Buckling of spherical shells adhering onto a rigid substrate

Deformation of a spherical shell adhering onto a rigid substrate due to van der Waals attractive interaction is investigated by means of numerical minimization (conjugate gradient method) of the sum of the elastic and adhesion energies. The conformation of the deformed shell is governed by two dimensionless parameters, i.e., C_s/epsilon and C_b/epsilon where C_s and C_b are respectively the stretching and the bending constants, and epsilon is the depth of the van der Waals potential between the shell and substrate. Four different regimes of deformation are characterized as these parameters are systematically varied: (i) small deformation regime, (ii) disk formation regime, (iii) isotropic buckling regime, and (iv) anisotropic buckling regime. By measuring the various quantities of the deformed shells, we find that both discontinuous and continuous bucking transitions occur for large and small C_s/epsilon, respectively. This behavior of the buckling transition is analogous to van der Waals liquids or gels, and we have numerically determined the associated critical point. Scaling arguments are employed to explain the adhesion induced buckling transition, i.e., from the disk formation regime to the isotropic buckling regime. We show that the buckling transition takes place when the indentation length exceeds the effective shell thickness which is determined from the elastic constants. This prediction is in good agreement with our numerical results. Moreover, the ratio between the indentation length and its thickness at the transition point provides a constant number (2–3) independent of the shell size. This universal number is observed in various experimental systems ranging from nanoscale to macroscale. In particular, our results agree well with the recent compression experiment using microcapsules.     

Interionic potentials and force constant models for rocksalt structure crystals

It is suggested that the observed departure from the Cauchy relation in alkali halide structure crystals is due to ionic deformations. Interionic forces may then be taken to be central and a comparison between lattice dynamical models and interionic potential models becomes possible. In this paper attention is restricted to MgO, NaCl, LiF and KI for all of which (i) an isotropic (breathing) deformation can account for the difference C₄₄–C₁₂ and (ii) only the negative ion need be considered deformable. The interionic potential is assumed to consist of Coulombic and van der Waals terms, which are taken as known, and short range repulsive terms with an exponential dependence on separation. The constants in these repulsive terms are determined from the force constants of the lattice dynamical models. Satisfactory agreement with measured cohesive energies can be achieved only if the charge on the ions is very close to the electronic charge (2e in the case of MgO). This leads to a sacrifice in accuracy of the lattice dynamical models but this is shown to be small so that reasonable compatibility between the two sets of models is thus demonstrated. The interionic potentials are compared with those of other workers.     

Messungen der van der Waals-Wechselwirkung zwischen Edelgasatomen

Total cross sections for collisions of Helium atoms with other rare gases have been measured by modulated molecular beam technique. The results are used to determine the interaction constants of the van der Waals potential (V(r)～ ?C/r ⁶). For this purpose, an indirect procedure is adopted, since the well known approximation ofMassey andMohr (Q～C ^2/5) is not applicable for Helium scattering experiments at thermal energies. The van der Waals constants obtained are in agreement with values determined from experimental data on transport properties in gases.     

Development of a force field for molecular simulation of the phase equilibria of perfluoromethylpropyl ether

A first step towards the development of a general, realistic potential model for perfluoroether compounds has been to parameterize a united atom model for a short chain perfluoroether perfluoromethylpropyl ether (CF₃CF₂CF₂OCF₃). The potential model takes the usual form in which separate bond bending and torsional terms describe the intramolecular interactions with the addition of van der Waals and electrostatic terms to describe the non-bonded interactions. Ab initio quantum calculations have been carried out to obtain the partial charges and intramolecular torsional and bending potentials. Phase equilibrium data were then used to optimize the van der Waals interaction parameters through Gibbs ensemble Monte Carlo simulations. The resulting model reproduces vapour-liquid equilibrium densities, the critical temperature and the critical density of perfluoromethylpropyl ether, in good agreement with those from experiment.     

Selective Reflection of Laser Radiation from Ultrathin Layers of Cesium Atomic Vapors Confined in a Nanocell

The effect of the van der Waals interaction of cesium atoms with the sapphire windows of a nanocell was experimentally investigated using the selective reflection process. The distance L between the windows varied in the range of 50–2000 nm and the nanocell was filled with the vapors of cesium atoms. For the Cs atoms (the transition 6S_1/2 → 6P_1/2), the C₃ coefficient of the van der Waals interaction with the sapphire windows of the nanocell is measured. It is shown that it is possible to determine the magnetic fields with the spatial resolution of 70 nm using the selective reflection spectrum and, consequently, both the homogeneous and highly gradient magnetic fields can be measured.     

The plastic state of C2Cl6

A model structure of the plastic phase of C₂Cl₆ generated by a Monte Carlo method is compared with single crystal neutron data. The model simulates the bcc-structure by an (8 + 1) molecular cluster with a gaussian a priori molecular centre of mass distribution and hard core Cl-Cl interaction. The effective closest Cl-Cl approach is about 10 per cent smaller than the van der Waals radius observed in the low temperature normal crystalline phase of C₂Cl₆. The effect of the hard core interaction on the distribution of the molecular axes, the density of Cl, and the centre of mass distribution is clearly demonstrated.     

Improved van der Waals potentials for alkali halide crystals

Improved values of the van der Waals energy coefficients are presented for 16 alkali halides using more recent electronic polarizabilities and, for each ion, three alternative values of the effective number of electrons. The statistical method of calculating interionic potentials is used to obtain the correlation energy at small interionic separations and the values are scaled to fit the van der Waals energy at large separation. The resultant correlation energy as a function of interionic separation is fitted to both a cubic polynomial and a cr^?6 analytic form. The extent to which the van der Waals interactions are quenched by ionic overlap is derived and contrasted with Catlow et al. work on this effect.     

Anomalous character of the interaction of C<Subscript>60</Subscript> molecules with the sulfur-saturated Ta(100) surface

It is shown that, contrary to all previously studied systems, heating to ～800 K in the C₆₀? TaS² monolayer-Ta(100) adsorption system leads to the complete removal of the deposited fullerene molecules. A model is proposed that explains the observed phenomenon by a very weak nonchemisorption interaction between the C₆₀ molecules and the valence-saturated surface of tantalum disulfide that forms layered crystals with van der Waals interaction between layers.     

Calculated pressure effects on spectral lines for long-range interatomic potentials: Rb and Cs with heavy rare gases

We have calculated the impact broadening and shift of the first and second doublets of Rb and Cs. The interaction potential of the collision pair is assumed to be a long-range van der Waals potential. The van der Waals constants involved are provided by recent theoretical calculations. We obtain good agreement between the calculated and experimental values for both the P_{$\text{1}\text{2}$} and P_{$\text{3}\text{2}$} component. Comparison of our calculated values is also made with those of Granier, Granier and Schuller.     

High-accuracy calculations of dipole, quadrupole, and octupole electric dynamic polarizabilities and van der Waals coefficients C 6, C 8, and C 10 for alkaline-earth dimers

The static and dynamic electric dipole, quadrupole, and octupole polarizabilities of the alkaline-earth atoms (beryllium, magnesium, calcium, strontium, and barium) in the ground state were calculated. The dynamic polarizabilities obtained were used to calculate the van der Waals coefficients C ₆, C ₈, and C ₁₀ of alkaline-earth metal dimers for the interaction of two like atoms in the ground state. The results are compared with other theoretical and experimental data.     

The generalised Huggins-Mayer form of born repulsive potentials for NaCl-type alkali halides

The generalised Huggins-Mayer form of Born repulsive potentials for NaCl-type alkali halides have been re-evaluated using more reliable, recently published thermodynamic data and van der Waals energy coefficients. As with older versions of these potentials excellent agreement between model and experimental values of interionic distance and cohesive energy is achieved. Further, the earlier shortcomings in the failure of the stability condition and predicted elastic constants are significantly reduced. For the majority of salts the new short-range interactions have stronger van der Waals attractions and slider repulsions. The model gives average crystal radii for the alkali ions about ~0.3 Å larger than traditional free ion radii and ~0.08 Å larger than Tosi-Fumi crystal radii. The predicted halogen crystal radii are correspondingly smaller by the same amounts.     

Mixing rules and effective potentials in gaseous mixtures

We generate exact mixing rules for dilute gaseous mixtures with nonconformal interactions by introducing an adequate effective potential. The general mixing rule leads to several approximations of the van der Waals type. The work uses nonconformal model pair potentials that accurately describe the pure fluid properties. The validity of the approximate mixing rules is assessed by comparison with exact results for binary mixtures over wide ranges of temperature and composition. Large differences in energy, size and potential profile are considered. The simplest mixing rules are straightforward generalizations of the van der Waals rules and one version, based on a square-well (SW) approximation, performs with high precision for all systems except for those with extreme differences in molecular size. The SW mixing rule is used to predict excess virial coefficients of mixtures involving Ar, Kr, H₂ and CF₄.     

Lattice dynamics and ionic charge of VI2

We present an Extended Shell Model calculation of the phonon dispersion curves in VI₂. The dynamical matrix is derived from interionic potentials including Coulomb monopole and dipole, van der Waals, nearest-neighbor and next-nearest-neighbor Born-Mayer repulsive interactions. The potential parameters are either known in literature or derived from lattice constants and cohesive energy. A suitable choice of only three adjustable parameters (net charge Z, shell charge and shell-core displacement) yields an excellent fit of the five optical frequencies and of the anion static dipole. The resulting ionic charge Z = 0.75 is very well consistent with the recent neutron data on transferred hyperfine interaction.     

Packing of linearly arranged benzene molecules inside single walled carbon nanotubes: The high pressure study

The high pressure behaviors and electronic properties of (C₆H₆)_n@SWCNT peapod structure with the different encapsulation densities are studied by the DFT calculation. The weak van der Waals interaction and electronic orbital hybridization interaction between the host and guest molecules are exhibited in the pressure lower and higher than 3 GPa, respectively. The encapsulation density of C₆H₆ molecules plays an important role in the structural deformation, the bonding behaviors, and the electronic orbital hybridization interaction of the considered four hybrid systems under the pressures.     

Parametrization of the hybrid potential for pairs of neutral atoms

The hybrid form is a combination of the Rydberg potential and the London inverse-sixth-power energy. It is accurate at all relevant distance scales and simple enough for use in all-atom simulations of biomolecules. One may compute the parameters of the hybrid potential for the ground state of a pair of neutral atoms from their internuclear separation, the depth and curvature of their potential at its minimum, and from their van der Waals coefficient of dispersion C₆.     

Modeling of the structure and electronic structure of condensed phases of small fullerenes C<Subscript>28</Subscript> and Zn@C<Subscript>28</Subscript>

A comparative analysis of the stability factors and electronic structure of two possible crystalline forms of small fullerene C₂₈ and endohedral fullerene Zn@C₂₈ with diamond and lonsdaleite structures is performed using a cluster model. Atoms of elements that, when placed inside C₂₈ cages, have no significant effect on the stability of free small-fullerene molecules are shown to be able to dramatically change the electronic properties and reactivity of the C₂₈ skeleton and to be favorable for forming small-fullerene crystalline modifications, which are covalent crystals. In contrast, if the presence of foreign atoms inside C₂₈ cages stabilizes the isolated nanoparticles, then molecular crystals (such as C₆₀ fullerites) are formed due to weak van der Waals forces.     

Caloric properties of liquid alcohols - H-bonded liquids continuum or spectroscopic determined mixture model,is that really the question?

It is discussed that the spectroscopic based mixture model of H-bonded liquids is qualified as efficient approximation to calculate caloric properties. The specific heat, enthalpy and heat of evaporization of liquid CH₃OH and C₂H₅OH are calculated from the melting point till overcritical temperature with the spectroscopic determined content O_f of non H-bonded OH groups and the H-bond energy. The good agreement between the results of water and the two alcohols shows the efficiency of the simplified model although O_f, the ratio of van der Waals to H-bond energy and the coordination numbers are totally different in both cases.     

Electronic structure of solid C48N12 aza-fullerene

I report electronic structures and the cohesive energy for face-centered-cubic (fcc) solid C₄₈N₁₂ using generalized-gradient density-functional theory. The full vibrational spectrum of the C₄₈N₁₂ cluster is calculated within the harmonic approximation at the B3LYP/6-31G* level of theory. The results show that fcc is energetically preferred and a more stable crystal form than body-centered-cubic (bcc). C₄₈N₁₂ clusters are found to condense by a weak (0.29 eV) van der Waals force. The band gap of fcc C₄₈N₁₂ is calculated to be 1.3 eV at the GGA-PW91 level, whereas the HOMO-LUMO gap is calculated to be 2.74 eV using B3LYP/6-31G*.     

Evidence for a solid phase of dodecahedral C 20

Evidence is presented for the formation of a solid phase based on the smallest fullerene, C₂₀, in thin diamond-like carbon films deposited by ultraviolet laser ablation from diamond onto nickel substrates at room temperature in the presence of 10^-4 torr of cyclohexane or benzene. Laser desorption mass spectrometry from the films shows the presence of C₂₀, C₂₁ and C₂₂ species, while micro-Raman spectroscopy and electron diffraction from selected particles together with first principle density-functional calculations, indicate a cubic solid with dodecahedral C₂₀ cages as building blocks. Unlike solid C₆₀ and fully protonated C₂₀, which are bound by van der Waals forces, the proposed structure is stabilized by linking of the C₂₀ dodecahedra with bridging carbon atoms at interstitial tetrahedral sites to form a face-centered-cubic lattice with 22 carbon atoms per unit cell. Received 10 October 2002 / Received in final form 24 December 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: zafar.iqbal@njit.edu