Orientational Order in Self-Assembled Nanocrystal Superlattices

Effect of non-additive mixing on entropic bonding strength and phase behavior of binary nanocrystal superlattices

Non-additive mixing plays a key role in the properties of molecular fluids and solids. In this work, the potential for athermal order-disorder phase transitions is explored in non-additive binary colloidal nanoparticles that form substitutionally ordered compounds, namely, for equimolar mixtures of octahedra + spheres, which form a CsCl lattice compound, and cubes + spheres, which form a NaCl crystal. Monte Carlo simulations that target phase coexistence conditions were used to examine the effect on compound formation of varying degrees of negative non-additivity created by component size asymmetry and by size-tunable indentations in the polyhedra's facets, intended to allow the nestling of neighboring spheres. Our results indicate that the stabilization of the compound crystal requires a relatively large degree of negative non-additivity, which depends on particle geometry and the packing of the relevant phases. It is found that negative non-additivity can be achieved in mixtures of large spheres and small cubes having no indentations and lead to the athermal crystallization of the NaCl lattice. For similarly sized components, athermal congruent transitions are attainable and non-additivity can be generated through indentations, especially for the cubes + spheres system. Increasing indentation leads to lower phase coexistence free energy and pressure in the cubes + spheres system but has the opposite effect in the octahedra + spheres system. These results indicate a stronger stabilizing effect on the athermal compound phase by the cubes' indentations, where a deeper nestling of the spheres leads to a denser compound phase and a larger reduction in the associated pressure-volume free-energy term.

Two-Regime Conformation of Grafted Polymer on Nanoparticle Determines Symmetry of Nanoparticle Self-Assembly

One of the key design factors that regulate the properties of grafted nanoparticles (GNPs) and their self-assembly is the conformation of the grafted polymer. On the curved surface of the GNP core, the conformation of the polymer chain is not uniform in the radial direction. The segment is a non-Gaussian chain in the concentrated polymer brush (CPB) regime near the interface between GNP core and grafted polymer, while it is less constrained in the semidilute polymer brush (SDPB) regime near the surface of GNP. Here, the property of polymer conformation showing crossover behavior at the CPB/SDPB threshold through the coarse-grain molecular dynamics simulation of nanoparticles with explicit grafted chains is explored. Moreover, the self-assembly structure depends on the effective softness, which is defined as a function of the threshold of two regimes estimated from the conformation of the polymer.

Predictive Modeling of Nanocrystal Orientation in Superlattices: Insights from Ligand Entropy

The self-assembly of nanocrystals (NCs) into close-packed, ordered superlattices (SLs) is of broad, engineering interest. The coherent orientation of polyhedral nanocrystals within NC SLs enhances electronic, magnetic, and vibrational coupling, leading to a variety of emergent phenomena. Here, we show that coherent orientation of polyhedral NCs in many SLs can be understood simply by considering its effect on the conformational entropy of surface ligands. We report the predicted nanocrystal orientations and entropic driving force to orient for a broad range of nanocrystal shapes and superlattice unit cells, and we show that ligand entropy is sufficient to reproduce a host of reported experimental and computational observations. We additionally use this framework to predict the expected distribution of interstitial species such as solvent or unbound ligands in an oriented NC SL. This work offers intuition for understanding the orientation of NCs in superlattices and a future framework for analyzing multinary structures.

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.

Solvent Isotherms and Structural Transitions in Nanoparticle Superlattice Assembly

We introduce a Molecular Theory for Compressible Fluids (MOLT-CF) that enables us to compute free energies and other thermodynamic functions for nanoparticle superlattices with any solvent content, including the dry limit. Quantitative agreement is observed between MOLT-CF and united-atom molecular dynamics simulations performed to assess the reliability and precision of the theory. Among other predictions, MOLT-CF shows that the amount of solvent within the superlattice decreases approximately linearly with its vapor pressure and that in the late stages of drying, solvent-filled voids form at lattice interstitials. Applied to single-component superlattices, MOLT-CF predicts fcc-to-bcc Bain transitions for decreasing vapor pressure and for increasing ligand length, both in agreement with experimental results. We explore the stability of other single-component phases and show that the C14 Frank-Kasper phase, which has been reported in experiments, is not a global free-energy minimum. Implications for precise assembly and prediction of multicomponent nanoparticle systems are discussed.

Coarse-Grained Many-Body Potentials of Ligand-Stabilized Nanoparticles from Machine-Learned Mean Forces

Colloidal nanoparticles self-assemble into a variety of superstructures with distinctive optical, structural, and electronic properties. These nanoparticles are usually stabilized by a capping layer of organic ligands to prevent aggregation in the solvent. When the ligands are sufficiently long compared to the dimensions of the nanocrystal cores, the effective coarse-grained forces between pairs of nanoparticles are largely affected by the presence of neighboring particles. In order to efficiently investigate the self-assembly behavior of these complex colloidal systems, we propose a machine-learning approach to construct effective coarse-grained many-body interaction potentials. The multiscale methodology presented in this work constitutes a general bottom-up coarse-graining strategy where the coarse-grained forces acting on coarse-grained sites are extracted from measuring the vectorial mean forces on these sites in reference fine-grained simulations. These effective coarse-grained forces, i.e., gradients of the potential of mean force or of the free-energy surface, are represented by a simple linear model in terms of gradients of structural descriptors, which are scalar functions that are rotationally invariant. In this way, we also directly obtain the free-energy surface of the coarse-grained model as a function of all coarse-grained coordinates. We expect that this simple yet accurate coarse-graining framework for the many-body potential of mean force will enable the characterization, understanding, and prediction of the structure and phase behavior of relevant soft-matter systems by direct simulations. The key advantage of this method is its generality, which allows it to be applicable to a broad range of systems. To demonstrate the generality of our method, we also apply it to a colloid-polymer model system, where coarse-grained many-body interactions are pronounced.

Surface Sites and Ligation in Amine-capped CdSe Nanocrystals

Converting colloidal nanocrystals (NCs) into devices for various applications is facilitated by designing and controlling their surface properties. One key strategy for tailoring surface properties is thus to choose tailored surface ligands. In that context, amines have been universally used, with the goal to improve NCs synthesis, processing and performances. However, understanding the nature of surface sites in amine-capped NCs remains challenging, due to the complex surface compositions as well as surface ligands dynamic. Here, we investigate both surface sites and amine ligation in CdSe NCs by combining advanced NMR spectroscopy and computational modelling. Notably, dynamic nuclear polarization (DNP) enhanced 113 Cd and 77 Se 1D NMR helps to identify both bulk and surface sites of NCs, while 113 Cd 2D NMR spectroscopy enables to resolve amines terminated sites on both Se-rich and nonpolar surfaces. In addition to directly bonding to surface sites, amines are shown to also interact through hydrogen-bonding with absorbed water as revealed by 15 N NMR, augmented with computations. The characterization methodology developed for this work provides unique molecular-level insight into the surface sites of a range of amine-capped CdSe NCs, and paves the way to identify structure-function relationships and rational approaches towards colloidal NCs with tailored properties.

Real-Time In Situ Observation of CsPbBr3 Perovskite Nanoplatelets Transforming into Nanosheets

The manipulation of nano-objects through heating is an effective strategy for inducing structural modifications and therefore changing the optoelectronic properties of semiconducting materials. Despite its potential, the underlying mechanism of the structural transformations remains elusive, largely due to the challenges associated with their in situ observations. To address these issues, we synthesize temperature-sensitive CsPbBr₃ perovskite nanoplatelets and investigate their structural evolution at the nanoscale using in situ heating transmission electron microscopy. We observe the morphological changes that start from the self-assembly of the nanoplatelets into ribbons on a substrate. We identify several paths of merging nanoplates within ribbons that ultimately lead to the formation of nanosheets dispersed randomly on the substrate. These observations are supported by molecular dynamics simulations. We correlate the various paths for merging to the random orientation of the initial ribbons along with the ligand mobility (especially from the edges of the nanoplatelets). This leads to the preferential growth of individual nanosheets and the merging of neighboring ones. These processes enable the creation of structures with tunable emission, ranging from blue to green, all from a single material. Our real-time observations of the transformation of perovskite 2D nanocrystals reveal a route to achieve large-area nanosheets by controlling the initial orientation of the self-assembled objects with potential for large-scale applications.

Temperature-Responsive Nanoporous Membranes from Self-Assembly of Poly(N-isopropylacrylamide) Hairy Nanoparticles

Nanoporous membranes play a critical role in numerous separations on laboratory and industrial scales, ranging from water treatment to biotechnology. However, few strategies exist that allow for the preparation of mechanically robust nanoporous membranes whose separation properties can be easily tuned. Here, we introduce a new family of tunable nanoporous membranes based on nanoparticles decorated with temperature-responsive polymer brushes. We prepared mechanically robust membranes from hairy nanoparticles (HNPs) carrying PNIPAM polymer brushes. We assembled the HNPs into thin films through pressure-driven deposition of nanoparticle suspensions and measured the permeability and filtration cutoff of these membranes at different temperatures. The membrane pore diameter at room temperature varied between 10 and 30 nm depending on the polymer length. The water permeability of these membranes could be controlled by temperature, with the effective pore diameter increasing by a factor of 3-6 (up to 100 nm) when the temperature was increased to 60 °C. The size selectivity of these membranes in the filtration of nanoparticles could also be attenuated by temperature. Molecular dynamics computer simulations of a coarse-grained HNP model show that temperature-sensitive pores sizes are consistent with our experimental results and reveal the polymer configurations responsible for the observed filtration membrane permeability. We expect that these membranes will be useful for separations and in the preparation of responsive microfluidic devices.

Shape-induced crystallization of binary DNA-functionalized nanocubes

Leveraging the anisotropic shape of DNA-functionalized nanoparticles holds potential for shape-directed crystallization of a wide collection of superlattice structures. Using coarse-grained molecular dynamics simulations, we study the self-assembly of a binary mixture of cubic gold nanoparticles, which are functionalized by complementary DNA strands. We observe the spontaneous self-assembly of simple cubic (SC), plastic body-centered tetragonal (pBCT), and compositionally disordered plastic body-centered tetragonal (d-pBCT) phases due to hybridization of the DNA strands. We systematically investigate the effect of length, grafting density, as well as rigidity of the DNA strands on the self-assembly behavior of cubic nanoparticles. We measure the potential of mean force between DNA-functionalized nanocubes for varying rigidity of the DNA strands and DNA lengths. Using free-energy calculations, we find that longer and flexible DNA strands can lead to a phase transformation from SC to the pBCT phase due to a gain in entropy arising from the orientational degrees of freedom of the nanocubes in the pBCT phase. Our results may serve as a guide for self-assembly experiments on DNA-functionalized cubic nanoparticles.

Reversible Diffusionless Phase Transitions in 3D Nanoparticle Superlattices

Nanocomposite tectons (NCTs), polymer brush-grafted nanoparticles that use supramolecular interactions to drive their assembly, form ordered nanoparticle superlattices (NPSLs) with well-defined unit cell symmetries when thermally annealed. In this work, we demonstrate that appropriate assembly and processing conditions can also enable control over the microstructure of NCT lattices by balancing the enthalpic and entropic factors associated with ligand packing and supramolecular bonding during crystallization. Unary systems of NCTs are assembled via the addition of a small molecule capable of binding to multiple nanoparticle ligands; these NCTs initially form face-centered-cubic (FCC) structures in solvents that are favorable for the particles' polymer brushes. However, the FCC lattices undergo a reversible, diffusionless phase transition to body-centered-cubic (BCC) lattices when transferred to a solvent that induces polymer brush collapse. The BCC superlattices maintain the same crystal habit as the parent FCC phase but exhibit significant transformation twinning similar to that seen in martensitic alloys. This previously unseen diffusionless phase transformation in NPSLs enables unique microstructural features in the resulting assemblies, suggesting that NPSLs could serve as models for the investigation of microstructural evolution in crystalline systems and extend our understanding of NPSLs as atomic material analogues.

Nanoparticle Assembly and Oriented Attachment: Correlating Controlling Factors to the Resulting Structures

Nanoparticle assembly and attachment are common pathways of crystal growth by which particles organize into larger scale materials with hierarchical structure and long-range order. In particular, oriented attachment (OA), which is a special type of particle assembly, has attracted great attention in recent years because of the wide range of material structures that result from this process, such as one-dimensional (1D) nanowires, two-dimensional (2D) sheets, three-dimensional (3D) branched structures, twinned crystals, defects, etc. Utilizing in situ transmission electron microscopy techniques, researchers observed orientation-specific forces that act over short distances (∼1 nm) from the particle surfaces and drive the OA process. Integrating recently developed 3D fast force mapping via atomic force microscopy with theories and simulations, researchers have resolved the near-surface solution structure, the molecular details of charge states at particle/fluid interfaces, inhomogeneity of surface charges, and dielectric/magnetic properties of particles that influence short- and long-range forces, such as electrostatic, van der Waals, hydration, and dipole-dipole forces. In this review, we discuss the fundamental principles for understanding particle assembly and attachment processes, and the controlling factors and resulting structures. We review recent progress in the field via examples of both experiments and modeling, and discuss current developments and the future outlook.

Development of Self-Assembly Methods on Quantum Dots

Quantum dot materials, with their unique photophysical properties, are promising zero-dimensional materials for encryption, display, solar cells, and biomedical applications. However, due to the large surface to volume ratio, they face the challenge of chemical instability and low carrier transport efficiency, which have greatly limited their reliability and utility. In light of the current development bottleneck of quantum dot materials, the chemical stability and physical properties can be effectively improved by the self-assembly method. This review will discuss the research progress of the self-assembly methods of quantum dots and analyze the advantages and disadvantages of those self-assembly methods. Furthermore, the scientific challenges and improvement in the self-assembly method of quantum dots are prospected.

Discovery of two-dimensional binary nanoparticle superlattices using global Monte Carlo optimization

Binary nanoparticle (NP) superlattices exhibit distinct collective plasmonic, magnetic, optical, and electronic properties. Here, we computationally demonstrate how fluid-fluid interfaces could be used to self-assemble binary systems of NPs into 2D superlattices when the NP species exhibit different miscibility with the fluids forming the interface. We develop a basin-hopping Monte Carlo (BHMC) algorithm tailored for interface-trapped structures to rapidly determine the ground-state configuration of NPs, allowing us to explore the repertoire of binary NP architectures formed at the interface. By varying the NP size ratio, interparticle interaction strength, and difference in NP miscibility with the two fluids, we demonstrate the assembly of an array of exquisite 2D periodic architectures, including AB-, AB₂-, and AB₃-type monolayer superlattices as well as AB-, AB₂-, A₃B₅-, and A₄B₆-type bilayer superlattices. Our results suggest that the interfacial assembly approach could be a versatile platform for fabricating 2D colloidal superlattices with tunable structure and properties.

The Crucial Role of Solvation Forces in the Steric Stabilization of Nanoplatelets

The steric stability of inorganic colloidal particles in an apolar solvent is usually described in terms of the balance between three contributions: the van der Waals attraction, the free energy of mixing, and the ligand compression. However, in the case of nanoparticles, the discrete nature of the ligand shell and the solvent has to be taken into account. Cadmium selenide nanoplatelets are a special case. They combine a weak van der Waals attraction and a large facet to particle size ratio. We use coarse grained molecular dynamics simulations of nanoplatelets in octane to demonstrate that solvation forces are strong enough to induce the formation of nanoplatelet stacks and by that have a crucial impact on the steric stability. In particular, we demonstrate that for sufficiently large nanoplatelets, solvation forces are proportional to the interacting facet area, and their strength is intrinsically tied to the softness of the ligand shell.

Reversible assembly of nanoparticles: theory, strategies and computational simulations

The significant advances in synthesis and functionalization have enabled the preparation of high-quality nanoparticles that have found a plethora of successful applications. The unique physicochemical properties of nanoparticles can be manipulated through the control of size, shape, composition, and surface chemistry, but their technological application possibilities can be further expanded by exploiting the properties that emerge from their assembly. The ability to control the assembly of nanoparticles not only is required for many real technological applications, but allows the combination of the intrinsic properties of nanoparticles and opens the way to the exploitation of their complex interplay, giving access to collective properties. Significant advances and knowledge gained over the past few decades on nanoparticle assembly have made it possible to implement a growing number of strategies for reversible assembly of nanoparticles. In addition to being of interest for basic studies, such advances further broaden the range of applications and the possibility of developing innovative devices using nanoparticles. This review focuses on the reversible assembly of nanoparticles and includes the theoretical aspects related to the concept of reversibility, an up-to-date assessment of the experimental approaches applied to this field and the advanced computational schemes that offer key insights into the assembly mechanisms. We aim to provide readers with a comprehensive guide to address the challenges in assembling reversible nanoparticles and promote their applications.

Dual Atomic Coherence in the Self-Assembly of Patchy Heterostructural Nanocrystals

Advances in the synthesis and self-assembly of nanocrystals have enabled researchers to create a plethora of different nanoparticle superlattices. But while many superlattices with complex types of translational order have been realized, rotational order of nanoparticle building blocks within the lattice is more difficult to achieve. Self-assembled superstructures with atomically coherent nanocrystal lattices, which are desirable due to their exceptional electronic and optical properties, have been fabricated only for a few selected systems. Here, we combine experiments with molecular dynamics (MD) simulations to study the self-assembly of heterostructural nanocrystals (HNCs), consisting of a near-spherical quantum dot (QD) host decorated with a small number of epitaxially grown gold nanocrystal (Au NC) "patches". Self-assembly of these HNCs results in face-centered-cubic (fcc) superlattices with well-defined orientational relationships between the atomic lattices of both QD hosts and Au patches. MD simulations indicate that the observed dual atomic coherence is linked to the number, size, and relative positions of gold patches. This study provides a strategy for the design and fabrication of NC superlattices with large structural complexity and delicate orientational order.

Strengthening Engineered Nanocrystal Three-Dimensional Superlattices via Ligand Conformation and Reactivity

Nanocrystal assembly into ordered structures provides mesostructural functional materials with a precise control that starts at the atomic scale. However, the lack of understanding on the self-assembly itself plus the poor structural integrity of the resulting supercrystalline materials still limits their application into engineered materials and devices. Surface functionalization of the nanobuilding blocks with organic ligands can be used not only as a means to control the interparticle interactions during self-assembly but also as a reactive platform to further strengthen the final material via ligand cross-linking. Here, we explore the influence of the ligands on superlattice formation and during cross-linking via thermal annealing. We elucidate the effect of the surface functionalization on the nanostructure during self-assembly and show how the ligand-promoted superlattice changes subsequently alter the cross-linking behavior. By gaining further insights on the chemical species derived from the thermally activated cross-linking and its effect in the overall mechanical response, we identify an oxidative radical polymerization as the main mechanism responsible for the ligand cross-linking. In the cascade of reactions occurring during the surface-ligands polymerization, the nanocrystal core material plays a catalytic role, being strongly affected by the anchoring group of the surface ligands. Ultimately, we demonstrate how the found mechanistic insights can be used to adjust the mechanical and nanostructural properties of the obtained nanocomposites. These results enable engineering supercrystalline nanocomposites with improved cohesion while preserving their characteristic nanostructure, which is required to achieve the collective properties for broad functional applications.

Machine-learning effective many-body potentials for anisotropic particles using orientation-dependent symmetry functions

Spherically-symmetric atom-centered descriptors of atomic environments have been widely used for constructing potential or free energy surfaces of atomistic and colloidal systems and to characterize local structures using machine learning techniques. However, when particle shapes are non-spherical, as in the case of rods and ellipsoids, standard spherically-symmetric structure functions alone produce imprecise descriptions of local environments. In order to account for the effects of orientation, we introduce two- and three-body orientation-dependent particle-centered descriptors for systems composed of rod-like particles. To demonstrate the suitability of the proposed functions, we use an efficient feature selection scheme and simple linear regression to construct coarse-grained many-body interaction potentials for computationally-efficient simulations of model systems consisting of colloidal particles with anisotropic shape: mixtures of colloidal rods and nonadsorbing polymer, hard rods enclosed by an elastic microgel shell, and ligand-stabilized nanorods. We validate the machine-learning (ML) effective many-body potentials based on orientation-dependent symmetry functions by using them in direct coexistence simulations to map out the phase behavior of colloidal rods and non-adsorbing polymer. We find good agreement with results obtained from simulations of the true binary mixture, demonstrating that the effective interactions are well-described by the orientation-dependent ML potentials.

Self-Assembly of Colloidal Nanocrystals into 3D Binary Mesocrystals

ConspectusBiominerals are unique materials found in many living organisms that often display outstanding functionalities attributed to their mesocrystalline structure. Mesocrystals are nanocrystal superstructures with mutual crystallographic alignment of the building units. One could thus imagine these optimized evolutionary systems as archetypes to fabricate advanced materials. The main advantage of such systems relies on their ability to combine the features of the nanocrystals with those of single crystalline microscopic structures, yielding assemblies with directional, enhanced, and potentially emergent properties. Moreover, fueled by the promises of multifunctional materials with unprecedented and tunable properties, the rational design of mesocrystals assembled from two distinct colloidal nanocrystal ensembles has become a recent focus of research. However, the combination of dissimilar nanocrystals into ordered binary superstructures is still a major scientific challenge due to the nature of the coassembly process.We focus this Account on the growth of tridimensional (3D) binary mesocrystals and the understanding of the self-assembly of two colloidal nanocrystal ensembles with the ultimate goal to serve as a basis for more rational mesocrystal syntheses in the future. The formation of mesocrystals demands nanocrystals with defined surface faceting, the primary factor influencing their oriented self-assembly. Notably, such a process cannot be successfully afforded without functionalized nanocrystals with high and, in many cases, tunable colloidal stability. Besides, the nature and solvation degree of the surface ligand shell influences the effective shape of the nanocrystals and the kinetics of self-assembly. If the assembly is triggered by reducing the colloidal stability with nonsolvents, 3D single-component mesocrystals are often grown. Here, the different magnitude of the van der Waals attraction forces between nanocrystals with differing compositions, dimensions, and morphologies generally favors the segregation and growth of single component mesocrystals. This phenomenon was illustrated during the successful preparation of 3D binary mesocrystals composed of iron oxide and platinum nanocubes. Although the building blocks possessed comparable sizes and were stabilized by similar ligands, the amount of the second component could only be arbitrarily tuned up to some extent, even when the assembly conditions were rationally optimized to achieve 3D binary mesocrystals. Only a small amount of it was effectively incorporated into the matrix of the initial mesocrystal. The 3D binary mesocrystal growth process demands a delicate control over the size, shape, and surface chemistry of the nanocrystals, the solvent nature, and the self-assembly process. Hence, the improvement of our ability to control the synthesis of 3D binary mesocrystalline materials is critical to exploit their potential toward technological applications in catalysis, energy storage, or structural materials.

Nanoscale Faceting and Ligand Shell Structure Dominate the Self-Assembly of Nonpolar Nanoparticles into Superlattices

Self-assembly of nanoscale structures at liquid-solid interfaces occurs in a broad range of industrial processes and is found in various phenomena in nature. Conventional theory assumes spherical particles and homogeneous surfaces, but that model is oversimplified, and nanoscale in situ observations are needed for a more complete understanding. Liquid-phase scanning transmission electron microscopy (LP-STEM) is used to examine the interactions that direct the self-assembly of superlattices formed by gold nanoparticles (AuNPs) in nonpolar liquids. Varying the molecular coating of the substrate modulates short-range attraction and leads to switching between a range of different geometric structures, including hexagonal close-packed (hcp), simple hexagonal (sh), dodecahedral quasi-crystal (dqc), and body-centered cubic (bcc) lattices, as well as random distributions. Langevin dynamics simulations explain the experimental results in terms of the interplay between nanoparticle faceting, ligand shell structure, and substrate-NP interactions.

Ligand Interactions and Nanoparticle Shapes Guide the Pathways toward Interfacial Self-Assembly

Non-equilibrium molecular dynamics simulations are used to probe the driving forces behind the formation of highly ordered, epitaxially connected superlattices of polyhedral-shaped nanoparticles (NPs) at fluid-fluid interfaces. By explicitly modeling coarse-grained ligands that cap the NP surface, it is shown that differences in NP shapes and time-dependent facet-specific ligand densities give rise to drastically different transformation mechanisms. Our results indicate that the extent of screening of the inter-particle interactions by the surrounding solvation environment has a significant impact on reversibility and ultimately the coherence of the final two-dimensional superlattice obtained. For the particle shapes examined, a hexagonal pre-assembly and a square superlattice final assembly (upon preferential ligand desorption from {100} facets) were prevalent; however, cuboctahedral NPs formed intermediate epitaxially bonded branched clusters, which eventually grew and rearranged into a square lattice; in contrast, truncated octahedral NPs exhibited an abrupt rhombic-to-square transition driven by the clustering of their numerous {111}-ligands that favored the stacking of linear NP rods. To track the incipient order in the system, we also outline a set of novel order parameters that measure the local orientation alignment between nearest-neighbor pairs. The simulation protocols advanced in this work could pave the way forward for exploration of the vast phase space associated with the interfacial self-assembly of NPs.

On the Formation of Honeycomb Superlattices from PbSe Quantum Dots: The Role of Solvent-Mediated Repulsion and Facet-to-Facet Attraction in NC Self-Assembly and Alignment

Semiconductor superstructures made from assembled and epitaxially connected colloidal nanocrystals (NCs) hold promise for crystalline solids with atomic and nanoscale periodicity, whereby the band structure can be tuned by the geometry. The formation of especially the honeycomb superstructure on a liquid substrate is far from understood and suffers from weak replicability. Here, we introduce 1,4-butanediol as an unreactive substrate component, which is mixed with reactive ethylene glycol to tune for optimal reactivity. It shows us that the honeycomb superlattice has a NC precursor state before oriented attachment occurs, in the form of a self-assembled hexagonal bilayer. We propose that the difference between the formation of the square or honeycomb superstructure occurs during the self-assembly phase. To form a honeycomb superstructure, it is crucial to stabilize the hexagonal bilayer in the presence of solvent-mediated repulsion. In contrast, a square superstructure benefits from the contraction of a hexagonal monolayer due to the absence of a solvent. A second experiment shows the very last stage of the process, where the increasing alignment of NCs is quantified using selected-area electron diffraction (SAED). The combination of transmission electron microscopy (TEM), SAED, and tomography used in these experiments shows that the (100)/(100) facet-to-facet attraction is the main driving force for NC alignment and attachment. These findings are validated by coarse-grained molecular dynamic simulations, where we show that an optimal NC repulsion is crucial to create the honeycomb superstructure.

Emergent properties in supercrystals of atomically precise nanoclusters and colloidal nanocrystals

We provide a comprehensive account of the optical, electrical and mechanical properties that result from the self-assembly of colloidal nanocrystals or atomically precise nanoclusters into crystalline arrays with long-range order....

Formation Mechanism of Well-Ordered Densely Packed Nanoparticle Superlattices Deposited from Gas Phase on Template-Free Surfaces

Superlattices of nanoparticles are generally produced based on solution chemistry processes. In this paper, we demonstrate that self-assembled monolayer structures of nanoparticles with superlattice periodicities can also be produced on template-free surfaces in the gas-phase cluster beam deposition process. It is found that the packing of Fe nanoparticles corresponds to an average of two-dimensional densely packed lattice with a hexagonal summary. By controlling the nanoparticle coverage, the two-dimensional densely packed monolayer morphology can spread to the whole substrate surface being deposited. A formation mechanism of the ordered monolayers is proposed. The densely packed morphologies are formed by the balance between the diffusion rate of the nanoparticles and their filling speed on the substrate surface determined by the deposition rate, and the ordering of the nanoparticle arrays is driven by the inter-particle attractive interactions. The model is strongly supported by a series of carefully designed cluster deposition experiments.

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.

Neuroevolutionary Learning of Particles and Protocols for Self-Assembly

Within simulations of molecules deposited on a surface we show that neuroevolutionary learning can design particles and time-dependent protocols to promote self-assembly, without input from physical concepts such as thermal equilibrium or mechanical stability and without prior knowledge of candidate or competing structures. The learning algorithm is capable of both directed and exploratory design: it can assemble a material with a user-defined property, or search for novelty in the space of specified order parameters. In the latter mode it explores the space of what can be made, rather than the space of structures that are low in energy but not necessarily kinetically accessible.

Unconventional-Phase Crystalline Materials Constructed from Multiscale Building Blocks

Crystal phase, an intrinsic characteristic of crystalline materials, is one of the key parameters to determine their physicochemical properties. Recently, great progress has been made in the synthesis of nanomaterials with unconventional phases that are different from their thermodynamically stable bulk counterparts via various synthetic methods. A nanocrystalline material can also be viewed as an assembly of atoms with long-range order. When larger entities, such as nanoclusters, nanoparticles, and microparticles, are used as building blocks, supercrystalline materials with rich phases are obtained, some of which even have no analogues in the atomic and molecular crystals. The unconventional phases of nanocrystalline and supercrystalline materials endow them with distinctive properties as compared to their conventional counterparts. This Review highlights the state-of-the-art progress of nanocrystalline and supercrystalline materials with unconventional phases constructed from multiscale building blocks, including atoms, nanoclusters, spherical and anisotropic nanoparticles, and microparticles. Emerging strategies for engineering their crystal phases are introduced, with highlights on the governing parameters that are essential for the formation of unconventional phases. Phase-dependent properties and applications of nanocrystalline and supercrystalline materials are summarized. Finally, major challenges and opportunities in future research directions are proposed.

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

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

Library Design of Ligands at the Surface of Colloidal Nanocrystals

Surfaces-and interfaces-are ubiquitous at the nanoscale. Their relevance to nanoscience and nanotechnology is therefore inherent. Colloidal inorganic nanocrystals (NCs), which can show more than a half of their atoms at the surface, are paradigmatic of the role of surfaces in determining materials' form and functions. Therefore, colloidal NCs may be regarded as soluble surfaces, allowing convenient study of ensemble structure and properties in the solution phase.Colloidal NCs commonly bear chemical species at their surface. Such species (generally referred to as ligands) are introduced already in the synthetic procedures and are added postsynthesis in surface chemistry modification (ligand exchange) reactions. Ligands (i) affect the reactivity and diffusion of the synthetic precursors, (ii) mediate NC interactions with the surroundings, and (iii) contribute to the overall electronic structure. In principle, a vast amount of ligands, as large as our imagination, could be used to coordinate the surface of colloidal NCs. In practice and despite the plethora of studies on NC surface chemistry, a relatively limited number of ligands have been explored. In addition, the importance of designing a set of ligands with tailored features (a ligand library), which may permit comprehensive discussion and explanation of the role of surfaces in the NC structure and properties, is often overlooked. Ligand libraries may also foster heuristic access to novel, unexpected observations.Here, the rational design of ligand libraries is discussed, suggesting that it may be a general method to advance knowledge on colloidal NCs and nanomaterials at large.First, a general ligand framework is introduced. The main subunits are identified: ligands are constituted by a binding group and a pendant moiety, bearing functional substituent groups. On this basis, ligand binding at the NC surface is discussed borrowing concepts from coordination chemistry. Dynamic equilibria at the NC surface are highlighted, revealing the compromise between forming and breaking bonds at interfaces and its intricate interplay with the surroundings. Tailoring of the ligand subunits may impart functions to the whole ligand, eventually transposable to the ligated NC.On these bases, it is shown how ligand design may be exploited to (i) exert control on the size and shape of the NCs, (ii) determine NCs' dispersibility in a solvent and affect their self-assembly, and (iii) tune the NCs' optical and electronic properties. These observations point to a description of colloidal NCs as un-decomposable species: ligands may be conceived as an integral part of the overall chemical and electronic structure of the colloidal NC and should not be considered as mere appendages that weakly perturb the inorganic core features.Finally, a perspective on the ligand library design is given. Function-oriented design of the ligand subunits is foreseen as an effective strategy to explore the chemical diversity space. High-throughput screening processes by using computation may represent a valuable tool for such an exploration. The whole ligand features, which depend on the subunits, can be implemented in the final NCs, providing feedback for refined design, toward a priori materials design. Ligand libraries can be fundamental to enabling colloidal NCs as reliable luminophores and (photo)catalysts.

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.

Mechanistic Insights into Superlattice Transformation at a Single Nanocrystal Level Using Nanobeam Electron Diffraction

Understanding the mechanism and ultimately directing nanocrystal (NC) superlattice assembly and attachment have important implications on future advances in this emerging field. Here, we use 4D-STEM to investigate a monolayer of PbS NCs at various stages of the transformation from a hexatic assembly to a nonconnected square-like superlattice over large fields of view. Maps of nanobeam electron diffraction patterns acquired with an electron microscope pixel array detector (EMPAD) offer unprecedented detail into the 3D crystallographic alignment of the polyhedral NCs. Our analysis reveals that superlattice transformation is dominated by translation of prealigned NCs strongly coupled along the <11n>_AL direction and occurs stochastically and gradually throughout single grains. We validate the generality of the proposed mechanism by examining the structure of analogous PbSe NC assemblies using conventional transmission electron microscopy and selected area electron diffraction. The experimental results presented here provide new mechanistic insights into NC self-assembly and oriented attachment.

Coupled Dynamics of Colloidal Nanoparticle Spreading and Self-Assembly at a Fluid-Fluid Interface

We investigated the physicochemical and transport phenomena governing the self-assembly of colloidal nanoparticles at the interface of two immiscible fluids. By combining in situ grazing-incidence small-angle X-ray scattering (GISAXS) with a temporal resolution of 200 ms and electron microscopy measurements, we gained new insights into the coupled effects of solvent spreading, nanoparticle assembly, and recession of the vapor-liquid interface on the morphology of the self-assembled thin films. We focus on oleate-passivated PbSe nanoparticles dispersed across an ethylene glycol subphase as a model system and demonstrate how solvent parameters such as surface tension, nanoparticle solubility, aromaticity, and polarity influence the mesoscale morphology of the nanoparticle superlattice. We discovered that a nanoparticle precursor monolayer film spreads in front of the bulk solution and influences the fluid spreading across the subphase. Improved understanding of the impact of kinetic phenomena (i.e., solvent spreading and evaporation) on the superlattice morphology is important to describe the formation mechanism and ultimately enable the assembly of high-quality superlattices with long-range order.

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.

Learning to grow: Control of material self-assembly using evolutionary reinforcement learning

We show that neural networks trained by evolutionary reinforcement learning can enact efficient molecular self-assembly protocols. Presented with molecular simulation trajectories, networks learn to change temperature and chemical potential in order to promote the assembly of desired structures or choose between competing polymorphs. In the first case, networks reproduce in a qualitative sense the results of previously known protocols, but faster and with higher fidelity; in the second case they identify strategies previously unknown, from which we can extract physical insight. Networks that take as input the elapsed time of the simulation or microscopic information from the system are both effective, the latter more so. The evolutionary scheme we have used is simple to implement and can be applied to a broad range of examples of experimental self-assembly, whether or not one can monitor the experiment as it proceeds. Our results have been achieved with no human input beyond the specification of which order parameter to promote, pointing the way to the design of synthesis protocols by artificial intelligence.

Collective topo-epitaxy in the self-assembly of a 3D quantum dot superlattice

Epitaxially fused colloidal quantum dot (QD) superlattices (epi-SLs) may enable a new class of semiconductors that combine the size-tunable photophysics of QDs with bulk-like electronic performance, but progress is hindered by a poor understanding of epi-SL formation and surface chemistry. Here we use X-ray scattering and correlative electron imaging and diffraction of individual SL grains to determine the formation mechanism of three-dimensional PbSe QD epi-SL films. We show that the epi-SL forms from a rhombohedrally distorted body centred cubic parent SL via a phase transition in which the QDs translate with minimal rotation (~10°) and epitaxially fuse across their {100} facets in three dimensions. This collective epitaxial transformation is atomically topotactic across the 10³-10⁵ QDs in each SL grain. Infilling the epi-SLs with alumina by atomic layer deposition greatly changes their electrical properties without affecting the superlattice structure. Our work establishes the formation mechanism of three-dimensional QD epi-SLs and illustrates the critical importance of surface chemistry to charge transport in these materials.

Revealing Grain Boundaries and Defect Formation in Nanocrystal Superlattices by Nanodiffraction

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

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.

Modulating the Mechanical Properties of Supercrystalline Nanocomposite Materials via Solvent-Ligand Interactions

Supercrystalline nanocomposite materials with micromechanical properties approaching those of nacre or similar structural biomaterials can be produced by self-assembly of organically modified nanoparticles and further strengthened by cross-linking. The strengthening of these nanocomposites is controlled via thermal treatment, which promotes the formation of covalent bonds between interdigitated ligands on the nanoparticle surface. In this work, it is shown how the extent of the mechanical properties enhancement can be controlled by the solvent used during the self-assembly step. We find that the resulting mechanical properties correlate with the Hansen solubility parameters of the solvents and ligands used for the supercrystal assembly: the hardness and elastic modulus decrease as the Hansen solubility parameter of the solvent approaches the Hansen solubility parameter of the ligands that stabilize the nanoparticles. Moreover, it is shown that self-assembled supercrystals that are subsequently uniaxially pressed can deform up to 6 %. The extent of this deformation is also closely related to the solvent used during the self-assembly step. These results indicate that the conformation and arrangement of the organic ligands on the nanoparticle surface not only control the self-assembly itself but also influence the mechanical properties of the resulting supercrystalline material. The Hansen solubility parameters may therefore serve as a tool to predict what solvents and ligands should be used to obtain supercrystalline materials with good mechanical properties.

Angular X-Ray Cross-Correlation Analysis (AXCCA): Basic Concepts and Recent Applications to Soft Matter and Nanomaterials

Angular X-ray cross-correlation analysis (AXCCA) is a technique which allows quantitative measurement of the angular anisotropy of X-ray diffraction patterns and provides insights into the orientational order in the system under investigation. This method is based on the evaluation of the angular cross-correlation function of the scattered intensity distribution on a two-dimensional (2D) detector and further averaging over many diffraction patterns for enhancement of the anisotropic signal. Over the last decade, AXCCA was successfully used to study the anisotropy in various soft matter systems, such as solutions of anisotropic particles, liquid crystals, colloidal crystals, superlattices composed by nanoparticles, etc. This review provides an introduction to the technique and gives a survey of the recent experimental work in which AXCCA in combination with micro- or nanofocused X-ray microscopy was used to study the orientational order in various soft matter systems.

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.

Controlling Nanoparticle Orientations in the Self-Assembly of Patchy Quantum Dot-Gold Heterostructural Nanocrystals

Self-assembly of nanocrystals is a promising route for creating macroscale materials that derive function from the properties of their nanoscale building blocks. While much progress has been made assembling nanocrystals into different superlattices, controlling the relative orientations of nanocrystals in those lattices remains a challenge. Here, we combine experiments with computer simulations to study the self-assembly of patchy heterostructural nanocrystals (HNCs), consisting of near-spherical quantum dots decorated with regular arrangements of small gold satellites, into close-packed superlattices with pronounced orientational alignment of HNCs. Our simulations indicate that the orientational alignment is caused by van der Waals interactions between gold patches and is sensitive to the interparticle distance in the superlattice. We demonstrate experimentally that the degree and type of orientational alignment can be controlled by changing ligand populations on HNCs. This study provides guidance for the design and fabrication of nanocrystal superlattices with enhanced structural control.