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.

High-Precision Calculation of Nanoparticle (Nanocrystal) Potentials of Mean Force and Internal Energies.

Thermodynamic stability assessment of nanocrystal systems requires precise free energy calculations. This study highlights the importance of meticulous control over various factors, including the thermostat, time step, potential cutoff, initial configuration, sampling method, and overall simulation duration. Free energy computations in dry (solvent-free) systems are on the order of several hundred kBT but can be obtained with consistent accuracy. However, calculation of internal energies becomes challenging, as they are typically much larger in magnitude than free energies and exhibit significant noise and reduced reliability. To address this limitation, we propose a new internal energy estimate that drastically reduces the noise. We also present formulas that enable the optimization of the parameters of the harmonic bias potential for optimal convergence. Finally, we discuss the implications of these findings for the computation of free energies in nanocrystal clusters and superlattices.

Hydrogen Bond Network Disruption by Hydration Layers in Water Solutions with Salt and Hydrogen-Bonding Polymers (PEO).

A mean field theory model describing the interaction of ion hydration layers with the network of hydrogen bonds of both water and the nonionic polymer poly(ethylene oxide) (PEO) is presented. The predictions of the model for types and statistics of hydrogen bonds, the number of water molecules bound to PEO, or their dependence on temperature are successfully verified from all-atom simulations at different NaCl and PEO concentrations. Furthermore, our simulations show that the binding of cations to PEO increases monotonically with salt concentration, in agreement with recent experimental results, through a mechanism in which the sum of the number of bound water and cations is independent of salt concentration. The model introduced is general and can describe any salt or hydrogen-bond-forming polymer.

Two-dimensional assembly of gold nanoparticles grafted with charged-end-group polymers.

HYPOTHESIS: Introducing charged terminal groups to polymers that graft nanoparticles enable Coulombic control over their assembly by tuning the pH and salinity of their aqueous suspensions. EXPERIMENTS: Gold nanoparticles (AuNPs) are grafted with poly (ethylene glycol) (PEG) terminated with (charge-neutral), (negatively charged) or groups (positively charged), and characterized with dynamic light scattering, ζ-potential, and thermal gravimetric analysis. Liquid surface X-ray reflectivity (XR) and grazing incidence small-angle X-ray scattering (GISAXS) are used to determine the density profile and in-plane structure of the AuNPs assembly at the aqueous surface. FINDINGS: Assembly of PEG-AuNPs at the liquid/vapor interface is tunable by adjusting pH or salinity for COOH but less for terminals. The distinct assembly behaviors are attributed to the overall charge of PEG-AuNPs as well as PEG conformation. COOH-PEG corona is more compact than those of the other terminal groups, leading to a crystalline structure with a smaller superlattice. The net charge per particle depends not only on the PEG terminal groups but also on the cation sequestration of PEG and the intrinsic negative charge of the AuNP surface. [1] The closeness to overall charge neutrality, and hydrogen bonding in play, brought by -PEG, drive -PEG-AuNPs to assembly and crystallinity without additives to the suspensions.

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

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

Chiral assemblies of pinwheel superlattices on substrates.

The unique topology and physics of chiral superlattices make their self-assembly from nanoparticles highly sought after yet challenging in regard to (meta)materials1-3. Here we show that tetrahedral gold nanoparticles can transform from a perovskite-like, low-density phase with corner-to-corner connections into pinwheel assemblies with corner-to-edge connections and denser packing. Whereas corner-sharing assemblies are achiral, pinwheel superlattices become strongly mirror asymmetric on solid substrates as demonstrated by chirality measures. Liquid-phase transmission electron microscopy and computational models show that van der Waals and electrostatic interactions between nanoparticles control thermodynamic equilibrium. Variable corner-to-edge connections among tetrahedra enable fine-tuning of chirality. The domains of the bilayer superlattices show strong chiroptical activity as identified by photon-induced near-field electron microscopy and finite-difference time-domain simulations. The simplicity and versatility of substrate-supported chiral superlattices facilitate the manufacture of metastructured coatings with unusual optical, mechanical and electronic characteristics.

Exact Solution for Elastic Networks on Curved Surfaces.

The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity or through effective defect interaction models. In this Letter, we show that the problem can be solved by considering nonlinear elasticity in an exact form without resorting to any approximation in terms of geometric quantities. In this way, we are able to consider different effects that have been unwieldy or not viable to include in the past, such as a finite line tension, explicit dependence on the Poisson ratio, or the determination of the particle positions for the entire lattice. Several geometries with rotational symmetry are solved explicitly. Comparison with linear elasticity reveals an agreement that extends beyond its strict range of applicability. Implications for the problem of the characterization of virus assembly are also discussed.

Binary Superlattices of Gold Nanoparticles in Two Dimensions.

We have created two-dimensional (2D) binary superlattices by cocrystallizing gold nanoparticles (AuNPs) of two distinct sizes into √3 × âˆš3 and 2 × 2 complex binary superlattices, derived from the hexagonal structures of the single components. The building blocks of these binary systems are AuNPs that are functionalized with different chain lengths of poly(ethylene glycol) (PEG). The assembly of these functionalized NPs at the air-water interface is driven by the presence of salt, causing PEG-AuNPs to migrate to the aqueous surface and assemble into a crystalline lattice. We have used liquid surface X-ray reflectivity (XR) and grazing incidence small-angle X-ray scattering (GISAXS) to examine the assembly and crystallization at the liquid interface.

Structural Diversity in Multicomponent Nanocrystal Superlattices Comprising Lead Halide Perovskite Nanocubes.

Nanocrystal (NC) self-assembly is a versatile platform for materials engineering at the mesoscale. The NC shape anisotropy leads to structures not observed with spherical NCs. This work presents a broad structural diversity in multicomponent, long-range ordered superlattices (SLs) comprising highly luminescent cubic CsPbBr3 NCs (and FAPbBr3 NCs) coassembled with the spherical, truncated cuboid, and disk-shaped NC building blocks. CsPbBr3 nanocubes combined with Fe3O4 or NaGdF4 spheres and truncated cuboid PbS NCs form binary SLs of six structure types with high packing density; namely, AB2, quasi-ternary ABO3, and ABO6 types as well as previously known NaCl, AlB2, and CuAu types. In these structures, nanocubes preserve orientational coherence. Combining nanocubes with large and thick NaGdF4 nanodisks results in the orthorhombic SL resembling CaC2 structure with pairs of CsPbBr3 NCs on one lattice site. Also, we implement two substrate-free methods of SL formation. Oil-in-oil templated assembly results in the formation of binary supraparticles. Self-assembly at the liquid-air interface from the drying solution cast over the glyceryl triacetate as subphase yields extended thin films of SLs. Collective electronic states arise at low temperatures from the dense, periodic packing of NCs, observed as sharp red-shifted bands at 6 K in the photoluminescence and absorption spectra and persisting up to 200 K.

Nanocomposite tectons as unifying systems for nanoparticle assembly.

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

De novo endocytic clathrin coats develop curvature at early stages of their formation.

Sculpting a flat patch of membrane into an endocytic vesicle requires curvature generation on the cell surface, which is the primary function of the endocytosis machinery. Using super-resolved live cell fluorescence imaging, we demonstrate that curvature generation by individual clathrin-coated pits can be detected in real time within cultured cells and tissues of developing organisms. Our analyses demonstrate that the footprint of clathrin coats increases monotonically during the formation of pits at different levels of plasma membrane tension. These findings are only compatible with models that predict curvature generation at the early stages of endocytic clathrin pit formation. We also found that CALM adaptors associated with clathrin plaques form clusters, whereas AP2 distribution is more homogenous. Considering the curvature sensing and driving roles of CALM, we propose that CALM clusters may increase the strain on clathrin lattices locally, eventually giving rise to rupture and subsequent pit completion at the edges of plaques.

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

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

Perovskite-type superlattices from lead halide perovskite nanocubes.

Atomically defined assemblies of dye molecules (such as H and J aggregates) have been of interest for more than 80 years because of the emergence of collective phenomena in their optical spectra1-3, their coherent long-range energy transport, their conceptual similarity to natural light-harvesting complexes4,5, and their potential use as light sources and in photovoltaics. Another way of creating versatile and controlled aggregates that exhibit collective phenomena involves the organization of colloidal semiconductor nanocrystals into long-range-ordered superlattices6. Caesium lead halide perovskite nanocrystals7-9 are promising building blocks for such superlattices, owing to the high oscillator strength of bright triplet excitons10, slow dephasing (coherence times of up to 80 picoseconds) and minimal inhomogeneous broadening of emission lines11,12. So far, only single-component superlattices with simple cubic packing have been devised from these nanocrystals13. Here we present perovskite-type (ABO3) binary and ternary nanocrystal superlattices, created via the shape-directed co-assembly of steric-stabilized, highly luminescent cubic CsPbBr3 nanocrystals (which occupy the B and/or O lattice sites), spherical Fe3O4 or NaGdF4 nanocrystals (A sites) and truncated-cuboid PbS nanocrystals (B sites). These ABO3 superlattices, as well as the binary NaCl and AlB2 superlattice structures that we demonstrate, exhibit a high degree of orientational ordering of the CsPbBr3 nanocubes. They also exhibit superfluorescence-a collective emission that results in a burst of photons with ultrafast radiative decay (22 picoseconds) that could be tailored for use in ultrabright (quantum) light sources. Our work paves the way for further exploration of complex, ordered and functionally useful perovskite mesostructures.

Ligand structure and adsorption free energy of nanocrystals on solid substrates.

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

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.

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

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

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

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

Temperature-Induced Tunable Assembly of Columnar Phases of Nanorods.

We report on the assembly of gold nanorods functionalized with poly(ethylene glycol) in aqueous suspensions by electrostatic control and hydrogen bonds provided by polyelectrolyte linkers (i.e., interpolymer complexation processes). Small-angle X-ray scattering reveals that the quality and stability of the assemblies into the hexagonal columnar phases increase with temperature. Our study shows that the lattice constant of the ordered structures is tunable over a wide range of values by the interplay between electrostatic and hydrophobic effects.

The hard sphere diameter of nanocrystals (nanoparticles).

The hard sphere diameter dHS of a nanocrystal (or nanoparticle) is a very important parameter that determines the nearest neighbor separation of their assembled structure, even in those situations where the nanocrystals have large deformations of the ligand shell that prevent them from being described as hard spheres. The parameter dHS is a function of the number of grafted ligands and critically depends on the maximum ligand grafting density σMax, which we calculate by three different methods for the 351 gold nanocrystals with the number of atoms between 38 and 4033. The use of dHS in the interpretation of experimental results is analyzed.