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.     

Influence of surface roughness on dispersion forces

Surface roughness occurs in a wide variety of processes where it is both difficult to avoid and control. When two bodies are separated by a small distance the roughness starts to play an important role in the interaction between the bodies, their adhesion, and friction. Control of this short-distance interaction is crucial for micro and nanoelectromechanical devices, microfluidics, and for micro and nanotechnology. An important short-distance interaction is the dispersion forces, which are omnipresent due to their quantum origin. These forces between flat bodies can be described by the Lifshitz theory that takes into account the actual optical properties of interacting materials. However, this theory cannot describe rough bodies. The problem is complicated by the nonadditivity of the dispersion forces. Evaluation of the roughness effect becomes extremely difficult when roughness is comparable with the distance between bodies. In this paper we review the current state of the problem. Introduction for non-experts to physical origin of the dispersion forces is given in the paper. Critical experiments demonstrating the nonadditivity of the forces and strong influence of roughness on the interaction between bodies are reviewed. We also describe existing theoretical approaches to the problem. Recent advances in understanding the role of high asperities on the forces at distances close to contact are emphasized. Finally, some opinions about currently unsolved problems are also presented.     

Capillary forces between chemically different substrates

Motivated by experimental results, we present numerical and analytical calculations of the capillary force exerted by a capillary bridge spanning the gap between two parallel flat plates of asymmetric wettability. Depending on whether the sum of the two contact angles is smaller or larger than 180 degrees, the capillary force is either attractive or repulsive at small separations D between the plates. In either cases the magnitude of the force diverges as D approaches zero. The leading order of this divergence is captured by an analytical expression deduced from the geometry of the meniscus of a flat capillary bridge. The results for substrates with different wettability reveal an interesting behavior: with the sum of the contact angles fixed, the magnitude of the capillary force and the rupture separation decreases as the asymmetry in contact angles is increased. In addition, we present the rupture separation, i.e., the maximal extension of a capillary bridge, as a function of the contact angles. Our results provide an extensive picture of surface wettability effects on capillary adhesion.     

Charge heterogeneity of surfaces: mapping and effects on surface forces

The DLVO theory treats the total interaction force between two surfaces in a liquid medium as an arithmetic sum of two components: Lifshitz–van der Waals and electric double layer forces. Despite the success of the DLVO model developed for homogeneous surfaces, a vast majority of surfaces of particles and materials in technological systems are of a heterogeneous nature with a mosaic structure composed of microscopic and sub-microscopic domains of different surface characteristics. In such systems, the heterogeneity of the surface can be more important than the average surface character. Attractions can be stronger, by orders of magnitude, than would be expected from the classical mean-field DLVO model when area-averaged surface charge or potential is employed. Heterogeneity also introduces anisotropy of interactions into colloidal systems, vastly ignored in the past. To detect surface heterogeneities, analytical tools which provide accurate and spatially resolved information about material surface chemistry and potential — particularly at microscopic and sub-microscopic resolutions — are needed.Atomic force microscopy (AFM) offers the opportunity to locally probe not only changes in material surface characteristic but also charges of heterogeneous surfaces through measurements of force–distance curves in electrolyte solutions. Both diffuse-layer charge densities and potentials can be calculated by fitting the experimental data with a DLVO theoretical model. The surface charge characteristics of the heterogeneous substrate as recorded by AFM allow the charge variation to be mapped. Based on the obtained information, computer modeling and simulation can be performed to study the interactions among an ensemble of heterogeneous particles and their collective motions. In this paper, the diffuse-layer charge mapping by the AFM technique is briefly reviewed, and a new Diffuse Interface Field Approach to colloid modeling and simulation is briefly discussed.     

Capillary condensation in mesoporous silica with surface roughness

We construct an atomistic silica pore model mimicking templated mesoporous silica MCM-41, which has molecular-level surface roughness, with the aid of the electron density profile (EDP) of MCM-41 obtained from X-ray diffraction data. Then, we present the GCMC simulations of argon adsorption on our atomistic silica pore models for two different MCM-41 samples at 75, 80, and 87 K, and the results are compared with the experimental adsorption data. We demonstrate that accurate molecular modeling of the pore structure of MCM-41 by using the experimental EDP allows the prediction of experimental capillary evaporation pressures at all investigated temperatures. The experimental desorption branches of the two MCM-41 samples are in good agreement with equilibrium vapor–liquid transition pressures from the simulations, which suggests that the experimental desorption branch for the open-ended cylindrical pores is in thermodynamic equilibrium.     

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.     

Mimicking the lotus effect: influence of double roughness structures and slender pillars

Surface roughness is known to amplify hydrophobicity. The apparent contact angle of a drop on a rough surface is often modeled using either Wenzel's or Cassie's formulas. These formulas, along with an appropriate energy analysis, are critical in designing superhydrophobic substrates for applications in microscale devices. In this paper we propose that double (or multiple) roughness structures or slender pillars are appropriate surface geometries to develop "self-cleaning" surfaces. The key motivation behind the double structured roughness is to mimic the microstructure of superhydrophobic leaves (such as lotus). Theoretical analysis similar to that presented in the paper can be used to obtain optimal geometric parameters for the rough surface. The calculation procedure should result in surface geometries with excellent water repellent properties.     

Capillary forces between two spheres with a fixed volume liquid bridge: theory and experiment

Capillary forces are commonly encountered in nature because of the spontaneous condensation of liquid from surrounding vapor, leading to the formation of a liquid bridge. In most cases, the advent of capillary forces by condensation leads to undesirable events such as an increase in the strength of granules, which leads to flow problems and/or caking of powder samples. The prediction and control of the magnitude of capillary forces is necessary for eliminating or minimizing these undesirable events. The capillary force as a function of the separation distance, for a liquid bridge with a fixed volume in a sphere/plate geometry, was calculated using different expressions reported previously. These relationships were developed earlier, either on the basis of the total energy of two solid surfaces interacting through the liquid and the ambient vapor or by direct calculation of the force as a result of the differential gas pressure across the liquid bridge. It is shown that the results obtained using these methodologies (total energy or differential pressure) agree, confirming that a total-energy-based approach is applicable, despite the thermodynamic nonequilibrium conditions of a fixed volume bridge rupture process. On the basis of the formulas for the capillary force between a sphere and a plane surface, equations for the calculation of the capillary force between two spheres are derived in this study. Experimental measurements using an atomic force microscope (AFM) validate the formulas developed. The most common approach for transforming interaction force or energy from that of sphere/plate geometry to that of sphere/sphere geometry is the Derjaguin approximation. However, a comparison of the theoretical formulas derived in this study for the interaction of two spheres with those for sphere/plate geometry shows that the Derjaguin approximation is only valid at zero separation distance. This study attempts to explain the inapplicability of the Derjaguin approximation at larger separation distances. In particular, the area of a liquid bridge changes with the separation distance, H, and thereby does not permit the application of the "integral method," as used in the Derjaguin approximation.     

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.     

Colloid stability of synthetic titania and the influence of surface roughness

The colloid stability of synthetic titania particles was studied as a function of KCl concentration at pH values of 6.3, 6.7, and 8.4, using static light scattering to obtain stability ratios. Standard DLVO theory was then used to calculate the stability ratios as a function of salt concentration. Reasonable agreement between theory and experiment could only be obtained if an effective interaction radius, corresponding to surface asperities on the titania particles, was used in the calculation. High-resolution TEM images suggest that the effective interaction radius corresponds to the size of surface crystallites formed during synthesis.     

The influence of electrostatic forces on protein adsorption

In this paper we investigate the importance of electrostatic double layer forces on the adsorption of human serum albumin by UV-ozone modified polystyrene. Electrostatic forces were measured between oxidized polystyrene surfaces and gold-coated atomic force microscope (AFM) probes in phosphate buffered saline (PBS) solutions. The variation in surface potential with surface oxygen concentration was measured. The observed force characteristics were found to agree with the theory of electrical double layer interaction under the assumption of constant potential. Chemically patterned polystyrene surfaces with adjacent 5 microm x 5 microm polar and non-polar domains have been studied by AFM before and after human serum albumin adsorption. A topographically flat surface is observed before protein adsorption indicating that the patterning process does not physically modify the surface. Friction force imaging clearly reveals the oxidation pattern with the polar domains being characterised by a higher relative friction compared to the non-polar, untreated domains. Far-field force imaging was performed on the patterned surface using the interleave AFM mode to produce two-dimensional plots of the distribution of electrostatic double-layer forces formed when the patterned polystyrene surfaces is immersed in PBS. Imaging of protein layers adsorbed onto the chemically patterned surfaces indicates that the electrostatic double-layer force was a significant driving force in the interaction of protein with the surface.     

Numerical study on the adhesion and reentrainment of nondeformable particles on surfaces: the role of surface roughness and electrostatic forces

In this paper, the reentrainment of nanosized and microsized particles from rough walls under various electrostatic conditions and various hydrodynamic conditions (either in air or aqueous media) is numerically investigated. This issue arises in the general context of particulate fouling in industrial applications, which involves (among other phenomena) particle deposition and particle reentrainment. The deposition phenomenon has been studied previously and, in the present work, we focus our attention on resuspension. Once particles are deposited on a surface, the balance between hydrodynamic forces (which tend to move particles away from the surface) and adhesion forces (which maintain particles on the surface) can lead to particle removal. Adhesion forces are generally described using van der Waals attractive forces, but the limit of these models is that any dependence of adhesion forces on electrostatic forces (due to variations in pH or ionic strength) cannot be reproduced numerically. For this purpose, we develop a model of adhesion forces that is based on the DLVO (Derjaguin and Landau, Verwey and Overbeek) theory and which includes also the effect of surface roughness through the use of hemispherical asperities on the surface. We first highlight the effect of the curvature radius on adhesion forces. Then some numerical predictions of adhesion forces or adhesion energies are compared to experimental data. Finally, the overall effects of surface roughness and electrostatic forces are demonstrated with some applications of the complete reentrainment model in some simple test cases.     

Colloidal dynamics: influence of diffusion, inertia and colloidal forces on cluster formation

Computer simulations of colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. Comparison of two models, one taking into account inertial term in Langevin equation and another based on diffusional approximation proposed in [D.L. Ermak, J.A. McCammon, J. Chem. Phys. 69 (1978) 1352], has shown that both models enable the prediction of the correct values of the diffusion coefficient and residence time of particle in a doublet and are therefore suitable to study the dynamics of formation and breakage of clusters in colloidal suspensions. It is shown that the appropriate selection of the time step and taking into account inertia of particles provides also the correct value of the average kinetic energy of each particle during the simulations, what allows to use the model based on full Langevin equations as a reference model to verify the validity of the numerical scheme for simulation using diffusion approximation.     

Electrostatic interactions between double layers: influence of surface roughness, regulation, and chemical heterogeneities

Electrostatic interactions between two surfaces as measured by atomic force microscopy (AFM) are usually analyzed in terms of DLVO theory. The discrepancies often observed between the experimental and theoretical behavior are usually ascribed to the occurrence of chemical regulation processes and/or to the presence of surface chemical or morphological heterogeneities (roughness). In this paper, a two-gradient mean-field lattice analysis is elaborated to quantifying double layer interactions between nonplanar surfaces. It allows for the implementation of the aforementioned sources of deviation from DLVO predictions. Two types of ion-surface interaction ensure the adjustment of charges and potentials upon double layer overlap, i.e., specific ionic adsorption at the surfaces and/or the presence of charge-determining ions for the surfaces considered. Upon double layer overlap, charges and potentials are adjusted via reequilibrium of the different ion adsorption processes. Roughness is modeled by grafting asperities on supporting planar surfaces, with their respective positions, shapes, and chemical properties being assigned at will. Local potential and charge distributions are derived by numerically solving the nonlinear Poisson-Boltzmann equation under the boundary conditions imposed by the surface profiles and regulation mechanism chosen. Finite size of the ions is taken into account. A number of characteristic situations are briefly discussed. It is shown how the surface irregularities are reflected in the Gibbs energy of interaction.     

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.     

Melting mechanism of monolayers adsorbed in cylindrical pores: the influence of the pore wall roughness

We have analyzed the mechanism of melting of molecular layers adsorbed in porous materials with cylindrical pores and rough pore walls. The working example studied here is a monolayer of methane molecules adsorbed in MCM-41 pore of diameter 2R=4 nm. Both experimental (neutron scattering) and simulation (Monte Carlo) results demonstrate the strong influence of the wall roughness on the melting mechanism. In particular, the transformation between solidlike and liquidlike monolayer phases adsorbed on a rough surface is observed over a broad temperature range, and solidlike properties persist even above the bulk methane melting temperature.