Adhesion forces between wetted solid surfaces

We investigate in this paper the influence of wetting films on the adhesion forces between macroscopic solid surfaces connected by a liquid bridge. We show that the capillary forces are dependent on the interactions governing the wetting layers, and that those interactions may be determined from the measurement of the capillary force in the presence of a condensable vapor. We illustrate those results with a surface force apparatus experiment where the capillary force between high-energy surfaces is measured for different liquid pressures.     

Kinetics of liquid annulus formation and capillary forces

The dependence of the capillary adhesion force F(cap) between a silica microsphere and a flat silica surface versus a time period t of the samples' contact (i.e., dwell-in time) is experimentally investigated using atomic force microscopy (AFM). F(cap) was found to be dependent on t if the humidity was >30-35%. This dependence is exponential, with decay (characteristic) times of ～10 s. It is suggested that the kinetics of the adhesion process are related to the growth of the water annulus between surfaces. Furthermore, we propose that the growth kinetics has two components: (1) water vapor diffusion from the surrounding humid media into the gap between samples and (2) water drainage from the gap. The theory of diffusion through thin pores (i.e., gaps) is developed, and analytical formulas are obtained for the dependence of the meniscus radius r versus time t. However, the experimental dependence of F(cap) versus t and, consequently, r versus t obtained in this article disagrees with the theoretical prediction by several orders of magnitude. Similar results were obtained from the literature data for capillary forces between an AFM cantilever tip and a flat surface. Possible reasons for the deviation from diffusion theory are suggested: surface and Knudsen regimes of vapor diffusion, nonsteady state vapor flow, and tortuosity. Taking into account the viscous drainage of water from the multilayer gap can explain the experimental kinetics of bridge formation, but only if the viscosity of the adjacent multilayer of water is several orders of magnitude larger than the bulk viscosity.     

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.     

Temperature dependence of particle-particle adherence forces in ice and clathrate hydrates

Particle-particle pulloff adherence forces were measured as a function of temperature in the ice/n-decane/ice and tetrahydrofuran (THF) hydrate/n-decane/THF hydrate systems using a newly developed micromechanical testing technique. Experiments using approximately 200 microm radius particles were performed at atmospheric pressure over the temperature range 263-275 K. The ice and hydrate particles displayed very similar behavior. While the measured adherence forces had significant variation, the shapes of the cumulative force distribution curves were similar among the different sets of experiments. The measured adherence forces distributions shifted to lower force values as the temperature was decreased from the solid melting temperature. The observed forces and trends were explained by the capillary cohesion of rough surfaces, with the capillary bridging liquid being stabilized below its freezing point by the negative curvature of the bridging liquid/n-decane interface.     

Influence of surface topography on the interactions between nanostructured hydrophobic surfaces

Nanostructured particle coated surfaces, with hydrophobized particles arranged in close to hexagonal order and of specific diameters ranging from 30 nm up to 800 nm, were prepared by Langmuir-Blodgett deposition followed by silanization. These surfaces have been used to study interactions between hydrophobic surfaces and a hydrophobic probe using the AFM colloidal probe technique. The different particle coated surfaces exhibit similar water contact angles, independent of particle size, which facilitates studies of how the roughness length scale affects capillary forces (previously often referred to as "hydrophobic interactions") in aqueous solutions. For surfaces with smaller particles (diameter < 200 nm), an increase in roughness length scale is accompanied by a decrease in adhesion force and bubble rupture distance. It is suggested that this is caused by energy barriers that prevent the motion of the three-phase (vapor/liquid/solid) line over the surface features, which counteracts capillary growth. Some of the measured force curves display extremely long-range interaction behavior with rupture distances of several micrometers and capillary growth with an increase in volume during retraction. This is thought to be a consequence of nanobubbles resting on top of the surface features and an influx of air from the crevices between the particles on the surface.     

Forces between surfaces in liquids

The results and implications of direct force measurements between molecularly smooth mica surfaces in liquids are reviewed. These discussions include four interactions fundamental to colloid science: van der Waals forces, double layer forces, adhesion forces and structural or solvation forces (e.g. hydration forces). Also considered are the effects of preferential surface adsorption of solute molecules on these interactions, e.g. surfactant adsorptions from aqueous solutions and water condensation from non-aqueous solvents.In aqueous media it is apparent that the DLVO theory is valid at all surface separations down to the “force barrier”, but that under certain conditions hydration forces can become significant at distances below 30 Å.The measured adhesion force between two solid surfaces can be simply related to their surface energies and where meniscus forces are also present due to “capillary condensation” from vapor solvent, their effect on adhesion can be understood in terms of straightforward bulk thermodynamic principles. Here, too, it is concluded that structural forces cannot be ignored.Our results suggest that structural forces may either very monotonically with distance or be oscillatory with a periodicity equal to the molecular size. Their origin, nature, mode of action and importance for particle interactions will no doubt take many years to sort out.     

Isotherms of Capillary Condensation Influenced by Formation of Adsorption Films

Isotherms of capillary condensation are often used to determine the vapor sorption capacity of porous adsorbents as well as the pore size distribution by radii. In this paper, for calculating the volume of capillary condensate and of adsorption films in a porous body, an approach based on the theory of surface forces is used. Adsorption isotherms and disjoining pressure isotherms of wetting films are presented here in an exponential form discussed earlier. The calculations were made for straight cylindrical capillaries of different radii and slit pores of different width. The mechanisms of capillary condensation differ in cylindrical and slit pores. In cylindrical pores capillary condensation occurs due to capillary instability of curved wetting films on a capillary surface, when film thickness grows. In the case of slit pores, coalescence of wetting films formed on opposite slit surfaces proceeds under the action of attractive dispersion forces. Partial volumes of liquid in the state of both capillary condensate and adsorbed films are calculated dependent on the relative vapor pressure in a surrounding media. Copyright 2000 Academic Press.     

Decomposing bridging adhesion between polyelectrolyte layers into single molecule contributions

A novel approach to analyze the force response of multiple polymer strands, which are bridged between two surfaces, is proposed. The response of single polymer strands is experimentally accessible by measuring the force upon separation of two polymer-coated surfaces with the atomic force microscope. Our approach is based on the decomposition of the stretching and desorption sequence into contributions of independently bridged chains and of the elimination of loops formed on the opposite surface during contact. This approach was applied to investigate the bridging adhesion of surfaces coated with poly(vinylamine) (PVA). The force response of single PVA molecules was described on the basis of a recently proposed model, which accounts for the discrete chain character of the polymer at higher extension forces. As exemplary results, we determined the length distributions of the individual chains and the loop number distribution of these bridging chains on the polyelectrolyte-coated surfaces. The former were compared with scaling theories of polymer adsorption.     

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.     

Theoretical studies of solute vibrational energy relaxation at liquid interfaces

Recent advances in the theoretical understanding of solute vibrational energy relaxation at liquid interfaces and surfaces are described. Non-equilibrium molecular dynamics simulations of the relaxation of an initially excited solute molecule are combined with equilibrium force autocorrelation calculations to gain insight into the factors that influence the vibrational relaxation rate. Diatomic and triatomic nonpolar, polar, and ionic solute molecules adsorbed at the liquid/vapor interface of several liquids as well as at the water/CCl(4) liquid/liquid interface are considered. In general, the vibrational relaxation rate is significantly slower (a factor of 3 to 4) at the liquid/vapor and liquid/liquid interface than in the bulk due to the reduced density, which gives rise to a reduced contribution of the repulsive solvent-solute forces on the vibrational mode. The surface effects on the ionic solutes are much smaller (50% or less slower relaxation relative to the bulk). This is due to the fact that ionic solutes at the interface are able to keep part of their solvation shell to a degree that depends on their size. Thus, a significant portion of the repulsive forces is maintained. A high degree of correlation is found between the peak height of the solvent-solute radial distribution function and the vibrational relaxation rate. The relaxation rate at the liquid/liquid interface strongly depends on the location of the solute across the interface and correlates with the change in the density and polarity profile of the interface.     

Adhesion hysteresis from interdependent capillary and electrostatic forces

Adhesion hysteresis commonly occurs at the nanoscale in humid atmospheres, yet mechanisms are not entirely understood. Here, the adhesion forces between silicon (111) oxide surfaces and tungsten oxide probes have been examined using interfacial force microscopy. The results show that the adhesion forces during surface approach and separation differ not only in magnitude but also in mechanism, arising mainly from capillary and electrostatic forces, respectively. Surface contact leads to a transient intersurface potential on dewetting. This mechanism of adhesion hysteresis differs in not relying singly on hysteretic wetting. Furthermore, by biasing the surfaces, nonadditivity is demonstrated between the capillary and electrostatic forces at the onset of condensation. These results hold important implications on the interpretation of force in nanoprobe geometries in humid atmospheres.     

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.     

Choose sides: differential polymer adhesion

AFM-based single molecule desorption measurements were performed on surface end-grafted poly(acrylic acid) monolayers as a function of the pH of the aqueous buffer to study the adhesion properties of polymers that bridge two surfaces. These properties were found to depend on the adhesion forces of both surfaces in a differential manner, which is explained with a simple model in analogy to the Bell-Evans formalism used in dynamic force spectroscopy. The measured interaction forces between the poly(acrylic acid) chains and silicon nitride AFM tips depend on the grafting density of the polymer monolayers as well as on the contour length of the polymer chains. This study demonstrates that the stability of polymer bridges is determined by the adhesion strengths on both surfaces, which can be tuned by using pH-dependent polyelectrolyte monolayers.     

Universal Two-dimensional forces that Act on Particles at interfaces

This paper starts with a short tribute to the scientific legacy of Peter Kralchevsky and his role in the collaboration with the research group of Kuniaki Nagayama in Japan. Next it presents an overview of the lateral capillary forces, studied jointly by both authors and their groups. Analogies with some other forces in nature are highlighted where relevant. The lateral capillary forces emerge between objects dispersed at a liquid interface or in liquid film and act in direction parallel to the liquid interface, being caused by the liquid surface tension. The lateral capillary forces depend on the size of the objects and the wetting of the particle by the liquid and can be either attractive or repulsive. For fine particles the force–distance relationship follows an inverse-linear law. Their effect is seen in our everyday experience that dust particles and bubbles tend to aggregate on the water surface. These forces are universally acting between any objects regardless of scale and are described by equations similar to those describing the gravitational and electric forces in the two-dimensional (2D) world. The current KN & PK review article provides a didactic overview that is easy to digest as a 2D model of gravity in general relativity, because the origin of the latter force, namely the space distortion, can be clearly visualized.     

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.     

Electrostatic double-layer interaction between spherical particles inside a rough capillary

Predictions of electrostatic double-layer interaction forces between two similarly charged spherical colloidal particles inside an infinitely long "rough" capillary are presented. A simple model of a rough cylindrical surface is proposed, which assumes the capillary wall to be a periodic function of axial position. The periodic roughness of the wall is characterized by the wavelength and amplitude of the undulations. The electrostatic double-layer interaction force between two spherical particles located axially inside this rough capillary is determined by solving the nonlinear Poisson-Boltzmann equation employing finite element analysis. The effect of surface roughness of the cylindrical enclosure on the interaction force between two particles is extensively studied on the basis of this model. The simulations are carried out for dimensionless amplitudes (amplitude/particle radii) ranging from 0.05 to 0.15 and scaled wavelengths (wavelength/particle radii) ranging from 0.4 to 4.0. The interaction force between the particles is significantly modified by the proximity of the rough capillary wall. Generally, the interaction force for rough capillaries oscillates around the corresponding interaction force in a smooth capillary depending on the magnitudes of the scaled amplitude and wavelength of the roughness. The influence of roughness on the electrostatic interactions becomes more pronounced when the surface potential of the cylinder wall is different from the sphere surface potentials. When the cylinder and the particle surfaces have large potential differences, the axial force experienced by a particle is dominated by the capillary roughness. There are dramatic oscillations of the force, which alternately becomes repulsive and attractive as the particle moves from the crest to the trough of the rough capillary wall. These results suggest that manipulation of colloidal particles in narrow microchannels may be subject to significant force variations owing to the roughness inherent in microfabricated channels etched on metal films.     

A theory of adsorbate melting near the surfaces of adsorbents and in slit-shaped pores

Molecular principles of a theory of adsorbate melting near the open surfaces of adsorbents in the frozen state or in slit-shaped pores are discussed. The states of liquid and crystalline adsorbates are described in terms of a single molecular approach (the lattice gas model). The crystalline state is described using the concept of quasi-average distributions, for which the degeneracy of the density distribution function in the plane of the adsorbent is eliminated. Equations for the chemical potential of the adsorbate in defective crystals and vapor-liquid systems are derived with allowance for their vibrational motion, making it possible to calculate the concentration profile of the substance at the planar interface between two solid phases, between a solid and a liquid, and inside a slit-shaped pore.     

Transport mechanisms in capillary condensation of water at a single-asperity nanoscopic contact

Transport mechanisms involved in capillary condensation of water menisci in nanoscopic gaps between hydrophilic surfaces are investigated theoretically and experimentally by atomic force microscopy (AFM) measurements of capillary force. The measurements showed an instantaneous formation of a water meniscus by coalescence of the water layers adsorbed on the AFM tip and sample surfaces, followed by a time evolution of meniscus toward a stationary state corresponding to thermodynamic equilibrium. This dynamics of the water meniscus is indicated by time evolution of the meniscus force, which increases with the contact time toward its equilibrium value. Two water transport mechanisms competing in this meniscus dynamics are considered: (1) Knudsen diffusion and condensation of water molecules in the nanoscopic gap and (2) adsorption of water molecules on the surface region around the contact and flow of the surface water toward the meniscus. For the case of very hydrophilic surfaces, the dominant role of surface water transportation on the meniscus dynamics is supported by the results of the AFM measurements of capillary force of water menisci formed at sliding tip-sample contacts. These measurements revealed that fast movement of the contact impedes on the formation of menisci at thermodynamic equilibrium because the flow of the surface water is too slow to reach the moving meniscus.