Interface-induced nucleation, orientational alignment and symmetry transformations in nanocube superlattices

Defect Self-Elimination in Nanocube Superlattices Through the Interplay of Brownian, van der Waals, and Ligand-Based Forces and Torques

Understanding defect healing is necessary to control the electronic and optoelectronic performance of devices based on nanoparticle (NP) superlattices. However, a key challenge remains to understand how NP interactions and the resulting dynamics are coupled to defect self-elimination during assembly processes. Additional degrees of freedom that account for the anisotropic nature of NPs associated with rotational dynamics and torques further complicate the challenge. Here, we investigate nanocube (NC) superlattices by employing liquid-phase transmission electron microscopy, continuum theory, and molecular dynamics simulations. Our detailed analyses reveal that interparticle forces and torques due to ligand interactions dominate those from Brownian motions and van der Waals interactions. More importantly, NC translations and rotations induced by unbalanced forces and torques are transmitted to neighboring NCs, prompting "chain interactions" in a two-dimensional (2D) network and expediting self-elimination. The mechanistic understanding will further enable the design and fabrication of defect-free superlattices as well as those with tailored defects via assembly of anisotropic particles.

Molecular Dynamics Simulation Study on Self-Assembly of Polymer-Grafted Nanocrystals: From Isotropic Cores to Anisotropic Cores

The self-assembly of polymer-grafted nanocrystals (PGNCs) is an important method to manufacture novel nanomaterials. Herein, we focus on the self-assembly of three types of PGNCs with differently shaped cores including sphere, octahedron, and cube by molecular dynamics simulation. By characterizing the positional and orientational order of the assembled superlattices, we construct the phase diagrams as a function of the grafting density and polymer chain length. For PGNCs with spherical cores, we observe the transition from the FCC phase to the BCC phase due to the packing entropy of the ligand polymer chains. For PGNCs with anisotropic cores, the close-packed FCC phase is replaced by the C-BCC phase (octahedral cores) or the C-triclinic phase (cubic cores) due to the directional entropy of core shape. We also study the assembly dynamics by tracking the time evolution of the positional and orientational order. We elucidate the relationship of grafting density and polymer chain length to the packing entropy and directional entropy and reveal their important effects on assembled structures. In general, our simulation results provide useful guidelines for the programmable assembly of PGNCs.

Synthesis of Zwitterionic CsPbBr3 Nanocrystals with Controlled Anisotropy using Surface-Selective Ligand Pairs

Mechanistic studies of the morphology of lead halide perovskite nanocrystals (LHP-NCs) are hampered by a lack of generalizable suitable synthetic strategies and ligand systems. Here, the synthesis of zwitterionic CsPbBr3 NCs is presented with controlled anisotropy using a proposed "surface-selective ligand pairs" strategy. Such a strategy provides a platform to systematically study the binding affinity of capping ligand pairs and the resulting LHP morphologies. By using zwitterionic ligands (ZwL) with varying structures, majority ZwL-capped LHP NCs with controlled morphology are obtained, including anisotropic nanoplatelets and nanorods, for the first time. Combining experiments with density functional theory calculations, factors that govern the ligand binding on the different surface facets of LHP-NCs are revealed, including the steric bulkiness of the ligand, the number of binding sites, and the charge distance between binding moieties. This study provides guidance for the further exploration of anisotropic LHP-NCs.

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.

Structural Diversity in Dimension-Controlled Assemblies of Tetrahedral Gold Nanocrystals

Polyhedron packings have fascinated humans for centuries and continue to inspire scientists of modern disciplines. Despite extensive computer simulations and a handful of experimental investigations, understanding of the phase behaviors of synthetic tetrahedra has remained fragmentary largely due to the lack of tetrahedral building blocks with tunable size and versatile surface chemistry. Here, we report the remarkable richness of and complexity in dimension-controlled assemblies of gold nanotetrahedra. By tailoring nanocrystal interactions from long-range repulsive to hard-particle-like or to systems with short-ranged directional attractions through control of surface ligands and assembly conditions, nearly a dozen of two-dimensional and three-dimensional superstructures including the cubic diamond and hexagonal diamond polymorphs are selectively assembled. We further demonstrate multiply twinned icosahedral supracrystals by drying aqueous gold nanotetrahedra on a hydrophobic substrate. This study expands the toolbox of the superstructure by design using tetrahedral building blocks and could spur future computational and experimental work on self-assembly and phase behavior of anisotropic colloidal particles with tunable interactions.

Observation of an Orientational Glass in a Superlattice of Elliptically-Faceted CdSe Nanocrystals

Extensive prior work has shown that colloidal inorganic nanocrystals coated with organic ligand shells can behave as artificial atoms and, as such, form superlattices with different crystal structures and packing densities. Although ordered superlattices present a high degree of long-range positional order, the relative crystallographic orientation of the inorganic nanocrystals with respect to each other tends to be random. Recent works have shown that superlattices can achieve orientational alignment through combinations of nanocrystal faceting and ligand modification, as well as selective metal particle attachment to particular facets. These studies have focused on the assembly of high-symmetry nanocrystals, such as cubes and cuboctahedra. Here, we study the assembly of elliptically faceted CdSe/CdS core/shell nanocrystals with one distinctive crystallographic orientation along the major elliptical axis. We show that the nanocrystals form an unexpectedly well-ordered translational superlattice, with a degree of order comparable to that achieved with higher-symmetry nanocrystals. Additionally, we show that, due to the particles' faceted shape, the superlattice is characterized by an orientational glass phase in which only certain orientations are possible due to entropically frustrated crystallization. In this phase, the nanocrystals do not exhibit a local orientational ordering but rather have distinct orientations that emerge at different locations within the same domain. The distinct orientations are a result of a facet-to-facet lock-in mechanism that occurs during the self-assembly process. These facet-to-facet alignments force the nanocrystals to tilt on different lattice planes forming different projections that we termed apparent polydispersity. Our experimental realization of an orientational glass phase for multifaceted semiconducting nanocrystals can be used to investigate how this phase is formed and how it can be utilized for potential optical, electrical, and thermal transport applications.

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.

Using small-angle scattering to guide functional magnetic nanoparticle design

Magnetic nanoparticles offer unique potential for various technological, biomedical, or environmental applications thanks to the size-, shape- and material-dependent tunability of their magnetic properties. To optimize particles for a specific application, it is crucial to interrelate their performance with their structural and magnetic properties. This review presents the advantages of small-angle X-ray and neutron scattering techniques for achieving a detailed multiscale characterization of magnetic nanoparticles and their ensembles in a mesoscopic size range from 1 to a few hundred nanometers with nanometer resolution. Both X-rays and neutrons allow the ensemble-averaged determination of structural properties, such as particle morphology or particle arrangement in multilayers and 3D assemblies. Additionally, the magnetic scattering contributions enable retrieving the internal magnetization profile of the nanoparticles as well as the inter-particle moment correlations caused by interactions within dense assemblies. Most measurements are used to determine the time-averaged ensemble properties, in addition advanced small-angle scattering techniques exist that allow accessing particle and spin dynamics on various timescales. In this review, we focus on conventional small-angle X-ray and neutron scattering (SAXS and SANS), X-ray and neutron reflectometry, gracing-incidence SAXS and SANS, X-ray resonant magnetic scattering, and neutron spin-echo spectroscopy techniques. For each technique, we provide a general overview, present the latest scientific results, and discuss its strengths as well as sample requirements. Finally, we give our perspectives on how future small-angle scattering experiments, especially in combination with micromagnetic simulations, could help to optimize the performance of magnetic nanoparticles for specific applications.

Oriented Attachment: From Natural Crystal Growth to a Materials Engineering Tool

ConspectusIntuitively, chemists see crystals grow atom-by-atom or molecule-by-molecule, very much like a mason builds a wall, brick by brick. It is much more difficult to grasp that small crystals can meet each other in a liquid or at an interface, start to align their crystal lattices and then grow together to form one single crystal. In analogy, that looks more like prefab building. Yet, this is what happens in many occasions and can, with reason, be considered as an alternative mechanism of crystal growth. Oriented attachment is the process in which crystalline colloidal particles align their atomic lattices and grow together into a single crystal. Hence, two aligned crystals become one larger crystal by epitaxy of two specific facets, one of each crystal. If we simply consider the system of two crystals, the unifying attachment reduces the surface energy and results in an overall lower (free) energy of the system. Oriented attachment often occurs with massive numbers of crystals dispersed in a liquid phase, a sol or crystal suspension. In that case, oriented attachment lowers the total free energy of the crystal suspension, predominantly by removal of the nanocrystal/liquid interface area. Accordingly, we should start by considering colloidal suspensions with crystals as the dispersed phase, i.e., "sols", and discuss the reasons for their thermodynamic (meta)stability and how this stability can be lowered such that oriented attachment can occur as a spontaneous thermodynamic process. Oriented attachment is a process observed both for charge-stabilized crystals in polar solvents and for ligand capped nanocrystal suspensions in nonpolar solvents. In this last system different facets can develop a very different reactivity for oriented attachment. Due to this facet selectivity, crystalline structures with very specific geometries can be grown in one, two, or three dimensions; controlled oriented attachment suddenly becomes a tool for material scientists to grow architectures that cannot be reached by any other means. We will review the work performed with PbSe and CdSe nanocrystals. The entire process, i.e., the assembly of nanocrystals, atomic alignment, and unification by attachment, is a very complex and intriguing process. Researchers have succeeded in monitoring these different steps with in situ wave scattering methods and real-space (S)TEM studies. At the same time coarse-grained molecular dynamics simulations have been used to further study the forces involved in self-assembly and attachment at an interface. We will briefly come back to some of these results in the last sections of this review.

In Situ Study of Order Formation in Mesoporous Titania Thin Films Templated by a Diblock Copolymer during Slot-Die Printing

Slot-die printing, a large-scale deposition technique, is applied to fabricate mesoporous titania films. Printing is interesting, for example, for scaling up solar cells where titania films with an interconnected mesoporous network and a large surface-to-volume ratio are desired as photoanodes. A fundamental understanding of the structure evolution during printing is of high significance in tailoring these films. In this work, we provide important insights into the self-assembly of the slot-die-printed titania/polystyrene-block-poly(ethylene oxide) (PS-b-PEO) micelles into ordered hybrid structures in real time via in situ grazing-incidence small-angle X-ray scattering (GISAXS). GISAXS allows for tracking both vertical and lateral structure development of the film formation process. In the hybrid film, a face-centered cubic (FCC) structure is preferentially formed at the interfaces with air and with the substrate, while a defect-rich mixed FCC and body-centered cubic (BCC) structure forms in the bulk. After calcination, the surface and inner morphologies of the obtained nanostructured titania films are compared with the spin-coated analogues. In the printed films, the initially formed nanoscale structure of the hybrid film is preserved, and the resulting mesoporous titania film shows a superior order as compared with the spin-coated thin films which can be beneficial for future applications.

Probing the Consequences of Cubic Particle Shape and Applied Field on Colloidal Crystal Engineering with DNA

In a magnetic field, cubic Fe₃ O₄ nanoparticles exhibit assembly behavior that is a consequence of a competition between magnetic dipole-dipole and ligand interactions. In most cases, the interactions between short hydrophobic ligands dominate and dictate assembly outcome. To better tune the face-to-face interactions, cubic Fe₃ O₄ nanoparticles were functionalized with DNA. Their assembly behaviors were investigated both with and without an applied magnetic field. Upon application of a field, the tilted orientation of cubes, enabled by the flexible DNA ligand shell, led to an unexpected crystallographic alignment of the entire superlattice, as opposed to just the individual particles, along the field direction as revealed by small and wide-angle X-ray scattering. This observation is dependent upon DNA length and sequence and cube dimensions. Taken together, these studies show how combining physical and chemical control can expand the possibilities of crystal engineering with DNA.

Self-assembly of gold nanocubes into three-dimensional hollow colloidosomes and two-dimensional superlattices

Self-assembly of metal nanocubes (NCs) into periodic structures has applications in the fabrication of functional materials. Here, we propose a facile yet robust strategy for the fabrication of three-dimensional (3D) hollow colloidosomes and two-dimensional (2D) superlattices with highly ordered face-to-face configuration of gold NCs (AuNCs) via the hierarchical assembly of polymer-tethered AuNCs at the emulsion interface, providing a universal route for the preparation of hierarchical NC superstructures with applications in various fields.

An Implicit-Solvent Model for the Interfacial Configuration of Colloidal Nanoparticles and Application to the Self-Assembly of Truncated Cubes

This study outlines the development of an implicit-solvent model that reproduces the behavior of colloidal nanoparticles at a fluid-fluid interface. The center point of this formulation is the generalized quaternion-based orientational constraint (QOCO) method. The model captures three major energetic characteristics that define the nanoparticle configuration-position (orthogonal to the interfacial plane), orientation, and inter-nanoparticle interaction. The framework encodes physically relevant parameters that provide an intuitive means to simulate a broad spectrum of interfacial conditions. Results show that for a wide range of shapes, our model is able to replicate the behavior of an isolated nanoparticle at an explicit fluid-fluid interface, both qualitatively and often nearly quantitatively. Furthermore, the family of truncated cubes is used as a test bed to analyze the effect of changes in the degree of truncation on the potential-of-mean-force landscape. Finally, our results for the self-assembly of an array of cuboctahedra provide corroboration to the experimentally observed honeycomb and square lattices.

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.

Unravelling three-dimensional adsorption geometries of PbSe nanocrystal monolayers at a liquid-air interface

The adsorption, self-organization and oriented attachment of PbSe nanocrystals (NCs) at liquid-air interfaces has led to remarkable nanocrystal superlattices with atomic order and a superimposed nanoscale geometry. Earlier studies examined the NC self-organization at the suspension/air interface with time-resolved in-situ X-ray scattering. Upon continuous evaporation of the solvent, the NC interfacial layer will finally contact the (ethylene glycol) liquid substrate on which the suspension was casted. In order to obtain structural information on the NC organization at this stage of the process, we examined the ethylene glycol/NC interface in detail for PbSe NCs of different sizes, combining in-situ grazing-incidence small-and-wide-angle X-ray scattering (GISAXS/GIWAXS), X-ray reflectivity (XRR) and analytical calculations of the adsorption geometry of these NCs. Here, we observe in-situ three characteristic adsorption geometries varying with the NC size. Based on the experimental evidence and simulations, we reveal fully three-dimensional arrangements of PbSe nanocrystals at the ethylene glycol-air interface with and without the presence of rest amounts of toluene.

Revealing Grain Boundaries and Defect Formation in Nanocrystal Superlattices by Nanodiffraction

X-ray nanodiffraction is applied to study the formation and correlation of domain boundaries in mesocrystalline superlattices of PbS nanocrystals with face-centered cubic structure. Each domain of the superlattice can be described with one of two mesocrystalline polymorphs with different orientational orders. Close to a grain boundary, the lattice constant decreases and the superlattice undergoes an out-of-plane rotation, while the orientation of the nanocrystals with respect to the superlattice remains unchanged. These findings are explained with the release of stress on the expense of specific nanocrystal-substrate interactions. The fact that correlations between adjacent nanocrystals are found to survive the structural changes at most grain boundaries implies that the key to nanocrystal superlattices with macroscopic domain sizes are strengthened interactions with the substrate.

Orientational Disorder in Epitaxially Connected Quantum Dot Solids

Periodic arrays of strongly coupled colloidal quantum dots (QDs) may enable unprecedented control of electronic band structure through manipulation of QD size, shape, composition, spacing, and assembly geometry. This includes the possibilities of precisely engineered bandgaps and charge carrier mobilities, as well as remarkable behaviors such as metal-insulator transitions, massless carriers, and topological states. However, experimental realization of these theoretically predicted electronic structures is presently limited by structural disorder. Here, we use aberration-corrected scanning transmission electron microscopy to precisely quantify the orientational disorder of epitaxially connected QD films. In spite of coherent atomic connectivity between nearest neighbor QDs, we find misalignment persists with a standard deviation of 1.9°, resulting in significant bending strain localized to the adjoining necks. We observe and quantify a range of out-of-plane particle orientations over thousands of QDs and correlate the in-plane and out-of-plane misalignments, finding QDs misoriented out-of-plane display a statistically greater misalignment with respect to their in-plane neighbors as well. Using the bond orientational order metric ψ₄, we characterize the 4-fold symmetry and introduce a quantification of the local superlattice (SL) orientation. This enables direct comparison between local orientational order in the SL and atomic lattice (AL). We find significantly larger variations in the SL orientation and a statistically robust but locally highly variable correlation between the orientations of the two differently scaled lattices. Distinct AL and SL behaviors are observed about a grain boundary, with a sharp boundary in the AL orientations, but a more smooth transition in the SL, facilitated by lattice deformation between the neighboring grains. Coupling between the AL and SL is a fundamental driver of film growth, and these results suggest nontrivial underlying mechanics, implying that simplified models of epitaxial attachment may be insufficient to understand QD growth and disorder when oriented attachment and superlattice growth occur in concert.

Monitoring Nanocrystal Self-Assembly in Real Time Using In Situ Small-Angle X-Ray Scattering

Self-assembled nanocrystal superlattices have attracted large scientific attention due to their potential technological applications. However, the nucleation and growth mechanisms of superlattice assemblies remain largely unresolved due to experimental difficulties to monitor intermediate states. Here, the self-assembly of colloidal PbS nanocrystals is studied in real time by a combination of controlled solvent evaporation from the bulk solution and in situ small-angle X-ray scattering (SAXS) in transmission geometry. For the first time for the investigated system a hexagonal closed-packed (hcp) superlattice formed in a solvent vapor saturated atmosphere is observed during slow solvent evaporation from a colloidal suspension. The highly ordered hcp superlattice is followed by a transition into the final body-centered cubic superlattice upon complete drying. Additionally, X-ray cross-correlation analysis of Bragg reflections is applied to access information on precursor structures in the assembly process, which is not evident from conventional SAXS analysis. The detailed evolution of the crystal structure with time provides key results for understanding the assembly mechanism and the role of ligand-solvent interactions, which is important both for fundamental research and for fabrication of superlattices with desired properties.

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.

Impact of Crystallographic Orientation Disorders on Electronic Heterogeneities in Metal Halide Perovskite Thin Films

Metal halide perovskite thin films have achieved remarkable performance in optoelectronic devices but suffer from spatial heterogeneity in their electronic properties. To achieve higher device performance and reliability needed for widespread commercial deployment, spatial heterogeneity of optoelectronic properties in the perovskite thin film needs to be understood and controlled. Clear identification of the causes underlying this heterogeneity, most importantly the spatial heterogeneity in charge trapping behavior, has remained elusive. Here, a multimodal imaging approach consisting of photoluminescence, optical transmission, and atomic force microscopy is utilized to separate electronic heterogeneity from morphology variations in perovskite thin films. By comparing the degree of heterogeneity in highly oriented and randomly oriented polycrystalline perovskite thin film samples, we reveal that disorders in the crystallographic orientation of the grains play a dominant role in determining charge trapping and electronic heterogeneity. This work also demonstrates a polycrystalline thin film with uniform charge trapping behavior by minimizing crystallographic orientation disorder. These results suggest that single crystals may not be required for perovskite thin film based optoelectronic devices to reach their full potential.

Guiding kinetic trajectories between jammed and unjammed states in 2D colloidal nanocrystal-polymer assemblies with zwitterionic ligands

Mesostructured matter composed of colloidal nanocrystals in solidified architectures abounds with broadly tunable catalytic, magnetic, optoelectronic, and energy storing properties. Less common are liquid-like assemblies of colloidal nanocrystals in a condensed phase, which may have different energy transduction behaviors owing to their dynamic character. Limiting investigations into dynamic colloidal nanocrystal architectures is the lack of schemes to control or redirect the tendency of the system to solidify. We show how to solidify and subsequently reconfigure colloidal nanocrystal assemblies dimensionally confined to a liquid-liquid interface. Our success in this regard hinged on the development of competitive chemistries anchoring or releasing the nanocrystals to or from the interface. With these chemistries, it was possible to control the kinetic trajectory between quasi-two-dimensional jammed (solid-like) and unjammed (liquid-like) states. In future schemes, it may be possible to leverage this control to direct the formation or destruction of explicit physical pathways for energy carriers to migrate in the system in response to an external field.

Creating two self-assembly micro-environments to achieve supercrystals with dual structures using polyhedral nanoparticles

Organizing nanoparticles into supercrystals comprising multiple structures remains challenging. Here, we achieve one assembly with dual structures for Ag polyhedral building blocks, comprising truncated cubes, cuboctahedra, truncated octahedra, and octahedra. We create two micro-environments in a solvent evaporation-driven assembly system: one at the drying front and one at the air/water interface. Dynamic solvent flow concentrates the polyhedra at the drying front, generating hard particle behaviors and leading to morphology-dependent densest-packed bulk supercrystals. In addition, monolayers of nanoparticles adsorb at the air/liquid interface to minimize the air/liquid interfacial energy. Subsequent solvent evaporation gives rise to various structurally diverse dual-structure supercrystals. The topmost monolayers feature distinct open crystal structures with significantly lower packing densities than their densest-packed supercrystals. We further highlight a 3.3-fold synergistic enhancement of surface-enhanced Raman scattering efficiency arising from these dual-structure supercrystals as compared to a uniform one.

Crystals with multiple structures often perform special functions in nature, inspiring the creation of synthetic analogues. Here, the authors subject polyhedral nanoparticles to two self-assembly micro-environments to realize supercrystals with dual structures, in which the order of the surface layer differs from the bulk structure.

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.

Formation of self-assembled gold nanoparticle supercrystals with facet-dependent surface plasmonic coupling

Metallic nanoparticles, such as gold and silver nanoparticles, can self-assemble into highly ordered arrays known as supercrystals for potential applications in areas such as optics, electronics, and sensor platforms. Here we report the formation of self-assembled 3D faceted gold nanoparticle supercrystals with controlled nanoparticle packing and unique facet-dependent optical property by using a binary solvent diffusion method. The nanoparticle packing structures from specific facets of the supercrystals are characterized by small/wide-angle X-ray scattering for detailed reconstruction of nanoparticle translation and shape orientation from mesometric to atomic levels within the supercrystals. We discover that the binary diffusion results in hexagonal close packed supercrystals whose size and quality are determined by initial nanoparticle concentration and diffusion speed. The supercrystal solids display unique facet-dependent surface plasmonic and surface-enhanced Raman characteristics. The ease of the growth of large supercrystal solids facilitates essential correlation between structure and property of nanoparticle solids for practical integrations.

Macroscopically large supercrystals are very difficult to assemble from metallic nanoparticles. Here, the authors use a binary solvent diffusion method to form sub-millimeter gold nanoparticle supercrystals with rare hcp symmetry, and discover that they exhibit facet-dependent optical properties.

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.

A simulation study on the phase behavior of hard rhombic platelets

Using Monte Carlo simulations, we investigate the phase behavior of hard rhombic platelets as a function of the thickness of the platelets, T. The phase diagram displays a columnar phase and a crystal phase in which the platelets are stacked in columns that are arranged in a two-dimensional lattice. We find that the shape of the platelets determines the symmetry of the two-dimensional lattice, i.e., rhombic platelets form an oblique columnar phase and a simple monoclinic crystal phase. For sufficiently thick platelets, i.e., for a thickness-to-length ratio T/L>0.17, we find only an isotropic fluid, an oblique columnar phase, and a monoclinic crystal phase. Surprisingly, for an intermediate plate thickness, 0.083<T/L<0.17, we also find a region in between the isotropic (or nematic) phase and the columnar phase, where the smectic phase is stable. For sufficiently thin platelets, T/L<0.13, the phase diagram displays a nematic phase. With the exception of the smectic phase, our results resemble the phase behavior of discotic particles. Our results may guide the synthesis and future experiments on rhombic nanoplatelets.

Self-assembly of cubic colloidal particles at fluid-fluid interfaces by hexapolar capillary interactions

Colloidal particles adsorbed at fluid-fluid interfaces can self-assemble, thanks to capillary interactions, into 2D ordered structures. Recently, it has been predicted by theoretical and numerical calculations [G. Soligno et al., Phys. Rev. Lett., 2016, 116, 258001] that cubes with smooth edges adsorbed at a flat fluid-fluid interface generate hexapolar capillary deformations that cause the particles to self-assemble into honeycomb and hexagonal lattices, at equilibrium and for Young's contact angle π/2. Here we extend these results. Firstly, we show that capillary interactions induced by hexapolar deformations can drive the particles at the interface to form also thermodynamically-stable square lattices, in addition to honeycomb and hexagonal lattices. Then, we study the effects of tuning the particle shape on the particle self-assembly at the interface, considering, respectively, smooth-edge cubes, sharp-edge cubes, slightly truncated-edge cubes, and highly truncated-edge cubes. In our calculations, both capillary and hard-particle interactions are taken into account. We show that such variations in the particle shape significantly affect both qualitatively and quantitatively the self-assembly of the particles at the interface, and we sum up our results in the form of temperature-density phase diagrams. For example, using typical experimental parameters, our results show that only 4-to-5 nm sized sharp-edge and smooth-edge cubes can self-assemble into a honeycomb lattice, while slightly and highly truncated-edge cubes can form a honeycomb lattice only if they have a 8-to-12 and 10-to-16 nm size, respectively, for the same experimental parameters. Also, our results show that the capillarity-induced square lattice phase is stable only for the smooth-edge and truncated-edge cubes, but not for the sharp-edge cubes.

Bubble Assemblies of Nanocrystals: Superlattices without a Substrate

A method was developed to create free-standing nanocrystal films in the form of solidified bubbles. Bubbles of octadecanethiol-capped gold nanocrystals were studied by in situ grazing incidence small-angle X-ray scattering (GISAXS) to determine how the absence of an underlying substrate influences a disorder-order transition of a nanocrystal superlattice. We find that the presence of the substrate does not significantly change the nature of the disorder-order transition but does lead to reduced interparticle separation and reduced thermal expansion. Bubble assemblies of silicon and copper selenide nanocrystals are also demonstrated.

Quantifying Angular Correlations between the Atomic Lattice and the Superlattice of Nanocrystals Assembled with Directional Linking

We show that the combination of X-ray scattering with a nanofocused beam and X-ray cross correlation analysis is an efficient way for the full structural characterization of mesocrystalline nanoparticle assemblies with a single experiment. We analyze several hundred diffraction patterns at individual sample locations, that is, individual grains, to obtain a meaningful statistical distribution of the superlattice and atomic lattice ordering. Simultaneous small- and wide-angle X-ray scattering of the same sample location allows us to determine the structure and orientation of the superlattice as well as the angular correlation of the first two Bragg peaks of the atomic lattices, their orientation with respect to the superlattice, and the average orientational misfit due to local structural disorder. This experiment is particularly advantageous for synthetic mesocrystals made by the simultaneous self-assembly of nanocrystals and surface-functionalization with conductive ligands. While the structural characterization of such materials has been challenging so far, the present method now allows correlating the mesocrystalline structure with optoelectronic properties.

Superlattice growth and rearrangement during evaporation-induced nanoparticle self-assembly

Understanding the assembly of nanoparticles into superlattices with well-defined morphology and structure is technologically important but challenging as it requires novel combinations of in-situ methods with suitable spatial and temporal resolution. In this study, we have followed evaporation-induced assembly during drop casting of superparamagnetic, oleate-capped γ-Fe₂O₃ nanospheres dispersed in toluene in real time with Grazing Incidence Small Angle X-ray Scattering (GISAXS) in combination with droplet height measurements and direct observation of the dispersion. The scattering data was evaluated with a novel method that yielded time-dependent information of the relative ratio of ordered (coherent) and disordered particles (incoherent scattering intensities), superlattice tilt angles, lattice constants, and lattice constant distributions. We find that the onset of superlattice growth in the drying drop is associated with the movement of a drying front across the surface of the droplet. We couple the rapid formation of large, highly ordered superlattices to the capillary-induced fluid flow. Further evaporation of interstitital solvent results in a slow contraction of the superlattice. The distribution of lattice parameters and tilt angles was significantly larger for superlattices prepared by fast evaporation compared to slow evaporation of the solvent.

Droplets, Evaporation and a Superhydrophobic Surface: Simple Tools for Guiding Colloidal Particles into Complex Materials

The formation of complexly structured and shaped supraparticles can be achieved by evaporation-induced self-assembly (EISA) starting from colloidal dispersions deposited on a solid surface; often a superhydrophobic one. This versatile and interesting approach allows for generating rather complex particles with corresponding functionality in a simple and scalable fashion. The versatility is based on the aspect that basically one can employ an endless number of combinations of components in the colloidal starting solution. In addition, the structure and properties of the prepared supraparticles may be modified by appropriately controlling the evaporation process, e.g., by external parameters. In this review, we focus on controlling the shape and internal structure of such supraparticles, as well as imparted functionalities, which for instance could be catalytic, optical or electronic properties. The catalytic properties can also result in self-propelling (supra-)particles. Quite a number of experimental investigations have been performed in this field, which are compared in this review and systematically explained.

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.

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.

Orientationally Ordered Silicon Nanocrystal Cuboctahedra in Superlattices

Uniform silicon nanocrystals were synthesized with cuboctahedral shape and passivated with 1-dodecene capping ligands. Transmission electron microscopy, electron diffraction, and grazing incidence wide-angle and small-angle X-ray scattering show that these soft cuboctahedra assemble into face-centered cubic superlattices with orientational order. The preferred nanocrystal orientation was found to depend on the orientation of the superlattices on the substrate, indicating that the interactions with the substrate and assembly kinetics can influence the orientation of faceted nanocrystals in superlattices.

In situ study of the formation mechanism of two-dimensional superlattices from PbSe nanocrystals

Oriented attachment of PbSe nanocubes can result in the formation of two-dimensional (2D) superstructures with long-range nanoscale and atomic order. This questions the applicability of classic models in which the superlattice grows by first forming a nucleus, followed by sequential irreversible attachment of nanocrystals, as one misaligned attachment would disrupt the 2D order beyond repair. Here, we demonstrate the formation mechanism of 2D PbSe superstructures with square geometry by using in situ grazing-incidence X-ray scattering (small angle and wide angle), ex situ electron microscopy, and Monte Carlo simulations. We observed nanocrystal adsorption at the liquid/gas interface, followed by the formation of a hexagonal nanocrystal monolayer. The hexagonal geometry transforms gradually through a pseudo-hexagonal phase into a phase with square order, driven by attractive interactions between the {100} planes perpendicular to the liquid substrate, which maximize facet-to-facet overlap. The nanocrystals then attach atomically via a necking process, resulting in 2D square superlattices.

Site-Specific Ligand Interactions Favor the Tetragonal Distortion of PbS Nanocrystal Superlattices

We analyze the structure and morphology of mesocrystalline, body-centered tetragonal (bct) superlattices of PbS nanocrystals functionalized with oleic acid. On the basis of combined scattering and real space imaging, we derive a three-dimensional (3D) model of the superlattice and show that the bct structure benefits from a balanced combination of {100}PbS-{100}PbS and {111}PbS-{111}PbS interactions between neighboring layers of nanocrystals, which uniquely stabilizes this structure. These interactions are enabled by the coaxial alignment of the atomic lattices of PbS with the superlattice. In addition, we find that this preferential orientation is already weakly present within isolated monolayers. By adding excess oleic acid to the nanocrystal solution, tetragonal distortion is suppressed, and we observe assembly into a bilayered hexagonal lattice reminiscent of a honeycomb with grain sizes of several micrometers.

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.

Oleic Acid-Induced Atomic Alignment of ZnS Polyhedral Nanocrystals

Ordered two-dimensional (2D) superstructures of colloidal nanocrystals (NCs) can be tailored by the size, shape, composition, and surface chemistry of the NC building blocks, which can give directionality to the resulting superstructure geometry. The exact formation mechanism of 2D NC superstructures is however not yet fully understood. Here, we show that oleic acid (OA) ligands induce atomic alignment of wurtzite ZnS bifrustum-shaped NCs. We find that in the presence of OA ligands the {002} facets of the ZnS bifrustums preferentially adhere to the liquid-air interface. Furthermore, OA ligands induce inter-NC interactions that also orient the NCs in the plane of the liquid-air interface, resulting in atomically aligned 2D superstructures. We follow the self-assembly process in real-time with in situ grazing incidence small-angle X-ray scattering and find that the NCs form a hexagonal superstructure at early stages after which they come closer over time, resulting in a close-packed NC superstructure. Our results demonstrate the profound influence that surface ligands have on the directionality of 2D NC superstructures and highlight the importance of detailed in situ studies in order to understand the self-assembly of NCs into 2D superstructures.

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.

An Obtuse Rhombohedral Superlattice Assembled by Pt Nanocubes

We grew large single three-dimensional supercrystals from colloidal Pt nanocubes (NCs) suspended in hexane. A synchrotron-based two circle diffractometer was used to obtain an unprecedented level of detail from full sets of small/wide-angle X-ray scattering (SAXS/WAXS) patterns. Automatic indexing and simulations of X-ray patterns enabled detailed reconstruction of NC translation and shape orientation within the supercrystals from atomic to mesometric levels. The supercrystal has an obtuse rhombohedral (Rh) superlattice with space group R3m and a trigonal cell angle of 106.2°. Individual NCs orient themselves in a manner of atomic Pt[111] parallel to superlattice Rh[111]. We analyzed the superlattice structure in context of three spatial relationships of proximate NCs including face-to-face, edge-to-edge, and corner-to-corner configurations. Detailed analysis of supercrystal structure reveals nearly direct corner-to-corner contacts and a tight interlocking NC structure. We employed the correlations between strain and lattice distortion and established the first structural correlating mechanism between five superlattice polymorphs to elucidate the superlattice transformations and associated developing pathways. Together, the experimental and modeling results provide comprehensive structural information toward controlling design and efficient materials-processing for large fabrication of nanobased functional materials with tailored structures and desired properties.

Small-angle scattering of particle assemblies

Small-angle scattering formulae for crystalline assemblies of arbitrary particles are derived from powder diffraction theory using the decoupling approximation. To do so, the pseudo-lattice factor is defined, and methods to overcome the limitations of the decoupling approximation are investigated. Further, approximated equations are suggested for the diffuse scattering from various defects of the first kind due to non-ideal particles, including size polydispersity, orientational disorder and positional fluctuation about their ideal positions. Calculated curves using the formalism developed herein are compared with numerical simulations computed without any approximation. For a finite-sized assembly, the scattering from the whole domain of the assembly must also be included, and this is derived using the correlation function approach.

Entropic self-assembly of freely rotating polyhedral particles confined to a flat interface

The self-assembly of hard polyhedral particles confined to a flat interface is studied using Monte Carlo simulations. The particles are pinned to the interface by restricting their movement in the direction perpendicular to it while allowing their free rotations. The six different polyhedral shapes studied in this work are selected from a family of truncated cubes defined by a truncation parameter, s, which varies from cubes (s = 0) via cuboctahedra (s = 0.5) to octahedra (s = 1). Our results suggest that shapes with small values of s show square-like behavior whereas shapes with large values of s tend to show more disc-like behavior. At an intermediate value of s = 0.4, the phase behavior of the system shows both square-like and disc-like features. The results are also compared with the phase behavior of 3D bulk polyhedra and of 2D rounded hard squares. Both comparisons reveal key similarities in the number and sequence of mesophases and solid phases observed. These insights on 2D entropic self-assembly of polyhedral particles is a first step toward understanding the self-assembly of particles at fluid-fluid interfaces, which is driven by a complex interplay of entropic and enthalpic forces. A first-order analysis of the particle-surface energies associated with a fluid-fluid interface indicates that such enthalpic interactions will be particularly important in determining particle orientation behavior at low to intermediate concentrations.