Fast formation of opal-like columnar colloidal crystals

We demonstrate that highly polydisperse colloidal gibbsite platelets easily form an opal-like columnar crystal with striking iridescent Bragg reflections. The formation process can be accelerated by orders of magnitude under a centrifugation force of 900 g without arresting the system in a disordered glassy phase. Using transmission electron microscopy and small-angle X-ray scattering techniques, we find that the forced sedimentation is accompanied by particle size fractionation, leading to inversion of the iridescent colors. The relatively easy self-organization of the polydisperse colloidal particles into opal-like crystals may be explained on the basis of the observed particle fractionation and possibly also on hexatic-like ordering.     

Phase separations in liquid crystal-colloid mixtures

We present a mean-field theory to describe phase separations in mixtures of a nematic liquid crystal and a colloidal particle. The theory takes into account an orientational ordering of liquid crystals and a crystalline ordering of colloidal particles. We calculate phase diagrams on the temperature-concentration plane, depending on interactions between a liquid crystal and a colloidal surface and a coupling between nematic and crystalline ordering. We find various phase separation processes, such as a nematic-crystal phase separation and nematic-isotropic-crystal triple point. Inside binodal curves, we find new unstable and metastable regions which are important in phase ordering dynamics. We also find a stable nematic-crystalline (NC) phase, where colloidal particles dispersed in a nematic phase can form a crystalline structure. The coexistence between two NC phases with different concentrations can be appear though the coupling between nematic and crystalline ordering.     

Two-dimensional Monte Carlo simulations of a polydisperse colloidal dispersion composed of ferromagnetic particles for the case of no external magnetic field

We have investigated the aggregation phenomena in a polydisperse colloidal dispersion composed of ferromagnetic particles by means of the cluster-moving Monte Carlo method. The results have been compared with those for a monodisperse system. The internal structures of aggregates have been analyzed in terms of the radial distribution function in order to clarify the quantitative differences in the internal structures of clusters. In addition, the cluster size distribution and angular distribution function have been investigated. The results obtained in the present study are summarized as follows. In a monodisperse system, open necklacelike clusters are formed and they extend with increasing strength of the magnetic particle-particle interaction. In a polydisperse system with a small standard deviation in the particle size distribution, sigma=0.2, larger necklacelike clusters are formed and some looplike clusters can also be observed. In a polydisperse system with a larger standard deviation, sigma=0.35, clumplike clusters are formed for a weak magnetic particle-particle interaction. For a stronger magnetic interaction, larger size clusters that exhibit a complicated network structure are formed. These complicated cluster formations found in a polydisperse system are mainly due to the effect of the presence of larger particles.     

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.     

Size fractionation in a phase-separated colloidal fluid

Phase separation of a polydisperse colloidal dispersion implies size fractionation. An application of this effect is given by size-selective purification procedures associated with the colloidal synthesis of so-called monodisperse nanoparticles. We used electron microscopy to determine detailed particle size distributions of coexisting colloidal fluid phases containing highly polydisperse iron oxide nanoparticles with a log-normal distribution (sigma = 0.54 for the total system). Analysis of N approximately 10000 particles per phase yields the first five statistical moments of the distributions. Within experimental error, the interdependence of the statistical moments is in quantitative agreement with the "universal law of fractionation" proposed by Evans, Fairhurst, and Poon [Phys. Rev. Lett. 1998, 81, 1326], even though the theory was derived in the limit of slight polydispersity.     

Colloidal optomagnetic dimmer

We demonstrate a colloidal optomagnetic dimmer based on the interaction between micrometer-sized paramagnetic colloidal spheres and a magnetic film. The colloidal particles undergo Brownian motion, which when exposed to light results in characteristic intensity fluctuations, and we demonstrate that weak magnetic fields that are typically 200 A/m (2.5 G) can be used to control both the average intensity and the intensity fluctuations. The system can be used as a colloidal optical dimmer in microfluidic systems.     

Dynamic effects on colloidal electric interactions

Dynamic behaviors are abundant in field-responsive colloidal suspensions. Being beyond the usual point-dipole approximation, we develop a multiple image method of dipoles for two dynamic unequal colloidal dielectric spherical particles, which can be perfectly reduced to those for two static conducting particles. The method is applied to investigate colloidal electric interparticle forces under various conditions of dynamics. As a result, we find that the force can be enhanced, reduced, or even changed from attraction to repulsion, or vice versa. Some other interesting results are also reported. Our theoretical results are compared favorably with existing experimental observations. Therefore, it becomes possible to achieve desired colloidal structures by adjusting colloidal interactions by choosing appropriate dynamic phenomena.     

Two-dimensional Monte Carlo simulations of a colloidal dispersion composed of polydisperse ferromagnetic particles in an applied magnetic field

We have investigated aggregation phenomena in a polydisperse colloidal dispersion of ferromagnetic particles simulated by employing the cluster-moving Monte Carlo method in an applied magnetic field. The influence of both particle-particle and particle-field interactions on the aggregate structures is analyzed in terms of a pair correlation function. The results obtained in this study are summarized as follows: Under a strong magnetic field, chainlike clusters are formed along the magnetic field direction, and they become thickly clustered with an increase in the strength of the external magnetic field. Moreover, the thickly clustered chains are formed for a polydisperse system that has a large standard deviation of particle diameters. In contrast, for a very weak magnetic field, the strong interaction between the larger particles gives rise to the formation of various shapes in the chainlike clusters, including bending, looping, and branching. With an increase in the external magnetic field, these structures reorganize to form straight chainlike clusters. Furthermore, the thickness of the chainlike clusters for the polydisperse system is found to depend on the standard deviation of the particle-size distribution but is found to be independent of the magnetic field strength.     

Binary Colloidal Nanoparticles with a Large Size Ratio in Analytical Ultracentrifugation

Sedimenting colloidal particles may feel a surprisingly strong buoyancy in a mixture with other particles of a considerably larger size. In this paper we investigated the buoyancy of colloidal particles in a concentrated binary suspension in situ in a centrifugal field. After dispersing two different fluorescence-labeled silica nanoparticles with a large size ratio (90 nm and 30 nm, size ratio: 3) in a refractive index matching solvent, we used a multi-wavelength analytical ultracentrifuge to measure the concentration gradients of both particles in situ. The concentration of the 90 nm silica nanoparticles was used to calculate the effective solvent density for the 30 nm silica nanoparticles. The exponential Boltzmann equation for the sedimentation-diffusion equilibrium with locally varying effective solvent density was then used to theoretically predict the concentration gradient of 30 nm silica nanoparticles, which describes the experimental results very well. This finding proves the validity of effective buoyancy in colloidal mixtures and provides a good model to study sedimenting polydisperse colloids.     

Anomalous potentials from inverse analyses of interfacial polydisperse attractive colloidal fluids

This paper investigates effects of using monodisperse inverse analyses to extract particle-particle and particle-surface potentials from simulated interfacial colloidal fluids of polydisperse attractive particles. Effects of polydispersity are investigated as functions of particle concentration and attractive well depth and range for van der Waals and depletion potentials. Forward Monte Carlo simulations are used to generate particle distribution functions for polydisperse interfacial colloidal fluids from which inverted potentials are obtained using an inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method. Attractive potentials are successfully recovered for monodisperse colloidal fluids, but polydispersity that is unaccounted for in inverse analyses produces (1) apparent softening of strong forces, (2) anomalous repulsive and attractive interactions, and (3) aphysical particle overlaps. This investigation provides insights into the role of polydispersity in altering the equilibrium structure and corresponding inverted potentials of attractive colloidal fluids near surfaces. These findings should assist the design and interpretation of optical microscopy experiments involving interfacial colloidal fluids similar to the simulated experiments reported here.     

Formation of a colloidal band via pH-dependent electrokinetics

Electroosmosis on nonuniformly charged surfaces often gives rise to intriguing flow behaviors, which can be utilized in applications such as mixing processes and designing micromotors. Here, we demonstrate nonuniform electroosmosis induced by electrochemical reactions. Water electrolysis creates pH gradients near the electrodes that cause a spatiotemporal change in the wall zeta potential, leading to nonuniform electroosmosis. Such nonuniform EOFs induce multiple vortices, which promote the continuous accumulation of particles that subsequently form a colloidal band. The band develops vertically into a “wall” of particles that spans from the bottom to the top surface of the chamber. Such a flow-driven colloidal band can be potentially used in colloidal self-assembly and separation processes irrespective of the particle surface properties. For instance, we demonstrate these vortices can promote rapid segregation of soft colloids such as oil droplets and fat globules.     

Effect of quenched size polydispersity on the fluid-solid transition in charged colloidal suspensions

We study the effect of quenched size polydispersity on the phase behavior of charged colloidal suspensions using free-energy calculations in Monte Carlo simulations. The colloids are assumed to interact with a hard-core repulsive Yukawa (screened-Coulomb) interaction with constant surface potential, so that the particles are polydisperse both in size and charge. In addition, we take the size distribution to be fixed in both the fluid and crystal phase (no size fractionation is allowed). We study the fluid-solid transition for various screening lengths and surface potentials, finding that upon increasing the size polydispersity the freezing transition shifts toward higher packing fractions and the density discontinuity between the two coexisting phases diminishes. Our results provide support for a terminal polydispersity above which the freezing transition disappears.     

Depletion-induced phase separation in colloid-polymer mixtures

Phase separation can be induced in a colloidal dispersion by adding non-adsorbing polymers. Depletion of polymer around the colloidal particles induces an effective attraction, leading to demixing at sufficient polymer concentration. This communication reviews theoretical and experimental work carried out on the polymer-mediated attraction between spherical colloids and the resulting phase separation of the polymer-colloid mixture. Theoretical studies have mainly focused on the limits where polymers are small or large as compared to the colloidal size. Recently, however, theories are being developed that cover a wider colloid-polymer size ratio range. In practical systems, size polydispersity and polyelectrolytes (instead of neutral polymers) and/or charges on the colloidal surfaces play a role in polymer-colloid mixtures. The limited amount of theoretical work performed on this is also discussed. Finally, an overview is given on experimental investigations with respect to phase behavior and results obtained with techniques enabling measurement of the depletion-induced interaction potential, the structure factor, the depletion layer thickness and the interfacial tension between the demixed phases of a colloid-polymer mixture.     

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.     

Potential barrier gravitational field-flow fractionation based on the variation of the pH solution for the analysis of colloidal materials

Summary Potential barrier gravitational field-flow fractionation (PBGFFF) is a new technique for the separation and characterization of colloidal materials. It consists in changing the potential energy of interaction between the colloidal particles and the channel wall by varying the solution ionic strength or the Hamaker constant and the surface potential of the particles. In this work the PBGFFF technique based on the particles' surface potential variation, by varying the pH, is presented. Polydisperse colloidal particles of the sulphide CuZnS (with molar ratio Cu/Zn-10/90) are used as a model sample. Comparison of the results obtained by PBGFFF with those given by conventional gravitational fieldflow fractionation and laser counter measurements, shows that one could use PBGFFF not only for the separation and characterization of colloidal materials, but also for the investigation of the interactions between colloids and solid surfaces.     

Effects of colloid polydispersity on the phase behavior of colloid-polymer mixtures

We study theoretically the equilibrium phase behavior of a mixture of polydisperse hard-sphere colloids and monodisperse polymers, modeled using the Asakura-Oosawa model [S. Asakura and F. Oosawa, J. Chem. Phys. 22, 1255 (1954)] within the free volume approximation of H. N. W. Lekkerkerker, W. C. K. Poon, P. N. Pusey, A. Stroobants, and P. B. Warren [Europhys. Lett. 20, 559 (1992)]. We compute full phase diagrams in the plane of colloid and polymer volume fractions, using the moment free energy method. The intricate features of phase separation in pure polydisperse colloids combine with the appearance of polymer-induced gas-liquid coexistence to give a rich variety of phase diagram topologies as the polymer-colloid size ratio xi and the colloid polydispersity delta are varied. Quantitatively, we find that polydispersity disfavors fluid-solid against gas-liquid separation, causing a substantial lowering of the threshold value xi(c) above which stable two-phase gas-liquid coexistence appears. Phase splits involving two or more solids can occur already at low colloid concentration, where they may be kinetically accessible. We also analyze the strength of colloidal size fractionation. When a solid phase separates from a fluid, its polydispersity is reduced most strongly if the phase separation takes place at low colloid concentration and high polymer concentration, in agreement with experimental observations. For fractionation in gas-liquid coexistence we likewise find good agreement with experiment, as well as with perturbative theories for near-monodisperse systems.     

Phase separation behavior of whey protein isolate particle dispersions in the presence of xanthan

In this study, phase separation of colloidal whey protein isolate (WPI) particle dispersions was studied using a rod-like polysaccharide xanthan. Effects of different xanthan concentration, particle volume fraction, and temperature were analyzed by visual observations, turbidity measurements, and particle mobility tracking method. Particle mobility was determined using a diffusing wave spectroscopy (DWS) set up. Xanthan concentration was kept low in order not to increase the viscosity of dispersions, so that the phase separation could be observed easily. Visual observations showed that there was a minimum concentration of xanthan to induce phase separation at a constant particle volume fraction, and xanthan concentration was found to have an important effect on the degree of phase separation. The temperature was also found to have an effect on depletion mechanism. Phase separation was mainly a result of different sizes of WPI particles, and xanthan induced the depletion interaction between WPI particles, as supported by the data obtained from DWS. The results of this study explained both the mechanism and the stability range of particle dispersions in the presence of xanthan, which is important for the design of stable systems, including colloidal particles.     

Multiphase coexistence in polydisperse colloidal mixtures

The authors study the phase behavior of mixtures of monodisperse colloidal spheres with a depletion agent which can have arbitrary shape and can possess a polydisperse size or shape distribution. In the low concentration limit considered here, the authors can employ the free-volume theory and take the geometry of particles of the depletion agent into account within the framework of fundamental measure theory. The authors apply their approach to study the phase diagram of a mixture of (monodisperse) colloidal spheres and two polydisperse polymer components. By fine tuning the distribution of the polymer, it is possible to construct a complex phase diagram which exhibits two stable critical points.     

On the Theory of the Dynamic Properties of Dense Magnetic Fluids: Polydisperse Media

The theoretical model was proposed for determining functions of the dynamic response of moderately concentrated ferrofluids on the external magnetic field and their rheological properties. Ferrofluids are considered to be polydisperse colloidal systems with the interacting (albeit individual) particles. The model is based on the regular approximation of virial expansion in powers of the particle concentration and on the well-known effective field method. The effect of system polydispersity and the magnetodipole and hydrodynamic interactions between particles on the macroscopic and dynamic properties of ferrofluids was estimated. Calculations demonstrated that the interparticle interaction results in an increase in the dynamic functions of uniform ferrocolloids up to several tens of percents.     

The role of the electron tunneling effect in the coagulation kinetics of polydisperse metal nanocolloids

The energy of pair interactions between metal nanoparticles of different sizes is shown to be able to increase upon coagulation due to the additional electrostatic effect resulting from mutual heteropolar charging of the particles. The tunnel electron transfer occurring upon the collisions between particles of different sizes may be the reason for the charging. The transfer is caused by the dependence of the electron work function on the particle size. The electron transfer through the interparticle gap equalizes the Fermi levels in particles of different sizes and is associated with this dependence. Using the example of bimodal silver nanocolloids, it is shown that mutual heteropolar charging of particles with different sizes may accelerate the coagulation of polydisperse colloidal systems by an order of magnitude or more as compared with monodisperse systems, in which this effect is absent.