Interactions between colloidal particles induced by polymer brushes grafted onto the substrate

We investigate the interaction energy between two colloidal particles on or immersed in nonadsorbing polymer brushes grafted onto the substrate as a function of the separation of the particles by the use of a self-consistent-field theory calculation. Depending on the colloidal size and the penetration depth, we demonstrate the existence of a repulsive energy barrier of several kBT, which can be interpreted by separating the interaction energy into three parts: colloid-polymer interfacial energy, entropic contribution due to "depletion zone" overlap of colloidal particles, and entropic elastic energy of grafted chains by the compression of particles. The existence of a repulsive barrier which is of entirely entropic origin can lead to kinetic stabilization of the mixture rather than depletion flocculation or phase separation. Therefore, the present result may suggest an approach for controlling the self-assembling behavior of colloids for the formation of target structures, by tuning the colloidal interaction on the grafting substrate under appropriate selection of colloidal size, effective gravity (influencing the penetration depth), and brush coverage density.     

Inverse density-functional theory as an interpretive tool for measuring colloid-surface interactions in dense systems

Recent advances in optical microscopy, such as total internal reflection and confocal scanning laser techniques, now permit the direct three-dimensional tracking of large numbers of colloidal particles both near and far from interfaces. A novel application of this technology, currently being developed by one of the authors under the name of diffusing colloidal probe microscopy (DCPM), is to use colloidal particles as probes of the energetic characteristics of a surface. A major theoretical challenge in implementing DCPM is to obtain the potential energy of a single particle in the external field created by the surface, from the measured particle trajectories in a dense colloidal system. In this paper we develop an approach based on an inversion of density-functional theory (DFT), where we calculate the single-particle-surface potential from the experimentally measured equilibrium density profile in a nondilute colloidal fluid. The underlying DFT formulation is based on the recent work of Zhou and Ruckenstein [Zhou and Ruckenstein, J. Chem. Phys. 112, 8079 (2000)]. For model hard-sphere and Lennard-Jones systems, using Monte Carlo simulation to provide the "experimental" density profiles, we found that the inversion procedure reproduces the true particle-surface-potential energy to an accuracy within typical DCPM experimental limitations (approximately 0.1 kT) at low to moderate colloidal densities. The choice of DFT closures also significantly affects the accuracy.     

Distribution of colloidal particles in a spherical cavity

The spatial distribution of colloidal particles in a confined space is frequently a key issue to many phenomena of practical significance. This problem is investigated by considering the distribution of colloidal particles in a spherical cavity under the conditions of relatively large cavities, low cavity and colloidal particles potentials, and low monovalent electrolyte and colloidal concentrations. The analytical expression for the particle-cavity pair interaction energy is derived under various surface conditions. The results obtained are used to evaluate the direct correlation functions in the hypernetted chain approximation employed for the resolution of an Ornstein-Zernike equation. For a fixed particle number concentration at the center of a cavity, we make the following conclusions: (i) the spatial distribution of particles increases in an oscillatory manner with the distance away from the cavity surface, (ii) increasing the particle-cavity pair interaction energy has the effect of reducing the free space of particles inside a cavity, and (iii) the greater the pair interaction energy between two particles, the higher the average concentration of particles.     

Fabrication of colloidal grid network by two-step convective self-assembly

We explored a "template-free" approach to arranging colloidal particles into a network pattern by a convective self-assembly technique. In this approach, which we call "two-step convective self-assembly," a stripe pattern of colloidal particles is first prepared on a substrate by immersing it in a suspension. The substrate with the stripes is then rotated by 90° and again immersed in the suspension to produce stripes perpendicular to the first ones, resulting in a grid-pattern network of colloidal arrays. The width of the colloidal grid lines can be controlled by changing the particle concentration while maintaining an almost constant spacing between the lines. On the basis of these results, we propose a mechanism for grid pattern formation. Our method is applicable to various types of particles. In addition, the wide applicability of this method was employed to create a hybrid grid pattern.     

Collodial cluster arrays by electrohydrodynamic printing

A "stable" electrohydrodynamic jet is used to print arrays of colloidal suspensions on hydrophobic surfaces. Printed lines break up into sessile drops, and capillary forces guide the self-assembly of colloidal particles during the evaporation of the liquid, resulting in arrays of colloidal single particles or particle clusters depending on the concentration of the suspensions. The clusters differ from those formed in the absence of a substrate when the number of particles is larger than three. Multiple structures are found for the same number of particles.     

Janus balance of amphiphilic colloidal particles

We introduce the notion of "Janus balance" (J), defined as the dimensionless ratio of work to transfer an amphiphilic colloidal particle (a "Janus particle") from the oil-water interface into the oil phase, normalized by the work needed to move it into the water phase. The J value can be calculated simply from the interfacial contact angle and the geometry of Janus particles, without the need to know the interfacial energy. It is demonstrated that Janus particles of the same chemical composition but different geometries will have the highest adsorption energy when J = 1. Even for particles of homogeneous chemical makeup, the Janus balance concept can be applied when considering the contact angle hysteresis in desorbing the particle from equilibrium into the water or oil phase. The Janus balance concept may enable predictions of how a Janus particle behaves with respect to efficiency and function as a solid surfactant, as the Janus balance of solid surfactants is the analog of the classical hydrophile-lipophile balance of small surfactant molecules.     

Self-assembly of doublets from flattened polymer colloids

Bottom-up fabrication methods are used to assemble strong yet flexible colloidal doublets. Part of a spherical particle is flattened, increasing the effective interaction area with another particle having a flat region. In the presence of a moderate ionic strength, the flat region on one particle will preferentially "bond" to a flat region on another particle in a deep (≥10 kT) secondary energy minimum. No external field is applied during the assembly process. Under the right conditions, the flat-flat bonding strength is ≥10× that of a sphere-sphere interaction. Not only can flat-flat bonds be quite strong, but they are expected to remain freely rotatable and flexible, with negligible energy barriers for rotation because particles reside in a deep secondary energy minimum with a ~20-30 nm layer of fluid between the ~1 μm radius particles. We present a controlled technique to flatten the particles at room temperature, the modeling of the interparticle forces for flattened spheres, and the experimental data for the self-assembly of flat-flat doublets.     

Reversible coagulation of colloidal suspension in shallow potential wells: Direct numerical simulation

Brownian dynamics computer simulations of aggregation in 2D colloidal suspensions are discussed. The simulations are based on the Langevin equations, pairwise interaction between colloidal particles and take into account Brownian, hydrodynamic and colloidal forces. The chosen mathematical model enables to predict the correct values of diffusion coefficient of freely moving particle, the mean value of kinetic energy for each particle in ensemble of interacting colloidal particles and residence times of colloidal particles inside the potential wells of different depths. The simulations allow monitoring formation and breakage of clusters in a suspension as well as time dependence of the mean cluster size. The article is published in the original.     

Poly(ethylene glycol)-assisted two-dimensional self-assembly of zinc sulfide microspheres

A simple fabrication of two-dimensional zinc sulfide colloidal arrays with the assistance of a multihydroxy polymer is described, which can potentially be utilized in different technological fields, such as biosensor and electrooptical devices as well as a platform for studies of energy transfer between colloidal particles.     

Formation and dynamics of capillary-flow-induced colloidal rings

We have directly observed the ring formation of colloidal particles of 1 μm diameter at the contact lines of air, water, and oil using a laser scanning confocal microscope. Colloidal rings form and grow through the transport of particles induced by capillary flow due to water evaporation. In addition, we observe the sudden "jump in" of particles into the ring and the "depletion" of particles in the ring. Particle-tracking experiment shows that the particles within the ring exhibit 1D-like motion along the circular ring geometry, and the pair correlation function of the ring configuration suggests an equilibrium interparticle distance of approximately 2.8 μm. It is also found that the structure and formation speed of the colloidal rings can be controlled by accelerating water evaporation by the addition of methanol as a cosolvent.     

Laser-Induced "Regeneration" of Colloidal Particles: The Effects of Thermal Inertia on the Chemical Reactivity of Laser-Heated Particles

A size reduction of the suspended particles is observed upon irradiation of colloidal metal solutions by a high-power, pulsed laser, resulting in dramatic changes in their optical properties. The mechanism of change involves rapid production of ions as a consequence of laser heating, followed by diffusion and chemical reduction on a long time scale to form new colloidal particles. The process, by which large particles are differentially consumed relative to small ones, depends on the "thermal inertia" of the particles, which governs the temperature of the particles and hence their reactivity.     

Effect of charge asymmetry and charge screening on structure of superlattices formed by oppositely charged colloidal particles

Colloidal suspensions made up of oppositely charged particles have been shown to self-assemble into substitutionally ordered superlattices. For a given colloidal suspension, the structure of the superlattice formed from self-assembly depends on its composition, charges on the particles, and charge screening. In this study we have computed the pressure-composition phase diagrams of colloidal suspensions made up of binary mixtures of equal sized and oppositely charged particles interacting via hard core Yukawa potential for varying values of charge screening and charge asymmetry. The systems are studied under conditions where the thermal energy is equal or greater in magnitude to the contact energy of the particles and the Debye screening length is smaller than the size of the particles. Our studies show that charge asymmetry has a significant effect on the ability of colloidal suspensions to form substitutionally ordered superlattices. Slight deviations of the charges from the stoichiometric ratio are found to drastically reduce the thermodynamic stability of substitutionally ordered superlattices. These studies also show that for equal-sized particles, there is an optimum amount of charge screening that favors the formation of substitutionally ordered superlattices.     

Preparation of colloidal crystals with polyhedral building blocks through post-polymerization

An alternative approach was adopted to prepare colloidal crystal with polyhedral building blocks. First, monodisperse polystyrene particles that contained about 30% wt of monomer were obtained by emulsifier-free emulsion polymerization at 38 °C. These monomer-containing particles were used to prepare colloidal crystal on the surface of dispersion, before the spherical particles in the colloidal crystals underwent deformation between two quartz plates at 75 °C for 40 min by interfacial tensions, and finally the deformed particles were frozen through post-polymerization.     

Interactions between particles with an undulated contact line at a fluid interface: capillary multipoles of arbitrary order

A colloidal particle adsorbed at a fluid interface could have an undulated, or irregular contact line in the presence of surface roughness and/or chemical inhomogeneity. The contact-line undulations produce distortions in the surrounding liquid interface, whose overlap engenders capillary interaction between the particles. The convex and concave local deviations of the meniscus shape from planarity can be formally treated as positive and negative "capillary charges," which form "capillary multipoles." Here, we derive theoretical expressions for the interaction between two capillary multipoles of arbitrary order. Depending on the angle of mutual orientation, the interaction energy could exhibit a minimum, or it could represent a monotonic attraction. For undulation amplitudes larger than 5 nm, the interaction energy is typically much greater than the thermal energy kT. As a consequence, a monolayer from capillary multipoles exhibits considerable shear elasticity, and such monolayer is expected to behave as a two-dimensional elastic solid. These theoretical results could be helpful for the understanding of phenomena related to aggregation and ordering of particles adsorbed at a fluid interface, and for the interpretation of rheological properties of particulate monolayers. Related research fields are the particle-stabilized (Pickering) emulsions and the two-dimensional self-assembly of microscopic particles.     

Surfactant-induced Marangoni eddies alter the coffee-rings of evaporating colloidal drops

The influence of the small ionic surfactant sodium dodecyl sulfate (SDS) on the evaporation of drying colloidal droplets is quantitatively investigated. The addition of SDS leads to a significantly more uniform deposition of colloidal particles after evaporation (i.e., the so-called "coffee-ring effect" is dramatically altered). We understand this phenomenon in the context of circulating radial Marangoni flows induced by the variation of SDS concentration along the air-water interface. Video microscopy permits the direct visualization of the colloidal particles involved in these flows, revealing a surprisingly stable "Marangoni eddy" that prevents particle deposition at the drop perimeter.     

分散体系中任意形状的胶粒模型与相互作用能——Ⅲ. 园柱体型颗粒

在分散体系的研究中,也经常遇到园柱体型胶粒,例如蛋白质分子,海泡石和凸凹棒石粘土颗粒,它们都能用带电的园柱体型采近似处理。这种类型的颗粒以往研究不多,其原因大约有二,一是处理这类颗粒时,数学上的困难很大;二是这类颗粒之间的相互作用,和它们之间的取向有关。Sparnaay首先用Derjaguin法得出园柱体型颗粒处于平行和垂直位置时,相互排斥能的近似表达式。Brenner和McQuarrie(BM)对颗粒外的电位分布采     

Effect of colloidal particle size on adsorbed monodisperse and bidisperse monolayers

Coating hydrogel films or microspheres by an adsorbed colloidal shell is one synthesis method for forming colloidosomes. The colloidal shell allows control of the release rate of encapsulated materials, as well as selective transport. Previous studies found that the packing density of self-assembled, adsorbed colloidal monolayers is independent of the colloidal particle size. In this paper we develop an equilibrium model that correlates the packing density of charged colloidal particles in an adsorbed shell to the particle dimensions in monodisperse and bidisperse systems. In systems where the molar concentration in solution is fixed, the increase in adsorption energy with increasing particle size leads to a monotonic increase in the monolayer packing density with particle radius. However, in systems where the mass fraction of the particles in the adsorbing solutions is fixed, increasing particle size also reduces the molar concentration of particles in solution, thereby reducing the probability of adsorption. The result is a nonmonotonic dependence of the packing density in the adsorbed layer on the particle radius. In bidisperse monolayers composed of two particle sizes, the packing density in the layer increases significantly with size asymmetry. These results may be utilized to design the properties of colloidal shells and coatings to achieve specific properties such as transport rate and selectivity.     

Poly(ethyl cyanoacrylate) colloidal particles tagged with Rhodamine 6G: preparation and physicochemical characterization

This paper describes the preparation and characterization of poly(ethyl cyanoacrylate) colloidal particles loaded with the organic fluorophore Rhodamine 6G. We studied the physicochemical properties of the colloidal particles: morphology, size-distribution, ζ-potential, fluorescent properties and photobleaching upon UV-light illumination. The properties of the obtained colloidal particles, as well as the dye loading efficiency, were found to depend on the concentrations of ethyl cyanoacrylate monomer and Rhodamine 6G in the polymerization medium. The fluorophore release from the colloidal particles in aqueous buffer is also studied.      

Phase Transitions of the Liquid–Liquid Type and a Change in the Particle Charge in Colloidal Solutions

The thermodynamic properties are studied for the solutions of charged colloidal particles with ionizable surface groups. The microscopic mechanism of microion binding at surface groups is considered. The free energy of the system in the parameter range where the usual theory of such solutions is inadequate (a range of practical interest) is calculated using the method of the thermodynamic perturbation theory. The first-order phase transition of the liquid–liquid type is shown to be possible; in this phase transition, a phase with a high concentration of colloidal particles that have a higher charge coexists with a phase with a lower concentration of particles that have a lower charge.     

Eppur si muove,and yet it moves: Patchy (phoretic) swimmers

Advances in colloidal synthesis allow for the design of particles with controlled patches. This article reviews routes towards colloidal locomotion, where energy is consumed and converted into motion, and its implementation with active patchy particles. A special emphasis is given to phoretic swimmers, where the self-propulsion originates from an interfacial phenomenon, raising experimental challenges and opening up opportunities for particles with controlled anisotropic surface chemistry and novel behaviors.