasticities such as softening behavior, hysteresis loops and permanent set. In order to calculate the inelastic material behavior, constitutive models, that describe rubber as a homogeneous continuum, have to make use of damping or friction elements. On the nanoscale, there is no need to adopt such rheological models. Inelastic material behavior can be explained and simulated by a continuous rearrangement of bonds, in particular, the van der Waals interactions, and by the polymer chains transitioning between cis and trans equilibrium torsion angles. The discrete molecular dynamics simulations presented in this paper are performed in an explicit FEM environment using nonlinear but elastic force field potentials. From a structural mechanics point of view, topological changes of the polymer network can be interpreted as a sequence of local material instability problems due to negative tangential bond stiffnesses. In order to obtain representative results within reasonable computational time, the model is optimized with respect to the number of atoms and the loading velocity. It is shown that by increasing the model size, the stress–strain curves become independent of both the atoms initial state and the strain amplitudes.

The influence of van der Waals forces as interlayer non-bonded interactions on the elastic modules in graphene structures based on finite element modeling is the aim of this paper. The graphite layers and interlayer interactions were simulated using fully nonlinear spring-like elements. Detailed investigations were done for four various densities of interlayer interactions about different number of layers. Results indicate that flake’s properties show different behavior with respect to the various densities of interlayer forces. It is observed that the effect of van der Waals forces depends on the chirality of layers. Increasing the number of layers just intensify the effect of van der Waals forces. The results are compared with obtained results from molecular dynamic and finite element simulations in the open literature.

In this paper, the molecular structural mechanics method is employed to calculate the mechanical properties of a double-layered carbon graphene sheet more accurately. For this purpose, covalent bonds are modeled using nonlinear beam elements and van der Waals interactions are replaced by nonlinear truss elements. Morse potential and Lennard–Jones potential equations are used to simulate the covalent bonds and van der Waals interactions, respectively. For each atom, van der Waals forces are considered with respect to all the other atoms located in its cut-off radius. In addition to in-plane mechanical properties of single and double-layered graphene sheets some out-of-plane properties like the thickness-wise stiffness and shear modulus are studied. The results indicate that Young’s modulus of a double-layered carbon graphene sheet decreases linearly with strain while Poisson’s ratio is independent from it. Also it is noted that the thickness-wise stiffness significantly increases while the distance between the two layers declines however the shear modulus is independent from shear strain.

Thermo-elastic stress field in shock-induced multiwall carbon nanotubes (MWCNTs) is analyzed using an analytical method. The linear model of van der Waals forces is applied between two adjacent tubes in the MWCNTs with finite length to simulate the force between layers. The presented method is based on a dynamic continuum model of 3D elasticity solution in cylindrical shells. In addition, to create realistic physical properties, the temperature dependence of material properties is considered for the problem. All governing equations are transferred to frequency domain using Laplace transform technique to solve analytically the time dependent governing equations. The results in Laplace domain are transferred to time domain using an inverse Laplace transformation method. The accuracy of solution is verified by comparison with those obtained from literature. The results are obtained for two types of MWCNTs with 4 and 13 layers. To access a proper design of MWCNTs under thermal shock, the effects of their sizes on dynamic behaviors of thermal stresses are studied in details. It is found that thermal shock has a significant effect on disturbance of thermo-elastic stress filed in time domain, which is studied for various types of MWCNTs in this paper.

This paper investigates the combined bending stability of carbon nanotubes subjected to thermo-electro-mechanical loadings. Based on continuum mechanics, the Donnell shell theory is utilized to derive the critical buckling governing equations for carbon nanotubes subjected to combined thermo-electro-mechanical loadings. Both the van der Waals forces between adjacent nanotubes and the effect of the surrounding infinite elastic medium, the temperature change, the electric change, the axial loading are taken into consideration in the shell model. It is shown that the buckling bending moment only depends on the wave number of buckling modes under certain electric field and temperature field. All the related impact factors have enormous influence on the buckling bending moment for a certain buckling mode. The new features of the combined bending stability of carbon nanotubes subjected to thermo-electro-mechanical loadings will be helpful and valuable for the related applications and the dependent designs of CNT-based nano-structures serving in the complex electrical and thermal environment, especially for carbon nanotubes serving as electric conductors under combined bending load coupled with temperature change.

Detailed studies on the nanoscale vibration characteristics of multi-layered graphene sheets (MLGSs) that are embedded in an elastic medium are carried out using continuum-based modelling and Generalized Differential Quadrature (GDQ) method. Natural frequencies and their associated vibration modes of practical interest of single-layered and triple-layered graphene sheets, as well as general MLGSs that are embedded in an elastic medium are established. Numerical simulations are conducted to examine the effects of van der Waals (vdW) interactions, which are present as bonding forces between the layers, on nanoscale vibration natural frequencies and their mode shapes. The results show that for a general MLGSs embedded in an elastic medium, vibration modes can in general be classified into three families – lower classical synchronized modes which are independent of van der Waals forces and are somewhat sensitive to the surrounding elastic medium, middle van der Waals enhanced modes which are largely determined by the presence of van der Waals interactions and are hence less sensitive to the changes of the surrounding elastic medium, and higher mixed modes which are combinations of classical synchronized modes and van der Waals enhanced modes. Detailed characterizations of these modes from their derived mode shapes have been achieved for the typical case of an embedded triple-layered GSs, as well as general embedded MLGSs. Effects of Winkler modulus KW, the shear layer modulus Gb, different boundary conditions, aspect ratio β and the number L of graphene layers on nanoscale vibration properties have been examined in detail. The results presented in this paper, for the first time, provide accurate and wholesome studies and characterizations on the interesting nanoscale vibration properties of multi-layered graphene sheets embedded in an elastic medium and the results obtained will certainly be useful to those who are concerned with the dynamics of embedded graphene sheets which are increasingly being deployed for various innovative engineering applications such as nano-electro-mechanical systems (NEMS).

The mechanical stability of graphene nanoribbons (GNRs) is an important mechanical property to study, when GNRs are used as components in sensors or other nanodevices. In this paper, nonlocal effects are considered in a continuum model based theoretical analysis of the critical buckling stress of cantilevered double-layer GNRs (DLGNRs) that are subjected to an axial compressive load. The results show that the nonlocal effect has an inverse relationship with the buckling stress, and the nonlocal effect decreases with increasing aspect ratio of DLGNRs. Moreover, to the best of our knowledge this is the first report that, for DLGNRs in anti-phase modes, lower buckling mode can endure higher buckling stress because of van der Waals (vdW) interaction.

In this paper, we undertake a quantitative analysis of the reported metallic and semiconducting behaviour of electrical resistivity in perovskite manganites La1−xNaxMnO3 (x = 0.07, 0.13). We have formulated an effective inter-ionic interaction potential (EIoIP) with the long-range Coulomb, van der Waals (vdW) interaction and the short-range repulsive interaction up to second neighbor ions within the Hafemeister and Flygare approach to deduce Debye (θD), and Einstein temperature (θE). The temperature-dependent resistivity for temperatures less than metal–insulator transition (TMI), is theoretically analysed within the framework of the classical electron–phonon model of resistivity. Due to inherent low-frequency acoustic phonon as well high-frequency optical phonons, the contributions to the resistivity have been estimated. For low doping (x = 0.07; TMI = 194 K), the electron–phonon interaction is sufficient to describe the resistivity behaviour. However, additional electron–electron scattering (power temperature dependence) contribution to resistivity is required for higher doping as x = 0.13 (TMI = 301 K). For temperatures, T > TMI, the semiconducting nature is discussed with Mott’s variable range hopping (VRH) model and small polaron conduction (SPC) model. The SPC model consistently retraces the higher temperature resistivity behaviour (T > θD/2). The metallic and semiconducting behaviour of resistivity is theoretically discussed for the first time to our knowledge for La1−xNaxMnO3 in various compositions.

This paper represents the effect of nonlocal scale parameter on the wave propagation in multi-walled carbon nanotubes (MWCNTs). Each wall of the MWCNT is modeled as first order shear deformation beams and the van der Waals interactions between the walls are modeled as distributed springs. The studies shows that the scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or group speed tends to zero). The frequency at which this phenomenon occurs is called the ``Escape frequency''. The analysis shows that, for a given N-walled carbon nanotube (CNT). the nonlocal scaling parameter has a significant effect on the shear wave modes of the N - 1 walls. The escape frequencies of the flexural and shear wave modes of the N-walls are inversely proportionl to the nonlocal scaling parameter. It is also shown that the cut-off frequencies are independent of the nonlocal scale parameter. (C) 2009 Elsevier B.V. All rights reserved.

This paper investigates the effect of the geometric nonlinearity and the nonlinearity of van der Waals (vdW) force on the transverse vibration of the double-walled carbon nanotubes conveying fluid and the interaction between two types of nonlinearities. By using the Hamilton’s principle, the nonlinear governing equations of the double-walled carbon nanotubes conveying fluid are deduced. The effects of two types of nonlinearities on the coaxial and noncoaxial vibrations of the double-walled carbon nanotubes conveying fluid are discussed in numerical examples. The results show that the effect of geometric nonlinearity on the amplitude–frequency properties can be neglected if two types of nonlinearities are simultaneously considered. Compared with the uncoupling, the coupling between the longitudinal and transverse vibrations has little effect on the amplitude–frequency properties with considering two types of nonlinearities simultaneously. However, the coupling has significant effect on the amplitude–frequency properties with only considering the geometric nonlinearity.

This paper reports the result of an investigation into the wave propagation in a fluid-filled multi-walled carbon nanotubes embedded in elastic matrix, where multi-walled carbon nanotubes are considered as a multiple concentric shell coupled together through the van der Waals forces between two adjacent tubes, the surrounding matrix is considered as a spring element defined by the Winkler model, and a fluid loading term is induced by the presence of the fluid acoustic field in the innertube of multi-walled carbon nanotubes. Characteristics of wave propagation in a fluid-filled multi-walled carbon nanotubes are described through numerical examples considered the effect of matrix stiffness, van der Waals force and fluid velocity. The results obtained show that wave propagation in a fluid-filled carbon nanotubes embedded in elastic matrix exists some critical frequencies at which the velocity of wave drops dramatically and some cut-off frequencies before which the corresponding wave modes does not appear; the critical/cut-off frequency increases with the increase of matrix stiffness, and the influence of matrix is little on wave velocity in other frequency regions; there exists corresponding critical wave velocities for different wave modes when the effect of fluid velocity is considered. On the other hand, an approximate method is presented to effectively solve the wave propagation in a fluid-filled multi-walled carbon nanotubes with larger layers. This investigation may give a useful help in applications of nano-drive technology and nanopipes for conveying fluid.