Soft Skyrmions, Spontaneous Valence and Selection Rules in Nanoparticle Superlattices

Nanocrystal Assemblies: Current Advances and Open Problems

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

Theory and simulation of ligand functionalized nanoparticles - a pedagogical overview

Synthesizing reconfigurable nanoscale synthons with predictive control over shape, size, and interparticle interactions is a holy grail of bottom-up self-assembly. Grand challenges in their rational design, however, lie in both the large space of experimental synthetic parameters and proper understanding of the molecular mechanisms governing their formation. As such, computational and theoretical tools for predicting and modeling building block interactions have grown to become integral in modern day self-assembly research. In this review, we provide an in-depth discussion of the current state-of-the-art strategies available for modeling ligand functionalized nanoparticles. We focus on the critical role of how ligand interactions and surface distributions impact the emergent, pre-programmed behaviors between neighboring particles. To help build insights into the underlying physics, we first define an "ideal" limit - the short ligand, "hard" sphere approximation - and discuss all experimental handles through the lens of perturbations about this reference point. Finally, we identify theories that are capable of bridging interparticle interactions to nanoscale self-assembly and conclude by discussing exciting new directions for this field.

All-Perovskite Multicomponent Nanocrystal Superlattices

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

A multiscale approach to uncover the self-assembly of ligand-covered palladium nanocubes

Ligand-mediated superlattice assemblies of metallic nanocrystals represent a new type of mesoscale materials whose structural ordering directly influence emergent collective properties. However, universal control over the spatial and orientational ordering of their constitutive components remains an open challenge. One major barrier contributing to the lack of programmability in these nanoscale building blocks revolves around a gap in fundamental understanding of how ligand-mediated interactions at the particle level propagate to macroscopic and mesoscale behaviors. Here, we employ a combination of scaling theory and coarse-grained simulations to develop a multiscale modeling framework capable of bridging across hierarchical assembly length scales for a model system of ligand-functionalized nanocubes (here, Pd). We first employ atomistic simulations to characterize how specific ligand-ligand interactions influence the local behaviors between neighboring Pd nanocubes. We then utilize a mean-field scaling theory to both rationalize the observed behaviors as well as compute a coarse-grained effective pairwise potential between nanocubes capable of reproducing atomistic behaviors at the mesoscale. Furthermore, our simulations reveal that a complex interplay between ligand-ligand interactions is directly responsible for a shift in macroscopic ordering between neighboring nanocubes. Our results, therefore, provides a critical step forward in establishing a multiscale understanding of ligand-functionalized nanocrystalline assemblies that can be subsequently leveraged to design targeted structures exhibiting novel, emergent collective properties.

Anisotropy in Near-Spherical Colloidal Nanoparticles

Two major aspects of functional colloidal nanoparticles are their colloidal stability (dispersion) and controlled assembly of nanoparticles into ordered structures. Simplifying colloidal nanoparticles as isotropically interacting spheres is unsuitable for small nanoparticles capped with hydrocarbon chain ligands in which the ligand-ligand interaction plays a prominent role in the assembly processes. However, experimentally characterizing the ligand shell structure in solution presents significant challenges, and computer simulations yield divergent results without effective validation. Moreover, the connection between detailed information regarding ligand shell structures and interparticle interactions, in relation to the diverse dynamical behaviors of colloidal nanoparticles, remains poorly understood. In this study, we reveal the relationship between the ligand shell structures, interparticle interactions, and dynamical behaviors of few-nm-sized near-spherical nanoparticles capped with hydrocarbon chain ligands immersed in nonpolar solvents. Our study shows a transformation of the interparticle interactions from anisotropic attractions to isotropic repulsions as a result of the change in the ligand shell structures from order to disorder caused by varying temperature and other factors. The interplay between anisotropic attractions from ligand bundles and isotropic repulsions from disordered ligands dictates the nanoparticle dynamical behaviors of dispersion, uncontrolled aggregation, and controlled assembly.

Ligand Effects in Assembly of Cubic and Spherical Nanocrystals: Applications to Packing of Perovskite Nanocubes

We establish the formula representing cubic nanocrystals (NCs) as hard cubes taking into account the role of the ligands and describe how these results generalize to any other NC shapes. We derive the conditions under which the hard cube representation breaks down and provide explicit expressions for the effective size. We verify the results from the detailed potential of mean force calculations for two nanocubes in different orientations as well as with spherical nanocrystals. Our results explicitly demonstrate the relevance of certain ligand conformations, i.e., "vortices", and show that edges and corners provide natural sites for their emergence. We also provide both simulations and experimental results with single component cubic perovskite nanocrystals assembled into simple cubic superlattices, which further corroborate theoretical predictions. In this way, we extend the Orbifold Topological Model (OTM) accounting for the role of ligands beyond spherical nanocrystals and discuss its extension to arbitrary nanocrystal shapes. Our results provide detailed predictions for recent superlattices of perovskite nanocubes and spherical nanocrystals. Problems with existing united atom force fields are discussed.

Metal-Halide Perovskite Nanocrystal Superlattice: Self-Assembly and Optical Fingerprints

Self-assembly of nanocrystals into superlattices is a fascinating process that not only changes geometric morphology, but also creates unique properties that considerably enrich the material toolbox for new applications. Numerous studies have driven the blossoming of superlattices from various aspects. These include precise control of size and morphology, enhancement of properties, exploitation of functions, and integration of the material into miniature devices. The effective synthesis of metal-halide perovskite nanocrystals has advanced research on self-assembly of building blocks into micrometer-sized superlattices. More importantly, these materials exhibit abundant optical features, including highly coherent superfluorescence, amplified spontaneous laser emission, and adjustable spectral redshift, facilitating basic research and state-of-the-art applications. This review summarizes recent advances in the field of metal-halide perovskite superlattices. It begins with basic packing models and introduces various stacking configurations of superlattices. The potential of multiple capping ligands is also discussed and their crucial role in superlattice growth is highlighted, followed by detailed reviews of synthesis and characterization methods. How these optical features can be distinguished and present contemporary applications is then considered. This review concludes with a list of unanswered questions and an outlook on their potential use in quantum computing and quantum communications to stimulate further research in this area.

Strongly Confined CsPbBr3 Quantum Dots as Quantum Emitters and Building Blocks for Rhombic Superlattices

The success of the colloidal semiconductor quantum dots (QDs) field is rooted in the precise synthetic control of QD size, shape, and composition, enabling electronically well-defined functional nanomaterials that foster fundamental science and motivate diverse fields of applications. While the exploitation of the strong confinement regime has been driving commercial and scientific interest in InP or CdSe QDs, such a regime has still not been thoroughly explored and exploited for lead-halide perovskite QDs, mainly due to a so far insufficient chemical stability and size monodispersity of perovskite QDs smaller than about 7 nm. Here, we demonstrate chemically stable strongly confined 5 nm CsPbBr3 colloidal QDs via a postsynthetic treatment employing didodecyldimethylammonium bromide ligands. The achieved high size monodispersity (7.5% ± 2.0%) and shape-uniformity enables the self-assembly of QD superlattices with exceptional long-range order, uniform thickness, an unusual rhombic packing with an obtuse angle of 104°, and narrow-band cyan emission. The enhanced chemical stability indicates the promise of strongly confined perovskite QDs for solution-processed single-photon sources, with single QDs showcasing a high single-photon purity of 73% and minimal blinking (78% "on" fraction), both at room temperature.

Seeking regularity from irregularity: unveiling the synthesis-nanomorphology relationships of heterogeneous nanomaterials using unsupervised machine learning

Nanoscale morphology of functional materials determines their chemical and physical properties. However, despite increasing use of transmission electron microscopy (TEM) to directly image nanomorphology, it remains challenging to quantify the information embedded in TEM data sets, and to use nanomorphology to link synthesis and processing conditions to properties. We develop an automated, descriptor-free analysis workflow for TEM data that utilizes convolutional neural networks and unsupervised learning to quantify and classify nanomorphology, and thereby reveal synthesis-nanomorphology relationships in three different systems. While TEM records nanomorphology readily in two-dimensional (2D) images or three-dimensional (3D) tomograms, we advance the analysis of these images by identifying and applying a universal shape fingerprint function to characterize nanomorphology. After dimensionality reduction through principal component analysis, this function then serves as the input for morphology grouping through unsupervised learning. We demonstrate the wide applicability of our workflow to both 2D and 3D TEM data sets, and to both inorganic and organic nanomaterials, including tetrahedral gold nanoparticles mixed with irregularly shaped impurities, hybrid polymer-patched gold nanoprisms, and polyamide membranes with irregular and heterogeneous 3D crumple structures. In each of these systems, unsupervised nanomorphology grouping identifies both the diversity and the similarity of the nanomaterial across different synthesis conditions, revealing how synthetic parameters guide nanomorphology development. Our work opens possibilities for enhancing synthesis of nanomaterials through artificial intelligence and for understanding and controlling complex nanomorphology, both for 2D systems and in the far less explored case of 3D structures, such as those with embedded voids or hidden interfaces.

Nanopolymers for magnetic applications: how to choose the architecture?

Directional assembly of nanoscale objects results in morphologies that can broadly be classified as supra-molecular nanopolymers. Such morphologies, given a functional choice of the monomers used as building blocks, can be of ubiquitous utility in optical, magnetic, rheological, and medical applications. These applications, however, require a profound understanding of the interplay between monomer shape and bonding on one side, and polymeric properties - on the other. Recently, we fabricated nanopolymers using cuboid DNA nanochambers, as they not only allow fine-tuning of the resulting morphologies but can also carry magnetic nanoparticles. However, it is not known if the cuboid shape and inter-cuboid connectivity restrict the equilibrium confirmations of the resulting nanopolymers, making them less responsive to external stimuli. In this work, using Molecular Dynamics simulations, we perform an extensive comparison between various nanopolymer architectures to explore their polymeric properties, and their response to an applied magnetic field if magnetic nanoparticles are embedded. We explain the impact of monomer shape and bonding on the mechanical and magnetic properties and show that DNA nanochambers can build highly responsive and magnetically controllable nanopolymers.

Binary Superlattices of Gold Nanoparticles in Two Dimensions

We have created two-dimensional (2D) binary superlattices by cocrystallizing gold nanoparticles (AuNPs) of two distinct sizes into √3 × √3 and 2 × 2 complex binary superlattices, derived from the hexagonal structures of the single components. The building blocks of these binary systems are AuNPs that are functionalized with different chain lengths of poly(ethylene glycol) (PEG). The assembly of these functionalized NPs at the air-water interface is driven by the presence of salt, causing PEG-AuNPs to migrate to the aqueous surface and assemble into a crystalline lattice. We have used liquid surface X-ray reflectivity (XR) and grazing incidence small-angle X-ray scattering (GISAXS) to examine the assembly and crystallization at the liquid interface.

Nanocomposite tectons as unifying systems for nanoparticle assembly

Nanocomposite tectons (NCTs) are nanocomposite building blocks consisting of nanoparticle cores functionalized with a polymer brush, where each polymer chain terminates in a supramolecular recognition group capable of driving particle assembly. Like other ligand-driven nanoparticle assembly schemes (for example those using DNA-hybridization or solvent evaporation), NCTs are able to make colloidal crystal structures with precise particle organization in three dimensions. However, despite the similarity of NCT assembly to other methods of engineering ordered particle arrays, the crystallographic symmetries of assembled NCTs are significantly different. In this study, we provide a detailed characterization of the dynamics of hybridizations through universal (independent of microscopic details) parameters. We perform rigorous free energy calculations and identify the persistence length of the ligand as the critical parameter accounting for the differences in the phase diagrams of NCTs and other assembly methods driven by hydrogen bond hybridizations. We also report new experiments to provide direct verification for the predictions. We conclude by discussing the role of non-equilibrium effects and illustrating how NCTs provide a unification of the two most successful strategies for nanoparticle assembly: solvent evaporation and DNA programmable assembly.

Modeling of effective interactions between ligand coated nanoparticles through symmetry functions

Ligand coated nanoparticles are complex objects consisting of a metallic or semiconductor core with organic ligands grafted on their surface. These organic ligands provide stability to a nanoparticle suspension. In solutions, the effective interactions between such nanoparticles are mediated through a complex interplay of interactions between the nanoparticle cores, the surrounding ligands, and the solvent molecules. While it is possible to compute these interactions using fully atomistic molecular simulations, such computations are too expensive for studying self-assembly of a large number of nanoparticles. The problem can be made tractable by removing the degrees of freedom associated with the ligand chains and solvent molecules and using the potentials of mean force (PMF) between nanoparticles. In general, the functional dependence of the PMF on the inter-particle distance is unknown and can be quite complex. In this article, we present a method to model the two-body and three-body PMF between ligand coated nanoparticles through a linear combination of symmetry functions. The method is quite general and can be extended to model interactions between different types of macromolecules.

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

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

Macromolecular Ligand Engineering for Programmable Nanoprism Assembly

Ligands play a central role for the energetics and kinetics of nanocrystal assembly. Yet, the precise and simultaneous manipulation of ligands to dictate assembly outcome has proven difficult. Here, we present macromolecular ligand-engineering strategies to control, characterize, and model four molecular parameters of grafted polymer chains: chain length, chain dispersity, grafting density, and chain distribution. Direct ligand-exchange between nanoprisms and polymers functionalizes facets selectively and produces patchy nanocrystals. We develop a generalizable two-step ligand-exchange approach for the independent control of the two emergent brush parameters, brush thickness and brush softness. The resultant polymer-grafted prismatic nanocrystals with programmable ligand brushes self-assemble into thin-film superstructures of different wallpaper symmetries and faceted supracrystals. Our experiments are complemented by coarse-grained computer simulations of nanoprisms with directional, facet-specific interactions. This work paves the way for the precision synthesis of polymer-nanocrystal hybrid materials and enables the further refinement of theoretical models for particle brush materials.

Body centered tetragonal nanoparticle superlattices: why and when they form?

Body centered tetragonal (BCT) phases are structural intermediates between body centered cubic (BCC) and face centered cubic (FCC) structures. However, BCC ↔ FCC transitions may or may not involve a stable BCT intermediate. Interestingly, nanoparticle superlattices usually crystallize in BCT structures, but this phase is much less frequent for colloidal crystals of micrometer-sized particles. Two origins have been proposed for the formation of BCT NPSLs: (i) the influence of the substrate on which the nanoparticle superlattice is deposited, and (ii) non-spherical nanoparticle shapes, combined with the fact that different crystal facets have different ligand organizations. Notably, none of these two mechanisms alone is able to explain the set of available experimental observations. In this work, these two hypotheses were independently tested using a recently developed molecular theory for nanoparticle superlattices that explicitly captures the degrees of freedom associated with the ligands on the nanoparticle surface and the crystallization solvent. We show that the presence of a substrate can stabilize the BCT structure for spherical nanoparticles, but only for very specific combinations of parameters. On the other hand, a truncated-octahedron nanoparticle shape strongly stabilizes BCT structures in a wide region of the phase diagram. In the latter case, we show that the stabilization of BCT results from the geometry of the system and it does not require different crystal facets to have different ligand properties, as previously proposed. These results shed light on the mechanisms of BCT stabilization in nanoparticle superlattices and provide guidelines to control its formation.

Effect of Polymer Chain Length on the Superlattice Assembly of Functionalized Gold Nanoparticles

We report on the assembly of gold nanoparticle (AuNPs) superlattices at the liquid/vapor interface and in the bulk of their suspensions. Interparticle distances in the assemblies are achieved on multiple length scales by varying chain lengths of surface grafted AuNPs by polyethylene glycol (PEG) with molecular weights in the range 2000-40,000 Da. Crystal structures and lattice constants in both 2D and 3D assemblies are determined by synchrotron-based surface-sensitive and small-angle X-ray scattering. Assuming knowledge of grafting density, we show that experimentally determined interparticle distances are adequately modeled by spherical brushes close to the θ point (Flory-Huggins parameter, χ≈12) for 2D superlattices at a liquid interface and a nonsolvent (χ = ∞) for the 3D dry superlattices.

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

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

Perovskite-type superlattices from lead halide perovskite nanocubes

Atomically defined assemblies of dye molecules (such as H and J aggregates) have been of interest for more than 80 years because of the emergence of collective phenomena in their optical spectra^1-3, their coherent long-range energy transport, their conceptual similarity to natural light-harvesting complexes^4,5, and their potential use as light sources and in photovoltaics. Another way of creating versatile and controlled aggregates that exhibit collective phenomena involves the organization of colloidal semiconductor nanocrystals into long-range-ordered superlattices⁶. Caesium lead halide perovskite nanocrystals^7-9 are promising building blocks for such superlattices, owing to the high oscillator strength of bright triplet excitons¹⁰, slow dephasing (coherence times of up to 80 picoseconds) and minimal inhomogeneous broadening of emission lines^11,12. So far, only single-component superlattices with simple cubic packing have been devised from these nanocrystals¹³. Here we present perovskite-type (ABO₃) binary and ternary nanocrystal superlattices, created via the shape-directed co-assembly of steric-stabilized, highly luminescent cubic CsPbBr₃ nanocrystals (which occupy the B and/or O lattice sites), spherical Fe₃O₄ or NaGdF₄ nanocrystals (A sites) and truncated-cuboid PbS nanocrystals (B sites). These ABO₃ superlattices, as well as the binary NaCl and AlB₂ superlattice structures that we demonstrate, exhibit a high degree of orientational ordering of the CsPbBr₃ nanocubes. They also exhibit superfluorescence-a collective emission that results in a burst of photons with ultrafast radiative decay (22 picoseconds) that could be tailored for use in ultrabright (quantum) light sources. Our work paves the way for further exploration of complex, ordered and functionally useful perovskite mesostructures.

Ligand structure and adsorption free energy of nanocrystals on solid substrates

We present an investigation on the absorption of alkylthiolated nanocrystals on a solid substrate. We calculate adsorption free energies and report a number of effects induced by the substrate. Nearest neighbor distances and bonding free energies are significantly different than for a free floating case, there is a weakening of bonding free energies among nanocrystals, and the adsorption is manifestly anisotropic, i.e., stronger along certain directions of the nanocrystal core. We contend that this last result accounts for the Bain transition (fcc → bcc) observed in experimental results. We report the presence of vortices induced by the substrate, which explain the increased nearest neighbor distance among nanocrystals, which is in excellent quantitative agreement with experimental results and with the predictions of the Orbifold Topological Model. Implications for the assembly of nanostructures and future experiments are also discussed.

Engineering Organization of DNA Nano-Chambers through Dimensionally Controlled and Multi-Sequence Encoded Differentiated Bonds

Engineering the assembly of nanoscale objects into complex and prescribed structures requires control over their binding properties. Such control might benefit from a well-defined bond directionality, the ability to designate their engagements through specific encodings, and the capability to coordinate local orientations. Although much progress has been achieved in our ability to design complex nano-objects, the challenges in creating such nano-objects with fully controlled binding modes and understanding their fundamental properties are still outstanding. Here, we report a facile strategy for creating a DNA nanochamber (DNC), a hollow cuboid nano-object, whose bonds can be fully prescribed and complexly encoded along its three orthogonal axes, giving rise to addressable and differentiated bonds. The DNC can host nanoscale cargoes, which allows for the integration with functional nano-objects and their organization in larger-scale systems. We explore the relationship between the design of differentiated bonds and a formation of one-(1D), two-(2D), and three-(3D) dimensional organized arrays. Through the realization of different binding modes, we demonstrate sequence encoded nanoscale heteropolymers, helical polymers, 2D lattices, and mesoscale 3D nanostructures with internal order, and show that this assembly strategy can be applied for the organization of nanoparticles. We combine experimental investigations with computational simulation to understand the mechanism of structural formation for different types of ordered arrays, and to correlate the bonds design with assembly processes.

Softness- and Size-Dependent Packing Symmetries of Polymer-Grafted Nanoparticles

Achieving ordered arrays of nanoparticles (NPs) with controlled packing symmetry and interparticle spacing is of great importance to design complex metamaterials. Herein, we report softness- and size-dependent self-assembly behavior of polystyrene-grafted Au NPs (Au@PS NPs). We varied the core size of Au NPs from 1.9 to 9.6 nm and the number-average molecular weight (M_n) of thiol-terminated polystyrene from 1.8 to 7.9 kg mol^-1. The optimal packing model based on an "effective softness" parameter λ_eff that accounts for close-packed and semidilute brush regimes could predict the effective radius of Au@PS NPs (within ±9%) for a wide range of PS M_n, grafting density, and Au core size. With increasing λ_eff, the self-assembled Au@PS NP superlattices undergo a symmetry transition from hexagonal close packed (hcp) to body-centered tetragonal (bct) to body-centered cubic (bcc). This work demonstrates the effective softness model as a simple but robust tool for the design of NP superlattices with precisely controlled interparticle distance and packing symmetry, both of which are critical for the development of sophisticated materials through control of nanoscale structure.

Assembly of nanocrystal clusters by solvent evaporation: icosahedral order and the breakdown of the Maxwell regime

We carry out molecular dynamics simulations of N gold alkylthiolated nanocrystals (0 ≤ N ≤ 29) contained in liquid droplets of octane, nonane and decane coexisting with its vapor. The equilibrium structures that result when all the solvent dries up consist of highly symmetric nanocrystal clusters with different degrees of icosahedral order that are thoroughly characterized. We show that the relaxation times follow two regimes, a first for small nanocrystal packing fraction, dominated by the diffusion of vapor molecules (Maxwell regime, relaxation times independent of N) and another, for larger packing fractions, where the solvent diffuses through the cluster (with relaxation times growing like N2/3). We discuss the connection to the assembly of superlattices, prediction of lattice constants and evaporation models.

Close-Packed Ultrasmooth Self-assembled Monolayer of CsPbBr3 Perovskite Nanocubes

The use of colloidal self-assembly to form the complex multiscale patterns in many optoelectronic devices has been a long-standing dream of the nanoscience community. While great progress has been made using charged colloids in polar solvents, controlled assembly from nonpolar solvents is much more challenging. The major challenge is colloidal clustering caused by strong van der Waals (vdW) attraction between long-chain surface capping ligands passivating the surface of nanocrystals. Such clustering degrades ordering in packing during the self-assembly process. While ligand exchange to provide colloidal stability in polar phases is often an option, this is not the case for the exciting new class of halide perovskites due to the material's solubility in essentially all polar solvents. Here, we report surface-functionalized self-assembly of luminescent CsPbBr₃ perovskite nanocubes by partially replacing long-chain oleyl groups (18 carbon chain) with short-chain thiocyanate (SCN^-). This enables the fabrication of ultrasmooth monolayer thin films of nanocubes with a root-mean-square (RMS) roughness of around 4 Å. This ultrasmooth large area self-assembled layer could act as high-efficiency optoelectronic devices like solar cells, light-emitting diodes (LEDs), transistors, etc. We correlate our experimental results with simulations, providing detailed predictions for lattice constants with chain conformations showing reduced free energy for cubes grafted with short-chain thiocyanate compared to long-chain oleyl groups, thus facilitating better self-assembly.

Phase Diagram and Structure Map of Binary Nanoparticle Superlattices from a Lennard-Jones Model

A first-principles prediction of the binary nanoparticle phase diagram assembled by solvent evaporation has eluded theoretical approaches. In this paper, we show that a binary system interacting through the Lennard-Jones (LJ) potential contains all experimental phases in which nanoparticles are effectively described as quasi hard spheres. We report a phase diagram consisting of 53 equilibrium phases, whose stability is quite insensitive to the microscopic details of the potentials, thus giving rise to some type of universality. Furthermore, we show that binary lattices may be understood as consisting of certain particle clusters, i.e., motifs, that provide a generalization of the four conventional Frank-Kasper polyhedral units. Our results show that metastable phases share the very same motifs as equilibrium phases. We discuss the connection with packing models, phase diagrams with repulsive potentials, and the prediction of likely experimental superlattices.

The Phase Behavior of Nanoparticle Superlattices in the Presence of a Solvent

Superlattices of nanoparticles coated by alkyl-chain ligands are usually prepared from a stable solution by evaporation, therefore the pathway of superlattice self-assembly critically depends on the amount of solvent present within it. This work addresses the role of the solvent on the structure and the relative stability of the different supercrystalline phases of single-component superlattices (simple cubic, body-centered cubic (BCC), face-centered cubic (FCC), and hexagonal close-packed). The study is performed with a molecular theory for nanoparticle superlattices introduced in this work, which predicts the structure and thermodynamics of the supercrystals explicitly treating the presence and molecular details of the solvent and the ligands. The theory predicts a FCC-BCC transition with decreasing solvent content due to the competition between the translational entropy of the solvent and the entropy and internal energy of the ligands. This result provides an explanation for recent experimental observations by in situ X-ray scattering, which reported a FCC-BCC transition during solvent evaporation. The theory also predicts the effects of the length and surface coverage of the ligands and the radius of the core on the phase behavior in agreement with experimental evidence and previous molecular dynamics simulations. These results validate the use of the dimensionless softness parameter λ (ratio of ligand length to core radius) to predict the phase behavior of wet superlattices. Our results stress the importance of explicitly considering the presence of the solvent in order to reach a complete picture of the mechanisms that mediate the self-assembly of nanoparticle superlattices.

Mixing-demixing transition in polymer-grafted spherical nanoparticles

Polymer-grafted nanoparticles (PGNPs) can provide property profiles that cannot be obtained individually by polymers or nanoparticles (NPs). Here, we have studied the mixing-demixing transition of symmetric copolymer melts of polymer-grafted spherical nanoparticles by means of coarse-grained molecular dynamics simulation and a theoretical mean-field model. We find that a larger size of NPs leads to higher stability for a given number of grafted chains and chain lengths, reaching a point where demixing is not possible. Most importantly, the increase in the number of grafted chains, Ng, can initially favour the phase separation of PGNPs, but a further increase can lead to more difficult demixing. The reason is the increasing impact of an effective core that forms as the grafting density of the tethered polymer chains around the NPs increases. The range and exact values of Ng where this change in behaviour takes place depend on the NP size and the chain length of the grafted polymer chains. Our study elucidates the phase behaviour of PGNPs and in particular the influence of the grafting density on the phase behaviour of the systems, anticipating that it will open new doors in the understanding of these systems with implications in materials science and medicine.

Influence of Softness on the Stability of Binary Colloidal Crystals

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

Superlattice assembly by interpolymer complexation

We present a coarse grained model for a system where nanocrystals are functionalized with a polymer that is a hydrogen bond acceptor, such as polyethylene glycol (PEG), and are dispersed in a solution with a polymer whose monomers consist of a hydrogen bond donor, such as polyacrylic acid (PAA) at low pH (interpolymer complexation). We determine the minimum concentration of the polymer donor to induce aggregation and the structure and dynamics of the induced (fcc) superlattice. Our results are compared to previous and new experiments.

Supercrystallography-Based Decoding of Structure and Driving Force of Nanocrystal Assembly

Nanocrystal (NC) assembly appears as one promising method towards the controllable design and fabrication of advanced materials with desired property and functionality. The achievement of a “materials-by-design” requires not only a primary structural decoding of NC assembled supercrystal at a wide range of length scales, but also an improved understanding of the interactions and changeable roles of various driving forces over the course of nucleation and growth of NC superlattice. The recent invention of a synchrotron-based X-ray supercrystallographic approach makes it feasible to uncover the structural details of NC-assembled supercrystal at unprecedented levels from atomic through nano to mesoscale. Such structural documentations can be used to trace how various driving forces interact in a competitive way and thus change relatively in strength to govern the formation of individual superlattices under certain circumstances. This short review makes use of four single supercrystals typically made up of spherical, truncate, cubic and octahedral NCs, respectively, and provides a comparable description and a reasonable analysis of the use of a synchrotron-based supercrystallographic approach to reveal various degrees of translational and orientational ordering of NCs within various superlattices. In the connection of observed structural aspects with controlled environments of NC assembly, we further address how various driving forces interact each other to develop relatively changeable roles upon variation of the NC shape to respond to the nucleation and growth of various superlattices. With the guidance of such gained insights, we provide additional examples to illustrate how realistic environments are designed into delicate control of NC assembly to achieve particular interactions between NCs towards harvesting superlattice with NC translational symmetry and atomically crystallographic orientation as desired.

Assembly by solvent evaporation: equilibrium structures and relaxation times

We present a study describing the dynamics and equilibrium of the assembly of nanostructures by solvent evaporation. We first consider N nanocrystals stabilized by capping ligands in a spherical droplet of liquid solvent coexisting with its gas and show that, as the liquid solvent evaporates slowly, NCs crystallize into clusters of high symmetry based on tetrahedral and octahedral units: tetrahedron (N = 4), octahedron (N = 6), icosahedron (N = 13), Archimedean truncated tetrahedron (N = 16) and Z₂₀ (N = 21). We derive explicit formulas for the process and rigorously compute relaxation times, which drastically increase when the packing parameter reaches the hard-sphere liquid-solid transition η = 0.49. This result shows that contrary to what occurs in an evaporation of a single component system, the relaxation times are not determined by the diffusion constant of the vapor, but rather, are dominated by the residence time of solvent molecules trapped within the capping ligands. Our theory provides a number of predictions that enable the design of new structures while improving the control and quality of their assembly.

Coexistence of hcp and bct Phases during In Situ Superlattice Assembly from Faceted Colloidal Nanocrystals

We study the in situ self-assembly of faceted PbS nanocrystals from colloidal suspensions upon controlled solvent evaporation using time-resolved small-angle X-ray scattering and X-ray cross-correlation analysis. In our bulk-sensitive experiment in transmission geometry, the superlattice crystallization is observed in real time, revealing a hexagonal closed-packed (hcp) structure followed by formation of a body-centered cubic (bcc) superlattice. The bcc superlattice undergoes continuous tetragonal distortion in the solvated state shortly after its formation, resulting in the body-centered tetragonal (bct) structure. Upon solvent evaporation, the bct superstructure becomes more pronounced with the still coexisting hcp phase. These findings corroborate the existing simulations of assembling cuboctahedral-shaped particles and illustrate that we observed the predicted equilibrium states. This work is essential for a deeper understanding of the fundamental forces that direct nanocrystal assembly including nanocrystal shape and ligand coverage.

Dictating Nanoparticle Assembly via Systems-Level Control of Molecular Multivalency

Nanoparticle assembly can be controlled by multivalent binding interactions between surface ligands, indicating that more precise control over these interactions is important to design complex nanoscale architectures. It has been well-established in natural materials that the arrangement of different molecular species in three dimensions can affect the ability of individual supramolecular units to coordinate their binding, thereby regulating the strength and specificity of their collective molecular interactions. However, in artificial systems, limited examples exist that quantitatively demonstrate how changes in nanoscale geometry can be used to rationally modulate the thermodynamics of individual molecular binding interactions. As a result, the use of nanoscale design features to regulate molecular bonding remains an underutilized design handle to control nanomaterials synthesis. Here we demonstrate a polymer-coated nanoparticle material where supramolecular bonding and nanoscale structure are used in conjunction to dictate the thermodynamics of their multivalent interactions, resulting in emergent bundling of supramolecular binding groups that would not be expected on the basis of the molecular structures alone. Additionally, we show that these emergent phenomena can controllably alter the superlattice symmetry by using the mesoscale particle arrangement to alter the thermodynamics of the supramolecular bonding behavior. The ability to rationally program molecular multivalency via a systems-level approach therefore provides a major step forward in the assembly of complex artificial structures, with implications for future designs of both nanoparticle- and supramolecular-based materials.

Colloidal Self-Assembly of Inorganic Nanocrystals into Superlattice Thin-Films and Multiscale Nanostructures

The self-assembly of colloidal inorganic nanocrystals (NCs) offers tremendous potential for the design of solution-processed multi-functional inorganic thin-films or nanostructures. To date, the self-assembly of various inorganic NCs, such as plasmonic metal, metal oxide, quantum dots, magnetics, and dielectrics, are reported to form single, binary, and even ternary superlattices with long-range orientational and positional order over a large area. In addition, the controlled coupling between NC building blocks in the highly ordered superlattices gives rise to novel collective properties, providing unique optical, magnetic, electronic, and catalytic properties. In this review, we introduce the self-assembly of inorganic NCs and the experimental process to form single and multicomponent superlattices, and we also describe the fabrication of multiscale NC superlattices with anisotropic NC building blocks, thin-film patterning, and the supracrystal formation of superlattice structures.

Modeling Superlattices of Dipolar and Polarizable Semiconducting Nanoparticles

We present an analytical model to describe the stability of arbitrary semiconducting nanoparticle (NP) superlattices as a function of the dipole and polarizability of their constituents. We first validate our model by comparison with density functional theory calculations of simple cubic superlattices of small CdSe NPs, and we show the existence of a regime, relevant to experiments, where NP interactions are predominantly dipole-like. We then apply our model to binary superlattices and find striking differences between the stable geometries of lattices composed of polarizable and nonpolarizable NPs. Finally, we discuss the interplay of dipolar and ligand-ligand interactions in determining the stability of NP superlattices.

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.

Controlled Symmetry Breaking in Colloidal Crystal Engineering with DNA

The programmed crystallization of particles into low-symmetry lattices represents a major synthetic challenge in the field of colloidal crystal engineering. Herein, we report an approach to realizing such structures that relies on a library of low-symmetry Au nanoparticles, with synthetically adjustable dimensions and tunable aspect ratios. When modified with DNA ligands and used as building blocks for colloidal crystal engineering, these structures enable one to expand the types of accessible lattices and to answer mechanistic questions about phase transitions that break crystal symmetry. Indeed, crystals formed from a library of elongated rhombic dodecahedra yield a rich phase space, including low-symmetry lattices (body-centered tetragonal and hexagonal planar). Molecular dynamics simulations corroborate and provide insight into the origin of these phase transitions. In particular, we identify an unexpected asymmetry in the DNA shell, distinct from both the particle and lattice symmetries, which enables directional, nonclose-packed interactions.

Many Body Effects and Icosahedral Order in Superlattice Self-Assembly

We elucidate how nanocrystals "bond" to form ordered structures. For that purpose we consider nanocrystal configurations consisting of regular polygons and polyhedra, which are the motifs that constitute single component and binary nanocrystal superlattices, and simulate them using united atom models. We compute the free energy and quantify many body effects, i.e., those that cannot be accounted for by pair potential (two-body) interactions, further showing that they arise from coalescing vortices of capping ligands. We find that such vortex textures exist for configurations with local coordination number ≤6. For higher coordination numbers, vortices are expelled and nanocrystals arrange in configurations with tetrahedral or icosahedral order. We provide explicit formulas for the optimal separations between nanocrystals, which correspond to the minima of the free energies. Our results quantitatively explain the structure of superlattice nanocrystals as reported in experiments and reveal how packing arguments, extended to include soft components, predict ordered nanocrystal aggregation.

Relevance of packing to colloidal self-assembly

Since the 1920s, packing arguments have been used to rationalize crystal structures in systems ranging from atomic mixtures to colloidal crystals. Packing arguments have recently been applied to complex nanoparticle structures, where they often, but not always, work. We examine when, if ever, packing is a causal mechanism in hard particle approximations of colloidal crystals. We investigate three crystal structures composed of their ideal packing shapes. We show that, contrary to expectations, the ordering mechanism cannot be packing, even when the thermodynamically self-assembled structure is the same as that of the densest packing. We also show that the best particle shapes for hard particle colloidal crystals at any finite pressure are imperfect versions of the ideal packing shape.

Capping Ligand Vortices as "Atomic Orbitals" in Nanocrystal Self-Assembly

We present a detailed analysis of the interaction between two nanocrystals capped with ligands consisting of hydrocarbon chains by united atom molecular dynamics simulations. We show that the bonding of two nanocrystals is characterized by ligand textures in the form of vortices. These results are generalized to nanocrystals of different types (differing core and ligand sizes) where the structure of the vortices depends on the softness asymmetry. We provide rigorous calculations for the binding free energy, show that these energies are independent of the chemical composition of the cores, and derive analytical formulas for the equilibrium separation. We discuss the implications of our results for the self-assembly of single-component and binary nanoparticle superlattices. Overall, our results show that the structure of the ligands completely determines the bonding of nanocrystals, fully supporting the predictions of the recently proposed Orbifold topological model.

Metallurgy of soft spheres with hard core: From BCC to Frank-Kasper phases

Understanding how soft particles can fill the space is still an open question. Structures far from classical FCC or BCC phases are now commonly experimentally observed in many different systems. Models based on pair interaction between soft particles are at present much studied in 2D. Pair interactions with two different lengths have been shown to lead to quasicrystalline architectures. It is also the case for a hard core with a square repulsive shoulder potential. In 3D, global approaches have been proposed for instance by minimizing the interface area between the deformed objects in the case of foams or micellar systems or using a self-consistent mean-field theory in copolymer melts. In this paper we propose to compare a strong van der Waals attraction between spherical hard cores and an elastic energy associated to the deformation of the soft corona. This deformation is measured as the shift between the deformed shell compared to a corona with a perfect spherical symmetry. The two main parameters in this model are: the hard-core volume fraction and the weight of the elastic energy compared to the van der Waals one. The elastic energy clearly favours the BCC structure but large van der Waals forces favor Frank and Kasper phases. This result opens a route towards controlling the building of nanoparticle superlattices with complex structures and thus original physical properties.