Continuous phase transformation in nanocube assemblies

Engineering Anisotropy into Organized Nanoscale Matter

Programming the organization of discrete building blocks into periodic and quasi-periodic arrays is challenging. Methods for organizing materials are particularly important at the nanoscale, where the time required for organization processes is practically manageable in experiments, and the resulting structures are of interest for applications spanning catalysis, optics, and plasmonics. While the assembly of isotropic nanoscale objects has been extensively studied and described by empirical design rules, recent synthetic advances have allowed anisotropy to be programmed into macroscopic assemblies made from nanoscale building blocks, opening new opportunities to engineer periodic materials and even quasicrystals with unnatural properties. In this review, we define guidelines for leveraging anisotropy of individual building blocks to direct the organization of nanoscale matter. First, the nature and spatial distribution of local interactions are considered and three design rules that guide particle organization are derived. Subsequently, recent examples from the literature are examined in the context of these design rules. Within the discussion of each rule, we delineate the examples according to the dimensionality (0D-3D) of the building blocks. Finally, we use geometric considerations to propose a general inverse design-based construction strategy that will enable the engineering of colloidal crystals with unprecedented structural control.

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.

Effect of Mixed Morphology (Simple Cubic, Face-Centered Cubic, and Body-Centered Cubic)-Based Electrodes on the Electric Double Layer Capacitance of Supercapacitors

Supercapacitors store energy due to the formation of an electric double layer (EDL) at the interface of the electrodes and electrolyte. The present article deals with the finite element study of equilibrium electric double layer capacitance (EDLC) in the mixed morphology electrodes comprising all three fundamental crystal structures, simple cubic (SC), body-centered cubic (BCC), and face-centered cubic morphologies (FCC). Mesoporous-activated carbon forms the electrode in the supercapacitor with (C2H5)4NBF4/propylene carbonate organic electrolyte. Electrochemical interference is clearly demonstrated in the supercapacitors with the formation of the potential bands, as in the case of interference theory due to the increasing packing factor. The effects of electrode thickness varying from a wide range of 50 nm to 0.04 mm on specific EDLC have been discussed in detail. The interfacial geometry of the unit cell in contact with the electrolyte is the most important parameter determining the properties of the EDL. The critical thickness of the electrodes is 1.71 μm in all the morphologies. Polarization increases the interfacial potential and leads to EDL formation. The Stern layer specific capacitance is 167.6 μF cm-2 in all the morphologies. The maximum capacitance is in the decreasing order of interfacial geometry, as FCC > BCC > SC, dependent on the packing factor. The minimum transmittance in all the morphologies is 98.35%, with the constant figure of merit at higher electrode thickness having applications in the chip interconnects. The transient analysis shows that the interfacial current decreases with increasing polarization in the EDL. The capacitance also decreases with the increase of the scan rate.

Molecular Dynamics Simulations of Deformable Viral Capsomers

Most coarse-grained models of individual capsomers associated with viruses employ rigid building blocks that do not exhibit shape adaptation during self-assembly. We develop a coarse-grained general model of viral capsomers that incorporates their stretching and bending energies while retaining many features of the rigid-body models, including an overall trapezoidal shape with attractive interaction sites embedded in the lateral walls to favor icosahedral capsid assembly. Molecular dynamics simulations of deformable capsomers reproduce the rich self-assembly behavior associated with a general T=1 icosahedral virus system in the absence of a genome. Transitions from non-assembled configurations to icosahedral capsids to kinetically-trapped malformed structures are observed as the steric attraction between capsomers is increased. An assembly diagram in the space of capsomer-capsomer steric attraction and capsomer deformability reveals that assembling capsomers of higher deformability into capsids requires increasingly large steric attraction between capsomers. Increasing capsomer deformability can reverse incorrect capsomer-capsomer binding, facilitating transitions from malformed structures to symmetric capsids; however, making capsomers too soft inhibits assembly and yields fluid-like structures.

Solvent controlled 2D structures of bottom-up fabricated nanoparticle superlattices

We demonstrate that oleyl phosphate ligand-stabilized iron oxide nanocubes as building blocks can be assembled into 2D supercrystalline mono- and multilayers on flat YSZ substrates within a few minutes using a simple spin-coating process. As a bottom-up process, the growth takes place in a layer-by-layer mode and therefore by tuning the spin-coating parameters, the exact number of deposited monolayers can be controlled. Furthermore, ex situ scanning electron and atomic force microscopy as well as X-ray reflectivity measurements give evidence that the choice of solvent allows the control of the lattice type of the final supercrystalline monolayers. This observation can be assigned to the different Hansen solubilities of the solvents used for the nanoparticle dispersion because it determines the size and morphology of the ligand shell surrounding the nanoparticle core. Here, by using toluene and chloroform as solvents, it can be controlled whether the resulting monolayers are ordered in a square or hexagonal supercrystalline lattice.

Diffusion-Mediated Nucleation and Growth of fcc and bcc Nanocrystal Superlattices with Designable Assembly of Freestanding 3D Supercrystals

Diffusion-mediated assembly of octahedral PbS nanocrystals (NCs) in a confined antisolvent environment displays a primary burst nucleation and Ostwald ripening growth of rhombic bcc supercrystals, followed by a secondary seed-based nucleation and oriented attachment growth of triangle fcc supercrystals. As the diffusion proceeds from ethanol across a sharp interface into NC-suspended toluene, a burst nucleation of supercrystal seeds occurs, and such supercrystals are quickly developed into rhombic grains that have a bcc structure. At a critical size of 10 μm, an Ostwald ripening event appears to guide the supercrystal growth. Upon grain growth above 30 μm, the fcc supercrystals start a nucleation at two symmetrical tips of individual rhombic crystals. Such fcc supercrystals are developed with a triangle shape, and two triangles are combined with one bcc rhombus in-between to form a butterfly-like bowtie stacking structure. The fcc triangle wings grow larger at a reduction of bcc rhombus cores. As the bcc cores gradually fade, such butterfly-like bowtie crystals aggregate and undergo an oriented attachment process, leading to the formation of freestanding 3D triangle crystals that have a single fcc lattice. Analysis of experimental observations and defined diffusion parameters reveals that fast solvent diffusion and high-NC concentration promote the growth of rhombic bcc supercrystals, while slow solvent diffusion and low-NC concentration accelerate the development of triangle fcc supercrystals. Upon succeeding in designable growth of 3D fcc supercrystals, this study provides designing principles for controlled fabrication of supercrystals with desired superlattices for additional engineering and applications.

Shape control of deformable charge-patterned nanoparticles

Deformable nanoparticles (NPs) offer unprecedented opportunities as dynamic building blocks that can spontaneously reconfigure during assembly in response to environmental cues. Designing reconfigurable materials based on deformable NPs hinges on an understanding of the shapes that can be engineered in these NPs. We solve for the low-energy shapes of charge-patterned deformable NPs by using molecular dynamics-based simulated annealing to minimize a coarse-grained model Hamiltonian characterized with NP elastic and electrostatic energies subject to a volume constraint. We show that deformable spherical NPs of radius 50 nm whose surface is tailored with octahedrally distributed charged patches and double-cap charged patches adapt their shape differently in response to changes in surface charge coverage and ionic strength. We find shape transitions to rounded octahedra, faceted octahedra, faceted bowls, oblate spheroids, spherocylinders, dented beans, and dimpled rounded bowls. We demonstrate that similar shape transitions can be achieved in deformable NPs of different sizes. The effects of counterion condensation on the free-energetic drive associated with the observed deformations are examined via Manning model calculations that utilize simulation-derived estimates for the NP Coulomb energy under salt-free conditions. The charge-pattern-based shape control of deformable NPs has implications for the design of responsive nanocontainers and for assembling reconfigurable materials whose functionality hinges on the shape-shifting properties of their nanoscale building blocks.

Time-Resolved SAXS Study of Polarity- and Surfactant-Controlled Superlattice Transformations of Oleate-Capped Nanocubes During Solvent Removal

Structural transformations and lattice expansion of oleate-capped iron oxide nanocube superlattices are studied by time-resolved small-angle X-ray scattering (SAXS) during solvent removal. The combination of conductor-like screening model for real solvents (COSMO-RS) theory with computational fluid dynamics (CFD) modeling provides information on the solvent composition and polarity during droplet evaporation. Evaporation-driven poor-solvent enrichment in the presence of free oleic acid results in the formation of superlattices with a tilted face-centered cubic (fcc) structure when the polarity reaches its maximum. The tilted fcc lattice expands subsequently during the removal of the poor solvent and eventually transforms to a regular simple cubic (sc) lattice during the final evaporation stage when only free oleic acid remains. Comparative studies show that both the increase in polarity as the poor solvent is enriched and the presence of a sufficient amount of added oleic acid is required to promote the formation of structurally diverse superlattices with large domain sizes.

How fluorescent labels affect the kinetics of the toehold-mediated DNA strand displacement reaction

End modification of the toehold domain or near to it using fluorophore dyes or quenchers can significantly modulate the kinetics of the toehold-mediated strand displacement reaction (TMSDR) by almost two orders of magnitude. The labels at the end of the signal strand impede the TMSDR, while those at the end of the toehold domain of the substrate strand accelerate the TMSDR kinetics.

Designer Nanomaterials through Programmable Assembly

Nanoparticles have long been recognized for their unique properties, leading to exciting potential applications across optics, electronics, magnetism, and catalysis. These specific functions often require a designed organization of particles, which includes the type of order as well as placement and relative orientation of particles of the same or different kinds. DNA nanotechnology offers the ability to introduce highly addressable bonds, tailor particle interactions, and control the geometry of bindings motifs. Here, we discuss how developments in structural DNA nanotechnology have enabled greater control over 1D, 2D, and 3D particle organizations through programmable assembly. This Review focuses on how the use of DNA binding between nanocomponents and DNA structural motifs has progressively allowed the rational formation of prescribed particle organizations. We offer insight into how DNA-based motifs and elements can be further developed to control particle organizations and how particles and DNA can be integrated into nanoscale building blocks, so-called "material voxels", to realize designer nanomaterials with desired functions.

Designing Surface Charge Patterns for Shape Control of Deformable Nanoparticles

Designing reconfigurable materials based on deformable nanoparticles (NPs) hinges on an understanding of the energetically favored shapes these NPs can adopt. Using simulations, we show that hollow, deformable, patchy NPs tailored with surface charge patterns such as Janus patches, stripes, and polyhedrally distributed patches differently adapt their shape in response to changes in patterns and ionic strength, transforming into capsules, hemispheres, variably dimpled bowls, and polyhedra. The links between anisotropy in NP surface charge, shape, and the elastic energy density are discussed.

Self-assembly and entropic effects in pear-shaped colloid systems. I. Shape sensitivity of bilayer phases in colloidal pear-shaped particle systems

The role of particle shape in self-assembly processes is a double-edged sword. On the one hand, particle shape and particle elongation are often considered the most fundamental determinants of soft matter structure formation. On the other hand, structure formation is often highly sensitive to details of shape. Here, we address the question of particle shape sensitivity for the self-assembly of hard pear-shaped particles by studying two models for this system: (a) the pear hard Gaussian overlap (PHGO) and (b) the hard pears of revolution (HPR) model. Hard pear-shaped particles, given by the PHGO model, are known to form a bicontinuous gyroid phase spontaneously. However, this model does not replicate an additive object perfectly and, hence, varies slightly in shape from a "true" pear-shape. Therefore, we investigate in the first part of this series the stability of the gyroid phase in pear-shaped particle systems. We show, based on the HPR phase diagram, that the gyroid phase does not form in pears with such a "true" hard pear-shaped potential. Moreover, we acquire first indications from the HPR and PHGO pair-correlation functions that the formation of the gyroid is probably attributed to the small non-additive properties of the PHGO potential.

Self-assembly of anisotropic nanoparticles into functional superstructures

Self-assembly of colloidal nanoparticles (NPs) into superstructures offers a flexible and promising pathway to manipulate the nanometer-sized particles and thus make full use of their unique properties. This bottom-up strategy builds a bridge between the NP regime and a new class of transformative materials across multiple length scales for technological applications. In this field, anisotropic NPs with size- and shape-dependent physical properties as self-assembly building blocks have long fascinated scientists. Self-assembly of anisotropic NPs not only opens up exciting opportunities to engineer a variety of intriguing and complex superlattice architectures, but also provides access to discover emergent collective properties that stem from their ordered arrangement. Thus, this has stimulated enormous research interests in both fundamental science and technological applications. This present review comprehensively summarizes the latest advances in this area, and highlights their rich packing behaviors from the viewpoint of NP shape. We provide the basics of the experimental techniques to produce NP superstructures and structural characterization tools, and detail the delicate assembled structures. Then the current understanding of the assembly dynamics is discussed with the assistance of in situ studies, followed by emergent collective properties from these NP assemblies. Finally, we end this article with the remaining challenges and outlook, hoping to encourage further research in this field.

Programming colloidal bonding using DNA strand-displacement circuitry

As a strategy for regulating entropy, thermal annealing is a commonly adopted approach for controlling dynamic pathways in colloid assembly. By coupling DNA strand-displacement circuits with DNA-functionalized colloid assembly, we developed an enthalpy-mediated strategy for achieving the same goal while working at a constant temperature. Using this tractable approach allows colloidal bonding to be programmed for synchronization with colloid assembly, thereby realizing the optimal programmability of DNA-functionalized colloids. We applied this strategy to conditionally activate colloid assembly and dynamically switch colloid identities by reconfiguring DNA molecular architectures, thereby achieving orderly structural transformations; leveraging the advantage of room-temperature assembly, we used this method to prepare a lattice of temperature-sensitive proteins and gold nanoparticles. This approach bridges two subfields: dynamic DNA nanotechnology and DNA-functionalized colloid programming.

FCC ↔ BCC Phase Transitions in Convex and Concave Hard Particle Systems

Solid-solid transitions are ubiquitous in nature and are important for technology. Understanding and exploiting transitions are complicated by the fact that multiple transition pathways can exist between small unit cell structures such as face-centered cubic (FCC) and body-centered cubic (BCC). By symmetry, FCC ↔ BCC transitions can occur via a pair of continuous transitions or via a discontinuous, first-order transition. However, how to, or whether it is possible to, select between pathways is unclear. Here, we use particle shape change to induce FCC ↔ BCC transitions in systems where particle valence is malleable. Though some particle shapes can eliminate metastable HCP stacking faults, we find that for both convex and concave particles, transitions are first-order.

Tunable assembly of truncated nanocubes by evaporation-driven poor-solvent enrichment

Self-assembly of nanocrystals is extensively used to generate superlattices with long-range translational order and atomic crystallographic orientation, i.e. mesocrystals, with emergent mesoscale properties, but the predictability and tunability of the assembly methods are poorly understood. Here, we report how mesocrystals produced by poor-solvent enrichment can be tuned by solvent composition, initial nanocrystal concentration, poor-solvent enrichment rate, and excess surfactant. The crystallographic coherence and mesoscopic order within the mesocrystal were characterized using techniques in real and reciprocal spaces, and superlattice growth was followed in real time by small-angle X-ray scattering. We show that formation of highly ordered superlattices is dominated by the evaporation-driven increase of the solvent polarity and particle concentration, and facilitated by excess surfactant. Poor-solvent enrichment is a versatile nanoparticle assembly method that offers a promising production route with high predictability to modulate and maximize the size and morphology of nanocrystal metamaterials.

Versatile methods that can predictably assemble nanocrystals into large, well-ordered superlattices are rare. Here, the authors develop such a method–evaporation-driven poor-solvent enrichment–and rigorously determine the effect of various experimental parameters on the size, morphology, and mesoscopic order of the superlattices, giving the approach high predictive power.

Topological order in densely packed anisotropic colloids

The existence of topological order is frequently associated with strongly coupled quantum matter. Here, we demonstrate the existence of topological phases in classical systems of densely packed, hard, anisotropic polyhedrally shaped colloidal particles. We show that previously reported transitions in dense packings lead to the existence of topologically ordered thermodynamic phases, which we show are stable away from the dense packing limit. Our work expands the library of known topological phases, whose experimental realization could provide new means for constructing plasmonic materials that are robust in the presence of fluctuations.

Binary Assembly of PbS and Au Nanocrystals: Patchy PbS Surface Ligand Coverage Stabilizes the CuAu Superlattice

Self-assembly of two sizes of nearly spherical colloidal nanocrystals (NCs) capped with hydrocarbon surface ligands has been shown to produce more than 20 distinct phases of binary nanocrystal superlattices (BNSLs). Such structural diversity, in striking contrast to binary systems of micron-sized colloidal beads, cannot be rationalized by models assuming entropy-driven crystallization of simple spheres. In this work, we show that the PbS ligand binding equilibrium controls the relative stability of two closely related BNSL structures featuring alternating layers of PbS and Au NCs. At an intermediate size ratio, as-prepared PbS NCs assemble with Au NCs into CuAu BNSLs featuring orientational coherence of PbS NCs across the lattice. Measurement of interparticle separations within CuAu and modeling of the structure reveal that PbS inorganic cores are nearly in contact through (100) NC surfaces in the square tiling of the CuAu basal plane. On the other hand, AlB₂ BNSLs with PbS NCs packed in random orientations were found to be the dominant self-assembly product when the same binary NC solution was evaporated in the presence of added oleic acid (OAH). Solution nuclear magnetic resonance titration experiments confirmed that added OAH binds to PbS NCs, implicating ligand surface coverage as an important factor influencing the relative stability of CuAu and AlB₂ BNSLs at the experimental size ratio. From these results, we conclude that as-prepared PbS NCs feature sparsely covered (100) surfaces and thus effectively flat patches along NC x-, y-, and z-directions. Such anisotropic PbS-PbS interactions can be efficiently screened by restoring effectively spherical NC shape via addition of OAH to the binary assembly solution. Our findings underscore the important contribution of NC surfaces to superlattice phase stability and offer a strategy for targeted BNSL assembly.

Unusual packing of soft-shelled nanocubes

Space-filling generally governs hard particle packing and the resulting phases and interparticle orientations. Contrastingly, hard-shaped nanoparticles with grafted soft-ligands pack differently since the energetically interacting soft-shell is amenable to nanoscale sculpturing. While the interplay between the shape and soft-shell can lead to unforeseen packing effects, little is known about the underlying physics. Here, using electron microscopy and small-angle x-ray scattering, we demonstrate that nanoscale cubes with soft, grafted DNA shells exhibit remarkable packing, distinguished by orientational symmetry breaking of cubes relative to the unit cell vectors. This zigzag arrangement occurs in flat body-centered tetragonal and body-centered cubic phases. We ascribe this unique arrangement to the interplay between shape and a spatially anisotropic shell resulting from preferential grafting of ligands to regions of high curvature. These observations reveal the decisive role played by shell-modulated anisotropy in nanoscale packing and suggest a plethora of new spatial organizations for molecularly decorated shaped nanoparticles.

Manifestation of dipole-induced disorder in self-assembly of ferroelectric and ferromagnetic nanocubes

The colloidal processing of nearly monodisperse and highly crystalline single-domain ferroelectric or ferromagnetic nanocubes is a promising route to produce superlattice structures for integration into next-generation devices, whereas controlling the local behaviour of nanocrystals is imperative for fabricating highly-ordered assemblies. The current picture of nanoscale polarization in individual nanocrystals suggests a potential presence of a significant dipolar interaction, but its role in the condensation of nanocubes is unknown. We simulate the self-assembly of colloidal dipolar nanocubes under osmotic compression and perform the microstructural characterization of their densified ensembles. Our results indicate that the long-range positional and orientational correlations of perovskite nanocubes are highly sensitive to the presence of dipoles.

Understanding Fe3O4 Nanocube Assembly with Reconstruction of a Consistent Superlattice Phase Diagram

Nanocube (NC) assemblies display complex superlattice behaviors, which require a systematic understanding of their nucleation and growth as well transformation toward construction of a consistent superlattice phase diagram. This work made use of Fe₃O₄ NCs with controlled environments, and assembled NCs into three-dimensional (3D) superlattices of simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc), acute and obtuse rhombohedral (rh) polymorphs, and 2D superlattices of square and hexagon. Controlled experiments and computations of in situ and static small-angle X-ray scattering (SAXS) as well as electron microscopic imaging revealed that the fcc and bcc polymorphs preferred a primary nucleation at the early stage of NC assembly, which started from the high packing planes of fcc(111) and bcc(110), respectively, in both 3D and 2D cases. Upon continuous growth of superlattice grain (or domain), a confinement stress appeared and distorted fcc and bcc into acute and obtuse rh polymorphs, respectively. The variable magnitudes of competitive interactions between configurational and directional entropy determine the primary superlattice polymorph of either fcc or bcc, while emergent enhancement of confinement effect on enlarged grains attributes to late developed superlattice transformations. Differently, the formation of a sc polymorph requires a strong driving force that either emerges simultaneously or is applied externally so that one easy case of the sc formation can be achieved in 2D thin films. Unlike the traditional Bath deformation pathway that involves an intermediate body-centered tetragonal lattice, the observed superlattice transformations in NC assembly underwent a simple rhombohedral distortion, which was driven by a growth-induced in-plane compressive stress. Establishment of a consistent phase diagram of NC-based superlattices and reconstruction of their assembly pathways provide critical insight and a solid base for controlled design and scalable fabrication of nanocube-based functional materials with desired superlattices and collective properties for real-world applications.

Computer simulation study on the self-assembly of tethered nanoparticles with tunable shapes

We built a tethered nanoparticle (TNP) model that is composed of a nanoparticle with a hydrophobic tethered polymer chain. The shape of the nanoparticle can be tuned from a pure rigid cube to a soft sphere, mimicking the increase of grafting density on the nanocube surfaces. With this model, we study the self-assembly of TNPs in dilute solution using a dissipative particle dynamics simulation technique, and especially focus on the influence of particle shape, tethered chain length, and grafting density on the self-assembly structures. Some intriguing aggregates such as spherical micelles, pearl-necklace-like structures, cubic columnar structures, handshake structures, core–shell–corona micelles, and four-patch micelles have been observed when varying the interactions between cubes and solvents and the lengths of tethered chain. Modifying the nanocube surface with some hydrophilic grafted chains helps the TNPs form small micelles. Increased steric repulsion due to chain overlapping at larger grafting densities results in shape transformation of the nanoparticle from a rigid cube to a soft sphere. In these cases, the self-assembled structures are characterized by the packing of nanoparticles on the micelle surface, and the typical packing mode turns from rectangular (typical for cubes) to hexagonal (typical for spheres).

The self-assembled structures are characterized by the packing of nanoparticles on the micelle surface, and the typical packing mode turns from rectangular (typical for cubes) to hexagonal (typical for spheres).

Understanding the role of co-surfactants in microemulsions on the growth of copper oxalate using SAXS

SAXS study for evaluating the effect of variation of co-surfactants on the shape of reverse micelles and growth of copper oxalate nanostructures.

Intermediate crystalline structures of colloids in shape space

We computationally study the thermodynamic assembly of more than 40 000 hard, convex polyhedra belonging to three families of shapes associated with the triangle groups 323, 423, and 523. Each family is defined by vertex and/or edge truncation of symmetric polyhedra with equal edge length, producing shapes for which the majority are intermediates of more symmetric polyhedra found among the Platonic, Archimedean, and Catalan solids. In addition to the complex crystals cI16 lithium, BC8 silicon, γ-brass, β-manganese, and a dodecagonal quasicrystal, we find that most intermediate shapes assemble distorted variants of four basic cubic crystals: face-centered cubic, body-centered cubic, simple cubic, and diamond. To quantify the degree of distortion, we developed an algorithm that extracts lattice vectors from particle positions and then evaluates closeness to the four reference cubic crystals. This analysis allows us to group together in shape space related intermediate structures that would otherwise be placed in different lattice systems had we followed the lattice systems' strict definitions for angles and lengths of lattice vectors. The resulting landscapes show, as a function of shape, regions where ordered structures assemble, what is assembled and at what density, locations of transitions between regions of ordered structures, and regions of disorder. Our results provide a guide to self-assembling a host of related colloidal crystals through systematic design, by careful tweaking of the particle shape.

Synthesis of Hollow Silica Nanocubes with Tuneable Size and Shape, Suitable for Light Scattering Studies

We present a preparation method for hollow silica nanocubes with tuneable size and shape in the range required for light scattering studies. Cuprous oxide nanocubes are prepared by a water-assisted polyol method. By adjusting the water content, the size of the nanocubes can be tuned in the range of 40–120 nm. These cubes function as a shape template in the subsequent coating with Stöber silica, resulting in core-shell nanocubes. Dissolving the core with nitric acid results in hollow silica nanocubes with sizes ranging from 80–120 nm and cubicity shape parameters between 3 and 6.5.

Controlling the symmetry of supercrystals formed by plasmonic core-shell nanorods with tunable cross-section

Tailoring the crystal structure of plasmonic nanoparticle superlattices is a crucial step in controlling the collective physical response of these nanostructured materials. Various strategies can achieve this goal for isotropic nanoparticles, but few of them have been successful with anisotropic building blocks. In this work we use hybrid particles, consisting of gold nanorods encased in silver shells with a thickness that can be controlled from a few atomic layers to tens of nanometers. The particles were synthesized, characterized by a combination of techniques and assembled into supercrystals with a smectic B configuration, i.e. a 2D in-plane periodic order without interplane lateral correlations. We showed that, by tuning the silver shell thickness, the in-plane order can be changed from hexagonal to square and the lattice parameters can be adjusted. The spatial distribution of the supercrystal was systematically studied by optical and electron microscopy and by small-angle X-ray scattering. Through optimized surface chemistry, we obtain homogeneous, millimeter-size films of standing nanoparticles, which hold promise for all applications using plasmon-enhanced technologies.

Tools and Functions of Reconfigurable Colloidal Assembly

We review work in reconfigurable colloidal assembly, a field in which rapid, back-and-forth transitions between the equilibrium states of colloidal self-assembly are accomplished by dynamic manipulation of the size, shape, and interaction potential of colloids, as well as the magnitude and direction of the fields applied to them. It is distinguished from the study of colloidal phase transitions by the centrality of thermodynamic variables and colloidal properties that are time switchable; by the applicability of these changes to generate transitions in assembled colloids that may be spatially localized; and by its incorporation of the effects of generalized potentials due to, for example, applied electric and magnetic fields. By drawing upon current progress in the field, we propose a matrix classification of reconfigurable colloidal systems based on the tool used and function performed by reconfiguration. The classification distinguishes between the multiple means by which reconfigurable assembly can be accomplished (i.e., the tools of reconfiguration) and the different kinds of structural transitions that can be achieved by it (i.e., the functions of reconfiguration). In the first case, the tools of reconfiguration can be broadly classed as (i) those that control the colloidal contribution to the system entropy-as through volumetric and/or shape changes of the particles; (ii) those that control the internal energy of the colloids-as through manipulation of colloidal interaction potentials; and (iii) those that control the spatially resolved potential energy that is imposed on the colloids-as through the introduction of field-induced phoretic mechanisms that yield colloidal displacement and accumulation. In the second case, the functions of reconfiguration include reversible: (i) transformation between different phases-including fluid, cluster, gel, and crystal structures; (ii) manipulation of the spacing between colloids in crystals and clusters; and (iii) translation, rotation, or shape-change of finite-size objects self-assembled from colloids. With this classification in hand, we correlate the current limits on the spatiotemporal scales for reconfigurable colloidal assembly and identify a set of future research challenges.

Colloidal Assembly Approaches to Micro/Nanostructures of Complex Morphologies

The ability to programmatically assemble colloidal micro/nanostructures into highly ordered superstructures is of great importance in both fundamental studies and practical applications. In addition to the sophisticated manipulation of the short-range and long-range interactions imposed on the colloidal building blocks, the intrinsic shape elements including face, edge, corner, concave, convex, and curvature also play very important roles in solving the "jigsaw puzzle" of the superstructures. Here, the recent progress in the development of colloidal assembly strategies for the formation of complex superstructures is reviewed, with a primary focus on the unique effects of the morphology of the building blocks to the assembly processes and the final structures. Overall, this Review aims to shed light on the fundamental understanding of the colloidal behaviors of complex micro/nanostructures and promote the continued development of effective strategies for the creation of functional materials with complex compositions and morphologies.

Nonisotropic Self-Assembly of Nanoparticles: From Compact Packing to Functional Aggregates

Quantum strongly correlated systems that exhibit interesting features in condensed matter physics often need an unachievable temperature or pressure range in classical materials. One solution is to introduce a scaling factor, namely, the lattice parameter. Synthetic heterostructures named superlattices or supracrystals are synthesized by the assembling of colloidal atoms. These include semiconductors, metals, and insulators for the exploitation of their unique properties. Most of them are currently limited to dense packing. However, some of desired properties need to adjust the colloidal atoms neighboring number. Here, the current state of research in nondense packing is summarized, discussing the benefits, outlining possible scenarios and methodologies, describing examples reported in the literature, briefly discussing the challenges, and offering preliminary conclusions. Penetrating such new and intriguing research fields demands a multidisciplinary approach accounting for the coupling of statistic physics, solid state and quantum physics, chemistry, computational science, and mathematics. Standard interactions between colloidal atoms and emerging fields, such as the use of Casimir forces, are reported. In particular, the focus is on the novelty of patchy colloidal atoms to meet this challenge.

Interplay between spherical confinement and particle shape on the self-assembly of rounded cubes

Self-assembly of nanoparticles (NPs) inside drying emulsion droplets provides a general strategy for hierarchical structuring of matter at different length scales. The local orientation of neighboring crystalline NPs can be crucial to optimize for instance the optical and electronic properties of the self-assembled superstructures. By integrating experiments and computer simulations, we demonstrate that the orientational correlations of cubic NPs inside drying emulsion droplets are significantly determined by their flat faces. We analyze the rich interplay of positional and orientational order as the particle shape changes from a sharp cube to a rounded cube. Sharp cubes strongly align to form simple-cubic superstructures whereas rounded cubes assemble into icosahedral clusters with additionally strong local orientational correlations. This demonstrates that the interplay between packing, confinement and shape can be utilized to develop new materials with novel properties.

Colloidal nanoparticles self-assembled under spherical confinement can form a rich variety of structures. Here, the authors study the self-assembly of sharp and rounded nanocubes under such confinement, revealing the influence of particle and face geometry on positional and orientational behavior.

Structural Investigation of Cesium Lead Halide Perovskites for High-Efficiency Quantum Dot Light-Emitting Diodes

We have investigated the effect of reaction temperature of hot-injection method on the structural properties of CsPbX₃ (X: Br, I, Cl) perovskite nanocrystals (NCs) using small- and wide-angle X-ray scattering. It is confirmed that the size of the NCs decreased as the reaction temperature decreased, resulting in stronger quantum confinement. The cubic-phase perovskite NCs formed despite the fact that the reaction temperatures increased from 140 to 180 °C; however, monodispersive NC cubes that are required for densely packing self-assembly film were formed only at lower temperatures. From the X-ray scattering measurements, the spin-coated film from more monodispersive perovskite nanocubes synthesized at lower temperatures resulted in more preferred orientation. This dense-packing perovskite film with preferred orientation yielded efficient light-emitting diode (LED) performance. Thus the dense-packing structure of NC assemblies formed after spin-coating should be considered for high-efficient LEDs based on perovskite quantum dots in addition to quantum confinement effect of the quantum dots.

Shape-driven solid-solid transitions in colloids

Solid-solid phase transitions are the most ubiquitous in nature, and many technologies rely on them. However, studying them in detail is difficult because of the extreme conditions (high pressure/temperature) under which many such transitions occur and the high-resolution equipment needed to capture the intermediate states of the transformations. These difficulties mean that basic questions remain unanswered, such as whether so-called diffusionless solid-solid transitions, which have only local particle rearrangement, require thermal activation. Here, we introduce a family of minimal model systems that exhibits solid-solid phase transitions that are driven by changes in the shape of colloidal particles. By using particle shape as the control variable, we entropically reshape the coordination polyhedra of the particles in the system, a change that occurs indirectly in atomic solid-solid phase transitions via changes in temperature, pressure, or density. We carry out a detailed investigation of the thermodynamics of a series of isochoric, diffusionless solid-solid phase transitions within a single shape family and find both transitions that require thermal activation or are "discontinuous" and transitions that occur without thermal activation or are "continuous." In the discontinuous case, we find that sufficiently large shape changes can drive reconfiguration on timescales comparable with those for self-assembly and without an intermediate fluid phase, and in the continuous case, solid-solid reconfiguration happens on shorter timescales than self-assembly, providing guidance for developing means of generating reconfigurable colloidal materials.

Observation of solid-solid transitions in 3D crystals of colloidal superballs

Self-organization in anisotropic colloidal suspensions leads to a fascinating range of crystal and liquid crystal phases induced by shape alone. Simulations predict the phase behaviour of a plethora of shapes while experimental realization often lags behind. Here, we present the experimental phase behaviour of superball particles with a shape in between that of a sphere and a cube. In particular, we observe the formation of a plastic crystal phase with translational order and orientational disorder, and the subsequent transformation into rhombohedral crystals. Moreover, we uncover that the phase behaviour is richer than predicted, as we find two distinct rhombohedral crystals with different stacking variants, namely hollow-site and bridge-site stacking. In addition, for slightly softer interactions we observe a solid-solid transition between the two. Our investigation brings us one step closer to ultimately controlling the experimental self-assembly of superballs into functional materials, such as photonic crystals.

Maximally dense random packings of cubes and cuboids via a novel inverse packing method

The packings of cubes and cuboids (i.e., "elongated" or "compressed" cubes) are ubiquitous in nature. The high symmetry and space-tiling nature of such particles make them easily packable in dense configurations with a high degree of orientational and translational order. In this paper, we devise a novel inverse packing method that enables one to generate dense hard-particle packings with a controllable degree of disorder/order quantified by predefined order metrics via stochastic Monte Carlo optimizations. We employ the inverse packing method to generate and investigate the maximally dense random packings (MDRPs) of hard cubes and cuboids with aspect ratio α, in which a series of newly introduced normalized local cubatic order parameters sensitive to the onset of any spatial order in packings of cubes and cuboids is minimized. The density of the MDRP of cubes is φ ≈ 0.637, which increases as the shape deviates from the cube limit (α = 1) and reaches the maximal values for cuboids with aspect ratios α = 0.7 or 1.5. These special α values associated with local density extrema are almost identical for those associated with the random packings of spherocylinders, spheroids and superellipsoids, suggesting a universal influence of shape elongation on random packing density. Our inverse packing method can be readily utilized to study the MDRPs of other hard particles and the normalized local cubatic order parameter introduced here is applicable to other shaped particles characterized by three principal axes.

Entropy-Driven Pt3Co Nanocube Assembles and Thermally Mediated Electrical Conductivity with Anisotropic Variation of the Rhombohedral Superlattice

Understanding the shape-dependent superlattices and resultant anisotropies of both structure and property allows for rational design of materials processing and engineering to fabricate transformative materials with useful properties for applications. This work shows the structural evolution from square lattice of two-dimensional (2D) thin film to rhombic lattice of large three-dimensional (3D) assembles of Pt₃Co nanocubes (NCs). Synchrotron-based X-ray supercrystallography determines the superlattice of large 3D supercrystal into an obtuse rhombohedral (Rh) symmetry, which holds a long-range coherence of both NC translation and atomic crystallographic orientation. The Rh superlattice has a trigonal cell angle of 104°, and the constitute NCs orient their atomic Pt₃Co(111) planes to the superlattice Rh[111] direction. The temperature-dependent in situ small and wide-angle X-ray scattering (SAXS/WAXS) measurements reveal a thermally induced superlattice contraction of supercrystal, which maintains translational ordering but slightly develops orientational disordering. The observed increases of both the packing density and the rotation magnitude of NCs indicate a rational compromise between configurational and rotational entropies of NCs. The resultant minimization of the total free energy is responsible for the formation and stability of the obtuse Rh superlattice. The temperature-dependent in situ measurements of SAXS and electrical resistance reveal that, in conjunction with the thermally induced sharp contraction of superlattice at 160 °C, the supercrystal becomes measurable of electrical resistance, which was followed by a temperature-dependent linear increase. Upon rapid annealing from 250 °C, the supercrystal remains almost constant in both structure and electrical resistance. The heating-enabled electrical conductivity of the supercrystal at high temperature implies the formation of a NC-interconnected architecture. The experiments and overall analysis provide solid evidence and essential information for the use of shape-dependent structural anisotropies of supercrystal to create nanobased novel architecture with desired properties.

Exploring the zone of anisotropy and broken symmetries in DNA-mediated nanoparticle crystallization

In this work, we present a joint experimental and molecular dynamics simulations effort to understand and map the crystallization behavior of polyhedral nanoparticles assembled via the interaction of DNA surface ligands. In these systems, we systematically investigated the interplay between the effects of particle core (via the particle symmetry and particle size) and ligands (via the ligand length) on crystallization behavior. This investigation revealed rich phase diagrams, previously unobserved phase transitions in polyhedral crystallization behavior, and an unexpected symmetry breaking in the ligand distribution on a particle surface. To understand these results, we introduce the concept of a zone of anisotropy, or the portion of the phase space where the anisotropy of the particle is preserved in the crystallization behavior. Through comparison of the zone of anisotropy for each particle we develop a foundational roadmap to guide future investigations.

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.

Lattice engineering through nanoparticle-DNA frameworks

Advances in self-assembly over the past decade have demonstrated that nano- and microscale particles can be organized into a large diversity of ordered three-dimensional (3D) lattices. However, the ability to generate different desired lattice types from the same set of particles remains challenging. Here, we show that nanoparticles can be assembled into crystalline and open 3D frameworks by connecting them through designed DNA-based polyhedral frames. The geometrical shapes of the frames, combined with the DNA-assisted binding properties of their vertices, facilitate the well-defined topological connections between particles in accordance with frame geometry. With this strategy, different crystallographic lattices using the same particles can be assembled by introduction of the corresponding DNA polyhedral frames. This approach should facilitate the rational assembly of nanoscale lattices through the design of the unit cell.

Small Angle X-ray Scattering for Nanoparticle Research

X-ray scattering is a structural characterization tool that has impacted diverse fields of study. It is unique in its ability to examine materials in real time and under realistic sample environments, enabling researchers to understand morphology at nanometer and angstrom length scales using complementary small and wide angle X-ray scattering (SAXS, WAXS), respectively. Herein, we focus on the use of SAXS to examine nanoscale particulate systems. We provide a theoretical foundation for X-ray scattering, considering both form factor and structure factor, as well as the use of correlation functions, which may be used to determine a particle's size, size distribution, shape, and organization into hierarchical structures. The theory is expanded upon with contemporary use cases. Both transmission and reflection (grazing incidence) geometries are addressed, as well as the combination of SAXS with other X-ray and non-X-ray characterization tools. We conclude with an examination of several key areas of research where X-ray scattering has played a pivotal role, including in situ nanoparticle synthesis, nanoparticle assembly, and operando studies of catalysts and energy storage materials. Throughout this review we highlight the unique capabilities of X-ray scattering for structural characterization of materials in their native environment.

Self-Assembly of Shaped Nanoparticles into Free-Standing 2D and 3D Superlattices

This article describes a novel supramolecular assembly-mediated strategy for the organization of Au nanoparticles (NPs) with different shapes (e.g., spheres, rods, and cubes) into large-area, free-standing 2D and 3D superlattices. This robust approach involves two major steps: (i) the organization of polymer-tethered NPs within the assemblies of supramolecular comblike block copolymers (CBCPs), and (ii) the disassembly of the assembled CBCP structures to produce free-standing NP superlattices. It is demonstrated that the crystal structures and lattice constants of the superlattices can be readily tailored by varying the molecular weight of tethered polymers, the volume fraction of NPs, and the matrix of CBCPs. This template-free approach may open a new avenue for the assembly of NPs into 2D and 3D structures with a wide range of potential applications.

Switchable self-assembly of Prussian blue analogs nano-tiles triggered by salt stimulus

We showed fully reversible, ionic strength controlled self-assembly of Prussian blue analogues nano-tiles into large superlattice structures.

A versatile method to prepare size- and shape-controlled copper nanocubes using an aqueous phase green synthesis

A versatile, simple, and environmentally friendly method of preparing copper nanocubes with controlled morphology in aqueous solution at room temperature is demonstrated to make Cu nanocubes with sizes of 100 ± 35 nm.

Design strategies for self-assembly of discrete targets

Both biological and artificial self-assembly processes can take place by a range of different schemes, from the successive addition of identical building blocks to hierarchical sequences of intermediates, all the way to the fully addressable limit in which each component is unique. In this paper, we introduce an idealized model of cubic particles with patterned faces that allows self-assembly strategies to be compared and tested. We consider a simple octameric target, starting with the minimal requirements for successful self-assembly and comparing the benefits and limitations of more sophisticated hierarchical and addressable schemes. Simulations are performed using a hybrid dynamical Monte Carlo protocol that allows self-assembling clusters to rearrange internally while still providing Stokes-Einstein-like diffusion of aggregates of different sizes. Our simulations explicitly capture the thermodynamic, dynamic, and steric challenges typically faced by self-assembly processes, including competition between multiple partially completed structures. Self-assembly pathways are extracted from the simulation trajectories by a fully extendable scheme for identifying structural fragments, which are then assembled into history diagrams for successfully completed target structures. For the simple target, a one-component assembly scheme is most efficient and robust overall, but hierarchical and addressable strategies can have an advantage under some conditions if high yield is a priority.

Digital Alchemy for Materials Design: Colloids and Beyond

Starting with the early alchemists, a holy grail of science has been to make desired materials by modifying the attributes of basic building blocks. Building blocks that show promise for assembling new complex materials can be synthesized at the nanoscale with attributes that would astonish the ancient alchemists in their versatility. However, this versatility means that making a direct connection between building-block attributes and bulk structure is both necessary for rationally engineering materials and difficult because building block attributes can be altered in many ways. Here we show how to exploit the malleability of the valence of colloidal nanoparticle "elements" to directly and quantitatively link building-block attributes to bulk structure through a statistical thermodynamic framework we term "digital alchemy". We use this framework to optimize building blocks for a given target structure and to determine which building-block attributes are most important to control for self-assembly, through a set of novel thermodynamic response functions, moduli, and susceptibilities. We thereby establish direct links between the attributes of colloidal building blocks and the bulk structures they form. Moreover, our results give concrete solutions to the more general conceptual challenge of optimizing emergent behaviors in nature and can be applied to other types of matter. As examples, we apply digital alchemy to systems of truncated tetrahedra, rhombic dodecahedra, and isotropically interacting spheres that self-assemble diamond, fcc, and icosahedral quasicrystal structures, respectively. Although our focus is on colloidal systems, our methods generalize to any building blocks with adjustable interactions.

Controlling Chirality of Entropic Crystals

Colloidal crystal structures with complexity and diversity rivaling atomic and molecular crystals have been predicted and obtained for hard particles by entropy maximization. However, thus far homochiral colloidal crystals, which are candidates for photonic metamaterials, are absent. Using Monte Carlo simulations we show that chiral polyhedra exhibiting weak directional entropic forces self-assemble either an achiral crystal or a chiral crystal with limited control over the crystal handedness. Building blocks with stronger faceting exhibit higher selectivity and assemble a chiral crystal with handedness uniquely determined by the particle chirality. Tuning the strength of directional entropic forces by means of particle rounding or the use of depletants allows for reconfiguration between achiral and homochiral crystals. We rationalize our findings by quantifying the chirality strength of each particle, both from particle geometry and potential of mean force and torque diagrams.