Controlled particle placement through convective and capillary assembly

A wide variety of methods are now available for the synthesis of colloidal particle having controlled shapes, structures, and dimensions. One of the main challenges in the development of devices that utilize micro- and nanoparticles is still particle placement and integration on surfaces. Required are engineering approaches to control the assembly of these building blocks at accurate positions and at high yield. Here, we investigate two complementary methods to create particle assemblies ranging from full layers to sparse arrays of single particles starting from colloidal suspensions of gold and polystyrene particles. Convective assembly was performed on hydrophilic substrates to create crystalline mono- or multilayers using the convective flow of nanoparticles induced by the evaporation of solvent at the three-phase contact line of a solution. On hydrophobic surfaces, capillary assembly was investigated to create sparse arrays and complex three-dimensional structures using capillary forces to trap and organize particles in the recessed regions of a template. In both methods, the hydrodynamic drag exerted on the particle in the suspension plays a key role in the assembly process. We demonstrate for the first time that the velocity and direction of particles in the suspension can be controlled to perform assembly or disassembly of particles. This is achieved by setting the temperature of the colloidal suspension above or below the dew point. The influence of other parameters, such as substrate velocity, wetting properties, and pattern geometry, is also investigated. For the particular case of capillary assembly, we propose a mechanism that takes into account the relative influences of these parameters on the motion of particles and that describes the influence of temperature on the assembly efficiency.     

Mechanistic principles of colloidal crystal growth by evaporation-induced convective steering

We simulate evaporation-driven self-assembly of colloidal crystals using an equivalent network model. Relationships between a regular hexagonally close-packed array of hard, monodisperse spheres, the associated pore space, and selectivity mechanisms for face-centered cubic microstructure propagation are described. By accounting for contact line rearrangement and evaporation at a series of exposed menisci, the equivalent network model describes creeping flow of solvent into and through a rigid colloidal crystal. Observations concerning colloidal crystal growth are interpreted in terms of the convective steering hypothesis, which posits that solvent flow into and through the pore space of the crystal may play a major role in colloidal self-assembly. Aspects of the convective steering and deposition of high-Peclet-number rigid spherical particles at a crystal boundary are inferred from spatially resolved solvent flow into the crystal. Gradients in local flow through boundary channels were predicted due to the channels' spatial distribution relative to a pinned free surface contact line. On the basis of a uniform solvent and particle flux as the criterion for stability of a particular growth plane, these network simulations suggest the stability of a declining {311} crystal interface, a symmetry plane which exclusively propagates fcc microstructure. Network simulations of alternate crystal planes suggest preferential growth front evolution to the declining {311} interface, in consistent agreement with the proposed stability mechanism for preferential fcc microstructure propagation in convective assembly.     

Subcellular topological effect of particle monolayers on cell shapes and functions

We studied topological effects of subcellular roughness displayed by a closely packed particle monolayer on adhesion and growth of endothelial cells. Poly(styrene-co-acrylamide) (SA) particles were prepared by soap-free emulsion copolymerization. Particle monolayers were prepared by Langmuir–Blodgett deposition using particles, which were 527 (SA053) and 1270 nm (SA127) in diameter. After 24-h incubation, cells tightly adhered on a tissue culture polystyrene dish and randomly spread. On the other hand, cells attached on particle monolayers were stretched into a narrow stalk-like shape. Lamellipodia spread from the leading edge of cells attached on SA053 monolayer to the top of the particles and gradually gathered to form clusters. This shows that cell–cell adhesion became stronger than cell–substrate interaction. Cells attached to SA127 monolayer extended to the reverse side of a particle monolayer and engulfed particles. They remained immobile without migration 24 h after incubation. This shows that the inhibition of extensions on SA127 monolayer could inhibit cell migration and cell proliferation. Cell growth on the particle monolayers was suppressed compared with a flat TCPS dish. The number of cells on SA053 gradually increased, whereas that on SA127 decreased with time. When the cell seeding density was increased to 200,000 cells cm⁻², some adherent cells gradually became into contact with adjacent cells. F-actin condensations were formed at the frame of adherent cells and the thin filaments grew from the edges to connect each other with time. For the cell culture on SA053 monolayer, elongated cells showed a little alignment. Cells showed not arrangement of actin stress fibers but F-actin condensation at the contact regions with neighboring cells. Interestingly, the formed cell monolayer could be readily peeled from the particle monolayer. These results indicate that endothelial cells could recognize the surface roughness displayed by particle monolayers and the response was dependent on the pitch of particle monolayers.     

Effect of growth conditions on the structure of two-dimensional latex crystals: modeling

Essential experimental features of the nucleation and growth of a 2D colloidal crystal on a solid substrate are modeled. The crystal, composed of sub-micron-sized latex spheres, is grown by the evaporation of water from the particle suspension in a circular cell. The calculation of the meniscus profile in the cell allows the prediction of the particle volume fraction in the suspension surrounding the crystal as a function of time. This quantity enters into a convective-diffusion model for the crystal growth which calculates the crystal radius as a function of time. Comparison with experimental data for 2D latex particle crystals shows predominant convective growth over a wide range of evaporation rates set by varying the humidity of the air. Microscopic parameters of the particle assembly can also be estimated such as the particle velocity, diffusivity, characteristic time constants, Peclet number, etc. The nucleation is simulated by simultaneously solving the equations of motion for the ensemble of particles trapped in a thin liquid film using the discrete-element method. These equations account for the forces which are physically important in the system: contact particle–particle friction, increased viscous resistance during the particle motion in a wetting film, long-range capillary attraction between two particles screened by the rest of particles. The final result of the simulation is a particle cluster of hexagonal packing, whose structure resembles very much the monolayer nucleus of latex particles observed experimentally. The models proposed by us could also be implemented for the aggregation of species in a variety of practical processes such as coating, texturing, crystal growth from a melt or liquid solution, or a biological array. Received: 10 May 1999 Accepted in revised form: 6 July 1999     

Spontaneous pattern formation by dip coating of colloidal suspensions on homogeneous surfaces

We study the slow withdrawal of a partially wet vertical plate at velocity U from a suspension of well-wet particles. Periodic horizontal striped assemblies form spontaneously at the three-phase contact line on energetically uniform surfaces. Stripe width and spacing depend on the withdrawal velocity U relative to a transition velocity Ut. Thick stripes separated by large spaces form for UUt, thin stripes separated by small spaces form. The stripe spacing is reduced by an order of magnitude and varies weakly with U until a maximum velocity is reached at which the stripes fail to form. A partially wet surface can entrain a meniscus. For UUt, we infer that a film of thickness h is entrained above the meniscus. When h is smaller than the particle diameter D, particles aggregate where the entrained film thickens to match up to the wetting meniscus. When an entrained particle becomes exposed to air by evaporation, it becomes the new pinning site from which the next film is entrained. The film thickness h increases with U; at some velocity, h becomes comparable to D. Particles flow into the film and deposit there in a disordered manner. A diagram summarizing particle deposition is developed as a function of D, U, and h.     

Evaporation-induced particle microseparations inside droplets floating on a chip

We describe phenomena of colloidal particle transport and separation inside single microdroplets of water floating on the surface of dense fluorinated oil. The experiments were performed on microfluidic chips, where single droplets were manipulated with alternating electric fields applied to arrays of electrodes below the oil. The particles suspended in the droplets were collected in their top region during the evaporation process. Experimental results and numerical simulations show that this microsepration occurs as a result of a series of processes driven by mass and heat transfer. An interfacial tension gradient develops on the surface of the droplet as a result of the nonuniform temperature distribution during the evaporation. This gradient generates an internal convective Marangoni flow. The colloidal particles transported by the flow are collected in the top of the droplets by the hydrodynamic flux, compensating for evaporation through the exposed top surface. The internal flow pattern and temperature distribution within evaporating droplets were simulated using finite element calculations. The results of the simulation were consistent with experiments using tracer particles. Such microseparation processes can be used for on-chip synthesis of advanced particles and innovative microbioassays.     

Dynamic self-assembly of polymer colloids to form linear patterns

A dynamic self-assembling process is reported which involves drying a droplet of positively charged colloidal suspension on a flat negatively charged hydrophilic surface. This extremely simple method affords lines of colloidal particles with regular 1.5-4.5 microm line spacing and smaller than 2 microm line width over a broad surface area. The ordered region diffracts light to display an iridescent appearance and generates first-order diffraction spots when illuminated by a He-Ne laser. A periodic stick-slip motion of the drying liquid front is observed during the drying process using optical microscopy. The periodic motion must be related to the periodic particle deposition. We propose that the simultaneous deposition of the particles at a fixed distance (i.e., the line spacing) behind the previous line of particles where the contact line is pinned is in turn responsible for the periodic stick-slip motion. The key distinguishing feature of the present system is the attractive interaction between the particles and the surface, which instigates the periodicity of the particle deposition.     

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     

Colored thin films prepared from hydrogel microspheres

Ordered 2-D structures composed of poly(N-isopropylacrylamide) (PNIPAM) microgel particles that had regularity on a sub-micrometer length scale were prepared. By using sterically stabilized PNIPAM microgel particles as components, the ordered array was formed by a self-assembly process. The particle array was prepared by depositing a droplet of the microgel dispersion on a substrate. Atomic force microscopy observation of the resulting thin films revealed that they comprised a monolayer particle array. The periodic structure of the array produced iridescent colors due to optical diffraction. Since a homogeneous particle array can be prepared simply by drying the dispersion, this particle dispersion may be considered as a new ink whose color is generated from the microstructure in the films produced.     

Colloidal crystal layers of hexagonal nanoplates by convective assembly

Particles of the zeolite ZSM-2 prepared as nearly hexagonal nanoplatelets were coated onto flat substrates by a convective assembly technique. On the submillimeter scale, coatings ranged in patterns from striped to continuous. Particles were preferentially oriented out-of-plane, as supported by X-ray diffractometry. The novel observation is that where the particle coating was only a monolayer thick, particles were locally close-packed and uniformly oriented both in and out of plane in a hexagonal colloidal crystalline arrangement that may be described as being tiled (observations by scanning electron microscopy). This is the first documented demonstration of convective assembly applied to anisometric nanoparticles that resulted in particulate coatings with locally ordered microstructure, i.e., colloidal crystallinity.     

Influence of perpendicular external magnetic field on microstructures of monolayer composed of ferromagnetic particles: analysis by means of quasi-two-dimensional Monte Carlo simulation

We investigated the influences of the magnetic field strength and particle areal density on the microstructure of a quasi-two-dimensional monolayer composed of ferromagnetic particles by means of a Monte Carlo simulation. The magnetic field was applied along a direction perpendicular to the plane of the monolayer. Microstructures of the monolayer obtained in the simulations were analyzed in terms of radial distribution and orientational distribution functions. Formation of the microstructures is discussed from the perspective of particle-particle interaction energy and the perpendicular magnetic susceptibility of the monolayer was calculated from simulated magnetization curves. The obtained results are summarized as follows. For small areal density of particles, formation of chain-like structures is prevented by the repulsive magnetic interaction between particles due to orientations of the magnetic moments in the particles along the magnetic field direction. For intermediate areal density of particles, the chain-like structures remain even when a relatively strong magnetic field is applied, because contributions of the attractive magnetic interactions increase. For large areal density of particles, mixtures of chain-like and locally ordered structures appear due to the anisotropic attractive magnetic interactions in the absence of the magnetic field. However, when a sufficiently strong magnetic field is applied, the magnetic interactions between particles change to isotropic repulsive interactions, which results in the short-range repulsive steric interactions between particles becoming dominant with the appearance of hexagonal close packed structures.     

Attractive interactions in dispersions of identical charged colloidal particles: a Monte Carlo simulation

Using the Debye-Hückel pair potential, the collective interactions between identical charged particles were examined via Monte Carlo simulations. The results have shown that when the number of charges per particle and the particle volume fraction were sufficiently large, the pair long-range electrostatic repulsion generated an effective attractive interaction between identical charged particles because of many-body effects. Disordered liquid-like structures, ordered crystal-like structures, ordered structures dispersed in disordered ones, and disordered structures dispersed in ordered ones have been found. The structures are dependent on the volume fraction and charge of the particles, as well as on the electrolyte concentration.     

Numerical investigation into the effects of ordered particle packing and slip flow on the performance of chromatography

The pressure drop and the plate height of chromatography columns packed with particles in the face‐centered cubic, the body‐centered cubic and the simple cubic configurations are calculated by a volume averaging method model. It is found that the Kozeny‐Carman equation provides a reasonable prediction of the pressure drop when particles are in the face‐centered cubic configuration, but overestimates the pressure drop when particles are in the body‐centered cubic and the simple cubic configurations. The face‐centered cubic configuration has the advantage to provide a smaller longitudinal dispersion coefficient than the body‐centered cubic, the simple cubic, and the random configurations. The pressure drop and the plate height for slip flow through particles in the face‐centered cubic configuration are lower than that for no‐slip flow. The values of the smallest reduced plate height of columns packed with particles in the face‐centered cubic configuration for no‐slip flow and slip flow are about 0.084 and 0.059, respectively. The plate height of the ordered particle packing structures is smaller and the effect of slip flow on the plate height is less remarkable than results reported in literature.     

Geometric Model Describing the Banded Morphology of Particle Films Formed by Convective Assembly

Nanoparticle films coated on smooth substrates by convective assembly from dilute suspensions in dip‐coating configuration are known to have discrete film morphologies. Specifically, the film morphology is characterized by alternating bands of densely packed particles and bands of bare substrate. Convective assembly is a frontal film‐growth process that occurs at the three‐phase contact line formed by the substrate, the suspension in which it is submersed, and the surrounding air. The bands are parallel to this contact line and can be either monolayered or multilayered. Monolayered bands result whenever the substrate is withdrawn from the suspension at a rate too high for particles to assemble into a continuous film. We report a new insight to the mechanism behind this banding phenomenon, namely, that inter‐band spacing is strongly influenced by the constituent particle size. We therefore propose a geometric model relating the inter‐band spacing to the particle size. By making banded films with systematically varied particle sizes (silica/zeolite, 20 to 500 nm), we are able to quantitatively validate our model. Furthermore, the model correctly predicts that multilayered banded films have higher inter‐band spacings than monolayered banded films comprising the same particles.     

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.     

Formation and recovery of a cell sheet by a particle monolayer with the surface roughness

We studied the topographical effect of roughness displayed by a closely packed particle monolayer on formation of a cell monolayer (cell sheet). Particle monolayers were prepared by Langmuir-Blodgett deposition using particles, which were 527nm (SA053) and 1270nm (SA127) in diameter. Human umbilical vein endothelial cells (HUVECs) were seeded at a high density (2.0 x10(5)cells/cm(2)) onto particle monolayers. It was found that cells gradually became into contact with adjacent cells on the SA053 monolayer and the formed cell sheet could be readily detached from the particle monolayer by gentle pipetting. On the other hand, cells adhering onto the tissue culture polystyrene (TCPS) and the SA127 particle monolayer were difficult to peel off. At a low cell seeding density (5.0x10(4)cells/cm(2)), pre-coating with bovine plasma fibronectin (FN) allowed cell growth on an SA053 particle monolayer, and a confluent monolayer was able to be peeled as a cell sheet from the particle monolayer just by pipetting. By immunostaining of human fibronectin, we found that fibronectin was secreted and concentrated onto the substrate side of a cell sheet. The obtained cell sheet adhered and grew on the TCPS again within 20min.     

Forced convection heat transfer of nanofluids from a horizontal plate with convective boundary condition and a line heat source embedded in porous media

Journal of Thermal Analysis and Calorimetry - In this study, forced convective flow of nanofluids over a horizontal flat plate with convective boundary condition and a heated line source which are...     

Fabrication of binary colloidal crystals and non-close-packed structures by a sequential self-assembly method

Binary colloidal films of polystyrene (PS) spheres and silica spheres were fabricated with a sequential growth method using differently sized colloidal particles. In particular, we demonstrate the structures formed by a silica monolayer growing on top of a PS monolayer and a silica multilayer growing on top of a PS monolayer. By removal of the bottom PS layers, non-close-packed hexagonal, pentagonal, and square silica arrays were obtained at the original silica/PS interface. The possible formation mechanism of the non-close-packed structure was discussed, which may be used to explain how 3D colloidal crystals grow on patterned substrates.     

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.     

Deposition of poly(styrene/alpha-tert-butoxy-omega-vinyl-benzyl-polyglycidol) microspheres on mica plates crossing the liquid-air interface: formation of stripe pattern

Formation of stripelike assemblies of poly(styrene/alpha-tert-butoxy-omega-vinyl-benzyl-polyglycidol) microspheres adsorbed on nonpatterned mica plates moving perpendicularly from suspension of particles through the water-air interface has been observed. It was found that ordered assemblies were formed by capillary forces acting on particles crossing the water-air boundary. At sufficiently high rates of plate movement (i.e., at appropriate dynamic loading conditions) the adsorbed microspheres approaching the water surface begin sliding on the plate, due to capillary forces, in the direction opposite to the plate movement and are kept below the water surface. Plate movement brings new adsorbed particles to the water-air interface, where particles are assembled into aggregates. When particle aggregates are large, the capillary forces cannot overcome shearing forces and the particle assemblies are withdrawn on the plate above the water surface. This process repeated during continuous movement of the plate results in the formation of the quite regularly distributed stripes of adsorbed microspheres. Formation of the regularly distributed particle assemblies depends on concentration of microspheres in suspension.