Van der Waals interaction of membranes

The van der Waals interaction of hydrocarbon films in water is calculated using the exact expression derived by Parsegian and Ninham. The results are compared to an often used approximation, which fails for this system due to the large difference between the static dielectric constants of hydrocarbons and water. For large membrane separations the correct value of the van der Waals interaction is about a hundred times larger than the approximate result. The consequences for predicting unbinding transitions and interpreting experiments are discussed.Dedicated to Prof. Herbert Wagner on the occasion of his 60th birthday     

A van der Waals free energy in electrolytes revisited

A system of three electrolytes separated by two parallel planes is considered. Each region is described by a dielectric constant and a Coulomb fluid in the Debye-Hückel regime. In their book Dispersion Forces, Mahanty and Ninham have given the van der Waals free energy of this system. We rederive this free energy by a different method, using linear response theory and the electrostatic Maxwell stress tensor for obtaining the dispersion force.     

Subleading long-range interactions and violations of finite size scaling

We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor system. In the context of the mean spherical model with periodic boundary conditions we are able to identify, for temperatures close above T _c, finite-size contributions due to the subleading term in the interaction that are dominant in this region decaying algebraically as a function of L. This mechanism goes beyond the standard formulation of the finite-size scaling but is to be expected in real physical systems. We also discuss other ways in which critical point behavior is modified that are of relevance for analysis of Monte Carlo simulations of such systems. Received 21 November 2000 and Received in final form 28 February 2001     

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.     

Heterogeneous dynamics at the glass transition in van der Waals liquids, in the bulk and in thin films

It has been shown over the last few years that the dynamics close to the glass transition is strongly heterogeneous, both by measuring the diffusion coefficient of tagged particles or by NMR studies. Recent experiments have also demonstrated that the glass transition temperature of thin polymer films can be shifted as compared to the same polymer in the bulk. We propose here first a thermodynamical model for van der Waals liquids, which accounts for experimental results regarding the bulk modulus of polymer melts and the evolution of the density with temperature. This model allows us to describe the density fluctuations in such van der Waals liquids. Then, by considering the thermally induced density fluctuations in the bulk, we propose that the 3D glass transition is controlled by the percolation of small domains of slow dynamics, which allows to explain the heterogeneous dynamics close to T _g. We show then that these domains percolate at a lower temperature in the quasi-2D case of thin suspended polymer films and we calculate the corresponding glass transition temperature reduction, in quantitative agreement with experimental results of Jones and co-workers. In the case of strongly adsorbed films, we show that the strong adsorption amounts to enhance the slow domains percolation. This effect leads to 1) a broadening of the glass transition and 2) an increase of T _g in quantitative agreement with experimental results. For both strongly and weakly adsorbed films, the shift in T _g is given by a power law, the exponent being the inverse of that of the correlation length of 3D percolation. Received 21 March 2000 and Received in final form 4 December 2000     

Quantum theory of van der Waals interactions between excited atoms and birefringent dielectric surfaces

A theory of van der Waals (vdW) interaction between an atom (in ground or excited state) and a birefringent dielectric surface with an arbitrary orientation of the principal optic axis (C-axis) is presented. Our theoretical approach is based on quantum-mechanical linear response theory, using generalized susceptibilities for both atom and electromagnetic field. Resonant atom-surface coupling is predicted for excited-state atoms interacting with a dispersive dielectric surface, when an atom de-excitation channel gets into resonance with a surface polariton mode. In the non-retarded regime, this resonant coupling can lead to enhanced attractive or repulsive vdW surface forces, as well as to a dissipative coupling increasing the excited-state relaxation. We show that the strongly non-scalar character of the interaction with the birefringent surface produces a C-axis-dependent symmetry-breaking of the atomic wavefunction. Changes of the C-axis orientation may also lead to a frequency shift of the surface polariton mode, allowing for tuning on or off the resonant coupling, resulting in a special type of engineering of surface forces. This is analysed here in the case of cesium 6D _3/2 level interacting with a sapphire interface, where it is shown that an adequate choice of the sapphire C-axis orientation allows one to transform vdW surface attraction into repulsion, and to interpret recent experimental observations based on selective reflection methods [H. Failache etal., Phys. Rev. Lett. 83, 5467 (1999)]. Received 24 January 2001     

Wetting of Alkanes on Water from a Cahn-Type Theory: Effects of Long-Range Forces

We apply the phenomenological wetting theory of Cahn to fluids with van der Waals forces, and in particular to the wetting of pentane on water. Taking into account explicitly the long-range substrate–adsorbate interaction allows us to reproduce the experimentally observed critical wetting transition, which arises from the vanishing of the Hamaker constant at T53°C. This transition is preceded by a first-order transition between a thin and a thick film at a (much) lower temperature. If long-range forces are neglected, this thin–thick transition is the only wetting transition and critical wetting is missed. Our study focuses on the development of useful theoretical tools, such as phase portraits and interface potentials adapted to systems with van der Waals forces.     

Laser-induced fluorescence study of the influence of N <Emphasis Type="Bold">2</Emphasis> and CH <Emphasis Type="Bold">4</Emphasis> on the <Emphasis Type="Bold">114</Emphasis>Cd intercombination line

Using a laser-induced fluorescence method a detailed analysis of profiles of the ¹¹⁴Cd 326.1 nm line perturbed by N₂ and CH₄ was performed which revealed deviations from the ordinary Voigt profile. These deviations are shown to be consistent with fits of experimental profiles to an asymmetric Voigt profile. Coefficients of the pressure broadening, shift and collision-time asymmetry are determined and compared with those calculated for van der Waals interaction potential. Received 29 November 2001 / Received in final form 12 July 2002 Published online 4 February 2003     

Spinodal dewetting of thin liquid films at soft interfaces

We study theoretically the behavior of nanoscopic liquid films L (thickness e) intercalated between a solid S and a rubber R (elastic modulus μ). Thickness modulations involve a healing length , which results from a competition between elastic and disjoining pressure. With van der Waals interactions, , where a is a molecular size and h₀ the rubber capillary length ( , interfacial tension). If the Hamaker constant of the intercalated liquid is negative, the film dewets by amplification of peristaltic fluctuations (“spinodal dewetting”). The typical size of the contacts is predicted to scale like for films of thicknesses . The rise time of the fastest mode, predicted to scale like , should be very sensitive to the film thickness. Received 11 February 2000 and Received in final form 22 May 2000     

Electrostatic and van der Waals forces in the air contact between the atomic force microscope probe and a conducting surface

Electrostatic and van der Waals forces of interaction between commercial probes of atomic force microscopes (AFMs) and conducting surfaces under atmospheric conditions are measured using contact atomic force microscopy. An algorithm of statistical processing of the initial photocurrent-displacement dependences is developed, which makes it possible to transform these dependences into the force-distance dependences. The Hamaker constant at the platinum (probe)-graphite (sample) contact is determined. It is shown that the measurement of electrostatic forces makes it possible to determine geometrical parameters of the AFM probe and to independently calibrate the stiffness of the cantilever.     

Renormalization group treatment of the scaling properties of finite systems with subleading long-range interaction

The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r ^{- (d + σ)}, where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs to the short-range universality class it is shown that above the bulk critical temperature T _c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems. Received 8 August 2001     

Two-point correlation function in systems with van der Waals type interaction

The behavior of the bulk two-point correlation function G(;T| d ) in d-dimensional system with van der Waals type interactions is investigated and its consequences on the finite-size scaling properties of the susceptibility in such finite systems with periodic boundary conditions is discussed within mean-spherical model which is an example of Ornstein and Zernike type theory. The interaction is supposed to decay at large distances r as r ^{- (d + σ)}, with 2 < d < 4, 2 < σ < 4 and d + σ≤6. It is shown that G(;T| d ) decays as r ^{- (d - 2)} for 1 ≪r≪ξ, exponentially for ξ≪r≪r ^*, where r ^* = (σ - 2)ξlnξ, and again in a power law as r ^{- (d + σ)} for r≫r ^*. The analytical form of the leading-order scaling function of G(;T| d ) in any of these regimes is derived. Received 28 May 2001     

Dynamical van der Waals atom–surface interaction

We obtained new nonrelativistic expression for the dynamical van der Waals atom–surface interaction energy of a very convenient form for different applications. It is shown that classical result (Ferrell and Ritchie, 1980) holds only for a very slowly moving atom. In general case, the van der Waals atom–surface interaction energy manifests strong nonlinear dependence on the velocity and distance. In close vicinity of metal and dielectric surfaces and velocities ranging from 1 to 10 bohr units the dynamical van der Waals potential proves to be several times lower than in the static case and goes to the static values with increasing the distance and (or) decreasing the velocity.     

Metastable rare gas atoms scattered by nano- and micro-slit transmission gratings

The transmission of metastable argon atoms through nano-slit or micro-slit gratings is studied by use of time of flight and angular analysis. This transmission departs from the simple geometric one essentially by two ways: (i) the elastic or diagonal part of the van der Waals (vW) interaction with the solid causes an angular narrowing of the emerging beam; (ii) the off-diagonal vW interaction induces the exothermal fine structure transition ³ P ₀↦³ P ₂ (ΔE = 175 meV) leading to large scattering angles; the resulting angular distribution is very sensitive to the roughness of the surface in the direction of the depth. An extension of these experiments to transversally coherent beams is proposed. It should be considered as a first step towards a new type of interferometer in which the inelastic diffraction makes the gratings work as beam splitters or mirrors. Received 6 July 2001 and Received in final form 17 September 2001     

Acoustic instabilities in thin polymer films

The spatial confinement of a fluctuation spectrum leads to forces at the confining boundaries. While electromagnetic (EM) fluctuations lead to the well-known dispersion forces, the acoustic analogy has widely been neglected. We show that the strength of the forces resulting from confined acoustic modes may be of the same order of magnitude as van der Waals forces. Additionally, the predicted scaling behavior is identical to the non-retarded case of the EM fluctuations. Our results suggest that dewetting experiments using polymer films are strongly influenced by the acoustic dispersion forces. Received 5 March 2002 and Received in final form 21 May 2002     

Atomic scale mass delivery driven by bend kink in single walled carbon nanotube

The possibility of atomic scale mass delivery by bend kink in single walled carbon nanotube was investigated with the aid of molecular dynamics simulation. By keeping the bending angle while moving the tube end, the encapsulated atomic scale mass such as atom, molecule and atom group were successfully delivered through the nanotube. The van der Waals interaction between the encapsulated mass and the tube wall provided the driving force for the delivery. There were no dramatic changes in the van der Waals interaction, and a smooth and steady delivery was achieved when constant loading rate was applied. The influence of temperature on the atom group delivery was also analyzed. It is found raising temperature is harmful to the smooth movement of the atom group. However, the delivery rate can be promoted under higher temperature when the atom group is situated before the kink during the delivery.     

Exact results for Casimir interactions between dielectric bodies: the weak-coupling or van der Waals limit

In earlier papers, we have applied multiple-scattering techniques to calculate Casimir forces due to scalar fields between different bodies described by delta function potentials. When the coupling to the potentials became weak, closed-form results were obtained. We simplify this weak-coupling technique and apply it to the case of tenuous dielectric bodies, in which case the method involves the summation of van der Waals (Casimir-Polder) interactions. Once again, exact results for finite bodies can be obtained. We present closed formulas describing the interaction between spheres, between cylinders, and between an infinite plate and a rectangular slab of finite size. For such a slab, we consider the torque acting on it and find that nontrivial equilibrium points can occur.     

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.     

The Born repulsive parameters and dielectric behaviour of alkali halides

The dependence of the Born repulsive parameters of alkali halides on elastic and dielectric data has been discussed. The values of hardness parameter in alkali halides have been recalculated using the revised values of van der Waals energies. It is observed that the two sets of hardness parameter corresponding to elastic and dielectric data differ from each other but become compatible if an effective charge parameter for the ions is introduced. Its usefulness has been demonstrated by calculating the strain derivative of static dielectric constant of alkali halides.