The numerically exact evaluation of the van der Waals interaction, also known as Casimir interaction when including retardation effects, constitutes a challenging task. We present a new approach based on the plane-wave basis and demonstrate that it possesses advantages over the more commonly used multipole basis. The rotational symmetry of the plane-sphere and sphere-sphere geometries can be exploited by means of a discrete Fourier transform. The new technique is applied to a study of the interaction between a colloid particle made of polystyrene or mercury and another polystyrene sphere or a polystyrene wall in an aqueous solution. Special attention is paid to the influence of screening caused by a variable salt concentration in the medium. It is found that in particular for low salt concentrations the error implied by the proximity force approximation is larger than usually assumed. For a mercury droplet, a repulsive interaction is found for sufficiently large distances provided screening is negligible. We emphasize that the effective Hamaker parameter depends significantly on the scattering geometry on which it is based.
From microscopic fluid clusters to macroscopic droplets, the structure of fluids is governed by the Van der Waals force, a force that acts between polarizable objects. In this Letter, we derive a general theory that describes the non-equilibrium counterpart to the Van der Waals force, which emerges in spatially coherently fluctuating electromagnetic fields. We describe the formation of a novel and complex hierarchy of self-organized morphologies in magnetic and dielectric colloid systems. Most striking among these morphologies are dipolar foams - colloidal superstructures that swell against gr…
This contribution briefly reviews some recent work demonstrating the partial breakdown of the colloidal fluid <--> atomic fluid analogy. The success of liquid state theory for atomic fluids stems in part from the van der Waals picture, where steric interactions dominate the structure, and attractive interactions can be added as a perturbation. For complex fluids described by effective potentials, this picture may break down. In the first example discussed, depletion potentials in non-additive hard-sphere mixtures are shown to be surprisingly complex, leading to fluid structure and fluid-solid …
Fluctuations in fluid velocity and fluctuations in electric fields may both give rise to forces acting on small particles in colloidal suspensions. Such forces in part determine the thermodynamic stability of the colloid. At the classical statistical thermodynamic level, the fluid velocity and electric field contributions to the forces are comparable in magnitude. When quantum fluctuation effects are taken into account, the electric fluctuation induced van der Waals forces dominate those induced by purely fluid mechanical motions. The physical principles are applied in detail for the case of c…
We calculate the effective force mediated by thermally excited capillary waves between spherical or disklike colloids trapped at a fluid interface. This Casimir type interaction is shown to depend sensitively on the boundary conditions imposed at the three-phase contact line. For large distances between the colloids an unexpected cancellation of attractive and repulsive contributions is observed leading to a fluctuation force which decays algebraically very rapidly. For small separations the resulting force is rather strong and it may play an important role in two-dimensional colloid aggregati…
We investigate properties of dense suspensions and sediments of small spherical silt particles by means of a combined Molecular Dynamics (MD) and Stochastic Rotation Dynamics (SRD) simulation. We include van der Waals and effective electrostatic interactions between the colloidal particles, as well as Brownian motion and hydrodynamic interactions which are calculated in the SRD-part. We present the simulation technique and first results. We have measured velocity distributions, diffusion coefficients, sedimentation velocity, spatial correlation functions and we have explored the phase diagram …
For like charged colloidal particles two mechanisms of attraction between them survive when the interparticle distance is larger than the Debye screening length. One of them is the conventional van der Waals attraction and the second one is the attraction mechanism mediated by thermal fluctuations of particle positions. The latter is related to an effective variable mass (Euler mass) of the particle produced by a fluid motion. The most stronger attraction potential (up to the value of temperature T) corresponds to a situation of uncharged particles and a relatively large Debye screening length…
Physical properties of colloidal materials can be modified by addition of nanoparticles. Within a model of like-charged mixtures of particles governed by effective electrostatic interactions, we explore the influence of charged nanoparticles on the structure and thermodynamic phase stability of charge-stabilized colloidal suspensions. Focusing on salt-free mixtures of particles of high size and charge asymmetry, interacting via repulsive Yukawa effective pair potentials, we perform molecular dynamics simulations and compute radial distribution functions and static structure factors. Analysis o…
We studied the van der Waals interactions of two finite, solid, cylindrical rods at arbitrary angle and position with respect to each other. An analytic interpolative formula for the interaction potential energy is constructed, based on various asymptotic cases. The potential can be readily used for numerical and analytic description of multi-wall carbon nanotubes, metallic nanorods, rod-shaped colloids, or any other similar objects with significant van der Waals interactions.
We present a mechanism for the stabilization of colloids in liquid mixtures without use of surfactants or polymers. When a suitable salt is added to a solvent mixture, the coupling of the colloid's surface chemistry and the preferential solvation of ions leads to a repulsive force between colloids that can overcome van der Waals attraction. This repulsive force is substantial in a large range of temperatures, mixture composition and salt concentrations. The increased repulsion due to addition of salt occurs even for charged colloids. This mechanism may be useful in experimental situations wher…
The implications of soft `patchy' interactions on the orientational disorder-order transition of strongly elongated colloidal rods and flat disks is studied within a simple Onsager-van der Waals density functional theory. The theory provides a generic framework for studying the liquid crystal phase behaviour of highly anisometric cylindrical colloids, which carry a distinct geometrical pattern of repulsive or attractive soft interactions localised on the particle surface. In this paper, we apply our theory to the case of charged rods and disks for which the local electrostatic interactions can…
Concentrated colloidal suspensions and emulsions are amorphous soft solids, widespread in technological and industrial applications and studied as model systems in physics and material sciences. They are easily fluidized by applying a mechanical stress, undergoing a yielding transition that still lacks a unified description. Here, we investigate yielding in three classes of repulsive soft solids, using analytical and numerical modelling and experiments probing the microscopic dynamics and mechanical response under oscillatory shear. We find that at the microscopic level yielding consists in a …
We present a detailed numerical study of effective interactions between micron-sized silica spheres, induced by highly charged zirconia nanoparticles. It is demonstrated that the effective interactions are consistent with a recently discovered mechanism for colloidal stabilization. In accordance with the experimental observations, small nanoparticle concentrations induce an effective repulsion that counteracts the intrinsic van der Waals attraction between the colloids and thus stabilizes the suspension. At higher nanoparticle concentrations an attractive potential is recovered, resulting in r…
We theoretically study the polarizability and the interactions of neutral complexes consisting of a semi-flexible polyelectrolyte adsorbed onto an oppositely charged spherical colloid. In the systems we studied, the bending energy of the chain is small compared to the Coulomb energy and the chains are always adsorbed on the colloid. We observe that the polarizability is large for short chains and small electrical fields and shows a non-monotonic behavior with the chain length at fixed charge density. The polarizability has a maximum for a chain length equal to half of the circumference of the …
Within mean-field theory we calculate universal scaling functions associated with critical Casimir forces for a system consisting of three parallel cylindrical colloids immersed in a near-critical binary liquid mixture. For several geometrical arrangements and boundary conditions at the surfaces of the colloids we study the force between two colloidal particles along their center-to-center axis, analyzing the influence of the presence of a third particle on that force. Upon changing temperature or the relative positions of the particles we observe interesting features such as a change of sign …
Van der Waals interactions between flat surfaces in uniaxial anisotropic media are investigated in the nonretarded limit. The main focus is the effect of nonzero tilt between the optical axis and the surface normal on the strength of van der Waals attraction. General expressions for the van der Waals free energy are derived using the surface mode method and the transfer-matrix formalism. To facilitate numerical calculations a temperature-dependent three-band parameterization of the dielectric tensor of the liquid crystal 5CB is developed. A solid slab immersed in a liquid crystal experiences a…
We theoretically and experimentally investigate colloid-oil-water-interface interactions of charged, sterically stabilized, poly(methyl-methacrylate) colloidal particles dispersed in a low-polar oil (dielectric constant $ε=5-10$) that is in contact with an adjacent water phase. In this model system, the colloidal particles cannot penetrate the oil-water interface due to repulsive van der Waals forces with the interface whereas the multiple salts that are dissolved in the oil are free to partition into the water phase. The sign and magnitude of the Donnan potential and/or the particle charge is…
Using field-theoretical methods and exploiting conformal invariance, we study Casimir forces at tricritical points exerted by long-range fluctuations of the order-parameter field. Special attention is paid to the situation where the symmetry is broken by the boundary conditions (extraordinary transition). Besides the parallel-plate configuration, we also discuss the geometries of two separate spheres and a single sphere near a planar wall, which may serve as a model for colloidal particles immersed in a fluid. In the concrete case of ternary mixtures a quantitative comparison with critical Cas…
The past two decades have seen a remarkable progress in the development of synthetic colloidal agents which are capable of creating directed motion in an unbiased environment at the microscale. These self-propelling particles are often praised for their enormous potential to self-organize into dynamic nonequilibrium structures such as living clusters, synchronized super-rotor structures or self-propelling molecules featuring a complexity which is rarely found outside of the living world. However, the precise mechanisms underlying the formation and dynamics of many of these structures are still…
In its original formulation, the seminal Deryaguin-Landau-Verwey-Overbeek (DLVO) theory of colloidal stability seemed like a simple but realistic description of the world of colloid interactions in electrolyte solutions. It is based on a straightforward superposition of the mean-field Poisson-Boltzmann (PB) electrostatics with the electrodynamic van der Waals (vdW) interactions driven by thermal and quantum fluctuations. However, subsequent developments continued to reveal a much richer and deeper structure of fundamental interactions on the nano- and micro-scale: the granularity and structure…
We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response. We achieve this by rewriting the interaction energy expression 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 Waal…
We derive effective interaction potentials between hard, spherical colloidal particles and star-branched polyelectrolytes of various functionalities and smaller size than the colloids. The effective interactions are based on a Derjaguin-like approximation, which is based on previously derived potentials acting between polyelectrolyte stars and planar walls. On the basis of these interactions we subsequently calculate the demixing binodals of the binary colloid--polyelectrolyte star mixture, employing standard tools from liquid-state theory. We find that the mixture is indeed unstable at modera…
In the framework of the van-der-Waals model, analytical expressions for the locus of extrema (ridges) for heat capacity, thermal expansion coefficient, compressibility, density fluctuation, and sound velocity in the supercritical region have been obtained. It was found that the ridges for different thermodynamic values virtually merge into single Widom line only at $T<1.07 T_c, P<1.25P_c$ and become smeared at $T<2T_c, P<5P_c$, where $T_c$ and $P_c$ are the critical temperature and pressure. The behavior of the Batschinski lines and the pseudo-Gruneisen parameter $γ$ of a van-der-Waals fluid w…
The dimensionless value of critical compressibility factor in the van der Waals theory of gas-liquid critical point is a universal constant, $Z_\text{c} = 0.375$. Experimentally measured values of this quantity for simple fluids are considerably smaller than the theory prediction. Van der Waals once assumed that this discrepancy can be removed by taking account of the impact of the molecular pseudo-associations on the fluid criticality but he did not complete a proper modification of his theory following up on this idea. The communication is devoted to the filling of this gap.
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.
Colloidal structure, energy extensivity and Monte Carlo sampling properties of improved short-range interaction models for surfactant-coated magnetic nanoparticles
Although density functional theory (DFT) in principle includes even long-range interactions, standard implementations employ local or semi-local approximations of the interaction energy and fail at describing the van der Waals interactions. We show how to modify a recent density functional that includes van der Waals interactions in planar systems [Phys. Rev. Lett. 91, 126402 (2003)] to also give an approximate interaction description of planar molecules. As a test case we use this modified functional to calculate the binding distance and energy for benzene dimers, with the perspective of trea…
We investigate the dependence of the stickiness parameters $t_{ij}=1/(12τ_{ij})$ -- where the $τ_{ij}$ are the conventional Baxter parameters -- on the solute diameters $σ_{i}$ and $σ_{j}$ in multicomponent sticky hard sphere (SHS) models for fluid mixtures of mesoscopic neutral particles. A variety of simple but realistic interaction potentials, utilized in the literature to model \textit{short-ranged attractions} present in real solutions of colloids or reverse micelles, is reviewed. We consider: i) van der Waals attractions, ii) hard-sphere-depletion forces, iii) polymer-coated colloids, iv…
Working at the Lifshitz level, we investigate the van der Waals interactions across a series of layers with a periodic motif. We derive the complete form of the van der Waals interaction as an explicit function of the number of periodic layers. We then compare our result with an approximation based on an anisotropic-continuum representation of the stratified medium. Satisfactory agreement between discrete-layer and continuum models is reached only for thicknesses of ten or more layers.
We study the mutual interactions of simple, parallel polymers and nanotubes, and develop a scheme to include the van der Waals interactions in the framework of density functional theory (DFT) for these molecules at intermediate to long-range separations. We primarily focus on the polymers polyethylene, isotactic polypropylene, and isotactic polyvinylchloride, but our approach applies more generally to all simple polymers and nanotubes. From first-principle DFT calculations we extract the electron density of the polymers and their static electric response. We derive explicit expressions for the…
The method recently developed to include Van der Waals interactions in the Density Functional Theory by using the Maximally-Localized Wannier functions, is improved and extended to the case of atoms and fragments weakly bonded (physisorbed) to metal and semimetal surfaces, thus opening the way to realistic simulations of surface-physics processes, where Van der Waals interactions play a key role. Successful applications to the case of Ar on graphite and on the Al(100) surface, and of the H2 molecule on Al(100) are presented.
We consider a one-dimensional model allowing analytical derivation of the effective interactions between two charged colloids. We evaluate exactly the partition function for an electroneutral salt-free suspension with dielectric jumps at the colloids' position. We derive a contact relation with the pressure that shows there is like-charge attraction, whether or not the counterions are confined between the colloids. In contrast to the homogeneous dielectric case, there is the possibility for the colloids to attract despite the number of counter-ions ($N$) being even. The results are shown to re…
The transition of van der Waals to Casimir forces between macroscopic gold surfaces is investigated by Atomic Force Microscopy in the plane-sphere geometry. It was found that the transition appears to take place at separations about 10 % the plasma wavelength for evaporated gold surfaces, which compares to theoretical predictions by incorporation of experimental optical data and roughness corrections. Moreover, the force data allow estimation of the Hamaker constant AH in the van der Waals regime, which is in good agreement with the Lifshitz theory predictions (even if roughness corrections ar…
Electroconvection in rechargeable batteries enhances the growth of dendrites at the electrode surface. The addition of low molecular weight polymers to the electrolyte in batteries results in the formation of a thin layer of higher polymer concentration near the electrode. This is due to van der Waals forces of attraction between the metal electrode and the polymers dissolved in the electrolyte. The van der Waals forces act as a restoring body force on the electrolyte and oppose the growth of perturbations. Using linear stability analysis, we show that this force opposes electroconvective flow…
In systems composed of water and hydrocarbons Van der Waals-interactions are dominated by the non-retarded, classical (Keesom) part of the Lifshitz-interaction; the interaction is screened by salt and extends over mesoscopic distances of the order of the size of the (micellar) constituents of complex fluids. We show that these interactions are included intrinsically in a recently introduced local Monte Carlo algorithm for simulating electrostatic interactions between charges in the presence of non-homogeneous dielectric media.
The equations for Widom lines for the supercritical van der Waals fluid were considered in the paper J. Chem. Phys. 135, 084503 (2011). But the equations for the speed of sound and its special Widom line were incorrect. The correct equations are obtained.
We show that the usual sum of $R^{-6}$ contributions from elements separated by distance $R$ can give \emph{qualitatively} wrong results for the electromagnetically non-retarded van der Waals interaction between non-overlapping bodies. This occurs for anisotropic nanostructures that have a zero electronic energy gap, such as nanowires, conducting nanotubes, and nano-layered systems including metals and graphene planes. In all these cases our analytic microscopic calculations give an interaction falling off with a power of separation different from the conventional value. We discuss implication…
