Superlattice formation in binary mixtures of hard-sphere colloids

Coassembly of Complementary Polyhedral Metal-Organic Framework Particles into Binary Ordered Superstructures

Here we report the formation of a 3D NaCl-type binary porous superstructure via coassembly of two colloidal polyhedral metal-organic framework (MOF) particles having complementary sizes, shapes, and charges. We employed a polymeric-attenuated Coulombic self-assembly approach, which also facilitated the coassembly of these MOF particles with spherical polystyrene particles to form 2D binary superstructures. Our results pave the way for using MOFs to create sophisticated superstructures comprising particles of various sizes, shapes, porosities, and chemical compositions.

Frequency-Dependent Microelectrophoresis Study of Colloids with Tunable Surface Charge

Nonaqueous poly(methyl methacrylate) (PMMA) colloidal suspensions in a solvent that is simultaneously matched in both density and refractive index have been important for real-space studies of colloidal self-assembly, but their complex electrostatic character remains largely unexplored. Electrophoresis is a powerful tool for determining the surface potential and charge of the colloidal suspension; however, because of refractive index matching, standard electrophoresis measurements are not feasible. We carry out microscope-based microelectrophoresis measurements on PMMA colloids in cyclohexyl bromide and cis-trans decalin to measure particle charge as a function of salt concentration in both DC and frequency-variable AC fields. The colloid charge depends on salt concentration and reverses sign near 0.35 μM, providing evidence that solution ions are actively modifying the colloid surface. The frequency dependence of the electrophoretic mobility yields the characteristic time scale for electric double-layer polarization and provides intriguing evidence for Manning condensation and polyion formation.

All-Perovskite Multicomponent Nanocrystal Superlattices

Nanocrystal superlattices (NC SLs) have long been sought as promising metamaterials, with nanoscale-engineered properties arising from collective and synergistic effects among the constituent building blocks. Lead halide perovskite (LHP) NCs come across as outstanding candidates for SL design, as they demonstrate collective light emission, known as superfluorescence, in single- and multicomponent SLs. Thus far, LHP NCs have only been assembled in single-component SLs or coassembled with dielectric NC building blocks acting solely as spacers between luminescent NCs. Here, we report the formation of multicomponent LHP NC-only SLs, i.e., using only CsPbBr3 NCs of different sizes as building blocks. The structural diversity of the obtained SLs encompasses the ABO6, ABO3, and NaCl structure types, all of which contain orientationally and positionally locked NCs. For the selected model system, the ABO6-type SL, we observed efficient NC coupling and Förster-like energy transfer from strongly confined 5.3 nm CsPbBr3 NCs to weakly confined 17.6 nm CsPbBr3 NCs, along with characteristic superfluorescence features at cryogenic temperatures. Spatiotemporal exciton dynamics measurements reveal that binary SLs exhibit enhanced exciton diffusivity compared to single-component NC assemblies across the entire temperature range (from 5 to 298 K). The observed coherent and incoherent NC coupling and controllable excitonic transport within the solid NC SLs hold promise for applications in quantum optoelectronic devices.

Van der Waals Colloidal Crystals

A general guiding principle for colloidal crystallization is to tame the attractive enthalpy such that it slightly overwhelms the repulsive interaction. As-synthesized colloids are generally designed to retain a strong repulsive potential for the high stability of suspensions, encoding appropriate attractive potentials into colloids has been key to their crystallization. Despite the myriad of interparticle attractions for colloidal crystallization, the van der Waals (vdW) force remains unexplored. Here, it is shown that the implementation of gold cores into silica colloids and the resulting vdW force can reconfigure the pair potential well depth to the optimal range between -1 and -4 kB T at tens of nanometer-scale colloidal distances. As such, colloidal crystals with a distinct liquid gap can be formed, which is evidenced by photonic bandgap-based diffractive colorization.

The entropy-controlled strategy in self-assembling systems

Self-assembly of various building blocks has been considered as a powerful approach to generate novel materials with tailorable structures and optimal properties. Understanding physicochemical interactions and mechanisms related to structural formation and transitions is of essential importance for this approach. Although it is well-known that diverse forces and energies can significantly contribute to the structures and properties of self-assembling systems, the potential entropic contribution remains less well understood. The past few years have witnessed rapid progress in addressing the entropic effects on the structures, responses, and functions in the self-assembling systems, and many breakthroughs have been achieved. This review provides a framework regarding the entropy-controlled strategy of self-assembly, through which the structures and properties can be tailored by effectively tuning the entropic contribution and its interplay with the enthalpic counterpart. First, we focus on the fundamentals of entropy in thermodynamics and the entropy types that can be explored for self-assembly. Second, we discuss the rules of entropy in regulating the structural organization in self-assembly and delineate the entropic force and superentropic effect. Third, we introduce the basic principles, significance and approaches of the entropy-controlled strategy in self-assembly. Finally, we present the applications where this strategy has been employed in fields like colloids, macromolecular systems and nonequilibrium assembly. This review concludes with a discussion on future directions and future research opportunities for developing and applying the entropy-controlled strategy in complex self-assembling systems.

Tunable assembly of host-guest colloidal crystals

Entropy compartmentalization provides new self-assembly routes to colloidal host-guest (HG) structures. Leveraging host particle shape to drive the assembly of HG structures has only recently been proposed and demonstrated. However, the extent to which the guest particles can dictate the structure of the porous network of host particles has not been explored. In this work, by modifying only the guest shape, we show athermal, binary mixtures of star-shaped host particles and convex polygon-shaped guest particles assemble as many as five distinct crystal structures, including rotator and discrete rotator guest crystals, two homoporous host crystals, and one heteroporous host crystal. Edge-to-edge alignment of neighboring stars results in the formation of three distinct pore motifs, whose preferential formation is controlled by the size and shape of the guest particles. Finally, we confirm, via free volume calculations, that assembly is driven by entropy compartmentalization, where the hosts and guests contribute differently to the free energy of the system; free volume calculations also explain differences in assembly based on guest shape. These results provide guest design rules for assembling colloidal HG structures, especially on surfaces and interfaces.

Approaching the hard sphere limit in colloids suitable for confocal microscopy - the end of a decade lasting quest

PMMA-PHSA particles serve as the hard sphere model system since the 1980s. We investigate the fluid structure of fluorescent ones in three different solvents by laser scanning confocal microscopy: a decalin-tetrachloroethylene (TCE)-mixture and a decalin-cyclohexylbromide (CHB)-mixture with and without tetrabutylammoniumbromide (TBAB). The experimental 3D radial distribution functions are modeled by analytical theory and computer simulations taking polydispersity and the experimental position uncertainty into account. The quantitative comparison between experiment and simulation/theory establishes hard sphere like behavior for particles in decalin-TCE for a wide range of particle packing fractions. To the best of our knowledge, we present the first experimental dataset of a fluid structure that agrees convincingly with Percus-Yevick over a wide concentration range. Furthermore, charged sphere behavior is confirmed both for the decalin-CHB and the decalin-CHB-TBAB solvents, and it is demonstrated that a finite particle concentration reduces screening in the decalin-CHB-TBAB system compared to the bulk solvent.

Tuning assembly structures of hard shapes in confinement via interface curvature

Assembly in confinement is a problem of great interest in colloidal structure design, plasmonics, photonics, and industrial packaging. Along with the range of design choices provided by particle shape and attraction or repulsion, confined systems add an additional layer of complexity through the interactions between particles and the container holding them. The range of possible behaviors produced by these systems remains largely unexplored, yet has profound consequences on the resultant assembled structure. Here, we address this problem by exploring how the assembly of hard tetrahedral particles is affected by a spherical container. We simulate particle assemblies in containers holding 4 to 10 000 particles and analyze the range of resultant structures. We find that the presence of a curved wall causes organization into distinct concentric shells in containers holding up to thousands of particles. In addition, we see that wall curvature affects structural motifs in systems as large as 10 000 particles, promoting local environments that maximally conform to the wall and providing a seed for the propagation of these motifs into the interior of the container. Through this work, we show how confining interfaces can be used to promote the assembly of structures markedly distinct from those seen in the more commonly studied bulk systems.

Synthesis, crystal and electronic structure of BaLixCd13–x (x ≈ 2)

A new ternary phase has been synthesized and structurally characterized. BaLi_xCd_13–x (x ≈ 2) adopts the cubic NaZn₁₃ structure type (space group Fm3¯c, Pearson symbol cF112) with unit cell parameter a = 13.5548 (10) Å. Structure refinements from single-crystal X-ray diffraction data demonstrate that the Li atoms are exclusively found at the centers of the Cd₁₂-icosahedra. Since a cubic BaCd₁₃ phase does not exist, and the tetragonal BaCd₁₁ is the most Cd-rich phase in the Ba–Cd system, BaLi_xCd_13–x (x ≈ 2) has to be considered as a true ternary compound. As opposed to the typical electron count of ca. 27e-per formula unit for many known compounds with the NaZn₁₃ structure type, BaLi_xCd_13–x (x ≈ 2) only has ca. 26e-, suggesting that both electronic and geometric factors are at play. Finally, the bonding characteristics of the cubic BaLi_xCd_13–x (x ≈ 2) and tetragonal BaCd₁₁ are investigated using the TB-LMTO-ASA method, showing metallic-like behavior.

Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices

The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal cocrystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote-and, in some cases, may be necessary for-the self-assembly of a binary cocrystal. Using computer simulations, we identify two mechanisms responsible for this phenomenon. First, excess small particles act like plasticizers and enable systems to reach a greater supersaturation before kinetic arrest occurs. Second, they can disfavor competing structures that may interfere with the growth of the target structure. We find the phase behavior of simulated mixtures of nearly hard spheres closely matches published experimental results. We demonstrate the generality of our findings for mixtures of particles of arbitrary shape by presenting a binary mixture of hard shapes that only self-assembles with an excess of the smaller component.

Shape-Directed Co-Assembly of Lead Halide Perovskite Nanocubes with Dielectric Nanodisks into Binary Nanocrystal Superlattices

Self-assembly of colloidal nanocrystals (NCs) holds great promise in the multiscale engineering of solid-state materials, whereby atomically engineered NC building blocks are arranged into long-range ordered structures-superlattices (SLs)-with synergistic physical and chemical properties. Thus far, the reports have by far focused on single-component and binary systems of spherical NCs, yielding SLs isostructural with the known atomic lattices. Far greater structural space, beyond the realm of known lattices, is anticipated from combining NCs of various shapes. Here, we report on the co-assembly of steric-stabilized CsPbBr₃ nanocubes (5.3 nm) with disk-shaped LaF₃ NCs (9.2-28.4 nm in diameter, 1.6 nm in thickness) into binary SLs, yielding six columnar structures with AB, AB₂, AB₄, and AB₆ stoichiometry, not observed before and in our reference experiments with NC systems comprising spheres and disks. This striking effect of the cubic shape is rationalized herein using packing-density calculations. Furthermore, in the systems with comparable dimensions of nanocubes (8.6 nm) and nanodisks (6.5 nm, 9.0 nm, 12.5 nm), other, noncolumnar structures are observed, such as ReO₃-type SL, featuring intimate intermixing and face-to-face alignment of disks and cubes, face-centered cubic or simple cubic sublattice of nanocubes, and two or three disks per one lattice site. Lamellar and ReO₃-type SLs, employing large 8.6 nm CsPbBr₃ NCs, exhibit characteristic features of the collective ultrafast light emission-superfluorescence-originating from the coherent coupling of emission dipoles in the excited state.

Kinetically Controlled Self-Assembly of Binary Polymer-Grafted Nanocrystals into Ordered Superstructures via Solvent Vapor Annealing

Polymer-inorganic nanocomposites based on polymer-grafted nanocrystals (PGNCs) are enabling technologically relevant applications owing to their unique physical, chemical, and mechanical properties. While diverse PGNC superstructures have been realized through evaporation-driven self-assembly, this approach presents multifaceted challenges in experimentally probing and controlling assembly kinetics. Here, we report a kinetically controlled assembly of binary superstructures from a homogeneous disordered PGNC mixture utilizing solvent vapor annealing (SVA). Using a NaZn₁₃-type superstructure as a model system, we demonstrate that varying the solvent vapor pressure during SVA allows for exquisite control of the rate and extent of PGNC assembly, providing access to nearly complete kinetic pathways of binary PGNC crystallization. Characterization of kinetically arrested intermediates reveals that assembly follows a multistep crystallization pathway involving spinodal-like preordering of PGNCs prior to NaZn₁₃ nucleation. Our work opens up new avenues for the synthesis of multicomponent PGNC superstructures exhibiting multifunctionalities and emergent properties through a thorough understanding of kinetic pathways.

The diversity of three-dimensional photonic crystals

Many butterflies, birds, beetles, and chameleons owe their spectacular colors to the microscopic patterns within their wings, feathers, or skin. When these patterns, or photonic crystals, result in the omnidirectional reflection of commensurate wavelengths of light, it is due to a complete photonic band gap (PBG). The number of natural crystal structures known to have a PBG is relatively small, and those within the even smaller subset of notoriety, including diamond and inverse opal, have proven difficult to synthesize. Here, we report more than 150,000 photonic band calculations for thousands of natural crystal templates from which we predict 351 photonic crystal templates - including nearly 300 previously-unreported structures - that can potentially be realized for a multitude of applications and length scales, including several in the visible range via colloidal self-assembly. With this large variety of 3D photonic crystals, we also revisit and discuss oft-used primary design heuristics for PBG materials.

An Artificial Neural Network Reveals the Nucleation Mechanism of a Binary Colloidal AB13 Crystal

Colloidal suspensions of two species have the ability to form binary crystals under certain conditions. The hunt for these functional materials and the countless investigations on their formation process are justified by the plethora of synergetic and collective properties these binary superlattices show. Among the many crystal structures observed over the past decades, the highly exotic colloidal icosahedral AB₁₃ crystal was predicted to be stable in binary hard-sphere mixtures nearly 30 years ago, yet the kinetic pathway of how homogeneous nucleation occurs in this system is still unknown. Here we investigate binary nucleation of the AB₁₃ crystal from a binary fluid phase of nearly hard spheres. We calculate the nucleation barrier and nucleation rate as a function of supersaturation and draw a comparison with nucleation of single-component and other binary crystals. To follow the nucleation process, we employ a neural network to identify the AB₁₃ phase from the binary fluid phase and the competing fcc crystal with single-particle resolution and significant accuracy in the case of bulk phases. We show that AB₁₃ crystal nucleation proceeds via a coassembly process where large spheres and icosahedral small-sphere clusters simultaneously attach to the nucleus. Our results lend strong support for a classical pathway that is well-described by classical nucleation theory, even though the binary fluid phase is highly structured and exhibits local regions of high bond orientational order.

Ultracentrifugation Techniques for the Ordering of Nanoparticles

A centrifugal field can provide an external force for the ordering of nanoparticles. Especially with the knowledge from in-situ characterization by analytical (ultra)centrifugation, nanoparticle ordering can be rationally realized in preparative (ultra)centrifugation. This review summarizes the work back to the 1990s, where intuitive use of centrifugation was achieved for the fabrication of colloidal crystals to the very recent work where analytical (ultra)centrifugation is employed to tailor-make concentration gradients for advanced materials. This review is divided into three main parts. In the introduction part, the history of ordering microbeads in gravity is discussed and with the size of particles reduced to nanometers, a centrifugal field is necessary. In the next part, the research on the ordering of nanoparticles in analytical and preparative centrifugation in recent decades is described. In the last part, the applications of the functional materials, fabricated from centrifugation-induced nanoparticle superstructures are briefly discussed.

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.

Monte Carlo simulations of patch models with applications to soft matter

Patch models have been employed to describe anisotropic interactions in disparate soft matter systems. In this work, we present a unified study of a patch model to explore particle self-assembly in both monodisperse and polydisperse systems, with applications to both proteins and colloids. In the first case, we obtained a temperature-density phase diagram for a model of the protein polyglutamine from Monte Carlo simulations. These simulations evinced clusters in the gas phase and, via a comparison with the corresponding coarse-grained PLUM model for this system, we verified that dense clustering in the gas phase falls into the supersaturation region of the saturation curve. In the second case, we have investigated the effect of size polydispersity on the phase behavior of binary colloidal mixtures. It was found that the width of gas-liquid phase coexistence increases with increasing polydispersity and that, in addition to the aforementioned particle clustering, small particles decorate patches on large particles, thereby creating large-particle bridges. Our aim is to compare and contrast self-assembly in these two prototypical systems.

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.

Ionic solids from common colloids

From rock salt to nanoparticle superlattices, complex structure can emerge from simple building blocks that attract each other through Coulombic forces^1-4. On the micrometre scale, however, colloids in water defy the intuitively simple idea of forming crystals from oppositely charged partners, instead forming non-equilibrium structures such as clusters and gels^5-7. Although various systems have been engineered to grow binary crystals^8-11, native surface charge in aqueous conditions has not been used to assemble crystalline materials. Here we form ionic colloidal crystals in water through an approach that we refer to as polymer-attenuated Coulombic self-assembly. The key to crystallization is the use of a neutral polymer to keep particles separated by well defined distances, allowing us to tune the attractive overlap of electrical double layers, directing particles to disperse, crystallize or become permanently fixed on demand. The nucleation and growth of macroscopic single crystals is demonstrated by using the Debye screening length to fine-tune assembly. Using a variety of colloidal particles and commercial polymers, ionic colloidal crystals isostructural to caesium chloride, sodium chloride, aluminium diboride and K₄C₆₀ are selected according to particle size ratios. Once fixed by simply diluting out solution salts, crystals are pulled out of the water for further manipulation, demonstrating an accurate translation from solution-phase assembly to dried solid structures. In contrast to other assembly approaches, in which particles must be carefully engineered to encode binding information^12-18, polymer-attenuated Coulombic self-assembly enables conventional colloids to be used as model colloidal ions, primed for crystallization.

Influence of Softness on the Stability of Binary Colloidal Crystals

Mixtures of two types of nanoparticles can self-assemble into a wide variety of binary colloidal crystals (also called binary nanoparticle superlattices), which are interesting for their structural diversity and potential applications. Although so-called packing models-which usually treat the particles as "hard" with only excluded volume interactions-seem to explain many reported dense crystalline phases, these models often fail to predict the right structure. Here, we examine the role of soft repulsive interparticle interactions on binary colloidal crystals comprising two sizes of spherical particles; such "softness" can arise due to ligand shells or screened electrostatics. We determine the ground state phase diagram of binary systems of particles interacting with an additive inverse power law potential using a basin hopping algorithm to calculate the enthalpy of an extremely large pool of candidate structures. We find that a surprisingly small amount of softness can destabilize dense packings in favor of less densely packed structures, which provides further evidence that considerations beyond packing are necessary for describing many of the observed phases of binary colloidal crystals. Importantly, we find that several of the phases stabilized by softness, which are characterized by relatively few interparticle contacts and a tendency for local icosahedral order, are more likely to be observed experimentally than those predicted by packing models. We also report a previously unknown dense AB₄ phase and conduct free energy calculations to examine how the stability of several crystals will vary with temperature. Our results further our understanding of why particular binary colloidal crystals form and will be useful as a reference for experimentalists working with softly repulsive colloids.

Effect of size disparity on the structure and dynamics of the small component in concentrated binary colloidal mixtures

We determined, using confocal microscopy, the structure and dynamics of the small component in concentrated binary colloidal mixtures with moderate and large size ratios and different compositions of Polymethyl methacrylate particles. We show that when increasing the content of small spheres at fixed total volume fraction, a transition in the local environment of the small particles is observed, from a mixed environment of other small and large particles to a local environment of only small particles. The transition is rather abrupt for moderate size ratios, while it becomes particularly broad for large size ratios. This can be associated with the improved ability of the small particles to pack in between the large particles for larger size ratios. The dynamics reflect the transition with an increase of the mobility observed at intermediate mixing. This increase becomes particularly pronounced for large size ratios, leading to diffusive dynamics of the small particles, in agreement with predictions of theories of the glass transition in binary hard-sphere mixtures. The composition at which the fastest dynamics are observed is apparently independent of the size ratio.

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.

Complex Crystals from Size-Disperse Spheres

Colloids are rarely perfectly uniform but follow a distribution of sizes, shapes, and charges. This dispersity can be inherent (static) or develop and change over time (dynamic). Despite a long history of research, the conditions under which nonuniform particles crystallize and which crystal forms is still not well understood. Here, we demonstrate that hard spheres with Gaussian radius distribution and dispersity up to 19% always crystallize if compressed slowly enough, and they do so in surprisingly complex ways. This result is obtained by accelerating event-driven simulations with particle swap moves for static dispersity and particle resize moves for dynamic dispersity. Above 6% dispersity, AB_{2} Laves, AB_{13}, and a region of Frank-Kasper phases are found. The Frank-Kasper region includes a quasicrystal approximant with Pearson symbol oS276. Our findings are relevant for ordering phenomena in soft matter and alloys.

Binary Colloidal Nanoparticle Concentration Gradients in a Centrifugal Field at High Concentration

Binary colloidal nanoparticles have been found to form different types of crystalline phases at varied radial positions in a centrifugal field by Chen et al. ( ACS Nano 2015, 9, 6944-50). The variety of binary phase behaviors resulted from the two different nanoparticle concentration gradients, but to date, the gradients can only be empirically controlled. For the first time, we are able to measure, fit, and simulate binary hard-sphere colloidal nanoparticle concentration gradients at high particle concentrations up to 30 vol %, which enables tailor-made gradients in a centrifugal field. By this means, a continuous range of binary particle concentration ratios can be accessed in one single experiment to obtain an extended phase diagram. By dispersing two differently sized silica nanoparticles labeled with two different fluorescence dyes in a refractive index matching solvent, we can use a multi-wavelength analytical ultracentrifuge (MWL-AUC) to measure the individual concentration gradient for each particle size in sedimentation-diffusion equilibrium. The influence of the remaining slight turbidity at high concentration can be corrected using the MWL spectra from the AUC data. We also show that the experimental concentration gradients can be fitted using a noninteracting nonideal sedimentation model. By using these fitted parameters, we are able to simulate nanoparticle concentration gradients, which agreed with the subsequent experiments at a high concentration of 10 vol % and thus allowed for the simulation of binary concentration gradients of hard-sphere nanoparticles in preparative ultracentrifuges (PUCs). Finally we demonstrated that by simulating the concentration gradients in PUCs, a continuous and extended binary nanoparticle phase diagram can be obtained by simply studying the structure evolution along the centrifugal field for one single sample instead of a large number of experiments with discrete compositions as in conventional studies.

Recent Advances in Multicomponent Particle Assembly

Particle assembly and co-assembly have been research frontiers in chemistry and material science in the past few decades. To achieve a large variety of intricate structures and functional materials, remarkable progress has been made in particle assembly principles and strategies. Essentially, particle assembly is driven by intrinsic interparticle interactions or the external control. In this article, we focus on binary or ternary particle co-assembly and review the principles and feasible strategies. These advances have led to new disciplines of microfabrication technology and material engineering. Although significant achievement on particle-based structures has been made, it is still challenging to fully develop general and facile strategies to precisely control the one-dimensional (1D) co-assembly. This article reviews the recent development on multicomponent particle co-assembly, which significantly increases structural complexity and functional diversity. In particular, we highlight the advances in the particle co-assembly of well-ordered 1D binary superstructures by liquid soft confinement. Finally, prospective outlook for future trends in this field is proposed.

Formation of Laves phases in buoyancy matched hard sphere suspensions

Colloidal Laves phases (LPs) are promising precursors for photonic materials. Laves phases have not yet been observed to form in experiments on colloidal suspensions of hard spheres (HS), even though they have been reported in computer simulations. LP formation so far has been achieved only for binary mixtures of colloidal charged spheres or ligand-stabilized nano-particles after drying. Using static light scattering, we monitored LP formation and annealing in a binary mixture of buoyant hard sphere approximants (size ratio Γ = 0.77, number or molar fraction of small spheres xS = 0.76) for volume fractions in the fluid-crystal coexistence regions. All samples spontaneously formed MgZn2 type LPs on the time scale of weeks to months via bulk nucleation and growth. Irrespective of the initial suspension volume fractions, the LP volume fraction at coexistence is ΦCOEX = 0.59 which is significantly below the close packing limit ΦMAX = 0.615 and remarkably close to the expectation from simulation. At low volume fractions, crystals anneal to high quality during coarsening which is in line with recent theoretical expectations for the thermodynamic stability of different LP types. At large volume fractions, however, the diffractograms evolve towards a more MgCu2-like appearance which we attribute to the formation of randomly stacked LPs. Such structures are not known from atomic systems.

Local order and crystallization of dense polydisperse hard spheres

Computer simulations give precious insight into the microscopic behavior of supercooled liquids and glasses, but their typical time scales are orders of magnitude shorter than the experimentally relevant ones. We recently closed this gap for a class of models of size polydisperse fluids, which we successfully equilibrate beyond laboratory time scales by means of the swap Monte Carlo algorithm. In this contribution, we study the interplay between compositional and geometric local orders in a model of polydisperse hard spheres equilibrated with this algorithm. Local compositional order has a weak state dependence, while local geometric order associated to icosahedral arrangements grows more markedly but only at very high density. We quantify the correlation lengths and the degree of sphericity associated to icosahedral structures and compare these results to those for the Wahnström Lennard-Jones mixture. Finally, we analyze the structure of very dense samples that partially crystallized following a pattern incompatible with conventional fractionation scenarios. The crystal structure has the symmetry of aluminum diboride and involves a subset of small and large particles with size ratio approximately equal to 0.5.

Dense colloidal mixtures in an external sinusoidal potential

Concentrated binary colloidal mixtures containing particles with a size ratio 1:2.4 were exposed to a periodic potential that was realized using a light field, namely, two crossed laser beams creating a fringe pattern. The arrangement of the particles was recorded using optical microscopy and characterized in terms of the pair distribution function along the minima, the occupation probability perpendicular to the minima, the angular bond distribution, and the average potential energy per particle. The particle arrangement was investigated in dependence of the importance of particle-potential and particle-particle interactions by changing the potential amplitude and particle concentration, respectively. An increase in the potential amplitude leads to a stronger localization, especially of the large particles, but also results in an increasing fraction of small particles being located closer to the potential maxima, which also occurs upon increasing the particle density. Furthermore, increasing the potential amplitude induces a local demixing of the two particle species, whereas an increase in the total packing fraction favors a more homogeneous arrangement.

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.

Hierarchically self-assembled hexagonal honeycomb and kagome superlattices of binary 1D colloids

Synthesis of binary nanoparticle superlattices has attracted attention for a broad spectrum of potential applications. However, this has remained challenging for one-dimensional nanoparticle systems. In this study, we investigate the packing behavior of one-dimensional nanoparticles of different diameters into a hexagonally packed cylindrical micellar system and demonstrate that binary one-dimensional nanoparticle superlattices of two different symmetries can be obtained by tuning particle diameter and mixing ratios. The hexagonal arrays of one-dimensional nanoparticles are embedded in the honeycomb lattices (for AB₂ type) or kagome lattices (for AB₃ type) of micellar cylinders. The maximization of free volume entropy is considered as the main driving force for the formation of superlattices, which is well supported by our theoretical free energy calculations. Our approach provides a route for fabricating binary one-dimensional nanoparticle superlattices and may be applicable for inorganic one-dimensional nanoparticle systems.

Binary mixtures of 1D particles are rarely observed to cooperatively self-assemble into binary superlattices, as the particle types separate into phases. Here, the authors design a system that avoids phase separation, obtaining binary superlattices with different symmetries by simply tuning the particle diameter and mixture composition.

Colloidal alloys with preassembled clusters and spheres

Self-assembly is a powerful approach for constructing colloidal crystals, where spheres, rods or faceted particles can build up a myriad of structures. Nevertheless, many complex or low-coordination architectures, such as diamond, pyrochlore and other sought-after lattices, have eluded self-assembly. Here we introduce a new design principle based on preassembled components of the desired superstructure and programmed nearest-neighbour DNA-mediated interactions, which allows the formation of otherwise unattainable structures. We demonstrate the approach using preassembled colloidal tetrahedra and spheres, obtaining a class of colloidal superstructures, including cubic and tetragonal colloidal crystals, with no known atomic analogues, as well as percolating low-coordination diamond and pyrochlore sublattices never assembled before.

Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials

Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self-assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micrometer colloids and block copolymer assembly. We outline the extensive catalog of superlattices prepared to date using hydrocarbon-capped nanocrystals with spherical, polyhedral, rod, plate, and branched inorganic core shapes, as well as those obtained by mixing combinations thereof. We also provide an overview of structural defects in nanocrystal superlattices. We then explore the unique possibilities offered by leveraging nontraditional surface chemistries and assembly environments to control superlattice structure and produce nonbulk assemblies. We end with a discussion of the unique optical, magnetic, electronic, and catalytic properties of ordered nanocrystal superlattices, and the coming advances required to make use of this new class of solids.

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.