Lateral Capillary Forces Research Articles

Substrate-dependent dispersion behavior of polymer-protected Pt colloid studied by SPM

The dispersion behavior of PVP-protected platinum colloids on mica and gold is studied by scanning probe microscopy (STM and AFM). Both the distribution pattern and morphology of colloids are different on the two substrates. It is found that the dispersion results are determined not only by lateral capillary force but also by the evaporation rate of solvent. For dispersion on mica surfaces, the colloids form regular patterns at the edges of polymer patches that are stripped off the colloids. On gold surfaces, the protected colloids disperse randomly and preserve their core-shell structures. The reason is attributed to the different evaporation rate of solvent on two substrates, which in turn induces the difference in the effect of the lateral capillary force.

Influence of the Evaporation Rate on the Packing Order of Polydisperse Latex Monofilms

A new strategy to create well-ordered latex particle monofilms from polydisperse latex solutions was developed. Due to size-dependent segregation, the spherical particles assemble in grains with a uniform sphere size within each grain. The size-dependent segregation process can be deduced from the action of a single force, the lateral capillary force. A strong temperature dependence can be observed, and the process becomes evident when the substrate is cooled. The samples are characterized by scanning force microscopy. Finally, to prove the theoretical model, a computer simulation is performed, supporting the experimental results.

LATERAL CAPILLARY FORCES AND TWO-DIMENSIONA ARRAYS OF COLLOID PARTICLES AND PROTEIN MOLECULES

This paper presents a review of our recent studies on the lateral capillary forces and on their role in the formation of two-dimensional ordered arrays of colloidal particles or protein molecules. To reveal the mechanism of protein ordering in liquid films we carried out model experiments with micrometer sized latex particles. The films were formed on solid or liquid substrates. By variation of the electrolyte concentration, the particle charge and volume fraction we proved that neither the double layer repulsion, nor the van der Waals attraction between the particles, was responsible for the formation of the two-dimensional arrays. Direct microscope observations revealed that the process of ordering was triggered by attractive lateral capillary forces due to the overlap of the menisci formed around the particles. Two types of lateral capillary forces, flotation and immersion, could be distinguished and theory of these interactions was developed. The lateral capillary forces between a floating particle and a wall were also studied; they could be employed for precise determination of the shear surface viscosity.

Self-Assembly of Mesoscale Objects into Ordered Two-Dimensional Arrays

Regular arrays of topologically complex, millimeter-scale objects were prepared by self-assembly, with the shapes of the assembling objects and the wettability of their surfaces determining the structure of the arrays. The system was composed of solid objects floating at the interface between perfluorodecalin and water and interacting by lateral capillary forces; patterning of the wettability of the surfaces of the objects directs these forces. Self-assembly results from minimization of the interfacial free energy of the liquid-liquid interface. Calculations suggest that this strategy for self-assembly can be applied to objects on a micrometer scale.

Lateral forces acting between particles in liquid films or lipid membranes

To investigate the mechanism of formation of 2D arrays of protein macromolecules in liquid films we carried out model experiments with μm-sized latex particles. The direct observations revealed that the process of ordering is triggered by attractive lateral capillary forces due to the overlap of the menisci formed around the particles. Two types of lateral capillary forces, flotation and immersion, can be distinguished, and a theory of these interactions is developed. Similar forces are operative between inclusions (proteins) incorporated in lipid membranes. We develop an appropriate model of a lipid bilayer, which is described as an elastic layer (the hydrocarbon chain region) sandwiched between two Gibbs dividing surfaces (the two headgroup regions). The range of the interaction between two cylindrical inclusions turns out to be of the order of several inclusion radii. The results, which are in qualitative agreement with the experimental observations, can be applied to the interpretation of membrane processes and mechanisms such as protein aggregation in lipid membranes.

Nonlinear Rupture Theory of a Thin Liquid Film on a Cylinder

The dynamic rupture process of a thin liquid film on a cylinder is investigated numerically. First a nonlinear differential equation that describes the long-wave evolution of the interface shape is derived. After the evolution equation is solved and analyzed, the results reveal that a decrease in the cylinder radius will induce a stronger lateral capillary force and consequently will accelerate the rupture process. Moreover, the tendency of acceleration becomes more explicit in the case of large surface tension.

Direct Measurement of Nanonewton Capillary Forces

We measured experimentally very weak interactions between microscopic particles by means of a torsion microbalance of sensitivity better than 10 −9N. The model system consists of two thin glass cylinders of radii 50 μm immersed vertically in a liquid at the liquid/air interface. The cylinders attract each other by a capillary immersion force due to deformation of the liquid surface around them. The magnitude of the measured force ranges between 4 × 10 −7and 10 −9N, depending on the separation distance and the surface tension. At a fixed interparticle distance the force for solution of sodium dodecyl sulfate is about twice as small as that for pure water due to the lower surface tension. The experimental data are well described by the theory of lateral capillary forces. The presented results can be applied to the explanation of the interaction between spherical particles forming two-dimensional arrays on substrate.

Two-Dimensional Patterns of Magnetic Particles at Air−Water or Glass−Water Interfaces Induced by an External Magnetic Field: Theory and Simulation of the Formation Process

We describe theoretically the formation process of two-dimensional patterns of magnetic particles at an interface under the action of an external magnetic field. First, we developed a theoretical model for the forces acting on the particles, which are the magnetic attraction toward the axis of symmetry, magnetic repulsion due to the induced dipoles, electrostatic repulsion due to the surface net charge and electric dipoles of the particles, and lateral capillary forces in the case of a liquid interface. Then, we developed a Brownian dynamics algorithm and simulated the pattern formation. Our simulations reproduced the hexagonally aligned two-dimensional patterns, which were experimentally observed and reported in the complementary experimental work, that is, they reproduced the distance between the particles and the time of pattern formation. Irregular patterns such as square and pentagonal ones that were experimentally observed were also simulated. We calculated that when the distance between particles i...

Lateral capillary forces measured by torsion microbalance.

The forces of capillary interaction between two thin cylindrical rods or two spherical particles placed at a liquid/air interface and immersed partially in the liquid are measured by a sensitive torsion microbalance. Cylindrical rods of radii 50, 165, and 365 \ensuremath{\mu}m are used. The spheres have radius 600 \ensuremath{\mu}m; they are modeling the lateral interaction between colloidal particles trapped in a thin liquid film. The measured forces range in magnitude between ${10}^{\ensuremath{-}4}$ and ${10}^{\ensuremath{-}9}\mathrm{N}$ depending on the particle size and the interparticle distance. The experimental data agree well with the theory of capillary immersion forces.

Lateral capillary interaction between particles protruding from a spherical liquid layer

The lateral capillary interaction between two particles immersed in a spherical thin liquid film is investigated. The interfacial shape, the lateral capillary force and the interparticle energy are calculated by using the numerical solution of the linearized Laplace equation of capillarity. Orthogonal bipolar coordinates on a sphere (inducing biconical coordinates in space) are introduced as a helpful instrument for solving this problem and other problems of similar geometry. We consider two types of boundary conditions at the particle surfaces: fixed contact angle and fixed contact line. We established that for particles of fixed contact angle the capillary interaction energy depends monotonically on the interparticle distance whereas for particles of fixed contact line the interaction energy exhibits a maximum. The numerical results show that in both cases the capillary interaction is much larger than the thermal energy kT and can induce aggregation and ordering of submicrometre particles. These theoretical findings can be important for understanding the properties of Pickering emulsions (stabilized by particles) and liposomes or biomembranes containing incorporated membrane proteins.

Size-Dependent Separation of Colloidal Particles In Two-Dimensional Convective Self-Assembly

We report a new phenomenon, size-dependent separation of colloidal particles in two-dimensional (2D) convective self-assembly that takes place in a wetting liquid film on a mercury surface [Two-dimensional (2D) convective assembly (Nagayama, K. Phase Transition 1993, 45, 185)]. During the drying of suspensions of colloidal particles in wetting films, homogeneously mixed particles in the suspensions separated and assembled according to their size. In this size-dependent separation of particles, large particles gathered in the center and were surrounded by small particles. To obtain a better understanding of this new phenomenon, we performed experiments on the convective assembly of particles on a mercury surface using binary mixtures of particles that ranged in size from 144 to 12 nm in diameter. To study the mechanism of this size-dependent separation, we also did computer simulations in which we accounted for two types of assembly forces, lateral capillary force and convective flow, that we have been extensively studying in actual assembly systems. The simulations successfully reproduced a size-dependent separation of particles that was identical to that for the actual assembly systems. From the results of our experiments and simulations, we found that the mechanism that was concluded for the convective assembly also governs the size-dependent separation of particles in the actual assembly systems.

Measurement of the Drag Coefficient of Spherical Particles Attached to Fluid Interfaces

The drag coefficient, β, of spherical particles attached to a pure air-water interface is determined. The method is based on the measurement of the particle velocity V, under the action of a well-defined lateral capillary force F. The capillary force is created by controlled deformation of the water surface by means of a Teflon barrier whose vertical position can be precisely adjusted. The magnitude of the force is calculated by means of the theory of capillary interaction between a sphere and a vertical wall (Kralchevsky et al., J. Colloid Interface Sci. 167, 47, 1994). The drag coefficient is calculated from the ratio β = F/V at small Reynolds numbers. The dependence of the drag coefficient on the particle size and the three-phase contact angle is determined. For small spheres, which do not create substantial deformation of the fluid interface, β is always smaller than the Stokes coefficient, βs - 6 πηa (η is the water viscosity and a is the particle radius). For large spheres, however, β can be greater than βs. This higher hydrodynamic resistance can be explained by the presence of a curved meniscus around heavier particles. The measured values of β are compared with theoretical calculations and very good agreement is reached. It is demonstrated that the method is sensitive to the presence of adsorbed surfactants and that it can be used for the determination of the surface viscosity of adsorbed layers.

Formation of two-dimensional colloid crystals in liquid films under the action of capillary forces

When two similar small particles are attached to a liquid interface they attract each other due to a lateral capillary force. This force appears because the gravitational potential energy of the floating particles decreases when they are approaching each other. This force is proportional to R6 (R is the particle radius), so it decreases very fast with particle size and becomes negligible for R<10 mu m. We found that the situation is quite different when the particles (instead of being freely floating) are partially immersed in a liquid layer on a substrate. In this case the energy of capillary attraction is proportional to R2 and turns out to be much larger than kT even with particles of diameter about 10 nm. The effect is related to the particle three-phase contact angle, i.e. to the intermolecular forces, rather than to gravity. The experiments show that the lateral capillary forces can bring about the formation of a two-dimensional array (2D-crystal) from both micrometre-size and submicrometre particles: latex spheres, protein globules, etc.

Theory of curved interfaces and membranes: Mechanical and thermodynamical approaches

The mechanical and thermodynamical approaches to the theory of the general curved interfaces are presented and compared. In the mechanical approach a curved interface or membrane is characterized by the tensors of surface stresses and moments. They are connected by the surface balances of the linear and angular momentum. On the other hand, in the thermodynamical approach the surface is characterized by the scalar dilation and shear tensions as well as by the bending and torsion moments. In this review we investigate the problem about the relationships connecting the mechanical and thermodynamical approaches. We find that these two approaches are in a good agreement, that they are complementary to each other and represent the two parts of a self-consistent theory. The latter can be applied to any system where curved interfaces, thin films or membranes are present: microemulsions, lamellar and sponge phases, lipid vesicles and cell membranes, capillary waves at interfaces, undulation and peristaltic surface forces, lateral capillary forces between particles in thin liquid films, etc.

Direct measurement of lateral capillary forces

Precise and convenient force balance has been constructed for direct measurement of the lateral capillary forces between two vertical cylinders and between a cylinder and a wall. The experiments with both hydrophilic and hydrophobic capillaries of submillimeter diameter show that at large distances the capillary forces obey simple universal laws. A theoretical interpretation of this fact is proposed, which is based on a nonlinear superposition approximation for the shape of the liquid meniscus. At separations comparable with the capillary diameter and large slopes of the liquid surface, the nonlinear Laplace equation of capillarity should be solved numerically to describe the measured capillary forces. The obtained results have direct relation to the lateral capillary interactions between spherical particles floating on a single fluid interface or confined in a thin liquid layer.

Lateral Capillary Forces between Floating Submillimeter Particles

A procedure for calculating the energy and force of capillary interaction between two floating spherical particles of submillimeter size attached to a liquid-fluid interface is proposed on the basis of a general expression for the grand thermodynamic potential of the system. The latter takes into account the gravitational, wetting, and meniscus surface energies. For large interparticle separations the derived equations reduce to the asymptotic formulas derived by Chan et al. (J. Colloid Interface Sci. 79, 410 (1981)). The effects of interfacial tension, particle size, density, and contact angle on the capillary interaction are investigated. The results of the energetical and force approaches to the capillary interactions turn out to be in a very good quantitative agreement.