Superlattice formation in binary mixtures of hard-sphere colloids

Ionic colloidal crystals: Ordered, multicomponent structures via controlled heterocoagulation

We propose a new type of ordered colloid, the "ionic colloidal crystal" (ICC), which is stabilized by attractive electrostatic interactions analogous to those in atomic ionic materials. The rapid self-organization of colloids via this method should result in a diversity of orderings that are analogous to ionic compounds. Most of these complex structures would be difficult to produce by other methods. We use a Madelung summation approach to evaluate the conditions where ICC's are thermodynamically stable. Using this model, we compare the relative electrostatic energies of various structures showing that the regions of ICC stability are determined by two dimensionless parameters representing charge balance and the spatial extent of the electrostatic interactions. Parallels and distinctions between ICC's and classical ionic crystals are discussed. Monte Carlo simulations are utilized to examine the glass transition and melting temperatures, between which crystallization can occur, of a model system having the rocksalt structure. These tools allow us to make a first-order prediction of the experimentally accessible regions of surface charge, particle size, ionic strength, and temperature where ICC formation is probable.

Colloidal crystal assembly on topologically patterned templates

A variety of methods have been successfully used to produce crystals of colloidal particles made of polymeric (or silica) microspheres. Achieving highly accurate growth and control of the packing symmetry, packing efficiency and packing quality of these crystals is of paramount importance for many applications, for example in photonics. If colloidal crystals are formed in self-assembly processes, it is usually the most densely packed (111) set of planes that terminates the crystal-air interface. However, often exposure of (given) different packing facets is required at the crystal surface. In addition, there is ( in photonics) need for crystals exhibiting lower than the tightest packing, and possessing also lower degrees of packing symmetry. These requirements demand development of various engineering approaches for controlled particle assembly in regular structures. The synthesis of polymer colloidal particles with different sizes, shapes and surface charge density is first briefly outlined. The various interactions and forces that control growth for a broad range of colloidal crystals are subsequently discussed. In the main section of this review we give an account of various template-assisted, graphoepitaxial assembly approaches to produce colloidal crystals with tailored packing structures and controlled crystal orientation with respect to the topologically patterned substrates used to direct the assembly process. In the outlook we also describe various selected emerging approaches, which have the potential to produce crystals with low degree of packing symmetries, for example using direct one-to-one colloidal particle assembly.

Three-dimensional binary superlattices of oppositely charged colloids

We report the equilibrium self-assembly of binary crystals of oppositely charged colloidal microspheres at high density. By varying the magnitude of the charge on near equal-sized spheres we show that the structure of the binary crystal may be switched between face-centered cubic, cesium chloride, and sodium chloride. We interpret these transformations in terms of a competition between entropic and Coulombic forces.

Stability of the binary colloidal crystals AB2 and AB13

Suspensions of binary mixtures of hard-sphere poly-methylmethacrylate colloidal particles were studied at six different size ratios alpha. The main aim was to determine the range of size ratios over which the binary colloidal crystals AB2 and AB13 are stable. Combining these results with those of earlier work, we found stability of AB2 for 0.60 approximately > alpha approximately > 0.425, in good agreement with theoretical predictions by computer simulation and cell model methods. AB13 was observed for 0.62 approximately > alpha approximately > 0.485, the lower limit being significantly smaller than the theoretical prediction of about 0.525. Rough measurements of crystallization rates showed that AB2 tended to crystallize fastest at small size ratios, whereas the opposite was true for AB13. These findings should provide a guide to the optimum conditions for materials applications of these binary colloidal crystals.

Polymorphism in AB13 Nanoparticle Superlattices: An Example of Semiconductor−Metal Metamaterials

Colloidal crystallization of nanoparticles with different functionalities into multicomponent assemblies provides a route to new classes of ordered nanocomposites with novel properties tunable by the choice of the constituent building blocks. While theories based on hard sphere approximation predict crystallization of only a few stable binary phases (NaCl-, AlB(2)- and NaZn(13)-type), we find that additional polymorphs of lower packing density are possible. We demonstrate that PbSe and Pd nanoparticles can be reproducibly crystallized into two polymorphs with AB(13) stoichiometry. One polymorph is isostructural with the intermetallic compound NaZn(13) and is consistent with dense packing of hard spheres driven by entropy. The second unanticipated polymorph is of lower packing density. This observation underscores the shortcomings of applying simple space-filling principles to the crystallization of organically passivated nanocrystals and further motivates the development of models that incorporate combinations of hard-sphere, van der Waals, dipolar, and hydrophobic forces. This work demonstrates that ordered periodic structures with lower packing density are achievable and provides the first example of a binary semiconductor-metal superlattice using a combination of PbSe-Pd nanocrystals.

Prewetting and layering in athermal polymer solutions

Coexistence conditions for prewetting and layering at a hard surface in additive hard sphere polymer solutions, where the solvent particles are smaller than the monomers, have been calculated by density functional methods. Various chain lengths and pressures have been investigated. An unexpected finding is that prewetting in these systems may proceed below the bulk critical pressure. We rationalize this behavior in terms of local properties of the pressure tensor. For longer chains, a different behavior is observed where the systems display a lower wetting pressure, i.e., a low pressure bound for surface wetting.

Structure of colloidal crystals in sedimenting mixed dispersions of latex and silica particles

We report bcc-fcc transitions of colloidal crystals in mixed aqueous dispersions of polystyrene-based latex particles (diameter: D=55.8 nm) and silica particles (diameter: D=170 nm). In the single systems, the silica particles formed bcc crystals and the latex particles did not crystallize. In the binary mixtures of these particles, colloidal crystals with fcc structures were found by the analysis of Kikuchi-Kossel diffraction images. Especially, the samples at low latex fractions started out as bcc structures, and then changed to fcc structures. Due to gravitational sedimentation, the lattice constant increased as the height from the bottom of the dispersion became larger. Furthermore, the lattice constant became smaller at a given silica fraction as the latex fraction increased.

Colloidal crystal microarrays and two-dimensional superstructures: a versatile approach for patterned surface assembly

A simple, fast, and robust approach to colloidal assembly on patterned surfaces was developed. The approach involves the rapid settling and dewetting of suspensions of spherical colloids on lithographically templated surfaces. Using this method, we can quickly and easily fabricate close-packed colloidal crystal microarrays of both silica and polystyrene spheres that range in size from 500 nm to 4.5 microm. The microarrays tend to induce the formation of monolayer colloidal crystals, which can be interconnected and removed from the templates as free-standing colloidal crystal slabs. The same approach can also be used to assemble two-dimensional colloidal crystal superlattices that can adopt a variety of structures. Graphite, kagome, body-centered cubic, open hexagonal, tetragonal, and linear chain structures can all be quickly accessed by adjusting the ratio of the sphere diameter to the template diameter.

Synthesis of colloidal aluminosilicate for light-scattering investigations

To develop a binary colloidal system with a slight index of refraction mismatch suitable for light scattering studies, pure silica particles synthesized by the method of Stöber were mixed with aluminosilicate colloids synthesized using a novel approach. With this, index-matching for one component allowed extraction of the spatial distribution of the other. In addition, it was observed that by varying the solvent, interactions between colloids could be tuned from purely repulsive to weakly attractive.

Observation of a smecticlike crystalline structure in polydisperse colloids

We present the results of crystallographic measurements on samples of two latexes: one with a relatively symmetric particle size distribution, and another with a highly skewed pseudobimodal distribution. For the skewed latex, crystallites are clearly visible, but they exhibit only a single Bragg reflection, indicating long-range order in only one direction. We propose a schematic model that explains this result in terms of stacks of planes, which are unregistered due to a high incidence of stacking faults caused by the incorporation of a large number of small particles.

Direct measurement of entropic forces induced by rigid rods

We present the first direct depletion potential measurements for a single colloidal sphere close to a wall in a suspension of rigid colloidal rods. Since all particle interactions are as good as hard-core-like, the depletion potentials are of entirely entropic origin. We developed a density functional theory approach that accurately accounts for this experimental situation. The depletion potentials calculated for different rod number densities are in very good quantitative agreement with the experimental results.

Entropically driven formation of hierarchically ordered nanocomposites

Using theoretical models, we undertake the first investigation into the rich behavior that emerges when binary particle mixtures are blended with microphase-separating copolymers. We isolate an example of coupled self-assembly in such materials, where the system undergoes a nanoscale ordering of the particles along with a phase transformation in the copolymer matrix. Furthermore, the self-assembly is driven by entropic effects involving all the different components. The results reveal that entropy can be exploited to create highly ordered nanocomposites with potentially unique electronic and photonic properties.

Controlled assembly of mesoscale structures using DNA as molecular bridges

Mesoscale polyhedral structures from binary mixtures of microspheres of specific size ratios were prepared by using DNA as a molecular bridge. Carboxy-modified polystyrene beads were decorated with fluorescently labeled single-stranded DNA via carboxydiimide chemistry. Fluorescent resonance electron transfer in a confocal microscopy setting was utilized to corroborate DNA hybridization. Tetrahedrons were made by combining DNA-containing 0.818 and 0.211 mum beads, while octahedrons were obtained by bridging 0.818 and 0.364 mum beads. Confocal data in the reflection mode and SEM provide evidence for the formation of mesoscale building blocks.

Kinetic bottleneck to the self-organization of bidisperse hard disk monolayers formed by random sequential adsorption

We study the self-organization of bidisperse mixtures of hard spheres in two dimensions by simulating random sequential adsorption (RSA) of tethered hard disks that undergo limited Monte Carlo surface diffusion. The tethers place a control on the local entropy of the disks by constraining their movement within a specified distance from their original adsorption positions. By tuning the tether length, from zero (the pure RSA process) to infinity (near-equilibrium conditions), the kinetic pathway to monolayer formation can be varied. Previously [J. J. Gray et al., Phys. Rev. Lett. 85, 4430 (2000); Langmuir 17, 2317 (2001)], we generated nonequilibrium phase diagrams for size-monodisperse and size-polydisperse hard disks as a function of surface coverage, size distribution, and tether length to reveal the occurrence of hexagonal close-packed, hexatic, and disordered phases. Bidisperse hard disks potentially offer increasingly diverse phase diagrams, with the possible occurrence of spatially and compositionally organized superlattices. Geometric packing calculations anticipate the formation of close-packed lattices in two dimensions for particle size ratios sigma=R(S)/R(L)=0.53, 0.414, and 0.155. The simulations of these systems presented here, however, reveal that RSA kinetics frustrate superlattice ordering, even for infinite tethers. The calculated jamming limits fall well below the minimum surface coverages necessary for stable ordering, as determined by melting simulations.

Layer-by-layer growth of binary colloidal crystals

We report the growth of binary colloidal crystals with control over the crystal orientation through a simple layer-by-layer process. Well-ordered single binary colloidal crystals with a stoichiometry of large (L) and small (S) particles of LS2 and LS were generated. In addition, we observed the formation of an LS3 superstructure. The structures formed as a result of the templating effect of the first layer and the forces exerted by the surface tension of the drying liquid. By using spheres of different composition, one component can be selectively removed, as is demonstrated in the growth of a hexagonal non-close-packed colloidal crystal.

Desorption behavior of quench-condensed argon-neon mixtures

The desorption behavior of quench-condensed rare gas films has been investigated using high frequency surface acoustic waves. Measurements of pure films of argon and neon and of the binary mixture Ar(1-c)/Ne(c) have been carried out. For small and very large neon concentration c(Ne) a behavior is found which indicates the existence of a substitutionally disordered solid. In contrast, in the wide range of concentration 0.25< c(Ne)< 0.92 two discrete temperatures for neon desorption exist. The data clearly indicate the occurrence of two separate phases, one of pure neon, the other of crystallites with either Ar(2)Ne or Ar(3)Ne structure.

Binary hard-sphere crystals with the cesium chloride structure

The possibility of binary hard-sphere colloids crystallizing with the cesium chloride (CsCl) structure was examined experimentally using poly (methyl methacrylate) particles dispersed in organic solvents. Towards this end, two dispersions were prepared that contained particles with a radius ratio alpha=R(B)/R(A), where A refers to the large particles and B the small, of 0.736. This is close to the optimum ratio of 0.732 at which this structure is predicted to form as determined by space-filling calculations. The phases found within the binary mixture were examined using laser light crystallography and scanning electromicroscopy, and some were shown to have the CsCl structure. Over a period of time some of the CsCl crystals disappeared indicating that they were metastable and that this structure may not be the most enduring phase at this size ratio.

Motions in binary mixtures of hard colloidal spheres: melting of the glass

Dynamic light-scattering experiments are performed on binary mixtures of hard-sphere-like colloidal suspensions with a size ratio of 0.6. The optical properties of the particles are such that the relative contrast of the two species is very sensitive to temperature, a feature that is exploited to obtain the three partial coherent intermediate scattering functions. The glass transition is identified by the onset of structural arrest, or arrest of the alpha process, on the time scale of the experiment. This is observed in a one-component suspension at a packing fraction of 0.575. The intermediate scattering functions measured on the mixtures quantify how, on introduction of the smaller spheres, the alpha process is released, i.e., how the glass melts. Increasing the fraction of smaller particles causes the alpha process to speed up but, at a given wave vector, also incurs a change to its amplitude in proportion to the change in the (partial) structure factor.

Diffusive growth of polydisperse hard-sphere crystals

Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e., mixtures of infinitely many components with sizes drawn from a continuous distribution. We model the crystallization of hard-sphere colloids (with/without attractions) from an initially amorphous phase. Although the polydisperse hard-sphere phase diagram has been widely studied, it is not straightforwardly applicable to real colloidal crystals, since they are inevitably out of equilibrium. The process by which colloidal crystals form determines the size distribution of the particles that comprise them. Once frozen into the crystal lattice, the particles are caged so that the composition cannot subsequently relax to the equilibrium optimum. We predict that the mean size of colloidal particles incorporated into a crystal is smaller than anticipated by equilibrium calculations. This is because small particles diffuse fastest and therefore arrive at the crystal in disproportionate abundance.

Real-space imaging of nucleation and growth in colloidal crystallization

Crystallization of concentrated colloidal suspensions was studied in real space with laser scanning confocal microscopy. Direct imaging in three dimensions allowed identification and observation of both nucleation and growth of crystalline regions, providing an experimental measure of properties of the nucleating crystallites. By following their evolution, we identified critical nuclei, determined nucleation rates, and measured the average surface tension of the crystal-liquid interface. The structure of the nuclei was the same as the bulk solid phase, random hexagonal close-packed, and their average shape was rather nonspherical, with rough rather than faceted surfaces.

Superlattice formation in mixtures of hard-sphere colloids

We report a detailed experimental study of the superlattice structures formed in dense binary mixtures of hard-sphere colloids. The phase diagrams observed depend sensitively on the ratio alpha=R(S)/R(L) of the radii of the small (S) and large (L) components. Mixtures of size ratio alpha=0.72, 0.52, 0.42, and 0.39 are studied. The structures of the colloidal phases formed were identified using a combination of light-scattering techniques and confocal fluorescent microscopy. At alpha=0.39, ordered binary crystals are formed in suspensions containing an equal number of large and small spheres which microscopy shows have a three-dimensional structure similar to either NaCl or NiAs. At the larger size ratio, alpha=0.52, we observe LS2 and LS13 superlattices, isostructural to the molecular compounds AlB2 and NaZn13, while at alpha=0.72 the two components are immiscible in the solid state and no superlattice structures are found. These experimental observations are compared with the predictions of Monte Carlo simulations and cell model theories.

Crystallization and phase separation in nonadditive binary hard-sphere mixtures

We calculate for the first time the full phase diagram of an asymmetric nonadditivehard-sphere mixture. The nonadditivity strongly affects the crystallization and the fluid-fluid phase separation. The global topology of the phase diagram is controlled by an effective size ratio y(eff), while the fluid-solid coexistence scales with the depth of the effective potential well.

Phase diagram of highly asymmetric binary hard-sphere mixtures

We study the phase behavior and structure of highly asymmetric binary hard-sphere mixtures. By first integrating out the degrees of freedom of the small spheres in the partition function we derive a formal expression for the effective Hamiltonian of the large spheres. Then using an explicit pairwise (depletion) potential approximation to this effective Hamiltonian in computer simulations, we determine fluid-solid coexistence for size ratios q=0.033, 0.05, 0.1, 0.2, and 1.0. The resulting two-phase region becomes very broad in packing fractions of the large spheres as q becomes very small. We find a stable, isostructural solid-solid transition for q< or =0.05 and a fluid-fluid transition for q< or =0.10. However, the latter remains metastable with respect to the fluid-solid transition for all size ratios we investigate. In the limit q-->0 the phase diagram mimics that of the sticky-sphere system. As expected, the radial distribution function g(r) and the structure factor S(k) of the effective one-component system show no sharp signature of the onset of the freezing transition and we find that at most points on the fluid-solid boundary the value of S(k) at its first peak is much lower than the value given by the Hansen-Verlet freezing criterion. Direct simulations of the true binary mixture of hard spheres were performed for q > or =0.05 in order to test the predictions from the effective Hamiltonian. For those packing fractions of the small spheres where direct simulations are possible, we find remarkably good agreement between the phase boundaries calculated from the two approaches-even up to the symmetric limit q=1 and for very high packings of the large spheres, where the solid-solid transition occurs. In both limits one might expect that an approximation which neglects higher-body terms should fail, but our results support the notion that the main features of the phase equilibria of asymmetric binary hard-sphere mixtures are accounted for by the effective pairwise depletion potential description. We also compare our results with those of other theoretical treatments and experiments on colloidal hard-sphere mixtures.

Self-assembly of ordered microporous materials from rod-coil block copolymers

Rod-coil diblock copolymers in a selective solvent for the coil-like polymer self-organize into hollow spherical micelles having diameters of a few micrometers. Long-range, close-packed self-ordering of the micelles produced highly iridescent periodic microporous materials. Solution-cast micellar films consisted of multilayers of hexagonally ordered arrays of spherical holes whose diameter, periodicity, and wall thickness depended on copolymer molecular weight and composition. Addition of fullerenes into the copolymer solutions also regulated the microstructure and optical properties of the microporous films. These results demonstrate the potential of hierarchical self-assembly of macromolecular components for engineering complex two- and three-dimensional periodic and functional mesostructures.