Van Der Waals Interaction Coefficient Research Articles

Applicability and Limitations of Ru’s Formulation for Vibration Modelling of Double-Walled Carbon Nanotubes

In this paper, a comparison is conducted between two different formulations of the van der Waals interaction coefficient between layers, as applied to the vibrations of double-walled carbon nanotubes (DWCNTs); specifically, the evaluation of the natural frequencies is achieved through Ru’s and He’s formulations. The actual discrete DWCNT is modelled by means of a couple of concentric equivalent continuous thin cylindrical shells, where Donnell shell theory is adopted to obtain strain-displacement relationships. In order to take into account the chirality effect of DWCNT, an anisotropic elastic shell model is considered. Simply supported boundary conditions are imposed and the Rayleigh–Ritz method is used to obtain approximate natural frequencies and mode shapes. A parametric analysis considering different values of diameters and numbers of waves along longitudinal and circumferential directions is performed by adopting Ru’s and He’s formulations. From the comparisons, it is evident that Ru’s formulation provides unsatisfactory results for relatively low values of diameters and relatively high numbers of circumferential waves with respect to the more accurate He’s formulation. This behaviour is observed for every number of longitudinal half-waves. Therefore, Ru’s formulation cannot be used for the vibration modelling of DWCNTs in a large range of diameters and wavenumbers.

Investigation of Interaction of Cs Atoms with Sapphire Surface by Means of an Ultrathin Cell and the Second-Derivative Spectrometry of Vapor Absorption

The influence of interaction of Cs atoms with a dielectric surface on position and shape of the hyperfine components of the D2 line in the case of nanometer-scale distance between the atom and the surface is investigated. Using a wedged nanocell enabled investigating the dependence of shift of all hyperfine components of the D2 line corresponding to Fg = 3 → Fe = 2, 3, 4 and Fg = 4 → Fe = 3, 4, 5 transitions on distance L between the atoms and the surface of a sapphire window in the interval from 50 to 400 nm. At L smaller than 100 nm, atomic transitions experience strong broadening due to van der Waals interaction and shift to lower frequencies (the red shift). Calculation of the second derivative (SD) of the absorption spectra of vapors in a nanocell allows spectrally resolving the hyperfine components of an atomic transition down to L ~ 50 nm and determining the van der Waals interaction coefficient C3. It is demonstrated that the spectrum experiences an additional red shift with increase in the density of atoms at L < 100 nm. In contrast, a blue shift occurs with increase in the density of atoms at relatively large distances between the atoms and the surface (L ~ 400 nm). The above results are important for development of miniature submicron-size devices containing alkali metals.

Vibration isolation of few-layer graphene sheets

This work shows that a few-layer graphene with two highly-tensioned outermost layers exhibits negative effective mass and behaves like an elastic metamaterial. Actually, our simulations based on simple elastic membrane model confirm the existence of a bandgap in terahertz range within which a tensioned few-layer graphene exhibits remarkable vibration isolation: forced vibration will be highly restricted to a narrow region around the site of the applied excitation while all other parts of the graphene remain essentially static. The values of terahertz bandgap frequencies are determined by the van der Waals interaction coefficient between adjacent layers, while the width of the bandgap is determined by the number of inner layers. This research may provide new perspectives for designing and analyzing graphene-based metamaterials and nano-resonators with potential applications in high-frequency vibration controlling.

Long-Range Interactions for Hydrogen: 6P–1S and 6P–2S Systems

The collisional shift of a transition constitutes an important systematic effect in high-precision spectroscopy. Accurate values for van der Waals interaction coefficients are required in order to evaluate the distance-dependent frequency shift. We here consider the interaction of excited hydrogen 6 P atoms with metastable atoms (in the 2 S state), in order to explore the influence of quasi-degenerate 2 P and 6 S states on the dipole-dipole interaction. The motivation for the calculation is given by planned high-precision measurements of the transition. Due to the presence of quasi-degenerate levels, one can use the non-retarded approximation for the interaction terms over wide distance ranges.

Negative effective mass of a filled carbon nanotube

The present paper shows that a carbon nanotube filled with a mass chain behaves like a metamaterial which exhibits negative effective mass density within a certain range of frequencies. Unlike the known elastic metamaterials proposed in literature which are all based on artificial design of their microstructure, a filled carbon nanotube offers an already fabricated metamaterial which exhibits negative effective mass density and achieves desirable metamaterial dynamic properties even without any artificial design of microstructure. To demonstrate metamaterial dynamic behaviors of such a filled carbon nanotube, a simple continuum model is used to study flexural vibration of a hinged filled carbon nanotube. It is confirmed that the locally resonant bandgap of a filled carbon nanotube is determined by the mass of the inserted mass chain and the van der Waals interaction coefficient between the inserted mass chain and the surrounding carbon nanotube, and the expected metamaterial behavior can be demonstrated by remarkable vibration isolation. Actually, our results show clearly that when the applied excitation frequency is within the bandgap, forced vibration of a filled carbon nanotube is highly restricted to a narrow region around the site of the applied external excitation whose width is only a few times the outer diameter of the carbon nanotube.

Torsional wave propagation in multiwalled carbon nanotubes using nonlocal elasticity

Torsional wave propagation in multiwalled carbon nanotubes is studied in the present work. Governing equation of motion of multiwalled carbon nanotube is obtained using Eringen’s nonlocal elasticity theory. The effect of van der Waals interaction coefficient is considered between inner and outer nanotubes. Dispersion relations are obtained and discussed in detail. Effect of nonlocal parameter and van der Waals interaction to the torsional wave propagation behavior of multiwalled carbon nanotubes is investigated. It is obtained that torsional van der Waals interaction between adjacent tubes can change the rotational direction of multiwalled carbon nanotube as in-phase or anti-phase. The group and escape velocity of the waves converge to a limit value in the nonlocal elasticity approach.

Measurement of the van der Waals interaction by atom trajectory imaging

We study the repulsive van der Waals interaction of cold rubidium $70S_{1/2}$ Rydberg atoms by analysis of time-delayed pair correlation functions. After excitation, Rydberg atoms are allowed to accelerate under the influence of the van der Waals force. Their positions are then measured using a single-atom imaging technique. From the average pair correlation function of the atom positions we obtain the initial atom-pair separation and the terminal velocity, which yield the van der Waals interaction coefficient $C_{6}$. The measured $C_{6}$ value agrees well with calculations. The experimental method has been validated by simulations. The data hint at anisotropy in the overall expansion, caused by the shape of the excitation volume. Our measurement implies that the interacting entities are individual Rydberg atoms, not groups of atoms that coherently share a Rydberg excitation.

On the influence of van der Waals coefficient on the transverse vibration of double walled carbon nanotubes

The influence of van der Waals interaction coefficient on the vibrational properties of double-walled carbon nanotubes (DWCNTs) is studied. A high order continuum beam model is used, which can be applied to study the transverse vibrations of MWCNTs, including those that could have initial deformations due to defects or external actions. A numerical study was carried out and it was found that the non-coaxial intertube frequencies are strongly influenced by the coefficient used. The importance of this result can be valued considering that the concentric structure of DWCNTs is a crucial geometrical characteristic and a non-coaxial vibration would affect their electronic and optical properties.

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 propagation in multiwall carbon nanotubes (MWCNTs) are investigated 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 MWCNTs are more sensible to temperature than the thin ones.

Publisher's Note: Third-order perturbation theory for van der Waals interaction coefficients [Phys. Rev. A84, 052502 (2011)

Publisher's Note: Third-order perturbation theory for van der Waals interaction coefficients [Phys. Rev. A<b>84</b>, 052502 (2011)

Vibration of Axially Strained Triple-Wall Carbon Nanotubes

A comprehensive study is conducted on the vibration of axially strained triple-wall carbon nanotubes (TWCNTs). The Flugge shell theory is used, which largely improves the accuracy and enhances the scope of the research. It is found that the tensile or compressive axial strain can strengthen or weaken the structural rigidity of a TWCNT and thus, substantially upor down-shift its fundamental frequency. The strongest effect occurs for the lowest frequency associated with bending mode with a circular cross-section and radial modes with two to three circumferential waves depending on the radius and axial wavelength of TWCNTs. In addition, torsional, longitudinal or intertube radial modes largely controlled by the material constants or the interlayer van der Waals interaction coefficient are insensitive to the initial axial strain.

Structural connectivity and ionic transport in molten ZnCl 2: Optimization of chlorine interaction parameters

We report molecular-dynamics simulations of pseudoclassical models of liquid ZnCl 2 near its standard freezing point (sfp) and in thermodynamic states at higher temperature and pressure. Our calculations are firstly aimed at investigating the model sensitivity of the results for the temperature-dependent self-diffusion coefficients of the two species and for the structural connectivity of the liquid as defined in terms of corner-sharing versus edge-sharing ZnCl 4 tetrahedra. Data from coherent neutron scattering experiments near the sfp and from ionic diffusivity measurements along the standard-pressure isobar guide us to a “best” choice of the model parameters describing the electric polarizability and the van der Waals interaction coefficient of the chlorine ions. This choice also provides a consistent picture of the behaviour of the liquid under pressure: with increasing pressure the Zn ions are progressively squeezed from fourfold into sixfold coordination sites, in correspondence to crystal structures built on these two coordination states. The proposed “best” interionic force law is further tested by comparing its predictions with existing first-principles calculations on the structure of the molecular dimer Zn 2Cl 4 and with new first-principles calculations on distorted configurations of the ZnCl 2 monomer as created by extensive bond stretching or bond bending.

Surface instability of a semi-infinite anisotropic elastic body under surface van der Waals forces

We investigate the surface instability of an anisotropic elastic half-plane subjected to surface van der Waals forces due to the influence of another rigid contactor by means of the Stroh formalism. It is observed that the surface of a generally anisotropic elastic half-plane subjected to van der Waals forces from another rigid flat is always unstable. The wave number of the surface wrinkling is only reliant on the positive M 22 component of the 3 × 3 surface admittance tensor M, the van der Waals interaction coefficient β and the surface energy γ of the elastic half-plane. The decay rate of surface perturbation along the direction normal to the surface of the anisotropic half-plane is different from the wave number, a phenomenon different from that observed for an isotropic half-plane.

The effect of dimensional factors on buckling of multiwall carbon nanotubes

Based on a multiple-shell model, a comprehensive investigation has been performed on the effect of three dimensional factors, i.e., aspect ratio, the innermost radius, and the number of layers, on buckling behavior of multiwall carbon nanotubes (MWCNTs) under axial compression or radial pressure. In contrast to previous shell models, which use the single Donnell equation [Wang et al., ASME J. Appl. Mech. 71, 622 (2004)] and thus are only adequate for buckling of MWCNTs of relatively small aspect ratio (e.g., not larger than 10), the present shell model based on the simplified Flugge equation [Wang et al., ASME J. Appl. Mech. 71, 622 (2004)] allows for the study of buckling behavior of MWCNTs without any limitation on their aspect ratios. In addition, the pressure dependence of the interlayer van der Waals interaction coefficient (defined as the second derivative of the interlayer potential energy-interlayer spacing relation) has been considered for pressure-induced buckling of MWCNTs. The relevance of the present shell model for buckling of MWCNTs has been confirmed by the good agreement between the present shell model and available discrete models or experiments. Here, distinct buckling behaviors under axial compression or radial pressure are identified for long and short MWCNTs, separated by a certain critical value of aspect ratio. On the other hand, while the critical buckling load usually changes monotonically with the innermost radius an optimum value of the number of layers associated with the maximum critical buckling pressure is obtained for MWCNTs under radial pressure. In particular, the present shell model shows that the three dimensional factors effecting buckling of MWCNTs are generally interacting with, rather than being independent of, one another.

Surface Instability of a Semi-Infinite Elastic Body Under Surface van der Waals Forces

Abstract It is shown that the surface of a semi-infinite linear elastic body attracted by a rigid flat through van der Waals-like forces is always unstable. The wavelength of the surface wrinkling is finite and decreases with the van der Waals interaction coefficient. In particular, this result implies that the deformation field of the semi-infinite linear elastic body attracted by a rigid flat cannot be determined uniquely.

Static and thermoelastic properties of alkali cyanide crystals

In the present paper an attempt has been made to analyse the thermoelastic properties of alkali cyanide crystals by estimating the values of their cohesive energy, bulk modulus and their pressure derivatives, Debye temperature and Gruneisen parameter. The modified form of the three-body force shell model used in the present study consists of long-range Coulomb and three-body interactions, short-range overlap repulsion of HZ-type, and van der Waals interactions. The van der Waals interaction coefficients are determined using the Kirkwood-Muller theory based on quantum mechanical considerations. Results obtained are compared with the available experimental data. A good agreement is found.

A theoretical calculation on Schottky defects in AgCl

AbstractThe formation of Schottky defects in crystalline AgCl is investigated using interatomic potentials compatible with the macroscopic dielectric response of the solid with consistent van der Waals interaction coefficients. It is shown that two‐body central interactions in a point dipole model can yield satisfactory defect formation energy provided the dielectric polarization of the distorted defect crystal is adequately simulated. The calculated formation energy of the Schottky defect is 2.0 eV according to the potential that includes dipole—quadrupole van der Waals forces. The variation of the defect energy with temperature is studied in a quasiharmonic approximation.

Static and Thermophysical Properties of Mixed Crystal Systems

AbstractAn analysis of the interionic potential is performed to study the static and thermal properties of KClKBr and KBrKI mixed crystals for the entire range of composition. The interionic potential consists of the long‐range Coulomb and three body interaction, the short‐range van der Waals attraction, and the overlap repulsion, effective up to the second neighbour ions. Instead of using the BM‐type short‐range potential the Hafemeister and Zarht (HZ)‐type repulsive potential is considered between the nearest as well as between the next nearest neighbours. The three body charge transfer parameter f(r) and repulsive hardness parameters are evaluated using respectively the Cochran formula and overlap integrals. The van der Waals interaction coefficients are determined using the Slater‐Kirkwood variational approach. The calculated values of cohesive energy, bulk modulus, and the pressure derivatives of bulk modulus for the mixed crystals under study agree fairly well with available experimental data. The results achieved by previous investigators are also shown for the sake of comparison with the present and experimental investigations.