Capillary and van der Waals forces between uncharged colloidal particles linked by a liquid bridge

This work presents a theoretical study of the forces established between colloidal particles connected by means of a concave liquid bridge, where the solid particles are partially wetted by a certain amount of liquid also possessing a dry portion of their surfaces. In our analysis, we adopt a two-particle model assuming that the solids are spherical and with the same sizes and properties and that the liquid meniscus features an arc-of-circumference contour. The forces considered are the typical capillary ones, namely, wetting and Laplace forces, as well as the van der Waals force, assuming the particles uncharged. We analyze different parameters which govern the liquid bridge: interparticle separation, wetting angle, and liquid volume, which later determine the value of the forces. Due to the dual characteristic of the particles' surfaces, wet and dry, the forces are to be determined numerically in each case. The results indicate that the capillary forces are dominant in most of the situations meanwhile the van der Waals force is noticeable at very short distances between the particles.     

Capillary forces between surfaces with nanoscale roughness

The flow and adhesion behavior of fine powders (approx. less than 10 microm) is significantly affected by the magnitude of attractive interparticle forces. Hence, the relative humidity and magnitude of capillary forces are critical parameters in the processing of these materials. In this investigation, approximate theoretical formulae are developed to predict the magnitude and onset of capillary adhesion between a smooth adhering particle and a surface with roughness on the nanometer scale. Experimental adhesion values between a variety of surfaces are measured via atomic force microscopy and are found to validate theoretical predictions.     

A mathematical model for the interactions between non-identical rough spheres, liquid bridge and liquid vapor

Investigation of the interactions between the skeleton of an unsaturated particulate material and the contained liquid involves the general interaction model consisting of a liquid bridge in contact with two rigid smooth spherical particles of unequal size and dissimilar material, at a separation determined by their actual surface roughness, and surrounded by a gas with a vapor pressure at equilibrium with the liquid. The liquid retention and capillary force of the system are related to the capillary suction, liquid-solid contact angles, filling angles, roughness of the particles, and the ratio of particle radii in normalized terms by assuming a circular arc for the shape of the liquid profile. The normalized suction is also related to the corresponding relative humidity of the pore air. The calculated equilibrium relations are shown to possess non-uniqueness, which is interpreted in terms of mechanical properties of unsaturated particulate materials. The model is able to provide new insights into the behavior of an unsaturated particulate material.     

Effects of liquid bridge between colloidal spheres and evaporation temperature on fabrication of colloidal multilayers

For the application of colloidal crystal films as "photonic band gap" materials, their domain size and thickness are significant. The substrate withdrawing speed, the colloidal suspension volume fraction, and the colloidal suspension temperature have been studied for the domain size and thickness controls of colloidal crystals in this study. Stable dispersions of monodispersed polystyrene spheres with a diameter of 245 nm were synthesized according to a general emulsion polymerization for colloidal crystal films. By experimental results and the theoretical relationship between the number of layers and other parameters, we could know that the water bridge between colloidal spheres (which is formed by capillary force) influences the number of colloidal crystal layers significantly.     

Capillary forces between spherical particles floating at a liquid-liquid interface

We study the capillary forces acting on sub-millimeter particles (0.02-0.6 mm) trapped at a liquid-liquid interface due to gravity-induced interface deformations. An analytical procedure is developed to solve the linearized capillary (Young-Laplace) equation and calculate the forces for an arbitrary number of particles, allowing also for a background curvature of the interface. The full solution is expressed in a series of Bessel functions with coefficients determined by the contact angle at the particle surface. For sub-millimeter spherical particles, it is shown that the forces calculated using the lowest order term of the full solution (linear superposition approximation; LSA) are accurate to within a few percents. Consequently the many particle capillary force is simply the sum of the isolated pair interactions. To test these theoretical results, we use video microscopy to follow the motion of individual particles and pairs of interacting particles at a liquid-liquid interface with a slight macroscopic background curvature. Particle velocities are determined by the balance of capillary forces and viscous drag. The measured velocities (and thus the capillary forces) are well described by the LSA solution with a single fitting parameter.     

Elastic constants of uniaxial nematic liquid crystals: A comparison between theory and experiment

Using the unified molecular theory developed in our earlier paper (1992, Phys. Rev. A, 45, 974) we study in detail the influence of molecular interactions on the fundamental elastic properties of uniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. The expressions for the elastic moduli associated with 'splay', 'twist' and 'bend' modes of deformations are written in terms of order parameters characterizing the nature and amount of ordering in the phase and the structural parameters which involve the generalized spherical harmonic coefficients of the direct pair correlation function of an effective isotropic liquid. Numerical calculations are done for a model system, the molecules of which have prolate ellipsoid of revolution symmetry and interact via a pair potential having both repulsive and attractive parts. The repulsive interaction is represented by a repulsion between hard ellipsoids of revolution. The attractive potential is represented by the dispersion and electrostatic interactions. Results for the elastic constants are reported for a range of molecular length-width ratio, temperature, density and molecular parameters and are compared with the experimental values of p-azoxyanisole (PAA) and 4'-n-octyloxy-4-cyanobiphenyl (8OCB). It is found that the inclusion of electrostatic interactions reduces the values of the ratios K₂/K₁ and K₃/K₁. The absolute values of the elastic constants and their ratios are in good agreement with the experimental and computer simulation values. The temperature dependence of the elastic constants and their ratios is studied. It is observed that the twist elastic constant has a weak temperature dependence but a pronounced influence is observed on the bend moduli. We also observed a pronounced increase in the values of the twist and bend elastic constants on approaching the nematic-smectic A transition temperature.     

Nodoids and toroids: comparison of two geometries for the meniscus profile of a wetting liquid between two touching isolated spheres and extensions to the model of a collection of packed spheres

In the mid 1960s the present authors published two papers dealing with penetration of nonwetting liquids such as mercury into the interstitial void spaces using the model of uniform packed spheres. A circular arc was used to approximate the liquid-vapor interface in both papers. However, our circular arc-toroid values for the pressure-volume relationship in the pendular ring which exists between two touching spheres was criticized. The authors concluded that our approximation led to unacceptably large differences compared to the values calculated from the exact nodoid shape. This incorrect conclusion was never rebutted and has, in fact, been misinterpreted by subsequent workers to include values calculated for the shape of the access opening and the associated pressure for penetration into the void space of a collection of spheres. This leaves a cloud of uncertainty, not only over our original work on nonwetting fluids, but on the application of our procedures to the field of wetting fluids. The contrast in the geometrical shapes of the toroid and nodoid is depicted and the pressure values are compared at equal volumes. In contrast to the claim of excessive error, we show the toroid geometry, in conjunction with a pressure-volume work derivation, to have a maximum error of 0.06% as compared to the nodoid at all liquid-solid contact angles. The toroid also has the advantage of using a readily derived work versus surface free energy balance rather than requiring the use of incomplete elliptic integrals to evaluate the nodoid. Attempts to use radii of curvature to evaluate the toroid shape are shown to give extremely poor approximations of the exact values for the pressure. Values reported for access to the interior void space of a collection of spheres still need adjustment for the effect of contact angles between 0 degrees and 180 degrees for characterizing assemblies of real solids by computing "equivalent spherical" particle size from porosity and mercury penetration data. However, there is no anticipation that use of the circular arc will introduce large errors in the results. This gives confidence to us and others working with wetting media to test the potential applicability of the packed sphere model to various diverse fields.     

On the comparison of the predictions of lifshitz theory with experiment: Van der Wads forces between mica plates

The behavior of the experimental force-separation curve for two crossed cylinders of mica is compared to theoretical force-separation curves for two flat parallel plates. The theoretical force is computed using a dielectric function for mica, which contains different ir and uv frequencies from that employed previously by Richmond and Ninham. A theoretical method is described for determining the variation in the force-power law with distance of separation.     

Fifth-order Raman spectroscopy of liquid benzene: experiment and theory

The heterodyned fifth-order Raman response of liquid benzene has been measured and characterized by exploiting the passive-phase stabilization of diffractive optics. This result builds on our previous work with liquid carbon disulfide and extends the spectroscopy to a new liquid for the first time. The all-parallel and Dutch Cross polarization tensor elements are presented for both the experimental results and a finite-field molecular dynamics simulation. The overall response characteristics are similar to those of liquid carbon disulfide: a complete lack of signal along the pump delay, an elongated signal along the probe delay, and a short-lived signal along the time diagonal. Of particular interest is the change in phase between the nuclear and electronic response along the probe delay and diagonal which is not seen in CS2. Good agreement is achieved between the experiment and the finite-field molecular dynamics simulation. The measurement of the low-frequency Raman two-time delay correlation function indicates the intermolecular modes of liquid benzene to be primarily homogeneously broadened and that the liquid loses its nuclear rephasing ability within 300 fs. This rapid loss of nuclear correlations indicates a lack of modal character in the low-frequency motions of liquid benzene. This result is a validation of the general nature of the technique and represents an important step forward with respect to the use of nonlinear spectroscopy to directly access information on the anharmonic motions of liquids.     

Hydrodynamic interaction between spheres coated with deformable thin liquid films

In this article, we considered the hydrodynamic interaction between two unequal spheres coated with thin deformable liquids in the asymptotic lubrication regime. This problem is a prototype model for drop coalescence through the so-called "film drainage" mechanism, in which the hydrodynamic contribution comes dominantly from the lubrication region apart from the van der Waals interaction force. First, a general formulation was derived for two unequal coated spheres that experienced a head-to-head collision at a very close proximity. The resulting set of the evolution equations for the deforming film shapes and stress distributions was solved numerically. The film shapes and hydrodynamic interaction forces were determined as functions of the separation distance, film thickness, viscosity ratios, and capillary numbers. The results show that as the two spheres approach each other, the films begin to flatten and eventually to form negative curvature (or a broad dimple) at their forehead areas in which high lubrication pressure is formed. The dimple formation occurs earlier as the capillary number increases. For large capillary numbers, the film liquids are drained out from their forehead areas and the coated liquid films rupture before the two films "touch" each other. Meanwhile, for small capillary numbers, the gap liquid is drained out first and the two liquid films eventually coalesce.     

Capillary forces: influence of roughness and heterogeneity

A formalism is described to calculate capillary forces between solid surfaces analytically. Assumptions are that the liquid menisci (1) have a much larger extension parallel to the gap than normal and (2) are formed by capillary condensation and are in equilibrium with the vapor. To calculate capillary forces, first the gap between the two surfaces is described by a height distribution function. Roughness is considered with an asperity distribution function. Both distributions can at least in principal be measured by light, electron, or atomic force microscopy or grazing incidence X-ray reflectivity. The total capillary force versus distance or vapor pressure is obtained by a convolution of both distributions and an integration. The formalism is applied to calculate the capillary force between rough spherical particles. In addition, a method to consider surface heterogeneity is suggested.     

Capillary columns in liquid chromatography: between conventional columns and microchips

Liquid chromatography on columns with small internal diameters has been reviewed as the intermediate technique between conventional liquid chromatography and microchip separations. The development of micro column separations in the early years has been described, starting with the papers of Horváth and co-workers and Ishii and co-workers, continuing into the first part of the eighties, then making a leap in time to recent innovations with small-bore columns. Based on internal diameters a classification of the different analytical HPLC columns has been suggested. The advantages of small-bore columns have been discussed, with particular emphasis on the advantage of coupling to concentration sensitive detectors when the sample amount is limited. Open tubular columns are treated as a part of the historic background. The recent developments include a brief look into the current status of monolithic columns, the use of packed nano columns and micro columns with electrospray mass spectrometry, and the potential of two-dimensional comprehensive liquid chromatography. Finally, the coupling of sample preparation to analytical columns and the future applications of the novel technological improvements to the microchip separation methods have been discussed.     

Surface forces in polymer fluids: a comparison between simulations and density functional theory

A polymer density functional theory is evaluated in terms of its ability to predict interactions between large surfaces in a polymer fluid. Comparisons are made with results from simulations in an expanded isotension ensemble. The variation of the net surface-surface interaction with adsorption strength is examined. Cases where the monomers interact via a pure hard sphere potential are investigated, but we have also studied the effect of attractions between the monomers. In all cases, we obtain an almost quantitative agreement between the simulated results and the predictions from the polymer density functional theory.     

Work function of metals: Relation between theory and experiment

Theoretical approaches to calculation of work function within jellium model and the problem of extension of this model to include the lattice corrections to the work function are briefly discussed. Lattice corrections to the work function obtained from the experiment are estimated and compared with those calculated theoretically.

It is found that the mean value of the experimental lattice correction <δψ_hkl>_hkl compared to the mean work function is negligible. It is stated that the mean work function can be treated as a material constant characterizing a given metal, such as, e.g., binding energy.An expression for the dependence of jellium work function on r_s, valid in a metallic range of r_s, is given. A comparison between then theoretical and experimental results is presented and the role of correlation energy is examined. It is shown that more accurate approximations of the correlation energy than that given by Wigner's formula lead to a better agreement with experiment. A simple model is presented for explanation of work function changes on single crystal planes. Some recent results concerning the thermal dependence of work function are given. The dependence of the work function on the degree of coverage is discussed both for alkali and non-alkali atoms adsorption. Theoretical models are briefly reviewed and comparison between theory and experiment is made. A simple model is presented for explanation of the work function variation on rough planes in metallic non-alkali atoms chemisorption.     

Lateral capillary forces between solid bodies on liquid surface: a lattice Boltzmann study

When two solid bodies are placed on the surface of a dense liquid under gravitation, they deform the liquid surface to experience a lateral capillary force between themselves that can be attractive and repulsive, depending on the wettabilities and weights of the bodies. In the present study, the lateral capillary force between two square bodies at a liquid-vapor interface has been examined using numerical simulations based on a two-dimensional two-phase lattice Boltzmann (LB) method. The particular situations were simulated, where every body was vertically constrained and had the fixed triple points at its upper or lower corners. Here, the triple point indicates the place at which vapor, liquid, and solid phases meet. The interaction force between these two bodies was calculated as a function of the separation distance, the interfacial tension, and the gravitational acceleration. The simulation results agree well with the analytical expression of the lateral capillary interaction, indicating that our LB method can reproduce the interaction force between two bodies of various wettabilities at a liquid-vapor interface in mechanical equilibrium.     

Anchoring and electro-optical dynamics of thin liquid crystalline films in a polyimide cell: experiment and theory

The surface-dependent anchoring and electro-optical (EO) dynamics of thin liquid crystalline films have been examined using Fourier transform infrared spectroscopy. A simple nematic liquid crystal, 4-n-pentyl-4'-cyanobiphenyl (5CB), is confined as 40, 50, and 390 nm thick films in nanocavities defined by gold interdigitated electrode arrays (IDEAs) patterned on polyimide-coated zinc selenide (ZnSe) substrates [Noble et al., J. Am. Chem. Soc. 124, 15020 (2002)]. New strategies for controlling the anchoring interactions and EO dynamics are explored based on coating a ZnSe surface with an organic polyimide layer in order to both planarize the substrate and induce a planar alignment of the liquid crystalline film. The polyimide layer can be further treated so as to induce a strong alignment of the nematic director along a direction parallel to the electrode digits of the IDEA. Step-scan time-resolved spectroscopy measurements were made to determine the rate constants for the electric-field-induced orientation and thermal relaxation of the 5CB films. In an alternate set of experiments, uncoated ZnSe substrates were polished unidirectionally to produce a grooved surface presenting nanometer-scale corrugations. The dynamical rate constants measured for several nanoscale film thicknesses and equilibrium organizations of the director in these planar alignments show marked sensitivities. The orientation rates are found to vary strongly with both the magnitude of the applied potential and the initial anisotropy of the alignment of the director within the IDEA. The relaxation rates do not vary in this same way. The marked variations seen in EO dynamics can be accounted for by a simple coarse-grained dynamical model.     

Capillary bridging and long-range attractive forces in a mean-field approach

When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope and surface force apparatus, it can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them. By minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis. We also show that similar phenomenon can be observed in a number of different systems, e.g., liquid crystals and polymer mixtures.