An investigation of the stable orientations of orthorhombic particles in a thin film and their effect on its critical failure pressure

The effects of shape and contact angle on the behaviour of orthorhombic particles at an interface and in thin films were investigated using Surface Evolver. It is shown that the energetically stable orientations of the particle change with its aspect ratio. Long, wide, flat particles with low contact angles are more stable in flat orientations, i.e. with two faces parallel to the flat film surface. More cubic particles with higher contact angles are more stable in twisted orientations, where the opposite sides of the film can be drawn together at the sharp edges of the particle. The combination of contact angle and orientation has been found to have a large effect on the capillary pressure required to rupture the film. A film containing a particle in a flat orientation will rupture at a capillary pressure up to three times greater than one containing an identical particle in a twisted orientation. Wider, flatter particles with low contact angles stabilise thin liquid films to a greater extent than cubic particles with high contact angles.     

Theoretical evaluation of nano- or microparticulate contact angle at fluid/fluid interfaces: analysis of the excluded area behavior upon compression

A novel method for the determination of the particle contact angle at the liquid/gas or liquid/liquid interface based on the excluded area concept revealed, in spite of its simplicity, some serious difficulties connected with the exact quantitative particle deposition at the interface and with changes in the particulate contact angle upon binary monolayer compression. The comprehensive theoretical consideration of the contact angle behavior made for such a system allowed considerable improvements: firstly, the prediction of direction of the particles' displacement at surface pressure increase is now possible and hence an unambiguous identification of particle hydrophobicity can be done. Secondly, the analytical relation describing the dependence of the particulate contact angle on the surface tension (surface pressure) was derived, allowing the prediction of whether or not particles of a given hydrophobicity will be expelled from the monolayer at certain surface pressure and of the area relinquished by the displaced particles. Thirdly, the transformation of this relation upon taking into consideration the initial conditions led to a linear dependence between excluded area and normalized surface tension allowing the determination of the particle contact angle and the exact number of deposited particles simultaneously and independently of each other. Finally, the application of the improved approach to the previously collected experimental data yielded reasonable values for both particle contact angle and number of deposited particles.     

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.     

Surface functionalization of SBA-15 and a nonordered mesoporous silica with a 1,4-diazabicyclo[2.2.2]octane derivative: study of CuCl2 adsorption from ethanol solution

The equilibrium position of a spherical or prolate spheroidal particle resembling a needle floating at the interface between two immiscible fluids is discussed. A three-dimensional meniscus attached to an a priori unknown contact line at a specified contact angle is established around the particle, imparting to the particle a capillary force due to surface tension that is balanced by the buoyancy force and the particle weight. An accurate numerical solution for a floating sphere is obtained by solving a boundary-value problem, and the results are compared favorably with an approximate solution where the effect of the particle surface curvature is ignored and the elevation of the contact line is computed using an analytical solution for the meniscus attached to an inclined flat plate. The approximate formulation is applied locally around the nearly planar elliptical contact line of a prolate spheroid to derive a nonlinear algebraic equation governing the position of the particle center and the mean elevation of the contact line. The effect of the fluid and particle densities, contact angle, and capillary length is discussed, and the shape of the contact line is reconstructed and displayed from the local solution.     

pH-Dependent Control of Particle Motion through Surface Interactions with Patterned Polymer Brush Surfaces

In this Article, we show that inclined silicon surfaces patterned with poly(methacrylic acid) brushes are able to control the position and movement of 20 μm silica particles, which are propelled across the patterned surface by sedimentation forces. Three different types of behavior were observed depending on the angle between the direction in which a particle sedimented and the orientation of the polymer-brush silicon interface. At small angles, particles were found to sediment to the brush interface and then sediment following the direction of the brush interface. At larger angles, particles sedimented to the interface and then followed the direction of the brush interface, but then after a certain distance changed direction to pass over the interface. At the largest angles where the brush interface was approximately perpendicular to the motion of the particle, particles were found to travel over the interface unperturbed. This behavior was also found to be pH dependent, allowing the formation of pH responsive "gates", which allow particles to pass at low pH but not at high pH. It was also found that if patterned polymer brush surfaces were oriented in the correct way, they were able to control the number of particles present at specific locations.     

Adsorption of acicular particles at liquid-fluid interfaces and the influence of the line tension

In this paper, the adsorption energy of an acicular (prolate and cylindrical) particle onto a liquid-fluid interface and the effect of the line tension are investigated. The results show that, without line tension, acicular particles always prefer to lie flat in the plane of the interface. However, line tension plays a significant role in determining the adsorption of an acicular particle. First, the line tension creates an energy barrier for the adsorption of particles onto an interface. The planar configuration has a larger energy barrier due to the longer contact line. Therefore, the particles prefer to enter the interface in a homeotropic configuration and then rearrange to a planar configuration or an oblique configuration with a small tilt angle. Second, for prolate particles, an energy maximum occurs at some tilt angles when the line tension is large. Therefore, once the prolate particle is adsorbed on the interface in a homeotropic configuration or with a larger tilt angle, it must conquer an energy barrier to rearrange to a planar configuration. For cylindrical particles, when the line tension is higher, the planar configuration will not be the most energy-favorable configuration. The cylindrical particles prefer to stay in the interface with a small tilt angle.     

Adsorption of microstructured particles at liquid-liquid interfaces

The solid particles are adsorbed at interfaces and form self-assembled structures when the particles have suitable wettability to both liquids. Here, we show theoretically how the microstructure on the particle surface affects their adsorption properties. The physical properties of the interface adsorbing a particle will be described by taking into account the surface roughness due to the microstructure. The microstructure on the surface changes drastically the wettability and the equilibrium position of the adsorbed particle. Therefore, the contact angle of the particle at the three-phase contact line shifts with the particle surface area, because the surface roughness enhances the interfacial properties of the particle surface. Moreover, the range of the interfacial tensions at which the particle is adsorbed becomes narrower with the increase of the surface roughness. The effect of the particle shape on the adsorption properties is also studied. In the case of disk-shaped particles, the energy changes discontinuously when the plane surface of the particle contacts the liquid-liquid interface. The adsorbing position does not change with the surface roughness. The orientation of a parallelepiped particle at the liquid-liquid interface is governed by the aspect ratio and the surface area of the particle. On the other hand, the particle which is partially covered with the microstructured surface is adsorbed firmly at the interface in an oriented state. We should consider not only the interfacial tensions but also the surface structure and the particle shape to control the adsorption behavior of the particle.     

Shape of the capillary meniscus around an electrically charged particle at a fluid interface: comparison of theory and experiment

Here, we consider in detail the problem of the shape of the capillary meniscus around a charged colloidal particle, which is attached to a fluid interface: oil/water or air/water. The meniscus profile is influenced by the electric field created by charges at the particle/nonpolar fluid boundary. We digitized the coordinates of points from the meniscus around silanized glass spheres (200-300 mum in radius) attached to the tetradecane/water interface. The theoretical meniscus shape is computed in three different ways that give numerically coincident results. It is proven that for sufficiently small particles the meniscus profile can be expressed as a superposition of pure electric and gravitational deformations. Special attention is paid to the comparison of theory and experiment. A procedure for data processing is developed that allows one to obtain accurate values of the contact angle and surface charge density from the fit of the experimental meniscus profile. For all investigated particles, excellent agreement between theory and experiment is achieved. The results indicate that the electric field gives rise to an interfacial deformation of medium range and considerable amplitude.     

Optical trapping forces for colloids at the oil-water interface

We calculate the optical trapping forces exerted by a single laser beam strongly focused on a dielectric sphere located at a two-dimensional (2D) oil-water interface. The calculated lateral trapping forces, based on the geometrical optics approximation (GOA), agree with experimental measurements of the trapping force. Importantly, the calculations verify that the radiation force exerted on particles perpendicular to the interface is not sufficient to induce capillary interactions between particle pairs, which could be mistaken for particle-particle interactions. Finally, we find that the trapping forces depend on the three-phase contact angle of the particle at the interface.     

Detachment of deposited colloids by advancing and receding air-water interfaces

Moving air-water interfaces can detach colloidal particles from stationary surfaces. The objective of this study was to quantify the effects of advancing and receding air-water interfaces on colloid detachment as a function of interface velocity. We deposited fluorescent, negatively charged, carboxylate-modified polystyrene colloids (diameter of 1 μm) into a cylindrical glass channel. The colloids were hydrophilic with an advancing air-water contact angle of 60° and a receding contact angle of 40°. After colloid deposition, two air bubbles were sequentially introduced into the glass channel and passed through the channel at different velocities (0.5, 7.7, 72, 982, and 10,800 cm/h). The passage of the bubbles represented a sequence of receding and advancing air-water interfaces. Colloids remaining in the glass channel after each interface passage were visualized with confocal microscopy and quantified by image analysis. The advancing air-water interface was significantly more effective in detaching colloids from the glass surface than the receding interface. Most of the colloids were detached during the first passage of the advancing air-water interface, while the subsequent interface passages did not remove significant amounts of colloids. Forces acting on the colloids calculated from theory corroborate our experimental results, and confirm that the detachment forces (surface tension forces) during the advancing air-water interface movement were stronger than during the receding movement. Theory indicates that, for hydrophilic colloids, the advancing interface movement generally exerts a stronger detachment force than the receding, except when the hysteresis of the colloid-air-water contact angle is small and that of the channel-air-water contact angle is large.     

Contact angles of colloid silica and gold particles at air-water and oil-water interfaces determined with the gel trapping technique

We have used the recently developed gel trapping technique (GTT) to determine the three-phase contact angles of submicrometer silica particles partially coated with octadecyl groups. The particles were spread at air-water and decane-water surfaces, and the aqueous phase was subsequently gelled with a nonadsorbing polysaccharide. The particles trapped at the surface of the aqueous gel were lifted by molding with curable poly(dimethylsiloxane) and imaged with scanning electron microscopy (SEM) to determine the particle contact line diameter which allows their contact angle at the original air-water or oil-water interface to be estimated. We report for the first time the use of the GTT for characterizing the contact angle of individual submicrometer particles adsorbed at liquid interfaces. The SEM images also reveal the structure of the particle monolayer at the interface and the structure of adsorbed particle aggregates. We have also determined the contact angles of agglomerated gold powder microparticles at the air-water and the decane-water interfaces. It was found that agglomerated gold particles demonstrate considerably higher contact angles than those on flat gold-coated surfaces.     

Molding block copolymer micelles: a framework for molding of discrete objects on surfaces

Soft lithography based on photocurable perfluoropolyether (PFPE) was used to mold and replicate poly(styrene-b-isoprene) block-copolymer micelles within a broad range of shapes and sizes including spheres, cylinders, and torroids. These physically assembled nanoparticles were first formed in a selective solvent for one block then deposited onto substrates having various surface energies in an effort to minimize the deformation of the micelles due to attractive surface forces. The successful molding of these delicate nanoparticles underscores two advantages of PFPE as a molding material. First, it allows one to minimize particle deformation due to adsorption by using low energy substrates. Second, PFPE is not miscible with the organic micelles and thus prevents their dissociation. For spherical PS-b-PI micelles, a threshold value of the substrate surface energy for the mold to lift-off cleanly, that is, the particles remain adhered to the substrate after mold removal was determined to be around gamma congruent with 54 mJ/m2. For substrates with higher surface energies (>54 mJ/m2), the micelles undergo flattening which increase the contact area and thus facilitate molding, although at the expense of particle deformation. The results are consistent with theoretical predictions of a molding range for substrate surface energies, which depends on the size, shape, and mechanical properties of the particles. In a similar fashion, cylindrical PS-b-PI micelles remain on the substrate at surface energies gamma>or=54 mJ/m2 after a mold removal. However, cylindrical micelles behaved differently at lower surface energies. These micelles ruptured due to their inability to slide on the surfaces during mold lift-off. Thus, the successful molding of extended objects is attainable only when the particle is adsorbed on higher energy substrates where deformation can still be kept at a minimum by using stronger materials such as carbon nanotubes for the master.     

The role of capillary and surface forces in the crossover behavior of solid nanoparticles at liquid interfaces

We investigate the interaction between a nanoparticle and an oil-water interface with particular emphasis on the particle crossing through the interface. The formation of a three-phase contact line is investigated in two cases, namely in the presence and in the absence of surface forces. We carefully examine the interplay between capillary and surface forces in such systems. Two instabilities of the interface (snap-in/snap-out) as the particle is moved through the interface are identified and quantitatively described. While the snap-in instability was observed in some AFM studies, the precise interface position and configuration relative to the particle at the instability depends on the nature of the surface forces present in the system. After the snap-in, the particle is adsorbed and must overcome an energy barrier due to the interface deformation in order to cross-over to the other liquid. We make quantitative predictions on the interface configuration at the instabilities and the free energy barrier height. The roles of particle size and different interaction parameters characterizing the system in determining the magnitude of the energy barrier for crossing and in the formation of a three-phase contact line are discussed. Ultimately, this study will enable us to make quantitative predictions on capillary effects in nanoparticle-microemulsions mixtures and other colloidal systems. For particles in the micrometer range and larger the capillary forces dominate over the surface forces and dictate how the snap-in occurs. However, the situation becomes different for particle sizes smaller than about 100 nm. The presence of surface forces modifies the interface configuration and the free energy jump at the snap-in instability.     

Analytical Dispersion Force Calculations for Nontraditional Geometries

Presented in this paper are first-principle-based approximate macroscopic models of the van der Waals adhesion force for a variety of particle shapes interacting with an infinite cylinder. In particular, expressions for the van der Waals adhesion force and interaction energy are developed for a (1) spherical particle/infinite cylinder, (2) disk-like particle/infinite cylinder, (3) disk-like particle oriented edgewise to an infinite cylinder, and (4) a deformed slice/infinite cylinder. The models presented depict expected trends in the behavior of both the force of adhesion and the interaction energy between different geometric configurations. These results are also used to demonstrate the impact of contact time on the adhesion force for cylindrical fibers in contact with a disk-shaped particle. After long time intervals where the disk-like particles have remained in contact with the cylinder, the adhesion force may lead to significant deformation of the attached particle. Hence, the adhesion force for a fourth geometric set which represents the most likely scenario for attached particles with long contact times is developed. As will be shown, this scenario results in the highest values of adhesion force and interaction energy. Copyright 2000 Academic Press.     

Flotation de-inking studies using model hydrophobic particles and non-ionic dispersants

A series of non-ionic alcohol ethoxylated surfactants (with HLB within the range of 11.1–12.5) were used as dispersants during flotation of mondisperse hydrophobised silica particles (representing ink particles) in de-inking formulations. Laboratory scale flotation experiments, contact angle, dynamic surface tension and thin film drainage experiments were carried out. The reduction in dynamic surface tension at the air/solution interface (which is dependent on the adsorption kinetics) followed the order C₁₀E₆>C₁₂E₈≈C₁₂E₆>C₁₄E₆ and these values were lower than sodium oleate, which is commonly used in de-inking systems. In addition the non-ionics adsorbed on the hydrophobised silica particles reducing the contact angle. These results indicated that the non-ionic surfactant with the highest CMC (C₁₀E₆) gave (a) the highest rate of adsorption at the air/solution interface (b) the froth with the greatest water content and higher froth volume (c) the lowest reduction in contact angle and (d) the highest flotation efficiency at concentrations above the CMC. It was also observed that flotation occurred, in spite of the fact that thin-film measurements indicated that the adsorption of non-ionic at the air/solution and silica/solution interfaces reduced the hydrophobicity of the particles, as indicated by an increase in stability of the aqueous thin film between the particle and air-bubble. This result suggests that the bubble-ink particle captures mechanism (occurring through rupture of the thin aqueous film separating the interfaces) is not the only mechanism controlling the flotation efficiency and that other parameters (such as the kinetics of surfactant adsorption, foaming characteristics, and bubble size) need to be taken into account. The kinetics is important with respect to the rate of adsorption of surfactant to both interfaces. Under equilibrium conditions, this may give rise to repulsive steric forces between the air-bubble and the particles (stable aqueous thin-films). However, a lower amount of surfactant adsorbed at a freshly formed air bubble or inkparticle (caused by slow adsorption rates) will produce a lower steric repulsive force allowing effective collection of particles by the bubble. Also, it was suggested that the influence of alcohol ethoxylates on bubble-size could effect the particle capture rate and mechanical entrainment of particles in an excessively buoyant froth, which will also play an important role in the flotation recovery.     

Microparticle sampling by electrowetting-actuated droplet sweeping

This paper describes a new microparticle sampler where particles can be efficiently swept from a solid surface and sampled into a liquid medium using moving droplets actuated by the electrowetting principle. We successfully demonstrate that super hydrophilic (2 microm and 7.9 microm diameter glass beads of about 14 degrees contact angle), intermediate hydrophilic (7.5 microm diameter polystyrene beads of about 70 degrees contact angle), and super hydrophobic (7.9 microm diameter Teflon-coated glass beads and 3 microm size PTFE particles of over 110 degrees contact angles) particles on a solid surface are picked up by electrowetting-actuated moving droplets. For the glass beads as well as the polystyrene beads, the sampling efficiencies are over 93%, in particular over 98% for the 7.9 microm glass beads. For the PTFE particles, however, the sampling efficiency is measured at around 70%, relatively lower than that of the glass and polystyrene beads. This is due mainly to the non-uniformity in particle size and the particle hydrophobicity. In this case, the collected particles staying (adsorbing) on the air-to-water interface hinder the droplet from advancing. This particle sampler requires an extremely small amount of liquid volume (about 500 nanoliters) and will thus be highly compatible and easily integrated with lab-on-a-chip systems for follow-up biological/chemical analyses.     

颗粒聚集体对两性SiO2颗粒无水泡沫表面性质的影响

基于Pickering乳液模板法, 合成了2种用于制备非水泡沫的不同相对两亲面积的Janus颗粒, 并合成了表面均匀修饰的颗粒作为对比. 通过调整油混合物的性质, 对颗粒在油气表面上的行为进行了测量和对比, 对颗粒团聚体在颗粒吸附中的作用进行了研究. 结果表明, 受颗粒表面接触角的影响, Janus颗粒的表面活性(表面张力降低能力与产生泡沫的体积)不总是大于均匀改性颗粒. 均匀改性颗粒和Janus颗粒均不是以单个颗粒形式从体相吸附至表面上, 而是以颗粒团聚体状态向表面移动, 并且需要颗粒团聚体的Cassie-Baxter复合表面的接触角约为90°, 而颗粒的本征接触角小于70.1°.     

Connect the drops: using solids as adhesives for liquids

Colloidal particles are shown to be capable of developing adhesion between liquid phases through a bridging mechanism by which intervening, micrometer-scaled, fluid films are stabilized. Particle dynamics leading to the assembly of the stabilizing structure are discussed. Models for the resulting adhesive force are developed from considerations of both interface shape perturbation and the force applied by surface tension on an individual particle. Finally, predictions from these models are compared to direct measurements of the forces that arise during the separation of adhering interfaces. Such comparisons lead to a novel method for determining the three-phase contact angle inherent to particles residing at fluid interfaces.     

Capillary force required to detach micron-sized particles from solid surfaces—Validation with bubbles circulating in water and 2 μm-diameter latex spheres

The adhesion forces holding micron-sized particles to solid surfaces can be studied through the detachment forces developed by the transit of an air–liquid interface in a capillary. Two key variables affect the direction and magnitude of the capillary detachment force: (i) the thickness of the liquid film between the bubble and the capillary walls, and (ii) the effective angle of the triple phase contact between the particles and the interface. Variations in film thickness were calculated using a two-phase flow model. Film thickness was used to determine the time-variation of the capillary force during transit of the bubble. The curve for particle detachment was predicted from the calculated force. This curve proved to be non-linear and gave in situ information on the effective contact angle developing at the particle–bubble interface during detachment. This approach allowed an accurate determination of the detachment force. This theoretical approach was validated using latex particles 2 μm in diameter.     

Small solid particles and liquid lenses at fluid/fluid interfaces

The behaviour of small solid particles and liquid droplets at fluid interfaces is of wide interest, in part because of the roles they play in the stability of foams and emulsions. Here we focus on solid particles at liquid interfaces, both singly and in highly structured monolayers. We briefly mention small oil lenses on water in connection with the determination of line tension, τ. Particles are surface-active in the sense that they often adhere quite strongly to liquid surfaces, although of course they are not usually amphiphilic. The three-phase contact line around a particle at an interface is associated with an excess free energy resulting in a tendency of the line to contract (positive τ, which is a 1D analogue of surface tension) or to expand (negative τ). Positive line tension acts so as to push the contact angle of a particle with the fluid interface further away from 90°, i.e. to force the particle towards the more “wetting” of the two bulk phases. It also leads to activation barriers to entry and departure of particles from an interface. The behaviour of particle monolayers at octane/water interfaces is also discussed . It is found that, for monodisperse spherical polystyrene particles containing ionisable sulphate groups at the surface, highly ordered monolayers are formed. This appears to result from very long range electrostatic repulsion mediated through the oil phase. Surface pressure–surface area isotherms are discussed for particle monolayers and it is shown, using light microscopy, that at monolayer “collapse” particles are not expelled from the monolayers but rather the monolayer folds, remaining intact. This has an important bearing on methods, involving the use of the Langmuir trough, for the experimental determination of contact angles and line tensions in particulate systems. Received: 18 July 1999/Accepted: 30 August 1999