Stability of the binary colloidal crystals AB2 and AB13

Crystal-to-Crystal Transitions in Binary Mixtures of Soft Colloids

In this article, we demonstrate a method for inducing reversible crystal-to-crystal transitions in binary mixtures of soft colloidal particles. Through a controlled decrease of salinity and increasingly dominating electrostatic interactions, a single sample is shown to reversibly organize into entropic crystals, electrostatic attraction-dominated crystals, or aggregated gels, which we quantify using microscopy and image analysis. We furthermore analyze crystalline structures with bond order analysis to discern between two crystal phases. We observe the different phases using a sample holder geometry that allows both in situ salinity control and imaging through confocal laser scanning microscopy and apply a synthesis method producing particles with high resolvability in microscopy with control over particle size. The particle softness provides for an enhanced crystallization speed, while altering the re-entrant melting behavior as compared to hard sphere systems. This work thus provides several tools for use in the reproducible manufacture and analysis of binary colloidal crystals.

Spontaneous Crystallization in Systems of Binary Hard Sphere Colloids

Computer simulations of the fluid-to-solid phase transition in the hard sphere system were instrumental for our understanding of crystallization processes. But while colloid experiments and theory have been predicting the stability of several binary hard sphere crystals for many years, simulations were not successful to confirm this phenomenon. Here, we report the growth of binary hard sphere crystals isostructural to Laves phases, AlB_{2}, and NaZn_{13} in simulation directly from the fluid. We analyze particle kinetics during Laves phase growth using event-driven molecular dynamics simulations with and without swap moves that speed up diffusion. The crystallization process transitions from nucleation and growth to spinodal decomposition already deep within the fluid-solid coexistence regime. Finally, we present packing fraction-size ratio state diagrams in the vicinity of the stability regions of three binary crystals.

High antisite defect concentrations in hard-sphere colloidal Laves phases

Binary mixtures of hard spheres can spontaneously self-assemble into binary crystals. Computer simulations have been especially useful in mapping out the phase behaviour of these mixtures, under the assumption that the stoichiometry of the binary crystal is ideal. Here we show that for a size ratio of q = 0.82 this assumption is not valid near the coexistence region between the fluid and the stable binary crystal, the MgZn2 Laves phase. Instead we find a surprisingly high number of antisite defects: up to 2% of the large spheres are replaced by small spheres in equilibrium. We demonstrate that the defect concentration can be estimated using simple approximations, providing an easy way to identify systems where antisite defects play an important role. Our results shed new light on the self-assembly of colloidal Laves phases, and demonstrate the importance of antisite defects in binary crystals.

Aluminium diboride-type structure in Ethiopian opal-CT revealed by fast Fourier transform

Invisible on a scanning electron microscope image of the surface of an Ethiopian opal rough fracture, a periodic arrangement was detected by fast Fourier transform. Using a mask to eliminate the continuous background and keeping only the bright spots in the reciprocal space (fast Fourier transform pattern), an image reconstructed by inverse fast Fourier transform (IFFT) emphasizes a very regular bidisperse array. Taken on a vicinal plane, the image of the successive steps of the stacking allows identification of the crystallographic structure and estimation of the parameters of this aluminium diboride-type photonic crystal. In addition, another more complex IFFT image allowed confirmation of the structure and determination of the crystallographic indexing of the steps, despite image deformation due to the tilt of the vicinal plane under the electron beam.

Binary Colloidal Crystal Films Grown by Vertical Evaporation of Silica Nanoparticle Suspensions

Despite intensive research efforts in the synthesis of binary colloidal crystals, the production of well ordered binary colloidal crystal films over large areas continues to be synthetically challenging. In this paper, we investigate the phase behavior of binary mixtures of l-arginine-stabilized 36 and 22 nm silica nanoparticles deposited as centimeter-scale thin films onto a vertical substrate via evaporative assembly. By adjusting the temperature and relative colloid composition under high humidity conditions, we controlled the order of the resultant colloidal crystal films. The domain size of the AB₂ binary crystalline phase increased with an excess of small (B) particles and a very slow evaporation rate below 45 °C, with the best results obtained at 30° and 35 °C.

Pressure-controlled formation of crystalline, Janus, and core-shell supraparticles

Binary mixtures of nanoparticles self-assemble in the confinement of evaporating oil droplets and form regular supraparticles. We demonstrate that moderate pressure differences on the order of 100 kPa change the particles' self-assembly behavior. Crystalline superlattices, Janus particles, and core-shell particle arrangements form in the same dispersions when changing the working pressure or the surfactant that sets the Laplace pressure inside the droplets. Molecular dynamics simulations confirm that pressure-dependent interparticle potentials affect the self-assembly route of the confined particles. Optical spectrometry, small-angle X-ray scattering and electron microscopy are used to compare experiments and simulations and confirm that the onset of self-assembly depends on particle size and pressure. The overall formation mechanism reminds of the demixing of binary alloys with different phase diagrams.

Note: An iterative algorithm to improve colloidal particle locating

Confocal microscopy of colloids combined with digital image processing has become a powerful tool in soft matter physics and materials science. Together, these techniques enable locating and tracking of more than half a million individual colloidal particles at once. However, despite improvements in locating algorithms that improve position accuracy, it remains challenging to locate all particles in a densely packed, three dimensional colloid without erroneously identifying the same particle more than once. We present a simple iterative algorithm that mitigates both the "missed particle" and "double counting" problems while simultaneously reducing sensitivity to the specific choice of input parameters. It is also useful for analyzing images with spatially varying brightness in which a single set of input parameters is not appropriate for all particles. The algorithm is easy to implement and compatible with existing particle locating software.

Hiding in Plain View: Colloidal Self-Assembly from Polydisperse Populations

We report small-angle x-ray scattering experiments on aqueous dispersions of colloidal silica with a broad monomodal size distribution (polydispersity, 14%; size, 8 nm). Over a range of volume fractions, the silica particles segregate to build first one, then two distinct sets of colloidal crystals. These dispersions thus demonstrate fractional crystallization and multiple-phase (bcc, Laves AB_{2}, liquid) coexistence. Their remarkable ability to build complex crystal structures from a polydisperse population originates from the intermediate-range nature of interparticle forces, and it suggests routes for designing self-assembling colloidal crystals from the bottom up.

Nano-beam X-ray microscopy of dried colloidal films

We report on a nano-beam small angle X-ray scattering study on densely-packed, dried binary films made out of spherical silica particles with radii of 11.2 and 19.3 nm. For these three-dimensional thin films prepared by drop casting, only a finite number of colloidal particles contributes to the scattering signal due to the small beam size of 400 × 400 nm(2). By scanning the samples, the structure and composition of the silica particle films are determined spatially resolved revealing spatial heterogeneities in the films. Three different types of domains were identified: regions containing mainly large particles, regions containing mainly small particles, and regions where both particle species are mixed. Using the new angular X-ray cross-correlations analysis (XCCA) approach, spatial maps of the local type and degree of orientational order within the silica particle films are obtained. Whereas the mixed regions have dominant two-fold order, weaker four-fold and marginal six-fold order, regions made out of large particles are characterized by an overall reduced orientational order. Regions of small particles are highly ordered showing actually crystalline order. Distinct differences in the local particle order are observed by analyzing sections through the intensity and XCCA maps. The different degree of order can be understood by the different particle size polydispersities. Moreover, we show that preferential orientations of the particle domains can be studied by cross-correlation analysis yielding information on particle film formation. We find patches of preferential order with an average size of 8-10 μm. Thus, by this combined X-ray cross-correlation microscopy (XCCM) approach the structure and orientational order of films made out of nanometer sized colloids can be determined. This method will allow to reveal the local structure and order of self-assembled structures with different degree of order in general.

Crystallization kinetics of colloidal binary mixtures with depletion attraction

In this work the crystallization kinetics of colloidal binary mixtures with attractive interaction potential (Asakura-Oosawa) has been addressed. Parameters such as fraction of crystals, linear crystal dimension and crystal packing have been quantified in order to understand how the crystal formation is driven in terms of the depth of the attractive potential and the composition of the binary mixture (described by the number ratio). It was found that inside the eutectic triangle, crystallization is mainly governed by nucleation and the crystal packing is close to the close-packing of hard spheres. Moving out from the eutectic triangle towards small component results in the crystallization of small spheres. Enrichment of the eutectic mixture with large component results in the crystallization of both large and small spheres, however, the kinetics are completely different from those of the eutectic composition. Crosslinked polystyrene microgels with nearly hard sphere interactions were used as model systems. Attraction was introduced by addition of linear polystyrene. The time evolution of crystallization has been followed by static light scattering.

Crystallization kinetics of colloidal model suspensions: recent achievements and new perspectives

Colloidal model systems allow studying crystallization kinetics under fairly ideal conditions, with rather well-characterized pair interactions and minimized external influences. In complementary approaches experiment, analytic theory and simulation have been employed to study colloidal solidification in great detail. These studies were based on advanced optical methods, careful system characterization and sophisticated numerical methods. Over the last decade, both the effects of the type, strength and range of the pair-interaction between the colloidal particles and those of the colloid-specific polydispersity have been addressed in a quantitative way. Key parameters of crystallization have been derived and compared to those of metal systems. These systematic investigations significantly contributed to an enhanced understanding of the crystallization processes in general. Further, new fundamental questions have arisen and (partially) been solved over the last decade: including, for example, a two-step nucleation mechanism in homogeneous nucleation, choice of the crystallization pathway, or the subtle interplay of boundary conditions in heterogeneous nucleation. On the other hand, via the application of both gradients and external fields the competition between different nucleation and growth modes can be controlled and the resulting microstructure be influenced. The present review attempts to cover the interesting developments that have occurred since the turn of the millennium and to identify important novel trends, with particular focus on experimental aspects.

Structure of nanoparticles embedded in micellar polycrystals

We investigate by scattering techniques the structure of water-based soft composite materials comprising a crystal made of Pluronic block-copolymer micelles arranged in a face-centered cubic lattice and a small amount (at most 2% by volume) of silica nanoparticles, of size comparable to that of the micelles. The copolymer is thermosensitive: it is hydrophilic and fully dissolved in water at low temperature (T ~ 0 °C), and self-assembles into micelles at room temperature, where the block-copolymer is amphiphilic. We use contrast matching small-angle neuron scattering experiments to independently probe the structure of the nanoparticles and that of the polymer. We find that the nanoparticles do not perturb the crystalline order. In addition, a structure peak is measured for the silica nanoparticles dispersed in the polycrystalline samples. This implies that the samples are spatially heterogeneous and comprise, without macroscopic phase separation, silica-poor and silica-rich regions. We show that the nanoparticle concentration in the silica-rich regions is about 10-fold the average concentration. These regions are grain boundaries between crystallites, where nanoparticles concentrate, as shown by static light scattering and by light microscopy imaging of the samples. We show that the temperature rate at which the sample is prepared strongly influence the segregation of the nanoparticles in the grain-boundaries.

Self-assembled simple hexagonal AB(2) binary nanocrystal superlattices: SEM, GISAXS, and defects

Binary superlattices (BSLs) of sterically stabilized, hydrophobic, large (A; 11.5 nm diameter) Fe(2)O(3) and small (B; 6.1 nm diameter) Au nanocrystals were assembled by slow evaporation of colloidal dispersions on tilted substrates. A detailed analysis of the BSL structure was carried out using transmission and scanning electron microscopy (TEM and SEM) and grazing incidence small-angle X-ray scattering (GISAXS). The BSLs were simple hexagonal (sh) AB(2) superlattices (isostructural with the compound AlB(2); space group 191, P6/mmm) of large nanocrystals occupying a simple hexagonal lattice with small nanocrystals in the interstitial spaces. SEM and GISAXS confirmed long-range order of the BSLs and GISAXS revealed that the superlattice is slightly contracted (8-12%) perpendicular to the substrate as a result of solvent drying in the deposition process. When the sh-AB(2) superlattice deposits on a (100) plane, this shrinkage occurs in the [210] direction and changes the lattice symmetry to centered orthorhombic. Additionally, nearly periodic superlattice dislocations consisting of inserted half-planes of gold nanocrystals were observed by SEM in some BSLs.

Crystallization of bidisperse repulsive colloids in two-dimensional space: a study of model systems constructed at the air-water interface

We report the structural behavior for mixtures of two differently sized ("bidisperse") silica microspheres at the air-water interface under three different size ratio conditions (alpha (identical with R(S)/R(L)) = 0.375, 0.500, and 0.579). These bidisperse silica monolayers were studied via measurement of the surface pressure-area isotherm and optical microscopy at various particle surface coverages (theta identical with theta(S) + theta(L)) during compression. The silica colloids used in these trials were found to possess purely repulsive pair interactions at the air-water interface, which was confirmed by the pair correlation function calculated from the analysis of many optical images of the particles taken at dilute concentrations. The results revealed that, at certain mixture compositions (beta identical with theta(L)/theta(S)), compression can lead to the formation of 2D binary crystal structures. Specifically, at a particle size ratio of alpha = 0.375, LS1 crystal domains were observed at a surface coverage of theta approximately 0.619 when beta = 7.00 and 3.50, although this LS1 structure was not observed at higher total particle densities (where the system became phase-separated). At a size ratio of alpha = 0.579, compression produced 2D LS2 binary crystals at particle surface coverages (theta) above 0.641 when beta = 3.00, 1.50, or 1.00. However, at a size ratio of alpha = 0.500, compression triggered macroscopic phase separation, leading to the formation of two separate hexagonal-close-packed domains consisting purely of either large or small particles. In general, when the mixture composition (beta) was too different from the stoichiometric ratio needed for the formation of LS1 or LS2 superlattices, the bidisperse monolayer was observed to remain in an amorphous state rather than evolving to an ordered phase under compression. These findings suggest that, in two dimensions, contrary to what has been speculated in the literature, (1) purely repulsive pair potentials can give rise to LS1 and LS2 binary crystals under compression and also (2) perfectly spherical particles can form LS2 crystals. This discrepancy between our results and the predictions of previous simulations might indicate that the capillary interaction and/or the many-body effects play a significant role in determining the structure of bidisperse colloids at the air-water interface.

Direct observation of size fractionation during colloidal crystallization

We present a confocal microscopy study of the quasi-two-dimensional crystallization of a binary mixture of spherical colloids coated with long DNA strands. Our experiments show that in the crystalline phase the two colloidal species are completely demixed. Analysis of the lattice spacings in the two types of colloidal crystal shows that the diameters of the two species of colloids differ by 10%. We argue that the demixing in the crystalline phase is due to size segregation during crystallization. This phenomenon had been predicted in several theoretical studies. To our knowledge, the present study provides the first 'real-space' experimental confirmation of this effect.

Phase behaviour of deionized binary mixtures of charged colloidal spheres

We review recent work on the phase behaviour of binary charged sphere mixtures as a function of particle concentration and composition. Both size ratios Γ and charge ratios Λ are varied over a wide range. Unlike the case for hard spheres, the long-ranged Coulomb interaction stabilizes the crystal phase at low particle concentrations and shifts the occurrence of amorphous solids to particle concentrations considerably larger than the freezing concentration. Depending on Γ and Λ, we observe upper azeotrope, spindle, lower azeotrope and eutectic types of phase diagrams, all known well from metal systems. Most solids are of body centred cubic structure. Occasionally stoichiometric compounds are formed at large particle concentrations. For very low Γ, entropic effects dominate and induce a fluid-fluid phase separation. Since for charged spheres the charge ratio Λ is also decisive for the type of phase diagram, future experiments with charge variable silica spheres are suggested.

Enhanced crystal stability in a binary mixture of charged colloidal spheres

We report on the phase behavior of a binary charged sphere mixture of size ratio Gamma=0.68 and charge ratio Lambda approximately 1 as a function of composition p and number density n . For p=0.1-0.3 we observe freezing at densities well below the freezing densities of the pure components. At all compositions our data indicate the formation of substitutional alloy crystals of body centered cubic structure. No indications for compound formation were observed. Rather, our findings point at the first observation of an upper azeotrope. Measurements of the crystallization kinetics reveal a combined density and composition dependence of growth velocities and nucleation rate densities, with small but significant anomalies at p*=0.2 . These correlated deviations can be rationalized within classical theories of solidification and suggest an increased similarity between melt and solid for this particular composition.

Prediction of binary hard-sphere crystal structures

We present a method based on a combination of a genetic algorithm and Monte Carlo simulations to predict close-packed crystal structures in hard-core systems. We employ this method to predict the binary crystal structures in a mixture of large and small hard spheres with various stoichiometries and diameter ratios between 0.4 and 0.84. In addition to known binary hard-sphere crystal structures similar to NaCl and AlB2, we predict additional crystal structures with the symmetry of CrB, gammaCuTi, alphaIrV, HgBr2, AuTe2, Ag2Se, and various structures for which an atomic analog was not found. In order to determine the crystal structures at infinite pressures, we calculate the maximum packing density as a function of size ratio for the crystal structures predicted by our GA using a simulated annealing approach.

Dielectrophoresis and AC-induced assembly in binary colloidal suspensions

Dielectrophoretic behaviors and assembly of a binary suspension in aqueous media are examined in the presence of nonuniform alternating current (AC) electric field. A peculiar low-frequency threshold and dielectrophoresis (DEP) crossover frequency determine the applicable frequency window for binary assembly under positive DEP, which can be effectively tuned by medium conductivity and particle size, suggesting that the dynamic double-layer effect is responsible for the interfacial polarization of micrometer to submicrometer-sized particles in aqueous suspensions. Strong effects of AC-field frequency, medium conductivity, and size ratio on binary assembly morphology have been observed. A frequency-medium conductivity phase diagram is obtained to illustrate the morphological transition of assembled colloidal aggregates from segregated, ordered assemblies to inverted segregation with the appearance of amorphous phases upon increasing frequency and/or medium conductivity, which is a direct consequence of the competition between DEP and hydrodynamic mobility. Significantly, our results demonstrate a rapid method to form hybrid nanostructured materials.

Superlattice formation in binary mixtures of block copolymer micelles

Two distinct diblock copolymers, poly(styrene-b-isoprene) (SI) and poly(styrene-b-dimethylsiloxane) (SD), were codissolved at various concentrations in the polystyrene selective solvent diethyl phthalate. Two SI diblocks, with block molar masses of 12,000-33,000 and 30,000-33,000, and two SD diblocks, with block molar masses of 19,000-6000 and 16,000-9000, were employed. The size ratio of the smaller SD micelles (S) to the larger SI micelles (L) varied from approximately 0.5 to 0.6, based on hydrodynamic radii determined by dynamic light scattering on dilute solutions containing only one polymer component. Due to incompatibility between the polyisoprene and polydimethylsiloxane blocks, a binary mixture of distinct SI and SD micelles was formed in each mixed solution, as confirmed by cryogenic transmission electron microscopy. When the total concentration of polymer was increased to 20-30%, the micelles adopted a superlattice structure. Small angle X-ray scattering revealed the lattice to be the full LS13 superlattice (space group Fm3c) in all cases, with unit cell dimensions in excess of 145 nm. A coexistent face-centered cubic phase composed of SD micelles was also observed when the number ratio of S to L micelles was large.

Exotic crystal superstructures of colloidal crystals in confinement

Colloidal model systems have been used for over three decades for investigating liquids, crystals, and glasses. Colloidal crystal superstructures have been observed in binary systems of repulsive spheres as well as oppositely charged sphere systems showing structures well known from atomic solids. In this work we study the structural transition of colloidal crystals under confinement. In addition to the known sequence of crystalline structures, crystal superstructures with dodecagonal and hexagonal symmetry are observed in one component systems. These structures have no atomic counterpart.

Frustration-induced magic number clusters of colloidal magnetic particles

We report the formation of stable two-dimensional clusters consisting of long-range-interacting colloidal particles with predefined magnetic moments. The symmetry and arrangement of the particles within the cluster are imposed by the magnetic frustration. By satisfying the criteria of stability, a series of magic number clusters is formed. The magic clusters are close packed and have compensating magnetic moments and chirality. Thus, the system can be regarded as a classical mesoscopic model for spin arrangements in two-dimensional triangular antiferromagnets, although the exact nature of the interactions between the macroscopic magnetic moments is different.

Lattice-switch Monte Carlo simulation for binary hard-sphere crystals

We show how to generalize the lattice-switch Monte Carlo method to calculate the phase diagram of a binary system. A global coordinate transformation is combined with a modification of particle diameters, enabling the multicomponent system in question to be explored and directly compared to a suitable reference state in a single Monte Carlo simulation. We use the method to evaluate the free energies of binary hard-sphere crystals. Calculations at moderate size ratios alpha=0.58 and 0.73 are in agreement with previous results, and confirm AB2 and AB13 as stable structures. We also find that the AB(CsCl) structure is not entropically stable at the size ratio and volume where it has been reported experimentally, and therefore that those observations cannot be explained by packing effects alone.

Characterization of magnetic colloids by means of magnetooptics

A new, efficient method for the characterization of magnetic colloids based on the Faraday effect is proposed. According to the main principles of this technique, it is possible to detect the stray magnetic field of the colloidal particles induced inside the magnetooptical layer. The magnetic properties of individual particles can be determined providing measurements in a wide range of magnetic fields. The magnetization curves of capped colloids and paramagnetic colloids were measured by means of the proposed approach. The registration of the magnetooptical signals from each colloidal particle in an ensemble permits the use of this technique for testing the magnetic monodispersity of colloidal suspensions.

Hypersonic acoustic excitations in binary colloidal crystals: big versus small hard sphere control

The phononic band structure of two binary colloidal crystals, at hypersonic frequencies, is studied by means of Brillouin light scattering and analyzed in conjunction with corresponding dispersion diagrams of the single colloidal crystals of the constituent particles. Besides the acoustic band of the average medium, the authors' results show the existence of narrow bands originating from resonant multipole modes of the individual particles as well as Bragg-type modes due to the (short-range) periodicity. Strong interaction, leading to the occurrence of hybridization gaps, is observed between the acoustic band and the band of quadrupole modes of the particles that occupy the largest fractional volume of the mixed crystal; the effective radius is either that of the large (in the symmetric NaCl-type crystalline phase) or the small (in the asymmetric NaZn(13)-type crystalline phase) particles. The possibility to reveal a universal behavior of the phononic band structure for different single and binary colloidal crystalline suspensions, by representing in the dispersion diagrams reduced quantities using an appropriate length scale, is discussed.

Fabrication of binary colloidal crystals and non-close-packed structures by a sequential self-assembly method

Binary colloidal films of polystyrene (PS) spheres and silica spheres were fabricated with a sequential growth method using differently sized colloidal particles. In particular, we demonstrate the structures formed by a silica monolayer growing on top of a PS monolayer and a silica multilayer growing on top of a PS monolayer. By removal of the bottom PS layers, non-close-packed hexagonal, pentagonal, and square silica arrays were obtained at the original silica/PS interface. The possible formation mechanism of the non-close-packed structure was discussed, which may be used to explain how 3D colloidal crystals grow on patterned substrates.

Superlattice formation in a binary mixture of block copolymer micelles

A binary solution mixture of distinct block copolymer micelles is found to adopt a superlattice. The larger micelles, formed from polystyrene-polyisoprene diblocks, have a nominal radius of 29 nm; the smaller micelles, formed from polystyrene-polydimethylsiloxane diblocks, have a nominal radius of 16 nm. The superlattice unit cell dimension is 156 nm and is assigned to space group Fm3c; it corresponds to the AB13 structure. As these diblocks are uncharged, the driving force for superlattice formation is primarily free volume entropy, as in sterically stabilized colloidal hard spheres.