Anisotropic nanocrystal shape and ligand design for co-assembly

Theory and simulation of ligand functionalized nanoparticles - a pedagogical overview

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

High-Throughput Computational Screening of Solid-Binding Peptides

Inspired by biomineralization, a naturally occurring, protein-facilitated process, solid-binding peptides (SBPs) have gained much attention for their potential to fabricate various shaped nanocrystals and hierarchical nanostructures. The advantage of SBPs over other traditionally used synthetic polymers or short ligands is their tunable interaction with the solid material surface via carefully programmed sequence and being solution-dependent simultaneously. However, designing a sequence with targeted binding affinity or selectivity often involves intensive processes such as phage display, and only a limited number of sequences can be identified. Other computational efforts have also been introduced, but the validation process remains prohibitively expensive once a suitable sequence has been identified. In this paper, we present a new model to rapidly estimate the binding free energy of any given sequence to a solid surface. We show how the overall binding of a polypeptide can be estimated from the free energy contribution of each residue based on the statistics of the thermodynamically stable structure ensemble. We validated our model using five silica-binding peptides of different binding affinities and lengths and showed that the model is accurate and robust across a wider range of chemistries and binding strengths. The computational cost of this method can be as low as 3% of the commonly used enhanced sampling scheme for similar studies and has a great potential to be used in high-throughput algorithms to obtain larger training data sets for machine learning SBP screening.

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

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

On-Demand Assembly of Nanocrystals into a Superstructure Library in Co(OH)2 Single-Walled Nanotubes

The hierarchical self-assembly of colloidal particles facilitates the bottom-up manufacturing of metamaterials with synergistically integrated functionalities. Here, we define a modular assembly methodology that enables multinary co-assembly of nanoparticles in one-dimensional confined space. A series of isotropic and anisotropic nanocrystals such as plasmonic, metallic, visible, and near-infrared responsive nanoparticles as well as transition-metal phosphides can be selectively assembled within the single-walled Co(OH)2 nanotubes to achieve various increasingly sophisticated assembly systems, including unary, binary, ternary, and quaternary superstructures. Moreover, the selective assembly of distinct functional nanoparticles produces different integrated functional superstructures. This generalizable methodology provides predictable pathways to complex architectures with structural programming and customization that are otherwise inaccessible.

Flexible Colloidal Molecules with Directional Bonds and Controlled Flexibility

Colloidal molecules are ideal model systems for mimicking real molecules and can serve as versatile building blocks for the bottom-up self-assembly of flexible and smart materials. While most colloidal molecules are rigid objects, the development of colloidal joints has made it possible to endow them with conformational flexibility. However, their unrestricted range of motion does not capture the limited movement and bond directionality that is instead typical of real molecules. In this work, we create flexible colloidal molecules with an in situ controllable motion range and bond directionality by assembling spherical particles onto cubes functionalized with complementary surface-mobile DNA. By varying the sphere-to-cube size ratio, we obtain colloidal molecules with different coordination numbers and find that they feature a constrained range of motion above a critical size ratio. Using theory and simulations, we show that the particle shape together with the multivalent bonds creates an effective free-energy landscape for the motion of the sphere on the surface of the cube. We quantify the confinement of the spheres on the surface of the cube and the probability to change facet. We find that temperature can be used as an extra control parameter to switch in situ between full and constrained flexibility. These flexible colloidal molecules with a temperature switching motion range can be used to investigate the effect of directional yet flexible bonds in determining their self-assembly and phase behavior, and may be employed as constructional units in microrobotics and smart materials.

Entropy compartmentalization stabilizes open host-guest colloidal clathrates

Clathrates are open crystals in which molecules are arranged in a hierarchy of polyhedral cages that encapsulate guest molecules and ions. As well as holding fundamental interest, molecular clathrates serve practical purposes, such as for gas storage, and their colloidal counterparts also appear promising for host-guest applications. Here using Monte Carlo simulations, we report the entropy-driven self-assembly of hard truncated triangular bipyramids into seven different host-guest colloidal clathrate crystals with unit cells ranging from 84 to 364 particles. The structures consist of cages that are either empty or occupied by guest particles, which can be different from or identical to the host particles. The simulations point to crystallization occurring through the compartmentalization of entropy between low- and high-entropy subsystems for the host and the guest particles, respectively. We use entropic bonding theory to design host-guest colloidal clathrates with explicit interparticle attraction, providing a route to realize such systems in the laboratory.

Structural diversity in three-dimensional self-assembly of nanoplatelets by spherical confinement

Nanoplatelets offer many possibilities to construct advanced materials due to new properties associated with their (semi)two-dimensional shapes. However, precise control of both positional and orientational order of the nanoplatelets in three dimensions, which is required to achieve emerging and collective properties, is challenging to realize. Here, we combine experiments, advanced electron tomography and computer simulations to explore the structure of supraparticles self-assembled from nanoplatelets in slowly drying emulsion droplets. We demonstrate that the rich phase behaviour of nanoplatelets, and its sensitivity to subtle changes in shape and interaction potential can be used to guide the self-assembly into a wide range of different structures, offering precise control over both orientation and position order of the nanoplatelets. Our research is expected to shed light on the design of hierarchically structured metamaterials with distinct shape- and orientation- dependent properties.

Nanoplatelets can be used as anisotropic building blocks for constructing novel optoelectronic materials. Here, Wang et al. show a route of assembling nanoplatelets with controllable positional and orientational order in three dimensions facilitated by the surface tension of drying emulsion droplets.

Mismatched ligand density enables ordered assembly of mixed-dimensional, cross-species materials

The ordered coassembly of mixed-dimensional species-such as zero-dimensional (0D) nanocrystals and 2D microscale nanosheets-is commonly deemed impracticable, as phase separation almost invariably occurs. Here, by manipulating the ligand grafting density, we achieve ordered coassembly of 0D nanocrystals and 2D nanosheets under standard solvent evaporation conditions, resulting in macroscopic, freestanding hybrid-dimensional superlattices with both out-of-plane and in-plane order. The key to suppressing the notorious phase separation lies in hydrophobizing nanosheets with molecular ligands identical to those of nanocrystals but having substantially lower grafting density. The mismatched ligand density endows the two mixed-dimensional components with a molecular recognition-like capability, driving the spontaneous organization of densely capped nanocrystals at the interlayers of sparsely grafted nanosheets. Theoretical calculations reveal that the intercalation of nanocrystals can substantially reduce the short-range repulsions of ligand-grafted nanosheets and is therefore energetically favorable, while subsequent ligand-ligand van der Waals attractions induce the in-plane order and kinetically stabilize the laminate superlattice structure.

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.

Expanding the toolbox of photon upconversion for emerging frontier applications

Photon upconversion in lanthanide-based materials has recently shown compelling advantages in a wide range of fields due to their exceptional anti-Stokes luminescence performances and physicochemical properties. In particular, the latest breakthroughs in the optical manipulation of photon upconversion, such as the precise tuning of switchable emission profiles and lifetimes, open up new opportunities for diverse frontier applications from biological imaging to therapy, nanophotonics and three-dimensional displays. A summary and discussion on the recent progress can provide new insights into the fundamental understanding of luminescence mechanisms and also help to inspire new upconversion concepts and promote their frontier applications. Herein, we present a review on the state-of-the-art progress of lanthanide-based upconversion materials, focusing on the newly emerging approaches to the smart control of upconversion in aspects of light intensity, colors, and lifetimes, as well as new concepts. The emerging scientific and technological discoveries based on the well-designed upconversion materials are highlighted and discussed, along with the challenges and future perspectives. This review will contribute to the understanding of the fundamental research of photon upconversion and further promote the development of new classes of efficient upconversion materials towards diversities of frontier applications in the future.

Assembly mechanism of surface-functionalized nanocubes

Faceted nanoparticles can be used as building blocks to assemble nanomaterials with exceptional optical and catalytic properties. Recent studies have shown that surface functionalization of such nanoparticles with organic molecules, polymer chains, or DNA can be used to control the separation distance and orientation of particles within their assemblies. In this study, we computationally investigate the mechanism of assembly of nanocubes grafted with short-chain molecules. Our approach involves computing the interaction free energy landscape of a pair of such nanocubes via Monte Carlo simulations and using the Dijkstra algorithm to determine the minimum free energy pathway connecting key states in the landscape. We find that the assembly pathway of nanocubes is very rugged involving multiple energy barriers and metastable states. Analysis of nanocube configurations along the pathway reveals that the assembly mechanism is dominated by sliding motion of nanocubes relative to each other punctuated by their local dissociation at grafting points involving lineal separation and rolling motions. The height of energy barriers between metastable states depends on factors such as the interaction strength and surface roughness of the nanocubes and the steric repulsion from the grafts. These results imply that the observed assembly configuration of nanocubes depends not only on their globally stable minimum free energy state but also on the assembly pathway leading to this state. The free energy landscapes and assembly pathways presented in this study along with the proposed guidelines for engineering such pathways should be useful to researchers aiming to achieve uniform nanostructures from self-assembly of faceted nanoparticles.

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....

Square-triangle tilings: an infinite playground for soft matter

Regular square and triangle, two very simple geometrical figures, can be used to construct a fascinating variety of tilings which cover the 2D plane without any overlaps or holes. Such tilings are observed in many soft matter systems. Here we present a way to describe all possible globally uniform square-triangle phases using a three dimensional composition space. This approach takes into account both the overall composition and the orientations of the two kinds of tiles. The geometrical properties of special phases encountered in soft matter systems are described: the Archimedean Σ and H phases, the striped phases and the 12-fold maximally symmetric phases. We show how this very rich behavior with either periodic or aperiodic phases appears here as a consequence of the inherent incommensurability between the areas of the two tiles related by the ratio . Geometrical constraints on boundary lines and junction points between domains of different compositions are given, a situation likely to be encountered in experimental and numerical studies. Future developments are suggested like considering the effect on phase behavior of possible symmetry breaking.

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

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