Melting line of charged colloids from primitive model simulations

We develop an efficient simulation method to study suspensions of charged spherical colloids using the primitive model. In this model, the colloids and the co- and counterions are represented by charged hard spheres, whereas the solvent is treated as a dielectric continuum. In order to speed up the simulations, we restrict the positions of the particles to a cubic lattice, which allows precalculation of the Coulombic interactions at the beginning of the simulation. Moreover, we use multiparticle cluster moves that make the Monte Carlo sampling more efficient. The simulations are performed in the semigrand canonical ensemble, where the chemical potential of the salt is fixed. Employing our method, we study a system consisting of colloids carrying a charge of 80 elementary charges and monovalent co- and counterions. At the colloid densities of our interest, we show that lattice effects are negligible for sufficiently fine lattices. We determine the fluid-solid melting line in a packing fraction eta-inverse screening length kappa plane and compare it with the melting line of charged colloids predicted by the Yukawa potential of the Derjaguin-Landau-Verwey-Overbeek theory. We find qualitative agreement with the Yukawa results, and we do not find any effects of many-body interactions. We discuss the difficulties involved in the mapping between the primitive model and the Yukawa model at high colloid packing fractions (eta>0.2).     

In situ monitoring of structural changes during colloidal self-assembly

Reflectance spectroscopy is utilized to monitor structural changes during the self-assembly of a monodisperse colloidal system at the meniscus of a sessile drop on an inert substrate. Treating the ordered colloidal structure as a photonic crystal is equivalent to monitoring the changes in the photonic band gap (PBG) as the colloidal system self-assembles heterogeneously into a crystal through solvent evaporation in ambient conditions. Using a modified Bragg's law model of the photonic crystal, we can trace the structural evolution of the self-assembling colloidal system. After a certain induction period, a face-centered cubic (FCC) structure emerges, albeit with a lattice parameter larger than that of a true close-packed structure. This FCC structure is maintained while the lattice parameter shrinks continuously with further increase in the colloidal concentration due to drying. When the structure reaches a lattice parameter 1.09 times the size of that of a true close-packed structure, it undergoes an abrupt decrease in lattice spacing, apparently similar to those reported for lattice-distortive martensitic transformations. This abrupt final lattice shrinkage agrees well with the estimated Debye screening length of the electric double layer of charged colloids and could be the fundamental reason behind the cracking commonly seen in colloidal crystals.     

Dynamic investigation of gold nanocrystal assembly using in situ grazing-incidence small-angle X-ray scattering

Here we investigate the dynamic self-assembly pathway of ordered gold nanocrystal arrays during the self-assembly of gold nanocrystal micelles, with and without the presence of colloidal silica precursors, using grazing-incidence X-ray scattering performed at a synchrotron source. With silica precursors present, a lattice with rhombohedral symmetry is formed from the partial collapse of a face-centered cubic structure. In the absence of silica, a transient body-centered orthorhombic phase appears, which rapidly collapses into a glassy nanocrystal film. The appearance of face-centered and body-centered structures is consistent with a phase diagram for charged colloidal particles with assembly modulated via Coulomb screening.     

Janus and multiblock colloidal particles

We review recent developments in the synthesis and self-assembly of Janus and multiblock colloidal particles, highlighting new opportunities for colloid science and technology that are enabled by encoding orientational order between particles as they self-assemble. Emphasizing the concepts of molecular colloids and colloid valence unique to such colloids, we describe their rational self-assembly into colloidal clusters, taking monodisperse tetrahedra as an example. We also introduce a simple method to lock clusters into permanent shapes. Extending this to 2D lattices, we also review recent progress in assembling new open colloidal networks including the kagome lattice. In each application, areas of opportunity are emphasized.     

Phase diagrams of colloidal spheres with a constant zeta-potential

We study suspensions of colloidal spheres with a constant zeta-potential within Poisson-Boltzmann theory, quantifying the discharging of the spheres with increasing colloid density and decreasing salt concentration. We use the calculated renormalized charge of the colloids to determine their pairwise effective screened-Coulomb repulsions. Bulk phase diagrams in the colloid concentration-salt concentration representation follow, for various zeta-potentials, by a mapping onto published fits of phase boundaries of point-Yukawa systems. Although the resulting phase diagrams do feature face-centered cubic and body-centered cubic phases, they are dominated by the (re-entrant) fluid phase due to the colloidal discharging with increasing colloid concentration and decreasing salt concentration.     

Alignment of particles in sheared viscoelastic fluids

We investigate the shear-induced structure formation of colloidal particles dissolved in non-Newtonian fluids by means of computer simulations. The two investigated visco-elastic fluids are a semi-dilute polymer solution and a worm-like micellar solution. Both shear-thinning fluids contain long flexible chains whose entanglements appear and disappear continually as a result of Brownian motion and the applied shear flow. To reach sufficiently large time and length scales in three-dimensional simulations with up to 96 spherical colloids, we employ the responsive particle dynamics simulation method of modeling each chain as a single soft Brownian particle with slowly evolving inter-particle degrees of freedom accounting for the entanglements. Parameters in the model are chosen such that the simulated rheological properties of the fluids, i.e., the storage and loss moduli and the shear viscosities, are in reasonable agreement with experimental values. Spherical colloids dispersed in both quiescent fluids mix homogeneously. Under shear flow, however, the colloids in the micellar solution align to form strings in the flow direction, whereas the colloids in the polymer solution remain randomly distributed. These observations agree with recent experimental studies of colloids in the bulk of these two liquids.     

Concentrating colloids with electric field gradients. II. Phase transitions and crystal buckling of long-ranged repulsive charged spheres in an electric bottle

We explored the usefulness of electric field gradients for the manipulation of the particle concentration in suspensions of charged colloids, which have long-ranged repulsive interactions. In particular, we studied the compression obtained by "negative" dielectrophoresis, which drives the particles to the regions of lowest field strength, thus preventing unwanted structural changes by induced dipole-dipole interactions. We used several sample cell layouts and suspension compositions, with a different range of the interparticle repulsions. For these systems, we obtained sufficient compression to observe a transition from the initial fluid phase to a random hexagonal close-packed crystal, as well as a body-centered cubic crystal. The heterogeneous dielectrophoretic crystallization mechanism involved an intriguing "pluglike" motion of the crystal, similar to what we have previously reported for hard-sphere suspensions. In this way, remarkably large single crystals were formed of several millimeters wide and a couple of centimeters long. Moreover, we found that these crystals could be compressed to such an extent that it led to an anisotropic deformation ("buckling") and, upon subsequent relaxation, a reorientation of the lattice, while stacking errors disappeared. These striking differences with the compressed hard-sphere crystals that we studied before [M. E. Leunissen et al., J. Chem. Phys. 128, 164508 (2008).] are likely due to the smaller elastic moduli of the present lower-density soft-sphere crystals.     

Stacking fault structure in shear-induced colloidal crystallization

We report measurements of the spatial distribution of stacking faults in colloidal crystals formed by means of an oscillatory shear field at a particle volume fraction of 52% in a system where the pair potential interactions are mildly repulsive. Stacking faults are directly visualized via confocal laser scanning microscopy. Consistent with previous scattering studies, shear orders the initially amorphous colloids into close-packed planes parallel to the shearing surface. Upon increasing the strain amplitude, the close-packed direction of the (111) crystal plane shifts from an orientation parallel to the vorticity direction to parallel the flow direction. The quality of the layer ordering, as characterized by the mean stacking parameter, decreases with strain amplitude. In addition, we directly observe the three-dimensional structure of stacking faults in sheared crystals. We observe and quantify spatial heterogeneity in the stacking fault arrangement in both the flow-vorticity plane and the gradient direction, particularly at high strain amplitudes (gamma> or =3). At these conditions, layer ordering persists in the flow-vorticity plane only over scales of approximately 5-10 particle diameters. This heterogeneity is one component of the random layer ordering deduced from previous scattering studies. In addition, in the gradient direction, the stacking registry shows that crystals with intermediate global mean stacking probability are comprised of short sequences of face-centered cubic and hexagonal close-packed layers with a stacking that includes a component that is nonrandom and alternating in character.     

Crystallization in charged two-component suspensions

We report on the crystallization of colloidal crystals comprising of charged particles with different size ratio dispersed in thoroughly deionized water. Single components were characterized carefully and their nucleation behavior was investigated before the preparation of mixtures. Mixtures investigated at constant particle number densities showed body centred cubic structure, conductivity, and shear moduli comply with the assumption of a randomly substituted crystal. Most importantly, for the first time we obtain the dependence of the nucleation rate densities in dependence on the composition and (for one fixed composition) the particle number density. The process of nucleation in random substitutional crystals is found to be similar to the one-component case.     

Shear thickening in a model colloidal suspension

We study the rheology of model colloidal suspensions using molecular-dynamics simulations. We relate the onset of shear thickening to the transition from a low-viscosity regime, in which the solvent facilitates the flow of colloids, to a high-viscosity regime associated with jamming of the colloids and the formation of chains of colloids. In the low-viscosity regime, the colloidal particles are, on average, surrounded by two layers of solvent particles. On the contrary, in the high-viscosity regime, the solvent is expelled from the interstice between the jammed colloids. The thickening in suspensions is shown to obey the same criterion as in simple fluids. This demonstrates that jamming, even without the divergence of lubrication interactions, is sufficient to observe shear thickening.     

Polystyrene@TiO2 core-shell microsphere colloidal crystals and nonspherical macro-porous materials

High-quality and stable PS@TiO(2) core-shell microsphere colloidal crystals were prepared by electrostatic colloid stabilization combined with two-substrate vertical deposition method. The polyelectrolyte stabilized colloids self-assembled into face-centered cubic arrays with the (111) face perpendicular to the substrate. These colloidal crystals are gifted with high mechanical stability toward the flow of solution. Structure-property correlations were made using scanning electron microscopy and UV-vis-NIR spectroscopy. Optical spectra showed the presence of an L-stopband peak in the photonic band structure. Besides, these PS@TiO(2) colloidal crystals can be used as templates to fabricate the nonspherical macro-porous materials, and complete band gaps can be more easily obtained from such structure than from their spherical counterparts due to their lower symmetries. This work will hold the promise of enhanced photonic band gap materials.     

Controlling nanocrystal superlattice symmetry and shape-anisotropic interactions through variable ligand surface coverage

The assembly of colloidal nanocrystals (NCs) into superstructures with long-range translational and orientational order is sensitive to the molecular interactions between ligands bound to the NC surface. We illustrate how ligand coverage on colloidal PbS NCs can be exploited as a tunable parameter to direct the self-assembly of superlattices with predefined symmetry. We show that PbS NCs with dense ligand coverage assemble into face-centered cubic (fcc) superlattices whereas NCs with sparse ligand coverage assemble into body-centered cubic (bcc) superlattices which also exhibit orientational ordering of NCs in their lattice sites. Surface chemistry characterization combined with density functional theory calculations suggest that the loss of ligands occurs preferentially on {100} than on reconstructed {111} NC facets. The resulting anisotropic ligand distribution amplifies the role of NC shape in the assembly and leads to the formation of superlattices with translational and orientational order.     

Smoluchowski equation and the colloidal charge reversal

Smoluchowski equation and the Monte Carlo simulations are used to study the conditions leading to the reversal of the electrophoretic mobility. Zeta (zeta) potential is identified with the diffuse potential at the shear plane which, we argue, must be placed at least one ionic diameter away from the colloidal surface. For sufficiently strongly charged colloids, zeta potential changes sign as a function of the multivalent electrolyte concentration, resulting in a reversal of the electrophoretic mobility. This behavior occurs even for very small ions of 4 A diameter as long as the surface charge density of the colloidal particles is sufficiently large and the concentration of 1:1 electrolyte is sufficiently low.     

Melting temperature of colloidal crystals of monodisperse silica spheres in ethanol-water and ethylene glycol-water mixtures

The melting temperature (T _m) of colloidal crystals of monodisperse silica spheres in ethanol-water and ethylene glycol-water suspensions has been measured by reflection spectroscopy. A sphere of 110 nm in diameter and 0.041 in monodispersity index is used after purification and deionization processes. Transformation from the body-centered cubic lattice to the face-centered cubic lattice subphases is observed as the suspension temperature rises, which is similar to the purely aqueous suspension of the same sphere. A phase diagram including liquid-like and crystal-like structures is obtained in the presence of ion-exchange resins coexisted. The data ofT _m are analyzed successfully with the theory of Williams, Crandall, and Wojtowicz. The heat of melting decreases by the addition of ethanol or ethylene glycol in the mixtures.     

Survival probabilities in three-dimensional random walks

We evaluate the survival probability for random walkers on lattices doped with traps. We consider nearest-neighborstep walks and walks mediated bi multipolar interactions, for which the probability of steps of length r is proportional to r^?s. The decay law due to trapping is calculated for the diamond, simple cubic and body- and face-centered cubic lattices. We establish validity domains of approximate expressions.     

Effective interactions in mixtures of silica microspheres and polystyrene nanoparticles

We investigate the effect of small concentrations of highly charged nanoparticles on the stability of uncharged colloidal microspheres using large-scale simulations. Employing pair potentials that accurately represent mixtures of silica microspheres and polystyrene nanoparticles as studied experimentally, we are able to demonstrate that nanoparticle-induced stabilization can arise from a relatively weak van der Waals attraction between the colloids and nanoparticles. This demonstrates that the nanoparticle haloing mechanism for colloidal stabilization is of considerable generality and potentially can be applied to large classes of systems. The range of optimal nanoparticle concentrations can be tuned by controlling the attraction between colloids and nanoparticles.     

Influence of poly(ethylene oxide) brushes on the rheological properties of MgO colloidal suspensions in water

A combined experimental and multiscale simulation study of the influence of polymer brush modification on interactions of colloidal particles and rheological properties of dense colloidal suspensions has been conducted. Our colloidal suspension is comprised of polydisperse MgO colloidal particles modified with poly(ethylene oxide) (PEO) brushes in water. The shear stress as a function of shear rate was determined experimentally and from multiscale simulations for a suspension of 0.48 volume fraction colloids at room temperature for both bare and PEO-modified MgO colloids. Bare MgO particles exhibited strong shear thinning behavior and a yield stress on the order of several Pascals in both experiments and simulations. In contrast, simulations of PEO-modified colloids revealed no significant yielding or shear thinning and viscosity only a few times larger than solvent viscosity. This behavior is inconsistent with results obtained from experiments where modification of colloids with PEO brushes formed by adsorption of PEO-based comb-branched chains resulted in relatively little change in suspension rheology compared to bare colloids over the range of concentration of comb-branch additives investigated. We attribute this discrepancy in rheological properties between simulation and experiment for PEO-modified colloidal suspensions to heterogeneous adsorption of the comb-branch polymers.     

Connected open structures from close-packed colloidal crystals by hyperthermal neutral beam etching

We report the fabrication of connected open structures from close-packed colloidal crystals by hyperthermal neutral beam etching. Colloidal crystal films of polystyrene microspheres were prepared by a vertical deposition method. Exposure of the colloidal crystal films to hyperthermal neutral beam made isolated microspheres in the face-centered cubic lattice, each of which was connected with its twelve nearest neighbors through very thin cylinders. Due to the charge neutrality of impinging gas molecules of the hyperthermal neutral beam, the spherical shape of polymer microspheres was almost maintained during the etching process. The Bragg reflection peaks were modulated by the etched volume of colloidal crystals. Finally, the inverse structures of such open structures were replicated by a simple room-temperature chemical vapor deposition and subsequently burning out polymer template spheres.     

A universal approach to fabricate ordered colloidal crystals arrays based on electrostatic self-assembly

We present a novel and simple method to fabricate two-dimensional (2D) poly(styrene sulfate) (PSS, negatively charged) colloidal crystals on a positively charged substrate. Our strategy contains two separate steps: one is the three-dimensional (3D) assembly of PSS particles in ethanol, and the other is electrostatic adsorption in water. First, 3D assembly in ethanol phase eliminates electrostatic attractions between colloids and the substrate. As a result, high-quality colloidal crystals are easily generated, for electrostatic attractions are unfavorable for the movement of colloidal particles during convective self-assembly. Subsequently, top layers of colloidal spheres are washed away in the water phase, whereas well-packed PSS colloids that are in contact with the substrate are tightly linked due to electrostatic interactions, resulting in the formation of ordered arrays of 2D colloidal spheres. Cycling these processes leads to the layer-by-layer assembly of 3D colloidal crystals with controllable layers. In addition, this strategy can be extended to the fabrication of patterned 2D colloidal crystals on patterned polyelectrolyte surfaces, not only on planar substrates but also on nonplanar substrates. This straightforward method may open up new possibilities for practical use of colloidal crystals of excellent quality, various patterns, and controllable fashions.     

Freezing of parallel hard cubes with rounded edges

The freezing transition in a classical three-dimensional system of rounded hard cubes with fixed, equal orientations is studied by computer simulation and fundamental-measure density functional theory. By switching the rounding parameter s from zero to one, one can smoothly interpolate between cubes with sharp edges and hard spheres. The equilibrium phase diagram of rounded parallel hard cubes is computed as a function of their volume fraction and the rounding parameter s. The second order freezing transition known for oriented cubes at s = 0 is found to be persistent up to s = 0.65. The fluid freezes into a simple-cubic crystal which exhibits a large vacancy concentration. Upon a further increase of s, the continuous freezing is replaced by a first-order transition into either a sheared simple cubic lattice or a deformed face-centered cubic lattice with two possible unit cells: body-centered orthorhombic or base-centered monoclinic. In principle, a system of parallel cubes could be realized in experiments on colloids using advanced synthesis techniques and a combination of external fields.