Generalized Hertzian model for the deformation and cracking of colloidal packings saturated with liquid

The process of drying colloidal dispersions generally produces particulate solids under stress as a result of capillary or interparticle forces. The derivation of a constitutive relation on the basis of Hertzian contact mechanics between spheres provides a model for quantitatively predicting the conditions under which close-packed colloidal layers form continuous void-free films or homogeneous porous films or crack under tensile stresses.     

Low Reynolds Number Interactions between Colloidal Particles near the Entrance to a Cylindrical Pore

The interaction between stable colloidal particles arriving at a pore entrance was studied using a numerical method for the case where the particle size is smaller than but of the same order as the pore size. The numerical method was adapted from a front-tracking technique developed for studying incompressible, multifluid flow by S. O. Unverdi and G. Tryggvason (J. Comp. Phys. 100, 25, 1992). The method is based on the finite difference solution of Navier-Stokes equation on a stationary, structured, Cartesian grid and the explicit representation of the particle-liquid interface using an unstructured grid that moves through the stationary grid. The simulations are in two dimensions, considering both deformable and nondeformable particles, and include interparticle colloidal interactions. The interparticle and particle-pore hydrodynamic interactions, which are very difficult to determine using existing analytical and semi-numerical, semi-analytical techniques in microhydrodynamics, are naturally accounted for in our numerical method and need not be explicity determined. Two- and three-particle motion toward a pore has been considered in our simulations. The simulations demonstrate how the competition between hydrodynamic forces and colloidal forces acting on particles dictate their flow behavior near the pore entrance. The predicted dependence of the particle flow behavior on the flow velocity and the ratio of pore size to particle size are qualitatively consistent with the experimental observations of V. Ramachandran and H. S. Fogler (J. Fluid Mech. 385, 129, 1999). Copyright 2000 Academic Press.     

Kinetic stages of single-component colloidal crystallization

To harness the full potential of colloidal self-assembly, the dynamics of the transition between colloids in suspension to a colloidal crystalline film should be better understood. In this report, the structural changes during the self-assembly process in a vertical configuration for colloids in the size range 200-400 nm are monitored in situ, using the transmission spectrum of the colloidal assembly treated as an emergent photonic crystal. It is found that there are several sequential stages of colloidal ordering: in suspension, with a larger lattice parameter than the solid state, in a close-packed wet state with solvent in the interstices, and, finally, in a close-packed dry state with air in the interstices. Assuming that these stages lead continuously from one to another, we can interpret colloidal crystallization as being initiated by interparticle forces in suspension first, followed by capillary forces. This result has implications for identifying the optimum conditions to obtain high-quality nanostructures of submicrometer-sized colloidal particles.     

Evolution of interparticle capillary forces during drying of colloidal crystals

Photonic crystals are periodic structures that have the capability to manipulate the photons in the same way as semiconductors do for electrons. The self-assembly strategy that utilizes colloidal crystals as a template to form photonic crystals has received a great deal of recent research interest because it is simple and cost-effective. Experimental studies and theoretical analysis have speculated that capillary forces play a pivotal role in forming the colloidal crystals during the crystal growth process and that particularly during the drying stage the changing of the magnitude of capillary forces is critical to the resultant microstructure. This paper presents a computational analysis of the changing capillary forces, which may throw light on a refined strategy for controlling colloidal crystal growth.     

Influence of humidity on the fabrication of high-quality colloidal crystals via a capillary-enhanced process

Three-dimensional colloidal crystals have attracted a great deal of attention because of their potential use in photonic crystal, sensors, and other applications, but the bottlenecks in fabricating colloidal crystals include longer processing time and the lack of large-area ordered samples. A proposed capillary-enhanced method, which is a novel, efficient process for fabricating high-quality colloidal crystals in 24 h, is reported. It is necessary for increasing the processing rate by elevating the evaporation temperature but commonly resulted in the deposition of less-ordered crystals. However, high-quality colloidal crystals can be obtained in a controlled high-humidity system, resulting from the existence of secondary capillary forces present in high ambient humidity. Furthermore, the effect of secondary capillary forces will be confirmed, and it will increase with increasing humidity levels according to the semiquantitative analysis view of the surface thermodynamic behavior of small particles, including the modified Kelvin and Young-Laplace equations. Therefore, it can fine tune the relative position of the neighboring particles in the microarray and efficiently decrease the number of defects, resulting in the formation of perfect colloidal crystals with the assistance of enhanced secondary capillary forces.     

Buckling and crumpling of drying droplets of colloid-polymer suspensions

Spray drying of complex liquids to form solid powders is important in many industrial applications. One of the challenges associated with spray drying is controlling the morphologies of the powders produced; this requires an understanding of how drying mechanics depend on the ingredients and conditions. We demonstrate that the morphology of powders produced by spray drying colloidal polystyrene (PS) suspensions can be significantly altered by changing the molecular weight of dissolved poly(ethylene oxide) (PEO). Samples containing high-molecular-weight PEO produce powders with more crumpled morphologies than those containing low-molecular-weight PEO. Observations of drying droplets suspended by a thin film of vapor suggest that this occurs because the samples with high-molecular-weight PEO buckle earlier in the drying process when the droplets are larger. Earlier buckling times are likely caused by the decreased stability, demonstrated by bulk rheology experiments, of PS particles in the presence of high-molecular-weight PEO at elevated temperatures. We present a consistent picture in which decreased particle stability hastens droplet buckling and leads to more crumpled powder morphologies; this underscores the importance of interparticle forces in determining the buckling of particle-laden droplets.     

Migration and precipitation of soluble species during drying of colloidal films

The evaporation-induced convection resulted in a transport of dissolved species, a water-soluble polymer (carboxymethylcellulose) and dissolved CaCO(3), to the drying front of silica and CaCO(3) dispersions where the material eventually precipitates. Scanning electron microscopy and chemical analysis showed that the concentration of carboxymethylcellulose, CMC, is highest in the centre of the dried silica film and decreases towards the perifery. The colloidal films of the monodisperse silica particles displayed a high degree of structural order even at high concentrations of the non-adsorbed polymer CMC, which suggests that any depletion induced interparticle attraction is insufficient to affect the assembly of the colloidal crystal. The CaCO(3) particles are slightly soluble and we found that rod-like crystals reprecipitated in the centre of the particle films on top of the polyacrylate-coated particles. Addition of CMC disturbs the formation of distinct crystal shapes which was attributed to a complexation of Ca(2+) in solution.     

Interfacial routes to colloidal gelation

Colloidal gelation is a rheological transition from fluid-like to solid-like viscoelasticity in a particulate suspension and is often instigated by causing the net interparticle interaction to be attractive. In this article, three routes to colloidal gelation that have been discovered recently and involve interfacial phenomena at a fluid interface are reviewed. As in conventional systems, gelation is due to a percolating particle network that imparts elasticity to the mixture, but the network formation involves interfacial particle jamming or bridging, or capillary interactions along or across interfaces, in a mixture of immiscible fluids. Gelation imparts mechanical stability to these multiphase mixtures and paves the way for their use as templates for the synthesis of functional, microstructured materials and composites. The gel mechanical properties are mediated by the interfacial forces and the mixture's microstructure, and therefore show different dependencies on particle volume fraction across the three systems.     

Importance of capillary forces in the assembly of carbon nanotubes in a polymer colloid lattice

We highlight the significance of capillary pressure in the directed assembly of nanorods in ordered arrays of colloidal particles. Specifically, we discuss mechanisms for the assembly of carbon nanotubes at the interstitial sites between latex polymer particles during composite film formation. Our study points to general design rules to be considered to optimize the ordering of nanostructures within such polymer matrices. In particular, gaining an understanding of the role of capillary forces is critical. Using a combination of electron microscopy and atomic force microscopy, we show that the capillary forces acting on the latex particles during the drying process are sufficient to bend carbon nanotubes. The extent of bending depends on the flexural rigidity of the carbon nanotubes and whether or not they are present as bundled ensembles. We also show that in order to achieve long-range ordering of the nanotubes templated by the polymer matrix, it is necessary for the polymer to be sufficiently mobile to ensure that the nanotubes are frozen into the ordered network when the film is formed and the capillary forces are no longer dominant. In our system, the polymer is plasticized by the addition of surfactant, so that it is sufficiently mobile at room temperature. Interestingly, the carbon nanotubes effectively act as localized pressure sensors, and as such, the study agrees well with previous theoretical predictions calculating the magnitude of capillary forces during latex film formation.     

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.     

Magnetite 3D colloidal crystals formed in the early solar system 4.6 billion years ago

Three-dimensional colloidal crystals made of ferromagnetic particles, such as magnetite (Fe(3)O(4)), cannot be synthesized in principle because of the strong attractive magnetic interaction. However, we discovered colloidal crystals composed of polyhedral magnetite nanocrystallites of uniform size in the range of a few hundred nanometers in the Tagish Lake meteorite. Those colloidal crystals were formed 4.6 billion years ago and thus are much older than natural colloidal crystals on earth, such as opals, which formed about 100 million years ago. We found that the size of each individual magnetite particle determines its morphology, which in turn plays an important role in deciding the packing structure of the colloidal crystals. We also hypothesize that each particle has a flux-closed magnetic domain structure, which reduces the interparticle magnetic force significantly.     

Structure and Rheology of Simulated Gels Formed from Aggregated Colloidal Particles

Soft, elastic, solvent-rich materials made from networks of aggregated colloidal particles are called particle gels. The networks may be regarded as being permanent or transient depending on whether the short-range attractive forces between the particles arise from strong irreversible bonding or weak reversible interactions. Understanding the relationships between the interparticle forces and the structure and rheology of particle gels is a challenging problem. This article shows how useful insight is being provided by Brownian dynamics simulations involving systems of spherical particles interacting with a combination of bonded and nonbonded interparticle potentials. Copyright 2000 Academic Press.     

Recent developments in the measurement of interparticle forces

In the last twenty years there has been an explosion of experimental work devoted to determining the forces between colloidal particles. There have been considerable experimental and theoretical advances. In this review we shall concentrate on the experimental aspects. Currently there is no technique which directly measures the interaction between two individual particles as a function of their separation. Particle - particle forces can only be inferred. In this paper we review the experimental procedures which have been used to determine the nature and range of interparticle forces in this indirect way. The many different experimental techniques which have been developed are outlined and typical data presented. The relative merits and demerits of each technique is discussed and the way forward to measuring particle - particle interactions directly is proposed.     

Experimental synthesis and characterization of rough particles for colloidal and granular rheology

We review the experimental synthesis of smooth and rough particles, characterization of surface roughness, quantification of the pairwise and bulk friction coefficients, and their effect on the rheology of wet particulate flows. Even in the absence of interparticle attraction or cohesion, such types of flows are broadly ubiquitous, spanning enormous length scales ranging from consumer and food products to earth movements. The increasing availability of model frictional particles is useful to advancing new understanding of particulate rheology. Although hard-sphere particles remain the most widely studied system due to their simplicity, their rigid and frictionless nature cannot predict many of the complex flow phenomena in colloidal and granular suspensions. Besides a myriad of interparticle forces, the presence of tangential interparticle friction arising from either hydrodynamics or solid contacts of asperities is now thought to be responsible for commonalities in shear thickening and jamming phenomena at high volume fractions and shear stresses. The overall richness of the suspension mechanics landscape points to the reunification of colloidal and granular physics in the near future: one in which it may become possible to apply a universal set of physical frameworks to understand the flows of model rough particles across multiple spatiotemporal scales. This can only be accomplished by properly distinguishing between microscopic and bulk friction and by decoupling hydrodynamics and contact contributions within the context of experimental observations.     

Directed assembly and rupture mechanics of colloidal aggregates

The macroscopic rheological behavior of colloidal gels arises from the micromechanical properties of the gel backbone, which are governed by nanoscale particle interactions. These colloidal interactions have been commonly understood in terms of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Recent work has shown, however, that nonidealities, such as surface roughness and charge nonuniformity, may cause the particle interactions to significantly deviate from DLVO predictions at near-contact separations. Here we present novel techniques for directing the assembly of colloidal aggregates that mimic the gel backbone, based on optical micromanipulation of multiple particles using laser tweezers. This also provides an in situ method for measuring near-contact interactions via single-bond rupture forces. We find that PMMA particles aggregated in the presence of nonorganic salts exhibit interparticle bond strengths more than 10 times greater than those predicted by DLVO theory. However, good agreement is found with DLVO predictions when the anionic surfactant sodium dodecyl sulfate (SDS) is used as the flocculant.     

The Film Formation of Polymer Particles in Drying Thin Films of Aqueous Acrylic Latices

The aim of this study is to determine the factors that contribute to the process of film formation of binder particles in drying aqueous dispersion coatings, based on acrylic polymers. It is known that concentrated latices of uniform size show iridescent, colored light patterns. These colors are caused by interparticle interference, and they are only present when the latex particles are ordered in a regular structure. The interparticle interference can be characterized by measuring the transmission as a function of wavelength of the incident light. It appeared that the changes of the interparticle interference of a drying latex film can be related to changes in the interparticle distance and displacement. It was also found that the interparticle distance becomes "negative" upon coalescence of the latex particles. This means that from this point on, the change in interparticle interference is directly related to the indentation or deformation of the latex particles. It became clear that the coalescence process differs from deformation mechanisms accepted in the literature. It seems that the deformation of the particles follows a biaxial mechanism. This means that the particles deform only in one direction, perpendicular to the film surface. Copyright 2000 Academic Press.     

Study of the evaporation of colloidal suspension droplets with the quartz crystal microbalance

In this Article, we report the application of the quartz crystal microbalance (QCM) to study the evaporation of colloidal suspension droplets. Droplets of alumina particle suspensions with varying particle size and solid concentration have been investigated. Characteristic responses of the resonance frequency of the QCM associated with the different evaporation stages have been established. Quantitative analysis of the experimental results has been performed by the proposed QCM models. An interesting finding is that frequency increase after complete drying has been observed in some cases. Interpretation of the frequency increase has been developed in terms of the contact stiffness. The possible physical mechanisms are also discussed and quantified in terms of various interparticle forces.     

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     

Drying dip-coated colloidal films

We present the results from a small-angle X-ray scattering (SAXS) study of lateral drying in thin films. The films, initially 10 μm thick, are cast by dip-coating a mica sheet in an aqueous silica dispersion (particle radius 8 nm, volume fraction ?(s) = 0.14). During evaporation, a drying front sweeps across the film. An X-ray beam is focused on a selected spot of the film, and SAXS patterns are recorded at regular time intervals. As the film evaporates, SAXS spectra measure the ordering of particles, their volume fraction, the film thickness, and the water content, and a video camera images the solid regions of the film, recognized through their scattering of light. We find that the colloidal dispersion is first concentrated to ?(s) = 0.3, where the silica particles begin to jam under the effect of their repulsive interactions. Then the particles aggregate until they form a cohesive wet solid at ?(s) = 0.68 ± 0.02. Further evaporation from the wet solid leads to evacuation of water from pores of the film but leaves a residual water fraction ?(w) = 0.16. The whole drying process is completed within 3 min. An important finding is that, in any spot (away from boundaries), the number of particles is conserved throughout this drying process, leading to the formation of a homogeneous deposit. This implies that no flow of particles occurs in our films during drying, a behavior distinct to that encountered in the iconic coffee-stain drying. It is argued that this type of evolution is associated with the formation of a transition region that propagates ahead of the drying front. In this region the gradient of osmotic pressure balances the drag force exerted on the particles by capillary flow toward the liquid-solid front.     

Cracking in drying latex films

Thin films of latex dispersions containing particles of high glass transition temperature generally crack while drying under ambient conditions. Experiments with particles of varying radii focused on conditions for which capillary stresses normal to the film deform the particles elastically and generate tensile stresses in the plane of the film. Irrespective of the particle size, the drying film contained, simultaneously, domains consisting of a fluid dispersion, a fully dried packing of deformed spheres, and a close packed array saturated with water. Interestingly, films cast from dispersions containing 95-nm sized particles developed tensile stresses and ultimately became transparent even in the absence of water, indicating that van der Waals forces can deform the particles. Employing the stress-strain relation for a drying latex film along with the well-known Griffith's energy balance concept, we calculate the critical stress at cracking and the accompanying crack spacing, in general agreement with the observed values.