Nonretarded Van Der Waals Interaction Research Articles

Long-Range Repulsion Between Spatially Confined van der Waals Dimers.

It is an undisputed textbook fact that nonretarded van der Waals (vdW) interactions between isotropic dimers are attractive, regardless of the polarizability of the interacting systems or spatial dimensionality. The universality of vdW attraction is attributed to the dipolar coupling between fluctuating electron charge densities. Here, we demonstrate that the long-range interaction between spatially confined vdW dimers becomes repulsive when accounting for the full Coulomb interaction between charge fluctuations. Our analytic results are obtained by using the Coulomb potential as a perturbation over dipole-correlated states for two quantum harmonic oscillators embedded in spaces with reduced dimensionality; however, the long-range repulsion is expected to be a general phenomenon for spatially confined quantum systems. We suggest optical experiments to test our predictions, analyze their relevance in the context of intermolecular interactions in nanoscale environments, and rationalize the recent observation of anomalously strong screening of the lateral vdW interactions between aromatic hydrocarbons adsorbed on metal surfaces.

Effect of surface roughness on van der Waals and Casimir-Polder/Casimir attraction energies

A theoretical model is devised to assess effects of surface roughness on dispersion interactions between macroscopic bodies, bounded by self-affine fractal surfaces and separated by a vacuum gap. The rough-surface profiles are described statistically by the saturation values of surface width and the correlation lengths; i.e., in terms of experimentally measurable quantities. The model devised takes into account the separation distance-dependent nature of dispersive interactions. The case of non-retarded van der Waals interactions, known to operate at smaller separation distances between the bodies, and that of retarded attractions, operative at larger separation length-scales, are treated separately in this work. Analytical formulae for the roughness corrections are deduced for the two aforementioned types of attractions. The model is employed to compute roughness corrections to interactions between an extended body, bounded by a self-affine surface, and: a) a point-like adherent; and b) a planar half-space. Furthermore, the roughness-induced corrections to dispersive interaction energies between half-spaces, both bounded by self-affine surfaces, are obtained under assumption that the corresponding surface profiles are not correlated. The predictions of the model are compared with some previously reported theoretical studies and available experimental data on the theme of dispersive adhesion between macroscopic bodies.

Van der Waals interaction between a moving nano-cylinder and a liquid thin film.

We study the static and dynamic interaction between a horizontal cylindrical nano-probe and a thin liquid film. The effects of the physical and geometrical parameters, with a special focus on the film thickness, the probe speed, and the distance between the probe and the free surface are analyzed. Deformation profiles have been computed numerically from a Reynolds lubrication equation, coupled to a modified Young-Laplace equation, which takes into account the probe/liquid and the liquid/substrate non-retarded van der Waals interactions. We have found that the film thickness and the probe speed have a significant effect on the threshold separation distance below which the jump-to-contact instability is triggered. These results encourage the use of horizontal cylindrical nano-probes to scan thin liquid films, in order to determine either the physical or geometrical properties of the latter, through the measurement of interaction forces.

Casimir-Lifshitz interaction between ZnO and SiO2nanorods in bromobenzene turns repulsive at intermediate separations due to retardation effects

We consider the interaction between a ZnO nanorod and a SiO${}_{2}$ nanorod in bromobenzene. Using optical data for the interacting objects and ambient we calculate the force (from short-range attractive van der Waals force to intermediate-range repulsive Casimir-Lifshitz force to long-range entropically driven attraction). The nonretarded van der Waals interaction is attractive at all separations. We demonstrate a retardation-driven repulsion at intermediate separations. At short separations (in the nonretarded limit) and at large separations (in the classical limit) the interaction is attractive. These effects can be understood from an analysis of multiple crossings of the dielectric functions of the three media as functions of imaginary frequencies.

The boundary element approach to Van der Waals interactions

We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response of a general boundary shape. We achieve this by rewriting the interaction energy expression presented in Phys. Rev. B, 62 (2000) 6997 exclusively in terms of surface integrals of surface operators. We validate this approach in the Lifshitz case and give numerical results for the interaction of two spheres as well as the van der Waals self-interaction of a uniaxial ellipsoid. Our method is simple to implement and is particularly suitable for a full, non-perturbative numerical evaluation of non-retarded van der Waals interactions between objects of a completely general shape.

Effect of polyimide layer surfaces on pretilt angles and polar anchoring energy of liquid crystals

Considering the surface distribution of polyimide chains, the properties of the unidirectional out-of-plane nematic liquid crystal tilt angle are investigated in view of the van der Waals interaction between nematic liquid crystal molecules and two polyimide layers: the anisotropic upper layer and the isotropic lower layer. The dependence of the pretilt angle upon the thickness of the upper polyimide layer oriented by rubbing is estimated from experiment and theory. Another experimental result shows that the relation between the anchoring energy and the thickness of the polyimide layer could be dependent on lower material. This was also explained in view of the nonretarded van der Waals interaction.

Excess free energy and Casimir forces in systems with long-range interactions of van der Waals type: General considerations and exact spherical-model results

We consider systems confined to a d-dimensional slab of macroscopic lateral extension and finite thickness L that undergo a continuous bulk phase transition in the limit L --> infinity and are describable by an O(n) symmetrical Hamiltonian. Periodic boundary conditions are applied across the slab. We study the effects of long-range pair interactions whose potential decays as bx-(d+sigma) as x --> infinity, with 2<sigma<4 and 2<d+sigma< or =6, on the Casimir effect at and near the bulk critical temperature Tc,infinity, for 2<d<4. These interactions decay sufficiently fast to leave bulk critical exponents and other universal bulk quantities unchanged--i.e., they are irrelevant in the renormalization group (RG) sense. Yet they entail important modifications of the standard scaling behavior of the excess free energy and the Casimir force Fc. We generalize the phenomenological scaling Ansätze for these quantities by incorporating these long-range interactions. For the scaled reduced Casimir force per unit cross-sectional area, we obtain the form LdFc/kBt approximately Xi0(L/xi infinity) + g omegaL -omega Xi omega (L/Xi infinity) + g sigma L -omega sigma Xi sigma (L/Xi infinity). Here Xi0, Xi omega, and Xi sigma are universal scaling functions; g omega and g sigma are scaling fields associated with the leading corrections to scaling and those of the long-range interaction, respectively; omega and omega sigma = sigma + eta - 2 are the associated correction-to-scaling exponents, where eta denotes the standard bulk correlation exponent of the system without long-range interactions; xi infinity is the (second-moment) bulk correlation length (which itself involves corrections to scaling). The contribution proportional variant g sigma decays for T not = Tc,infinity algebraically in L rather than exponentially, and hence becomes dominant in an appropriate regime of temperatures and L. We derive exact results for spherical and Gaussian models which confirm these findings. In the case d + sigma = 6, which includes that of nonretarded van der Waals interactions in d = 3 dimensions, the power laws of the corrections to scaling proportional to b of the spherical model are found to get modified by logarithms. Using general RG ideas, we show that these logarithmic singularities originate from the degeneracy omega = omega sigma = 4 - d that occurs for the spherical model when d + sigma = 6, in conjunction with the b dependence of g omega.

Observation of Atom Wave Phase Shifts Induced by Van Der Waals Atom-Surface Interactions

The development of nanotechnology and atom optics relies on understanding how atoms behave and interact with their environment. Isolated atoms can exhibit wavelike (coherent) behavior with a corresponding de Broglie wavelength and phase which can be affected by nearby surfaces. Here an atom interferometer is used to measure the phase shift of Na atom waves induced by the walls of a 50 nm wide cavity. To our knowledge this is the first direct measurement of the de Broglie wave phase shift caused by atom-surface interactions. The magnitude of the phase shift is in agreement with that predicted by Lifshitz theory for a nonretarded van der Waals interaction. This experiment also demonstrates that atom waves can retain their coherence even when atom-surface distances are as small as 10 nm.

Retarded and nonretarded van der Waals interactions between a cluster and a second cluster or a conducting surface

In some respects, a cluster consisting of many atoms may be regarded as a single large atom. Knowing the dielectric properties of such a cluster permits one to evaluate the form of the van der Waals (dispersion) interactions between two clusters or between one cluster and a surface. In this paper, we derive these interactions in two extreme opposite regimes of separation: fully retarded and nonretarded. In the fully retarded regime (very large separation), the magnitude of the interaction is determined by just the static polarizability of the cluster(s). In the nonretarded regime (small separation), we employ a single resonant frequency model of thecluster polarizability to derive expressions for the interactions' coefficients. Numerical examples are presented to demonstrate that many-body screening of these interactions can be significant. The results represent the corrections to the commonly used approximation of pairwise additivity of interatomic interactions.

Line tension behavior of a first-order wetting system.

Line tension of hexaethylene glycol on a silicon wafer is measured with positive values up to +2.5x10(-11) N below a contact angle of 6 degrees and negative values down to -2x10(-10) N above 6 degrees, as expected for a first-order wetting system. From the measured interface potentials, a semiquantitative model function for the overall interface potential is derived as a superposition of a constant nonretarded van der Waals interaction with a Hamaker constant of -2.6x10(-19) J and an exponentially decaying term, allowing the prediction of a finite positive line tension at the wetting transition.

Modelling and asymptotic analysis of particle-interface interaction

An asymptotic study of the interaction between a foreign particle and a solidifying interface is undertaken. The analysis focuses primarily on the influence of the disjoining pressure on particle pushing or engulfment. The analysis considers only thermal effects in a pure substance in which a neutrally buoyant spherical particle, whose thermal conductivity is equal to that of the melt, is positioned near the solid-liquid interface. The interface equilibrium temperature includes the undercooling effects due to both the front curvature (the Gibbs-Thomson effect) and the long-range intermolecular forces (nonretarded van der Waals interactions) in the thin film behind the particle. A uniformly valid asymptotic representation for the front shape is derived and used to infer the gap width separating the particle from the solid front. The latter is utilized to calculate the growth rate that results from a balance of the van der Waals and Stokes forces. An attempt is also made at deriving an expression for the critical velocity for continuous pushing from the balance of forces.

Morphology of a solidifying interface near a spherical particle: disjoining pressure effects.

Numerical simulations were conducted to determine the morphology of a solid-liquid interface near an insoluble spherical particle. The model accounts for the undercoolings due to the front's curvature and to the nonretarded van der Waals interactions. Our numerical results show that, in the near-contact region, the interface profile develops a sharp peak whose curvature has a logarithmic singularity. This is in agreement with the asymptotic analysis of a previously published equation for the interface profile.

Particle trapping at an advancing solidification front with interfacial-curvature effects

We predict the maximum solidification rate, or critical velocity, V c at which an insoluble particle suspended in a melt is pushed ahead of an advancing solidification front by intermolecular forces. At higher solidification rates the particle is incorporated within the solid. The net intermolecular force pushing the particle and the viscous resistance opposing it are both significantly influenced by the shape of the front as it conforms to the particle in response to interfacial pre-melting. We predict the entire shape of the front, within a thin-film approximation, accounting for the freezing-point depression due to curvature. We show how the interface shape varies with the magnitude of the surface energy and the closeness of the particle, and compare these to previous, ad hoc representations of the interface. We confirm the scaling results of previous, more approximate, analyses for the case in which the intermolecular forces are dominated by non-retarded van der Waals interactions, and provide new results for other power-law interactions. We examine how the particle behaviour changes as its radius increases so that the effect of interfacial curvature is diminished.

DLVO interaction energy between spheroidal particles and a flat surface

The orientation dependent interaction energy between a spheroidal particle and an infinite planar surface is determined using the surface element integration (SEI) technique. The interaction energy predictions of SEI are shown to be considerably more accurate than the corresponding predictions based on Derjaguin’s approximation (DA). Comparison with the Hamaker approach for evaluating the non-retarded van der Waals interaction energy reveals that SEI predicts the orientation dependent interaction energy for spheroidal particles with remarkable accuracy. It is further shown that both SEI and DA give nearly identical predictions of the electrostatic double layer interaction energy between a spheroidal particle and a flat plate at high electrolyte concentrations. However, at low electrolyte concentrations, considerable deviations are noted between the predictions of SEI and DA, particularly for very small aspect ratios of the particle (aspect ratio=length of minor axis/length of major axis). It is also noted that when the spheroidal particle is oriented with its major axis parallel to the planar surface, DA incorrectly predicts the interaction energy as that of a spherical particle with a radius equal to the semi-major axis of the spheroid. This limitation of DA is avoided in SEI, which accounts for the dependence of the interaction energy on the actual shape (aspect ratio) of the particle at any orientation. Predictions of the DLVO interaction energy based on SEI indicate that, at high electrolyte concentrations, the orientation dependence of the interaction energy is not significant at large separation distances, and assumption of an equivalent spherical particle may be sufficient. However, significant deviation of the interaction energy from that of a spherical particle is observed at small separation distances, particularly at low electrolyte concentrations. At these small separation distances, where the correct orientation dependence of the interaction energy must be considered for proper calculations of particle interaction phenomena with flat surfaces (e.g. particle deposition), SEI provides a facile route to perform such calculations.

Surface Element Integration: A Novel Technique for Evaluation of DLVO Interaction between a Particle and a Flat Plate

A novel method, the surface element integration (SEI), is developed to determine the van der Waals and electrostatic double layer interactions between a particle and an infinite flat plate from the corresponding interactions per unit area between two infinite flat plates. Comparison with the Hamaker expression for nonretarded van der Waals interaction reveals that the new technique gives the exact interaction energy between a spherical particle and a flat plate. Available analytical expressions for the electrostatic double layer interaction energy between two infinite flat plates, based on the linearized Poisson–Boltzmann equation, are used in SEI to obtain the sphere–flat plate interaction energy. These sphere–flat plate interaction energies determined using SEI are compared with the corresponding interaction energies obtained from a detailed numerical solution of the Poisson–Boltzmann equation based on finite element analysis. The comparisons reveal that SEI scales the flat plate interaction to the corresponding sphere–flat plate geometry exactly, while the scaling based on the conventional Derjaguin approximation technique grossly overpredicts the interaction energy for small particles and low electrolyte concentrations.

On the contribution of macroscopic van der Waals interactions to frictional force

The equation for the frictional force caused by non-retarded van der Waals interactions has been found in the régime linear with respect to velocity. This force is generated because of the effect of field intrainment by a moving medium.

Contribution of macroscopic van der Waals interactions to friction forces

Using an approximation linear in velocities, an expression is obtained for friction forces due to nonretarded macroscopic van der Waals interactions. These forces are generated when field drag effects by a moving medium are taken into account.

Dielectric continuum theory of the Van der Waals interaction

We extend our local dielectric model of surface properties to encompass the calculation of the (nonretarded) Van der Waals interaction between two dissimilar media separated by a third. As established earlier, the computation of this energy reduces to the evaluation of the classical electrostatic fields associated with a point charge in the three-medium geometry. Explicit results are given for three media separated by parallel planar boundaries, in which case the requisite electrostatic fields may be evaluated simply by the method of images. These results reduce to those obtained earlier for two identical media separated by a vacuum.

Non-retarded van der Waals interactions between two spatially dispersive media

A method is described which permits the derivation of the van der Waals interaction free energy between two spatially dispersive media separated by a vacuum. A result which agrees with that of Lushnikov and Malov is obtained. We demonstrate that subject to certain assumptions about the dielectric permittivity (which are reasonable for a macroscopic system) the results is equivalent to that given by applying the method of surface modes.

Nonretarded van der waals interaction between two metal spheres

An approximate solution is found to an equation defining the spectrum of surface plasmons in systems of two equal metal spheres and two plane metal surfaces. The spectrum obtained is then used for calculation of the van der Waals interaction energy between these spheres at large and small separations and between the plane metal surfaces.