Soft epitaxy of nanocrystal superlattices

Epitaxial growth in one dimension

The final structure and properties of layers grown by epitaxy techniques are determined in the very early stage of the process. This review describes one-dimensional models for epitaxial growth, emphasizing the basic theoretical concepts employed to analyze nucleation and aggregation phenomena in the submonolayer regime. The main findings regarding the evolution of quantities that define the properties of the system, such as monomer and island densities, and the associated island size, gap length, and capture zone distributions are discussed, as well as the analytical tools used to evaluate them. This review provides a concise overview of the most widely used algorithms for simulating growth processes, discusses relevant experimental results, and establishes connections with existing theoretical studies.

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.

Colloidal model for nucleation and aggregation in one dimension: Accessing the interaction parameters

Through a one-dimensional colloidal model for epitaxial growth, we characterize the nucleation and aggregation processes occurring in a gap between adjacent islands. The timescales associated with deposition, diffusion, aggregation, and nucleation inside the gap are studied in terms of the parameters defining the interaction between colloidal particles. Numerical results from molecular-dynamics (MD) simulations are compared with analytical models and good agreement is found between both data sets. The results for the timescales are used to calculate the associated rates to generate kinetic Monte Carlo (KMC) simulations, which allow exploring larger systems and longer timescales in comparison with MD simulations. The KMC simulations reproduce the global behavior of the densities of islands and monomers as well as the gap length distribution between adjacent islands.

Chemical and Physical Properties of Photonic Noble-Metal Nanomaterials

Colloidal noble metal nanoparticles (NPs) are composed of metal cores and organic or inorganic ligand shells. These NPs support size- and shape-dependent plasmonic resonances. They can be assembled from dispersions into artificial metamolecules which have collective plasmonic resonances originating from coupled bright and dark optical electric and magnetic modes that form depending on the size and shape of the constituent NPs and their number, arrangement, and interparticle distance. NPs can also be assembled into extended 2D and 3D metamaterials that are glassy thin films or ordered thin films or crystals, also known as superlattices and supercrystals. The metamaterials have tunable optical properties that depend on the size, shape, and composition of the NPs, and on the number of NP layers and their interparticle distance. Interestingly, strong light-matter interactions in superlattices form plasmon polaritons. Tunable interparticle distances allow designer materials with dielectric functions tailorable from that characteristic of an insulator to that of a metal, and serve as strong optical absorbers or scatterers, respectively. In combination with lithography techniques, these extended assemblies can be patterned to create subwavelength NP superstructures and form large-area 2D and 3D metamaterials that manipulate the amplitude, phase, and polarization of transmitted or reflected light.

Colloidal model of two-step protocol for epitaxial growth in one dimension

We explore the application of a two-step growth protocol to a one-dimensional colloidal model. The evolution of the system is described in terms of the time-dependence of both monomer and island densities,N₁andN, while its structure is characterized by using distributions of the gap length, the capture zone, the inter-island distance, and the island length. Analytical results obtained from rate equations are compared with these from molecular dynamics simulations. Since the two-step growth protocol deals with nucleation and aggregation processes in two completely separated time regimes, it makes possible to gain better understanding and control on the island formation mechanism than the standard one-step protocol. The predicted features and advantages of the two-step process could be experimentally tested using deposition of colloidal spheres on pattern substrates.

Morphological and Orientational Controls of Self-Assembly of Gold Nanorods Directed by Evaporative Microflows

Evaporative self-assembly of noble metal nanoparticles into ordered structures holds great promise for fabricating optical and plasmonic devices by virtue of its low cost, high efficiency, and ease of operation. However, poor control of Marangoni flows is one of the challenges accounting for realizing a well-defined assembly. Herein, based on the theoretical analysis of the influence of evaporative intensity on the assembly, two simple but reliable flow-field-confinement platforms are designed to control the evaporative microflows and to work concurrently with depletion forces to enable the regulated self-assembly of gold nanorods. Orientationally ordered assemblies are realized by the designed strong unidirectional microflow in a capillary, and a device-scale assembly of monolayer membrane is obtained by the created weak convection in homemade glass cells. Morphologically diversified superstructure assemblies, such as spherulite-like, boundary-twisted, chiral spiral assemblies, and merging membranes with a π-twisted domain wall, are obtained due to the spontaneous symmetry breaking or in the presence of defects, such as surface steps and screw dislocations. Optical anisotropy and polarization-dependent behaviors of these assemblies are further revealed, implying the potential applications in plasmonic coupling devices and optoelectronic components. An understanding of the entropy-driven assembly behaviors and control of evaporative microflows to guide the self-assembly of gold nanorods provides insights into the general bottom-up approach that is helpful for constructing complex yet robust nanosuperstructures.

Building ordered nanoparticle assemblies inspired by atomic epitaxy

Self-assembly of inorganic nanoparticles into mesoscopic or macroscopic nanoparticle assemblies is an efficient strategy to fabricate advanced devices with emergent nanoscale functionalities. Furthermore, assembly of nanoparticles onto substrates may enable the fabrication of substrate-integrated devices, akin to atomic crystal growth on a substrate. Recent progress in nanoparticle assembly suggests that ordered nanoparticle assemblies could be well produced on a selected substrate, referred to as soft epitaxial growth. Herein, recent advances in soft epitaxial growth of a nanoparticle assembly are presented, including the assembly strategies, the choice of substrate and the epitaxial modes. Perspectives are also discussed for the material design based on substrate-integrated soft epitaxial growth.

Roll-To-Roll Friendly Solution-Processing of Ultrathin, Sintered CdTe Nanocrystal Photovoltaics

Roll-to-roll (R2R) device fabrication using solution-processed materials is a cheap and versatile approach that has attracted widespread interest over the past 2 decades. Here, we systematically introduce and investigate R2R-friendly modifications in the fabrication of ultrathin, sintered CdTe nanocrystal (NC) solar cells. These include (1) scalable deposition techniques such as spray-coating and doctor-blading, (2) a bath-free, controllable sintering of CdTe NCs by quantitative addition of a sintering agent, and (3) radiative heating with an infrared lamp. The impact of each modification on the CdTe nanostructure and solar cell performance was first independently studied and compared to the standard, non-R2R-friendly procedure involving spin-coating the NCs, soaking in a CdCl₂ bath, and annealing on a hot plate. The R2R-friendly techniques were then combined into a single, integrated process, yielding devices that reach 10.4% power conversion efficiency with a V_oc, J_sc, and FF of 697 mV, 22.2 mA/cm², and 67%, respectively, after current/light soaking. These advances reduce the barrier for large-scale manufacturing of solution-processed, ultralow-cost solar cells on flexible or curved substrates.

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.

Nanoscale Disorder Generates Subdiffusive Heat Transport in Self-Assembled Nanocrystal Films

Investigating the impact of nanoscale heterogeneity on heat transport requires a spatiotemporal probe of temperature on the length and time scales intrinsic to heat navigating nanoscale defects. Here, we use stroboscopic optical scattering microscopy to visualize nanoscale heat transport in disordered films of gold nanocrystals. We find that heat transport appears subdiffusive at the nanoscale. Finite element simulations show that tortuosity of the heat flow underlies the subdiffusive transport, owing to a distribution of nonconductive voids. Thus, while heat travels diffusively through contiguous regions of the film, the tortuosity causes heat to navigate circuitous pathways that make the observed mean-squared expansion of an initially localized temperature distribution appear subdiffusive on length scales comparable to the voids. Our approach should be broadly applicable to uncover the impact of both designed and unintended heterogeneities in a wide range of materials and devices that can affect more commonly used spatially averaged thermal transport measurements.

Debye vs. Casimir: controlling the structure of charged nanoparticles deposited on a substrate

Fine-tuning the interactions between particles can allow one to steer their collective behaviour and structure. A convenient way to achieve this is to use solvent criticality to control attraction, via critical Casimir forces, and to control repulsion via the Debye screening of electrostatic interactions. Herein, we develop a multiscale simulation framework and a method for controlled deposition of quantum dots to investigate how these interactions affect the structure of charged nanoparticles deposited on a substrate, altogether immersed in a binary liquid mixture intermixed with salt. We consider nanoparticles and substrates favouring the same component of the mixture and find that the critical Casimir interactions between the nanoparticles become drastically reduced at the substrate. In particular, the interactions can become a few k_BT weaker and their decay length a few orders of magnitude smaller than in the bulk. At off-critical compositions, the decay length increases upon approaching criticality, as expected, but the interaction strength decreases. With molecular dynamics simulations and experiments, we reveal that the nanoparticles can self-assemble into crystalline clusters which form superstructures resembling cluster fluids and spinodal morphology. The simulations additionally predict the formation of fractal-like nanoparticle gels and bicontinuous phases. Our results demonstrate that charged nanoparticles in a salty binary liquid mixture provide exciting opportunities to study the formation of complex structures experimentally and theoretically, which may lead to applications in optoelectronics and photonics.

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.

Single-crystal Winterbottom constructions of nanoparticle superlattices

Colloidal nanoparticle assembly methods can serve as ideal models to explore the fundamentals of homogeneous crystallization phenomena, as interparticle interactions can be readily tuned to modify crystal nucleation and growth. However, heterogeneous crystallization at interfaces is often more challenging to control, as it requires that both interparticle and particle-surface interactions be manipulated simultaneously. Here, we demonstrate how programmable DNA hybridization enables the formation of single-crystal Winterbottom constructions of substrate-bound nanoparticle superlattices with defined sizes, shapes, orientations and degrees of anisotropy. Additionally, we show that some crystals exhibit deviations from their predicted Winterbottom structures due to an additional growth pathway that is not typically observed in atomic crystals, providing insight into the differences between this model system and other atomic or molecular crystals. By precisely tailoring both interparticle and particle-surface potentials, we therefore can use this model to both understand and rationally control the complex process of interfacial crystallization.

Biowaste-Derived, Self-Organized Arrays of High-Performance 2D Carbon Emitters for Organic Light-Emitting Diodes

Low-cost flexible organic light-emitting diodes (OLEDs) with nanoemitter material from waste open up new opportunities for sustainable technology. The common emitter materials generated from waste are carbon dots (CDs). However, these have poor luminescent properties. Further solid-state emission quenching makes application in display devices challenging. Here, flexible and rigid OLED devices are demonstrated using self-assembled 2D arrays of CDs derived from waste material, viz., human hair. High-performance CDs with a quantum yield (QY) of 87%, self-assembled into 2D arrays, are achieved by improving the crystallinity and decreasing the CDs' size distribution. The CD island array exhibits ultrahigh hole mobility (≈10^-1 cm² V^-1 s^-1 ) and significant reduction in solid-state emission quenching compared to pristine CDs; hence, it is used here as an emitting layer in both indium tin oxide (ITO)-coated glass and ITO-coated flexible poly(ethylene terephthalate) (PET) substrate OLED devices, without any hole-injection layer. The flexible OLED device exhibits a stable, voltage-independent blue/cyan emission with a record maximum luminescence of 350 cd m^-2 , whereas the OLED device based on the rigid glass substrate shows a maximum luminescence of 700 cd m^-2 . This work sets up a platform to develop next-generation OLED displays using CD emitters derived from the biowaste material.

Application of the Spatial Distribution Function to Colloidal Ordering

2D colloidal assembly is a vital process in the fabrication of nanostructured devices and receives widespread attention in fundamental research. Characterizing the ordering is crucial to develop an understanding of the driving forces behind the assembly and to optimize processing conditions. Image analysis offers a direct evaluation pathway, typically via the radial distribution function or the 2D fast Fourier transform. Both methods have inherent limitations; the former provides no angular dependence, while the latter is challenged when confronted with imperfection on the mean size, spacing, and coverage of the building blocks. Here, we introduce the 2D spatial distribution function (SDF) as an alternative pathway to evaluate colloidal ordering. We benchmark the method in case studies of prominent examples and provide a tool kit for implementation, including an ImageJ plugin and the standalone software CORDERLY. Application and interpretation are straightforward and particularly powerful to analyze and compare colloidal assemblies with limited order.

Revealing Structure and Crystallographic Orientation of Soft Epitaxial Assembly of Nanocrystals by Grazing Incidence X-ray Scattering

We study the structural coherence of a self-assembled overlayer of PbS nanocrystal (NC) superlattice onto an underlying PbS NC monolayer, which acts as a template. We explore the effect of the templating layer on the structure of the overlayer asemblies by varying interfacial strain and determine the impact of new ligands on their superlattice structure. The overlayers and templates are analyzed by grazing-incidence X-ray scattering and microscopy. We find that differences in the lattice parameters of 7.7% between the two layers are tolerated in terms of a "soft epitaxial" assembly into the body-centered tetragonal superstucture and lead to structural registry within the overlayer. Conversely, at the interface, a lattice mismatch of 24.4% is too large for soft epitaxy and invokes a change in the superlattice. Upon ligand treatment, the overlayer superlattices transform their orientation axis and the NCs orient preferentially. These results provide new insights into mitigating defects in layered, heterostructured NC assemblies.

Controlling Superstructure-Property Relationships via Critical Casimir Assembly of Quantum Dots

The assembly of colloidal quantum dots (QDs) into dense superstructures holds great promise for the development of novel optoelectronic devices. Several assembly techniques have been explored; however, achieving direct and precise control over the interparticle potential that controls the assembly has proven to be challenging. Here, we exploit the application of critical Casimir forces to drive the growth of QDs into superstructures. We show that the exquisite temperature-dependence of the critical Casimir potential offers new opportunities to control the assembly process and morphology of the resulting QD superstructures. The direct assembly control allows us to elucidate the relation between structural, optical, and conductive properties of the critical Casimir-grown QD superstructures. We find that the choice of the temperature setting the interparticle potential plays a central role in maximizing charge percolation across QD thin-films. These results open up new directions for controlling the assembly of nanostructures and their optoelectronic properties.

Generalized Preparation of Two-Dimensional Quasi-nanosheets via Self-assembly of Nanoparticles

Two-dimensional (2D) nanomaterials are attracting increasing research interest because of their unique properties and promising applications. Here, we report a facile method to manipulate the assembly of nanoparticles (NPs) to fabricate free-standing 2D quasi-nanosheets. The as-generated 2D products are composed of few-layer NPs; that is, their thicknesses are only tens of nanometers but lateral dimensions could be up to several micrometers. Therefore, the novel structure was denoted as 2D "quasi-nanosheets (QNS)". Specifically, several types of building blocks could be assembled into 2D unary, binary, ternary, and even quaternary QNS by a universal procedure. The entire assembly process is carried out in solution and mediated simply by tuning the concentration of ligands surrounding the NPs. In contrast to traditional assembly techniques, even without any substrate or template, these QNS showed exceptionally high stability. They can remain intact for several days without any disassembly regardless of the solvent environment (e.g., water, ethanol, methanol, and hexane). In general, our method has effectively tackled several limitations associated with traditional assembly techniques and allows more freedom in manipulating assembly of NPs, which may hold great potential for future fabrication of 2D devices with rich functionalities.

Conforming nanoparticle sheets to surfaces with Gaussian curvature

Nanoparticle monolayer sheets are ultrathin inorganic-organic hybrid materials that combine highly controllable optical and electrical properties with mechanical flexibility and remarkable strength. Like other thin sheets, their low bending rigidity allows them to easily roll into or conform to cylindrical geometries. Nanoparticle monolayers not only can bend, but also cope with strain through local particle rearrangement and plastic deformation. This means that, unlike thin sheets such as paper or graphene, nanoparticle sheets can much more easily conform to surfaces with complex topography characterized by non-zero Gaussian curvature, like spherical caps or saddles. Here, we investigate the limits of nanoparticle monolayers' ability to conform to substrates with Gaussian curvature by stamping nanoparticle sheets onto lattices of larger polystyrene spheres. Tuning the local Gaussian curvature by increasing the size of the substrate spheres, we find that the stamped sheet morphology evolves through three characteristic stages: from full substrate coverage, where the sheet extends over the interstices in the lattice, to coverage in the form of caps that conform tightly to the top portion of each sphere and fracture at larger polar angles, to caps that exhibit radial folds. Through analysis of the nanoparticle positions, obtained from scanning electron micrographs, we extract the local strain tensor and track the onset of strain-induced dislocations in the particle arrangement. By considering the interplay of energies for elastic and plastic deformations and adhesion, we construct arguments that capture the observed changes in sheet morphology as Gaussian curvature is tuned over two orders of magnitude.

Au nanocrystal superlattices: nanocrystallinity, vicinal surfaces, and growth processes

Vicinal Au supracrystal surfaces were prepared from Ausingle single domain nanocrystals (NCs), whereas by replacing Ausingle with their polycrystalline counterparts common low-energy supracrystal surfaces were produced. By analogy to atomic crystalline surfaces, we propose a mechanism to explain the formation of such unexpected supracrystal vicinal surfaces, composed of only Ausingle NCs which are non-compact (bct structure) with a coherent alignment of the atomic planes oriented along the [111] superlattice axis and a slight tilt configuration (8.1°) of NCs. In the presence of Co(ε) NCs, these Ausingle supracrystals lose both the slightly tilted configuration of NCs and their orientational order leading to a superlattice transition from bct to fcc. In contrast, supracrystals of Aupoly NCs are insensitive to the presence of Co(ε) NCs. These intriguing structural changes obtained with Ausingle compared to Aupoly supracrystals in the absence and presence of Co(ε) NCs could explain the formation of vicinal surfaces. Note that the solvent used to disperse the nanocrystals plays a key role in the formation of supracrystal vicinal surfaces. Here, a new analogy between supracrystals and atomic crystals is presented.

Lattice Mismatch in Crystalline Nanoparticle Thin Films

For atomic thin films, lattice mismatch during heteroepitaxy leads to an accumulation of strain energy, generally causing the films to irreversibly deform and generate defects. In contrast, more elastically malleable building blocks should be better able to accommodate this mismatch and the resulting strain. Herein, that hypothesis is tested by utilizing DNA-modified nanoparticles as "soft," programmable atom equivalents to grow a heteroepitaxial colloidal thin film. Calculations of interaction potentials, small-angle X-ray scattering data, and electron microscopy images show that the oligomer corona surrounding a particle core can deform and rearrange to store elastic strain up to ±7.7% lattice mismatch, substantially exceeding the ±1% mismatch tolerated by atomic thin films. Importantly, these DNA-coated particles dissipate strain both elastically through a gradual and coherent relaxation/broadening of the mismatched lattice parameter and plastically (irreversibly) through the formation of dislocations or vacancies. These data also suggest that the DNA cannot be extended as readily as compressed, and thus the thin films exhibit distinctly different relaxation behavior in the positive and negative lattice mismatch regimes. These observations provide a more general understanding of how utilizing rigid building blocks coated with soft compressible polymeric materials can be used to control nano- and microstructure.

Silicon Nanocrystal Superlattice Nucleation and Growth

Colloidal dodecene-passivated silicon (Si) nanocrystals were dispersed in hexane or chloroform and deposited onto substrates as face-centered cubic superlattices by slowly evaporating the solvent. The uniformity of the nanocrystals enables extended order; however, the solvent and the evaporation protocol significantly influence the self-assembly process, determining the morphology of the films, the extent of order, and the superlattice orientation on the substrate. Chloroform yielded superlattices with step-flow growth morphologies and (111)_SL, (100)_SL, and (110)_SL orientations. Hexane led to mostly island morphologies when evaporated at room temperature with exclusively (111)_SL orientations. Higher evaporation temperatures led to more extensive step-flow deposition. A model for the surface diffusion of nanocrystals adsorbed on the superlattice surface is developed.

Thermomechanical Response of Self-Assembled Nanoparticle Membranes

Monolayers composed of colloidal nanoparticles, with a thickness of less than 10 nm, have remarkable mechanical moduli and can suspend over micrometer-sized holes to form free-standing membranes. In this paper, we discuss experiments and coarse-grained molecular dynamics simulations characterizing the thermomechanical properties of these self-assembled nanoparticle membranes. These membranes remain strong and resilient up to temperatures much higher than previous simulation predictions and exhibit an unexpected hysteretic behavior during the first heating-cooling cycle. We show this hysteretic behavior can be explained by an asymmetric ligand configuration from the self-assembly process and can be controlled by changing the ligand coverage or cross-linking the ligand molecules. Finally, we show the screening effect of water molecules on the ligand interactions can strongly affect the moduli and thermomechanical behavior.

Epitaxy: Programmable Atom Equivalents Versus Atoms

The programmability of DNA makes it an attractive structure-directing ligand for the assembly of nanoparticle (NP) superlattices in a manner that mimics many aspects of atomic crystallization. However, the synthesis of multilayer single crystals of defined size remains a challenge. Though previous studies considered lattice mismatch as the major limiting factor for multilayer assembly, thin film growth depends on many interlinked variables. Here, a more comprehensive approach is taken to study fundamental elements, such as the growth temperature and the thermodynamics of interfacial energetics, to achieve epitaxial growth of NP thin films. Both surface morphology and internal thin film structure are examined to provide an understanding of particle attachment and reorganization during growth. Under equilibrium conditions, single crystalline, multilayer thin films can be synthesized over 500 × 500 μm² areas on lithographically patterned templates, whereas deposition under kinetic conditions leads to the rapid growth of glassy films. Importantly, these superlattices follow the same patterns of crystal growth demonstrated in atomic thin film deposition, allowing these processes to be understood in the context of well-studied atomic epitaxy and enabling a nanoscale model to study fundamental crystallization processes. Through understanding the role of epitaxy as a driving force for NP assembly, we are able to realize 3D architectures of arbitrary domain geometry and size.

Fracture in sheets draped on curved surfaces

Conforming materials to rigid substrates with Gaussian curvature-positive for spheres and negative for saddles-has proven a versatile tool to guide the self-assembly of defects such as scars, pleats, folds, blisters, and liquid crystal ripples. Here, we show how curvature can likewise be used to control material failure and guide the paths of cracks. In our experiments, and unlike in previous studies on cracked plates and shells, we constrained flat elastic sheets to adopt fixed curvature profiles. This constraint provides a geometric tool for controlling fracture behaviour: curvature can stimulate or suppress the growth of cracks and steer or arrest their propagation. A simple analytical model captures crack behaviour at the onset of propagation, while a two-dimensional phase-field model with an added curvature term successfully captures the crack's path. Because the curvature-induced stresses are independent of material parameters for isotropic, brittle media, our results apply across scales.

The nature and implications of uniformity in the hierarchical organization of nanomaterials

In this Perspective, we present a framework that defines how to understand and control material structure across length scales with inorganic nanoparticles. Three length scales, frequently discussed separately, are unified under the topic of hierarchical organization: atoms arranged into crystalline nanoparticles, ligands arranged on nanoparticle surfaces, and nanoparticles arranged into crystalline superlattices. Through this lens, we outline one potential pathway toward perfect colloidal matter that emphasizes the concept of uniformity. Uniformity is of both practical and functional importance, necessary to increase structural sophistication and realize the promise of nanostructured materials. Thus, we define the nature of nonuniformity at each length scale as a means to guide ongoing research efforts and highlight potential problems in the field.

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.

Strong Resistance to Bending Observed for Nanoparticle Membranes

We demonstrate how gold nanoparticle monolayers can be curled up into hollow scrolls that make it possible to extract both bending and stretching moduli from indentation by atomic force microscopy. We find a bending modulus that is 2 orders of magnitude larger than predicted by standard continuum elasticity, an enhancement we associate with nonlocal microstructural constraints. This finding opens up new opportunities for independent control of resistance to bending and stretching at the nanoscale.