AI/참고/ontocast-main/data/chunks/chem.bassani-et-al-2024-nanocrystal-assemblies-current-advances-and-open-problems.json

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    "chunks": [
        "<!-- image --> ## Nanocrystal Assemblies: Current Advances and Open Problems\n\n\u0303\n\nCarlos L. Bassani, Greg van Anders, Uri Banin, Dmitry Baranov, Qian Chen, Marjolein Dijkstra, Michael S. Dimitriyev, Efi Efrati, Jordi Faraudo, Oleg Gang, Nicola Gaston, Ramin Golestanian, G. Ivan Guerrero-Garcia, Michael Gruenwald, Amir Haji-Akbari, Maria Ib \u00e1 nez, Matthias Karg, Tobias Kraus, Byeongdu Lee, Reid C. Van Lehn, Robert J. Macfarlane, Bortolo M. Mognetti, Arash Nikoubashman, Saeed Osat, Oleg V. Prezhdo, Grant M. Rotskoff, Leonor Saiz, An-Chang Shi, Sara Skrabalak, Ivan I. Smalyukh, Mario Tagliazucchi, Dmitri V. Talapin, Alexei V. Tkachenko, Sergei Tretiak, David Vaknin, Asaph Widmer-Cooper, Gerard C. L. Wong, Xingchen Ye, Shan Zhou, Eran Rabani, Michael Engel, and Alex Travesset *\n\n<!-- image -->\n\nCite This: https://doi.org/10.1021/acsnano.3c10201\n\nRead Online\n\n<!-- image --> ## ACCESS\n\nMetrics &amp; More\n\nArticle Recommendations\n\n<!-- image -->\n\nABSTRACT: 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\n\n<!-- image -->\n\noptimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.\n\nKEYWORDS: nanocrystal, nanoparticle, quantum dots, nanocrystal assembly, colloidal crystal, superlattice, self-assembly, assembly protocols, structure prediction, material properties ## 1. INTRODUCTION\n\nNanocrystals (NCs), a term used herein interchangeably with nanoparticles, provide building blocks for nanomaterials. 1 -4 NC superstructures are a form of matter possible by the progress in synthesizing NCs with different shapes, sizes, and chemical compositions with monodispersed distributions, 5,6 allowing tuning superlattice parameters from tens to hundreds of nanometers. This permits creating materials with properties and functionalities believed unattainable on the basis of the crystallization of atoms into lattices at the \u00c5-scale. An important challenge is to assemble materials that perform many functions simultaneously and undergo structural transformations on demand. Robust assembly that is precise and configurable or programmable is particularly desirable.\n\n<!-- image -->\n\nThe assembly of NCs can be rationalized by drawing an analogy to atoms, their constituents, interactions, and the emergence of structures, as depicted in Figure 1. That is, NCs can be regarded as big atoms, 7 or programmable atom equivalents 8 (PAEs), defining a virtually infinite-dimensional periodic table of NCs with degrees of freedom including shape, size, chemical composition, the capping ligand, and others. The shape of NC cores (Figure 1b) is partially responsible for\n\nPublished:\n\nMay 30, 2024\n\nFigure 1. Analogy between NCs and atoms. (a, b) NC cores play the role of atomic nuclei. (c, d) Ligands such as polymers and DNA are equifunctional to the electron shell. (e, f) Their combination gives rise to NC building blocks analogous to atoms. (g, h) Similarly to atoms, NCs can interact and bond. NCs interact via ligands through steric forces, van der Waals forces, or specific sites for hydrogen bonding. Solvent conditions modulate NC interactions. NCs can also bond by hybridization of quantum states, forming NC molecules. (i) Quantum chemistry explains the formation of crystalline lattices at the \u00c5-scale. (j) NCs se
        "Geometric constructions cannot predict them as they jump scales from atomic (\u00c5) to NC (50 to 100 nm) scales. Synthesis of multiply-twinned particles has received high attention in the past decade, 66,71,99,100 and its mechanism of formation relates to strain accumulation that often spreads heterogeneously along the NC habit. 90 Direct measurement of time-dependent strain accumulation requires 3D atomic resolution in timescales compatible with the crystallization of atoms, beyond the limits of current measurement techniques. Detailed atomistic simulations (aka computer experiments) seem therefore the path to proving and better understanding such mechanisms. Molecular dynamics (MD) (Figure 4a) was extensively used to quantify and verify the different conceptual mechanisms\n\nFigure 3. Habits of NC cores. (a) The simplest NC habits comprise spheres and polyhedra that comply with the underlying symmetry of the crystalline structure, also known as Wulff shapes, such as octahedra, cubes, rhombic dodecahedra, and their truncations. More complex habits that break symmetry from the underlying structure comprise (a) tetrahedra, (b) 1D and 2D shapes as nanorods, nanodiscs, and nanoplates, (c, d) nanoframes and nanocages, (e) multiply-twinned NCs such as bitetrahedra, decahedra, decahedral nanorods, and icosahedra, (f) branched NCs, (g) NCs with a patterned surface by the deposition of another material, and (h, i) complex-shaped habits coming from the etching of core@shell NCs, and grown in the presence of adsorption of chiral molecules forming chiral-shaped NCs.\n\n<!-- image -->\n\nsimplified models for larger scales\n\n<!-- image -->\n\nFigure 4. Challenges in multiscale simulation of the synthesis of NC cores with defined habits. (a) Diffusion of precursors over ligand layers, with subsequent surface hopping and attachment to the surface, requires MD to fully predict trajectories. The use of KMC allows scaling to larger systems at the cost of the trajectory description. (b) Heat and mass transfer limitations because of the exothermic nature of crystallization, precursor depletion, and interaction between NCs in dense populations require the solution of concentration and temperature fields via, e.g., finite volume method. (c) Competitive growth velocities of different facets lead to the formation of different crystal habits and are typically captured by geometric construction models.\n\nproposed for NC synthesis. 73,96,100 -105 There are, however, some important bottlenecks in MD simulations for crystal growth of atoms into NCs, (i) the inability to simulate realistic-sized NCs, keeping in mind that NCs on a length scale of 50 to 100s of nanometers contain tens of millions of atoms, and the inclusion of a ligand layer adsorbed in their facets adds simulation of many long-chained hydrocarbons (Figure 4a); (ii) the complexity when inserting/removing particles from the system to simulate growth/dissolution of NCs by the use of grand-canonical (Gibbs) or semi-Gibbs ensembles, 106 and (iii) the inaccuracy of the modern force fields underpinning MD simulations to describe weak long-range electrostatic and dispersive interactions critical for NC formation.\n\nThe sampling of surface energetics via kinetic Monte Carlo (KMC) to grow and dissolve atoms in the crystal lattice circumvents the first two issues mentioned. 70,82,83,107 -110 The trade-offs of KMC are (i) not predicting full trajectories but only the most probable intermediate states of the kinetic pathway of growth, therefore lacking in a complete description of diffusion, which is key for crystallization; (ii) considering a perfect lattice, thus lacking information on strain accumulation due to the formation of defects and their displacement, 90 or lattice mismatch when growing over a seed composed of a different metal, 66 both related to symmetry-breaking of NC; 74 and (iii) the consideration of a homogeneous and constant chemical potential of the solution over the entire NC surface, thus not capturing (iii.a) ligand adsorption depending on the crystalline direc
        "## 3. INTERACTIONS BETWEEN NCs\n\nNC assembly is driven by both enthalpic and entropic effects. There are different strategies to promote interactions and/or bonding between NCs, (i) the hybridization of their quantum states (Figure 5a), (ii) by ligands with nonspecific interactions (steric forces), (iii) by ligands with specific hydrogen-bonding sites that induce valence in NC interactions (Figure 5b -d), and (iv) by modulating solvent conditions such as electrostatic forces and ionic strength (Figure 5e), by the use of nematic\n\nhosts (Figure 5f), and via complex, nonadditive (many-body) interactions of ligands in the solvent medium.\n\nIn the analogy between NCs and atoms of Figure 1, ligands play a similar role to electrons. Superlattices can be held together by delocalized mobile NCs. 120 Similar metallizationlike behaviors have been observed in models of hard-shape alloys, where size-asymmetric mixtures exhibit mobile small particles interspersed in a stable lattice of larger particles 121 and is reminiscent of depletion interactions in colloids. 122 This illustrates the relevance and promise of hard shape and other simple models to provide qualitative descriptions of many phases found in NC assemblies, further discussed in the section on structure prediction.\n\n\u0308\n\nThe superatomic concept, based on the recognition of electronic atom shells in atomically precise metal clusters, provides a direct mapping of interatomic bonding to interparticle bonding. 123 Entropy also suggests analogs for other forms of bonding. Entropic patches give rise to entropic bonds 124 that have a quantitative behavior similar to traditional electron-mediated bonds, where the Smoluchowski equation takes the role of the Schrodinger equation in describing the bond. 125 In all cases, the design dimensions of anisotropy/ valence and interactions available to NCs resemble those that quantum mechanics ascribes to atoms, allowing the use of NCs as the basis of metachemical structures not seen in conventional systems. 126 Understanding how metachemical structures are rationally perceived in the design of materials on demand is a grand challenge for nanoassembly engineering in the coming years.\n\n3.1. Hybridization of NC Quantum States. Wavefunction coupling between semiconductor NCs leads to the hybridization of their electronic states. The analogy between NCs and atoms (Figure 1) becomes even more tantalizing as such wavefunction coupling leads to artificial molecules of importance to creating a library of hybrid nanostructures with different optoelectronic properties, with relevance to applications that include quantum technologies. 24\n\nThe realization of artificial quantum molecules with sufficient coupling energy detectable at room temperature is a promising use of QDs. This can be achieved by conducting ligands or by the fusion of adjacent NCs to form a continuous inorganic bridge linking the neighbors (Figure 5a). The controlled bridge and the barrier height between two adjacent quantum dots are key variables for dictating the magnitude of the coupling energy of the confined wavefunctions.\n\nThe proof of concept is the formation of the simplest NC molecule, a homodimer formed from two core/shell NCs in analogy to a homonuclear diatomic molecule. 127 The shell material of the two NCs is structurally fused resulting in a continuous crystal. The direct manifestation of the hybridization reflects on the band edge transition shifting towards lower energy (Figure 5a) and is resolved at room temperature. The hybridization energy within the single homodimer molecule is strongly correlated with the degree of structural continuity. The barrier is affected by (i) the original shell thickness, (ii) the original core/shell building blocks, (iii) the relative orientation of the two core/shell building blocks, and (iv) the extent of neck filling. 128\n\nThe challenges ahead lie in gaining higher degrees of control over the architecture of colloidal quantum dot molecules (CQDMs). Firstly, the ability to fabricate robust heterodimers at 
        "Variation of chain statistics with distance creates a depth gradient in the ligand density. When combined with curvatureinduced variations and tension, careful design of depth gradients in polymer brush properties provides a versatile way of controlling NC interactions. Moreover, nonspherical cores give rise to brush environments that depend on both the mean and Gaussian curvatures of the particle. 147 The dependence of brush properties on surface gradients in grafting density and curvature remains an open problem in polymer physics. Moreover, the polydispersity of chain lengths can give\n\nFigure 6. Depiction of soft shells over NC hard cores. (a) Schematic of a hard core particle with a soft polymer brush or polymer gel shell that is thick relative to the core diameter. (b) Gradients in core curvature result in local variations in brush thickness h (blue dashed line) when compared to a flat brush of thickness h fl (magenta dashed line). (c) Interactions between brushes give rise to an interpenetration zone of thickness h inter and a dry zone of thickness h dry . (d) Brushes composed of different polymer lengths lead to layers of thickness h A and h B -h A with different compositions. (e) A shell composed of a temperature-responsive polymer can change in thickness, e.g., conforming to a potentially anisotropic core above a lower critical solution temperature. (f) Two-body interactions of an elastic shell involve a combination of compressive and expansive deformations (left). Many-body interactions involve more complex deformations and changes in contact surfaces (right). (g) Equilibration involving mass (solvent) exchange can lead to coexistence between particles of different volumes, resulting in different crystal phases, e.g., transitioning from a hexagonal lattice (top) to a square lattice (bottom).\n\n<!-- image -->\n\nrise to additional structures in brushes, namely the segregation of long and short polymers into different layers 148 -151 (Figure 6d). This can also be used in favor of tuning NC interactions.\n\nMany open questions regarding the effect of polydispersity in curved brushes remain. There are examples 152 where the assembly is not affected by polydispersities leading to up to 25% variations in the effective diameter of the NC. The ability of these highly dispersed systems to produce uniform superlattices was attributed to the greater polymer configurational freedom enabled by their curvature. The universality of this effect however needs to be assessed by further work.\n\nThe NC core shape has a nonlocal effect on brush properties, chain statistics, and brush interactions, which is of importance to tune properties. To what extent this is possible is an open issue and highlights fundamental questions in the basic statistical physics of how polymers and polymer brushes fill space. The interpenetration of two polymer brushes alters the local density of the monomers within a brush, modifying packing conditions elsewhere. Consequently, the nonlocal character of this alteration in chain-packing conditions changes the degree to which additional brushes can interpenetrate the shell. This leads to effective many-body interactions that have been modeled for shorter ligands, 153 but it remains unclear how to extrapolate these models to long brushes.\n\nlinked polymer chains 13 (Figure 6a). The total dimensions of such gels reach hundreds of nanometers for nanogels, and up to tens of micrometers for microgels. When using an appropriate solvent, microgels are swollen by large amounts of solvent molecules, making their physical classification nontrivial. The properties of microgels range somewhere between those of classical macromolecules, surfactants, and colloids. 156 Whereas the decoration of NCs with linear polymer chains (e.g., polymer brushes) is limited to rather small shell thicknesses, the encapsulation of NCs by microgel shells extends to larger length scales because of its cross-linked nature. 157 This is relevant for designing close-packed NC assemblies where the thickness of the shell and its c
        "Selecting a voxel shape and the placement of interframe DNA bonds define the valence and geometry of binding arrangement and, consequently, an assembled DNA framework. For example, the 4-, 6-, and 8-fold symmetries of the individual voxel bonds 80,202,212,231 -234 result in diamond, simple cubic, and body-centered cubic frameworks, providing different 3D scaffolds to place NCs. By adding a bond identity to the valence when using different sequences, or a composition of a number of sequences for different directional bonds, a higher degree of structural diversity is achieved. 191,232,235 This approach permits (i) coordinating different types of frames, empty or with cargo, to create increasingly complex organizations, 226,232,236 and (ii) establishing an inverse design of lattices through the selection of bonds with different identities for a set of voxels. However, the requirements of the bond encoding and their energy distribution for an effective assembly process are unknown. Relevant questions remain on (i) how to reduce the amount of information required for the inverse design of such systems, and (ii) which energy landscape of the bonds provides an assembly pathway with minimal metastability in such complex systems.\n\n3.3.2. Nanocomposite Tectons and Other Ligands. Hydrogen bonds provide a powerful bonding mechanism between polymer-grafted NCs, being the most prominent example DNA-mediated assembly discussed in the previous section. There are however other successful strategies that offer advantages in scalability, lower cost, and operation in organic solvents. Nanocomposite tectons 18,19 (NCTs) are one important example that consists of an NC core functionalized with a polymer brush, where each polymer chain terminates in a supramolecular binding group, also called tether (Figure 5d). The highest quality crystals are typically obtained with NCTs that bond via complementary diaminopyridine (DAP) and thymine (Thy) groups that form a hydrogen-bonding pair. The reversible nature of the individual supramolecular interactions is a critical design component to enable crystallization. The use of multivalent interparticle bonding mediated by these supramolecular complexes between particles allows for crystal formation, thus providing an example regarding the rules for robust assembly discussed in the previous section.\n\nNCTs present an interesting tool for assembly, as the composition and length of the polymer brush and the identity of the supramolecular complexes provide design handles to tune the crystallization behavior. The scalability of the polymer system also allows a wider range of experimental variables and conditions to be explored, as well as the investigation of largerscale effects on nanoscale assembly. 154 Furthermore, passivation of DAP or Thy results in an NC functionalized with a nonspecific polymer brush, 237 thus representing an interpolation that may optimize pros and cons of NC bonding by polymer brushes and DNA-mediated assembly discussed in the previous sections.\n\nAnother example of polymers interacting through hydrogen bonds is interpolymer complexation (IC), where a hydrogenbond acceptor (e.g., polyethylene oxide) is functionalized to an NC, whereas a hydrogen-bond donor (e.g., polyacrylic acid) is suspended in a water solution providing a bond linker. 20 NCTs and IC however do not yet provide the level of programmability of DNA. Future efforts will require the development of hydrogen-bond polymers that retain the significant advantages of these examples while enabling more sophisticated programmability that can rival the successes achieved in DNA assembly.\n\n3.4. Solvent Effects. 3.4.1. Electrostatic Forces and Ionic Strength. Long-range Coulomb interactions are screened by the ionic strength of the solvent and controlled through variations in both the salt concentration and the dielectric constant of the solvent. These effects provide a method to finely control NC interactions (Figure 5e). A recent strategy shows that metal (e.g., Au, Pd, Ni) and semiconductor (e.g., PbS, PbSe) NCs 
        "Strategies to achieve robust and large-scale NC assembly consist of varying temperature (annealing), varying concentration via solvent evaporation, changing the fluid composition, and utilizing interfaces as a means to induce or guide assembly are all valuable. Other techniques employ external fields, like electrophoretic deposition, a combination with top-down approaches, or are inspired by biological systems.\n\n4.1. Controlling NC Kinetics. Slow or non-ergodic dynamics caused by strong NC attractions can be problematic. In particular, the intrinsic sensitivity of effective NC-NC interactions may prevent reaching equilibrium in multivalent ligand suspensions, such as those with DNA-mediated and other valence-limited colloidal interactions driven by temperature, 285 often resulting in arrested aggregates. Another factor that slows kinetics is related to the stickiness of the multivalent interactions. Sticky interactions prevent pairs of NCs from diffusing around each other while remaining bound, which is a key step for the relaxation of crystal defects.\n\nTo improve assembly, it is essential to have access to strategies that accelerate NC kinetics. The relative diffusion between bound NCs can be improved using high ligand coating density, 190 which increases the melting temperature (as a result of combinatorial gain) and the rates at which pairs of ligand-receptor bridges form/open. 286,287 General computational approaches optimize interactions for model systems, 288 -290 but a comprehensive understanding of how molecular details affect the emerging motility of functionalized particles remains missing and warrants future investigations. The electronic properties of the relevant building blocks may also provide an avenue for further optimization and control. In the case of atomically precise superatomic NCs, 291 the use of dopants can change the electronic character and symmetry of the molecular valence orbitals and thus change the nature of these interactions. 292 Many experimental efforts have now demonstrated the electronic tunability of these building blocks. 293 The relative motility of NCs is also pivotal to the development of dynamic materials, such as crystals glued by mobile NCs. 120\n\nEmpirical protocols of NC assembly that slowly decrease and increase temperature have been widely used. It is therefore necessary to understand how to optimize protocols and to identify general principles that guide the choice of cooling rates. At the next level, it would be crucial to embed protocols with on-the-fly feedback to scan parameter spaces autonomously. Advances in this direction have been made, for example, in experiments studying microphase separations in block copolymer systems. 294 Similarly, theoretical work has explored the optimization of experimental protocols for assembly using reinforcement learning. 295,296\n\n4.2. Varying Solvent Conditions. The most common assembly protocols consist of changing the interaction between NCs by modulating solvent conditions. Solvent-induced selfassembly has been demonstrated in various systems, offering control over NC assembly and disassembly and, in some instances, reversibility. 22,297 Additionally, advances have been made in assembling NCs with complex morphologies, such as Janus NCs. 298 Dynamic self-assembly using solvent gradients and localized solvent addition has also been explored, 299 -301 leading to the formation of patterned NC films. 302 To further advance in NC assembly, it is crucial to understand the role of surface ligands, 303 especially in those systems where a single NC can host a multitude of ligands, 304 as well as balancing attractive van der Waals interactions and steric repulsion.\n\n4.2.1. Assembly by Solvent Evaporation. Solvent evaporation is a strategy to assemble at near-equilibrium conditions. 6 The initial state is usually a stable dispersion, and the final state is solvent-free (dry). If solvent evaporation is slow enough, then it may be regarded as a quasi-static process, i.e., a succession of equilibrium states at the particular 
        "Furthermore, typical Langmuir trough setups operate with uniaxial compression, which can change the isotropy of monolayers made from soft, deformable particles. It is still required to measure and understand such influences and to compare them to radial compression.\n\n4.4. Electrophoretic Deposition. Electrophoretic deposition (EPD) involves the use of an electric field to direct the assembly of charge-stabilized NCs onto a solid substrate (Figure 7d). Initially used to assemble gold NCs into densely packed monolayers, 372 it has since assembled rod-shaped NCs with permanent dipoles into dense monoand multilayer structures. 373 More recently, EPD on patterned substrates was used to control both the position and orientation of individual particles over large areas, including millions of gold nanorods arranged either horizontally or vertically. 374 -376 Two important factors comprise (i) using nanoscale lithography to create cavities within an insulating layer deposited on top of the electrode and (ii) optimizing the deposition conditions. Depositing a wide range of different particle types into welldefined patterns in a scalable way with surface-templated EPD presents some limitations. For example, it is difficult to deposit NCs with diameters below 10 nm due to constraints in surface\n\ncharge density and the strength of the applied electric field. 376 Whereas clustering or shelling (e.g., with SiO ) can be used to 2 deposit smaller quantum dots, 376 finding alternative strategies is desirable. Another open question is how close the NCs can be spaced. Charged NCs approaching the surface pull counterions, creating complex flow patterns near cavities and electro-osmotic effects that still require characterization. Depositing NC mixtures into more complex patterns remains a challenge. Finally, the range and diversity of structures that can be assembled from EPD remain an open question.\n\n4.5. 3D Printing Superstructures. Self-assembly is a bottom-up strategy that can be combined with the top-down strategy 3D printing or additive manufacturing. Research efforts in this direction targeted the creation of 3D-printed nanomaterials using NCs as the ink. To maximally exploit the properties of the NCs in this process without disturbance from the matrix material, usually a polymeric matrix, 377 organic content should be minimal.\n\nA breakthrough was the creation of bulk superstructures by locally controlling NC aggregation (disordered assembly) in solution, triggered by light-induced reactions that connect NCs via shared organic molecules 378 (Figure 7e). This approach initially required specific NC inorganic cores and highly specialized ligands. 379 The concept has since evolved to a stage where the inorganic cores no longer directly contribute to the assembly process. Instead, a light-sensitive additive is added to the particle suspension. Upon irradiation, the additive converts into a molecule terminated with nitrene radicals, which react forming bonds connecting hydrocarbon chains. 380,381 Nitrene radicals can connect (i) ligands of the same NC, locally reducing colloidal stability and bringing the particles closer together, or (ii) ligands of different NCs, thereby creating interparticle links. These developments are promising towards expanding additive manufacturing capabilities to a broad range of NC building blocks.\n\n4.6. Bioinspired Assembly Protocols. 4.6.1. StimuliResponse Assembly. To mimic and exploit the intricate functions of natural living systems, research recently focused on systems of NCs that are dynamic and respond to external stimuli by initiating the ordering process (Figure 7f). 382 The challenge is to realize stimuli-responsive NC assembly that is capable of storing information and executing programmed tasks. 383,384 The wealth of available ligands, coupled with the diverse sizes, shapes, and properties of the inorganic cores provides sufficient flexibility to control NC solubility and guides the self-assembly process. Yet, it remains imperative to broaden the scope of NC cores beyond the cur
        "## 5. SUPERSTRUCTURE PREDICTION\n\nA general framework that reliably and autonomously predicts the equilibrium superstructure of a given set of building blocks does not yet exist. The development of such a framework is challenging and therefore relies on starting with simple models where superstructure prediction is more tractable. Among the simplest NC descriptions are hard shape (HS) models. 408 These models capture many aspects of the equilibrium structure and dynamics of NC assemblies surprisingly well and provide an excellent first level of approximation. However, HS models completely ignore enthalpic (i.e., non-entropic) NC interactions. They also omit the compressibility and conformations of ligands, which are critical for NC assembly as discussed in previous sections.\n\nWhereas HS models have been studied extensively and are generally well-understood, moving beyond HS models is a critical future challenge. Further research is also necessary to advance techniques for (i) estimating free energy at higher precision, (ii) better understanding the role of geometric frustration for superstructure formation, and (iii) advancing the treatment of inverse problems. The latter challenge, inverse problems, is particularly important, as it pushes superstructure\n\n5.1. Hard Shape NCs. Hard shape (HS) models have a long-standing history, in part owing to their elegance and simplicity. Building on the success of analogous models for ionic solids 409 and amphiphiles, 410 the advent of NCs as building blocks for assembly has prompted a flurry of research in this area. Assembly of HS NCs is commonly simulated via Monte Carlo (MC) (Figure 10a,b), and assembly diagrams 411 exist to categorize different polyhedral NC shapes into crystal, liquid crystal, plastic crystal, and glass superstructures (Figure 10c).\n\nEarly work on hard tetrahedra showed that instead of a dense packing structure, particles self-assemble into a dodecagonal quasicrystal. 412 It was a big success of the hard tetrahedron model that this highly nontrivial simulation prediction was eventually confirmed in experiments. 413 Other hard shapes self-assemble into a host of mesophases that differ from their densest packing. 414 Many of these mesophases occur in NCs that do not tile space, raising the question of whether mismatches with packing expectations 411,415 were due to some form of geometric frustration. Indeed, many shapes that fill space do not assemble in their densest packing structures. 416,417 The discrepancy between solutions to optimal packing problems and the self-assembled equilibrium structures of HS systems appears to work both ways. Not only do HS generally not form the superstructures in which they pack most densely, 412, -416 materials design of superstructures via digital alchemy also shows a thermodynamic preference for shapes that do not tile them perfectly. 59,417 -419\n\nFor systems in which the shapes are approximately hard, more accurate predictions are beginning to emerge from supramolecular chemistry-motivated models. These models are\n\nbased on the notion that entropy gives rise to emergent, directional entropic forces among particles 420 that induce a form of bonding. 124,125 This perspective has been corroborated by evidence from the creation of entropically patchy particles , 421 -423 and by the study of cluster packing, 424 doping simulations, 425 and inverse design. 59 For a given target superstructure, it has been argued that an eigenshape should exist \ue0d5 that is, an idealized HS that minimizes the free energy of that structure. 419\n\nAs it relates to NC assembly, the adoption of HS goes back to binary superlattices. 6,317,426 The HS model presents obvious limitations: (i) superlattices exist even at zero pressure, so significant NC attraction (enthalpic contribution) must be present for assembly, and (ii) the shell around the core is usually quite compressible. The HS description can be improved by mapping a given NC to an effective HS eigenshape. For spherical NCs, this is another spherical HS with a diameter th
        "Development of various charge equilibration schemes and explicit integration of electronic charges and spins into ML architectures accurately describe molecular charged species, long-range electron transfer, and dispersive forces. 462,467\n\nAnother critical feature of NC assemblies is their immense structural and conformational diversity. This complexity poses challenges when implementing active learning techniques to generate training databases, often requiring a trade-off between the generality and specificity of the resulting models.\n\n5.3. Free Energy Estimations. The equilibrium nature of binary nanocrystal superlattices (BNSL) observed in the literature remains uncertain. It is not yet established whether they represent stable configurations or metastable states that should eventually phase separate into two single-component superlattices. 6 The fact that different experimental strategies \ue0d5\n\nincluding microfluidics, 468 evaporation of a solvent on solid support, 317,469,470 and emulsification of the solvent 309,310,471 into large micelles \ue0d5 lead to the same BNSL phases corroborates with the argument that BNSLs are equilibrium states. Methods consisting of tuning hydrophobic interactions by solvent quality 22,472,473 predict interesting structures for a small number of NCs 474,475 but are unsuccessful in assembling BNSLs and always lead to single-component phase-separated systems. 476\n\nFree energy calculations with all-atom models could settle the question of whether BNSLs are equilibrium or metastable states. Unfortunately, the few free energy calculations available using all-atom 446 or coarse-grained models 477 have shown a difference in free energy between the BNSL and a phaseseparated single component of a few k T B per NC, which is within the accuracy of free energy estimations. Despite these calculations being somewhat inconclusive, the free energy estimations show that regardless of what is the equilibrium state, it is only marginally stable. Therefore, interactions that may appear as subleading (e.g., dipole-dipole and van der Waals forces between NC cores) may ultimately be critical in stabilizing the superstructure. It remains an outstanding challenge to quantify these subtle free-energy balances.\n\n5.4. Geometric Frustration. Geometric frustration is a cooperative phenomenon where the pairwise interactions in a structure cannot be all simultaneously minimized. Whenever the locally favored relative arrangement of the building blocks cannot be realized globally, the resulting structure will inevitably be frustrated. In some cases, frustration can be resolved locally at the scale of a single or a few unit cells (for example, through the proliferation of defects), leading to a uniform strain. However, if the mechanisms for locally resolving frustration are energetically unfavorable, frustration will build up and manifest as a nonuniform strain that grows in magnitude as the assembly grows in size. The associated elastic energy grows super extensively and, in its early stages, follows one of a handful of universal growth exponents. This phenomenon was recently termed as cumulative geometric f rustration . 31 However, the super-extensive growth of the elastic energy cannot persist indefinitely, and different systems show different mechanisms for frustration saturation. Thus, systems that exhibit cumulative geometric frustration are typically small in size and are associated with weak frustration. Moreover, their building blocks (or their interactions) are soft enough to allow for the required relative strains. If g is a geometric length scale associated with the frustration, and s is the typical linear dimension of the system, then s \u226a g is necessary for frustration accumulation.",
        "Frustration has been shown to play an important role in determining the shape, residual stress profile, and response properties in a wide variety of assemblies including liquid crystals, 478 filament bundles, 479 twisted molecular crystals, 480 -482 and frustrated xy -like lattice spin models. 483,484 A recently introduced framework aimed at the continuous description of frustrated assemblies 31 has enabled the quantification and classification of the different types of frustration. Consequently, the super-extensive energy exponent \u03bb &gt; 1, which satisfies E \u221d M \u03bb , where M is the mass of the system, can assume only a handful of values according to \u03bb = 1 + 2 \u03b7 / d , where d = 1, 2, 3 is the dimensionality of the system, and \u03b7 = 0, 1, 2, 3, ... denotes the first non-homogeneous order in the expansion of the compatibility conditions. 31 The rate at which the strain energy builds up in an assembly as it grows predicts if a given assembly will saturate at a finite size 485 or determines the spacing between the packing defects that absorb growing strains.\n\nWhile it is possible to tile a plane with equilateral triangles, it is not possible to tile the 3D space with regular tetrahedra, 486 which is the analog of an equilateral triangle in 3D. However, tetrahedra can tile certain types of curved spaces. Such curved spaces represent the ideal ground state for general crystals, and the actual crystal state in 3D is just a frustrated version that is unattainable due to the lack of curvature. 486 Frank-Kasper phases , 487 which are quite common in NC assemblies, 33 are phases in which the frustration inherent in regular tetrahedra is relieved by topological defects (disclinations). Frustration in tetrahedral (also known as topologically closed-packed) networks also connects to theories of the glass state. 488 -490 There are examples of the role of tetrahedral order (and closely related icosahedral) in NC assemblies. 32,33 The role of geometric frustration is ubiquitous in NC assemblies, and its systematical study is important to design frustrated interactions to produce desired complex structures.\n\n5.5. Mean-Field Theory. Self-consistent f ield theory (SCFT), a type of mean-field theory, has been successful in the study of ordered phases self-assembled from polymeric systems such as block copolymers. 491 Recently, SCFT and other mean-field approaches have been applied to the assembly of NCs by solvent evaporation 492 -494 and to NCs dispersed in polymer melts. 495,496 Existing approaches can be categorized into two types. In the first type, the cores, the ligands, and the solvent are all described in terms of density fields. 496 A major challenge in this strategy is to capture core-core excluded volume correlations. In this context, f undamental measure theory (FMT, a hard-sphere functional) stands out as a promising solution to predict the thermodynamic stability of hard-sphere superlattices. 494 FMT has also been combined with SCFT to model ligand-coated NCs 497,498 and was applied to single-component and binary mixtures of hard spheres. 499 It remains a challenge to combine these breakthroughs into a theory of ligand-coated NC superlattices.\n\nThe second type of mean-field approach to model NC assembly keeps a field-based representation of the ligands and the solvent but adopts a particle-based representation for the NC cores \ue0d5 i.e., the cores are modeled as regions inaccessible for the ligands and solvents. 492,493,495 The diffusion timescale of NCs is much larger than the characteristic timescales of molecular motion. Therefore, in a classical analogy to the Born-Oppenheimer approximation, the solvent/ligand degrees of freedom can be integrated for fixed core positions. A hybrid simulation scheme based on this approach was developed, 495 in which the interparticle forces obtained by solving the solvent/ligand problem were used to evolve the position of the cores in a small-time step. This strategy does not require any a priori knowledge of the final structure, but its long equi
        "Experimentally, it is fairly challenging to predict heterogeneous nucleation rates due to uncertainties in the types of impurities present within a solution. 520 Moreover, it has been recently demonstrated that traditional definitions of crystallinity break down in describing the physics of heterogeneous nucleation even on the simplest surfaces, 516 even when nucleation is still a single-step process. This highlights the importance of devising more robust descriptions of structure and its interplay with the outcome of heterogeneous nucleation. It is also imperative to understand situations in which heterogeneous nucleation exhibits\n\ndeviations from the classical picture provided by Turnbull and Vonnegut. 521 These explorations are critical for constructing predictive models that can be used for estimating the rate of heterogeneous nucleation as a function of operational variables under different experimental conditions.\n\nAn important case for models that go beyond critical nucleation is the two-step nucleation mechanism introduced for globular proteins. 522 It involves the formation of an intermediate disordered phase with a high concentration of particles, so nucleation occurs within the intermediate phase (Figure 11a), with a lowered nucleation barrier. Computational\n\nFigure 11. Nucleation of NC assemblies. (a) Schematic representation of one-step and two-step nucleation processes. (b) Probability of superlattice nucleation represented by color gradients, where green is high, blue is intermediate, and yellow is a low probability. The axes represent the depth u 0 and range \u03bb of a square-well potential, as represented in the inset, for colloidal particles with radius R and a volume fraction of 0.1. The diagram shows the regions of (I) one-step nucleation, (II) two-step nucleation, (III) the coexistence of two metastable fluids with a slow nucleation rate, (IV) gel formation, and (V) a thermodynamically stable colloidal fluid. The dashed line is the metastable fluidfluid binodal curve. The solid black curve is the thermodynamic boundary for the stability of an fcc crystal. Adapted with permission from ref 27. Copyright 2022 The American Association for the Advancement of Science. Based on data of ref 21.\n\n<!-- image -->\n\n<!-- image -->\n\nstudies predicted two-step nucleation for spherical colloids with short-ranged attractive potentials (Figure 11b). 21 More recently, simulations considering complex hard polyhedral shapes showed a two-step nucleation process where nucleation occurs from a high-density precursor fluid phase with prenucleation motifs in the form of clusters, fibers and layers, and networks. 518 In addition to these computational efforts, advanced in situ characterization methods allow experimental observations of nucleation. Two-step nucleation of NC superlattices was observed by transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS) studies of NC assemblies, 27,523,524 where crystalline structures grow from amorphous aggregates. While SAXS provides bulk ensemble characterization of structural evolution in reciprocal space, liquid-phase TEM \ue0d5 sealing solution samples against the high vacuum of TEM for imaging at the nanometer and millisecond resolution \ue0d5 resolves NC dynamics, interaction, and crystallization pathways in real space with single-particle tracking.\n\n6.2. Superstructure Growth. The length and energy scales associated with NC assembly are dramatically different than those in atoms or simple molecules. The larger timescales and sizes of NCs make direct, real-space observation of these assembly processes more feasible than their atomic counterparts, permitting detailed experimental verification. Nevertheless, the length scale has a major effect during crystal growth. For example, larger crystalline clusters of NCTs 154 are associated with (i) slower cooling rates, consistent with classical nucleation theory, but also (ii) higher concentration of NCTs, opposing classical nucleation theory. This unexpected behavior was explained as a funct
        "Fundamental understandings of the effects of multiple length scales, from inter-NC interactions to hydrodynamic flows and other effects due to external fields, are lacking when it comes to nanoscale building blocks. More efforts are required to establish the field of nanoscale active matter, where external energy drives the actions of NCs near or far from thermodynamic equilibrium.\n\nFigure 14. Electronic properties of metallic NCs. (a) Bulk, surface, and plasmon states in Ag 104 . Plasmons extend far beyond NC, providing strong coupling to other NCs, substrates, molecules, and light. Plasmon states couple to vibrations more weakly than bulk and surface states. Adapted with permission from ref 579. Copyright 2010 American Physical Society. (b) Evolution of hot electron energy in Au55. 570 Metallic NCs have no band gap, in contrast to semiconducting NCs (Figure 13). Nevertheless, smaller gaps do appear, giving rise to excited states that remain populated for a picosecond. Adapted with permission from ref 570. Copyright 2016 American Chemical Society. (c) Surface atoms of metallic NCs can undergo slow fluctuations, creating longer-lived states and (photo-) catalytic sites. Adapted with permission from ref 571. Copyright 2020 American Chemical Society. (d) Active absorbers of light, surface plasmons are collective electronic excitations that lose coherence within femtoseconds. Hot charges need to be extracted prior to electron-hole recombination (top). If metallic NCs are strongly coupled to charge acceptors, plasmon excitations produce charge-separated states immediately, enhancing charge extraction (bottom). Adapted with permission under a Creative Commons CC BY license from ref 572. Copyright 2014 American Chemical Society. (e) By extending far away from metal, plasmons enable efficient coupling to substrates over long distances, facilitating charge and energy transport. Adapted with permission from ref 573. Copyright 2020 American Chemical Society. (f) Metallic NCs support ensembles of hot charges, but simultaneous transfer of many charges are forbidden (top). Instead, hot electrons can transfer energy by scattering with substrate electrons (bottom), enabling energy transport devices. Adapted with permission from ref 574. Copyright 2021 Springer Nature BV.\n\n<!-- image --> ## 7. FUNCTIONS AND APPLICATIONS\n\nThe diversity of NC cores with different shapes, sizes, chemical compositions, and capping ligands defines a staggering design space for materials. The obvious challenge is identifying the regions of this space that contain NC assemblies with given properties or superior performance compared to traditional materials structured solely at the atomic and molecular scale. There are many strategies for expanding the inventory of NC assemblies. For example, so far only superstructures containing up to three NC species (ternary systems) have been considered, 449,476,533 yet analogues to high entropy alloys 534 may soon be investigated. Adding active NCs to the system during synthesis or operation, in which the environment supplies energy or momentum, further expands the design space.\n\nwindows, flexible sensors, displays, and efficient catalysts, 537 and assisted by 3D nanoprinting, 379 will be key. Given the breadth of the field, we do not attempt an exhaustive description of all phenomena that have been proposed or are under investigation. Instead, we highlight a few selected examples, for which nanoscale structural order plays a central role in achieving desired functional properties. Significant potential with open challenges exists for NC assemblies in the application fields of thermoelectric materials, batteries, plasmonics, high mobility semiconductors, flexible electronics, and light-emitting devices. 60 Assembled QD solids permit solution-processed functional optoelectronic nanomaterials. 535 Phononics has recently been identified as an as-of-yet untapped area. 536 Bridging the scales from functional nanocomposites to robust macroscale devices, such as smart\n\n7.1. Electronic Properties. The rational
        "Alternatively, one can consider combining periodic solidstate physics treatments of bulk NC regions with explicit consideration of surfaces by using, e.g., embedding methods. 551 Excitonic effects are typically treated by the Bethe-Salpeter theory, which is computationally demanding. Simpler descriptions involving approximations to the dielectric function 552 and stochastic sampling 553 are valuable.\n\nThe main function of ligands is to enable various synthetic routes for manufacturing colloidal NCs, passivate the electronic defects, and protect the NC surface. Moreover, ligands interact strongly with NC surfaces leading to substantial charge redistribution and polarization effects on the surface. 543 Hybridized states form, in which the electronic density is spread over the NC and the ligands. In fully passivated NCs, neither the ligand-localized nor hybridized molecular orbitals appear as trap states inside or near the band gap. Instead, being mostly optically dark, dense hybridized states open channels of relaxation of high-energy electronic excitations (Figure 13a). Loss of passivating ligands leads to either optically dark or bright additional states inside of the band gap, depending on the position of the leaving ligand. Mid-gap trap states are eliminated by surface reconstruction in certain magic-size NCs, such as Cd33S33 (Figure 13b). However, surface passivation is typically required. 554,555 Modeling of electronic properties of passivated NCs requires proper placement of ligands on NC surfaces to satisfy charge neutrality and realistic synthesis conditions. Achieving precise control over the placement of molecular ligands remains an outstanding synthetic challenge. It often brings forward properties and applications, such as chiroptical features, which is of interest to structure determination, polarized photo-detectors, sensing, and spintronics. Typically, semiconducting NCs are nonchiral structures with significant optical activity in the UV-Vis range. In contrast, chiral molecular systems generally have a significant band gap. One approach to induce chiroptical signatures in semiconducting NC is by creating chirality in their surrounding environment, often referred to as chirality transfer . This can be achieved by embedding inorganic NCs within chiral superstructures or by using achiral molecular ligands to passivate the semiconductor surfaces. While some experimental and theoretical reports are encouraging, 556 -558 understanding of the physical processes underpinning chirality transfer is yet to be achieved. For example, structural templating, state hybridization, and longrange dipolar interactions were proposed as mechanisms to be employed by fabrication strategies. 559 -562\n\nNC composition is often not fully stoichiometric, and the NC surface can be rich in a particular element. Metal-rich surfaces behave differently from non-metal-rich surfaces. 544 The stoichiometric CdS NC maintains a large band gap. However, an S-rich surface creates a larger number of defect states with energies everywhere inside the band gap (lower-left panel of Figure 13b), leading to rapid electron-vibrational relaxation and impeding light emission. In contrast, defect states created by a Cd-rich surface form a sub-band inside the\n\nbandgap (lower-right panel of Figure 13b), leaving a large energy gap between the CB minimum and the defect band. The nonradiative energy relaxation is limited, and the NC emits both at the main peak corresponding to the band-gap transition and broadly at lower energy corresponding to transitions into and out of the defect sub-band. 544 The differences arise due to the bonding properties of metals and non-metals. S, Se, and other non-metals require directional covalent bonds, and all the bonding requirements cannot be satisfied on the S-rich surface. Metals, such as Cd and Pb, can form bonds more easily and in a less directional manner, reducing the number of defect levels. Such general chemical bonding principles, as reflected in the covalent bond classification scheme and charge-orbit
        "Controlling the core/shell semiconductor band offsets of the composing NC monomers is also important. In type II core/ shell semiconductor NCs, the staggered band alignment allows extensive delocalization of the carrier type to the shell. 587 A higher degree of delocalization can facilitate the transfer of charge carriers to neighboring NCs. This could facilitate color switching under the application of an external electric field. Furthermore, a long-lived charge carrier that is of relevance for light-harvesting applications can be designed and achieved by staggered band alignment of the two cores. Because the electron and hole wave functions are in two different dots, their overlap is reduced, increasing charge carrier lifetimes.\n\nThe description of the electronic and optical properties of single NCs is a great challenge, even to modern computers. Accurate techniques developed to study small molecules or solids are limited to small system sizes and computationally too expensive to be applicable to NCs. 34,35 Early work utilized\n\nFigure 15. Conductivity and electronic coupling of NCs assembled by ligands. (a) TEM images comparing interparticle spacing for selfassembled Au NCs of 5 mm in size, capped with 1-dodecanethiol (DDT) and Sn2S6 4 -ligands. (b) Order-coupling diagram for existing NC assemblies. The data points correspond to superlattices of DDT-capped Ag NCs 600 (orange diamond), film of inorganically capped HgTe NCs 601 (blue triangle), and epitaxially connected PbSe superlattice by oriented attachment 268 (navy blue pentagon). (c) X-ray scattering patterns of superlattices of Au NCs with Sn2S6 4 -ligands, showing crystalline order at both the supercrystal and atomic length scales for a superlattice of Au NCs of size 5 mm. (d) In the strong coupling regime, NC assemblies are expected to develop a hierarchical band structure, but their Fermi surface remains to be understood. (a -c) Adapted with permission from ref 27. Copyright 2022 The American Association for the Advancement of Science.\n\n<!-- image -->\n\ncontinuum approaches based on the effective mass model and its multiband generalization for realistic-sized NCs. 2,538,588 Atomistic models based on semiempirical pseudopotentials 589 -591 were developed for NC inhomogeneities that cannot be captured by continuum models. These atomistic models can be applied to describe electronic couplings, alloys, heterostructures, and vibronic and polaritonic effects, 592 but are still limited to single NC properties. Moreover, understanding surface effects, defects, and the inclusion of passivation of dangling bonds remains a challenge even for a single NC.\n\nThe description of the electronic and optical properties of NC assemblies is even more daunting. Ideally, an accurate description should (i) cover the atomistic scale of a single NC including electrons, holes, excitons, and their coupling to lattice vibrations, while (ii) bridging the time and length scales relevant for the emergent properties of NC assemblies. A promising bottom-up approach is coarse-grained electronic structure models, which utilize linear-scaling techniques at the single-particle level and then use them to parameterize a coarse-grained model for NC assembly. Along this line, it was recently shown that electron transfer in a NC dimer can be driven from the damped nonadiabatic limit to the coherent adiabatic limit even at room temperature, thereby increasing the transfer rate by orders of magnitude. 593 This was achieved by carefully designing the interface between the NCs that act as donors and acceptors, resulting in the discovery of large differences in coupling strength between NC molecules and bulk assemblies. Finally, moving beyond dimers requires accounting for collective phenomena and coupling between the NCs, as well as the inclusion of superlattice modes, 536 superradiance, and other many-body effects.\n\n7.3. Conductivity. Ordered NC assemblies are candidates for the bottom-up design of materials with hierarchically engineered electronic structures. Traditional approaches 8
        "Furthermore, superstructures prepared by lithography are often limited in total array size, and the fabrication is not scalable, requiring expensive equipment. Alternative preparation schemes using an assembly of plasmonic NCs have attracted significant interest in recent years. 157 While literature offers many robust wet-chemical protocols for the synthesis of noble metal NCs with excellent control over particle size, shape, and size distribution, their assembly into periodic, non-close-packed superstructures with precise lattice parameters (symmetry, periodicity) is a remaining scientific challenge.\n\nIn this sense, two assembly protocols have been proven suitable: (i) template-assisted assembly, where topographic templates are used to guide NC assembly 610,611 and (ii) polymer-guided (template-free) self-assembly of NCs that are encapsulated in sufficiently thick polymer shells. 361 While the symmetry and periodicity of the template control the final array structure in template-assisted assembly, template-free self-assembly of polymer-encapsulated NCs typically yields hexagonally ordered superstructures. In the latter, the periodicity of the lattice can be controlled by the thickness of the polymer shell and its degree of compression in the 2D confinement. 355 Another direction is superstructures that provide chiral SLRs. Chiral SLRs can be realized by fabricating superlattices with chiral plasmonic nanostructures 612,613 or by inducting optical chirality into otherwise achiral superstructures using chiral molecules. 614\n\nChallenges regarding SLRs comprise (i) the fabrication of non-close-packed superstructures that are periodic in all directions, (ii) understanding the role of defects and structural imperfections on the quality factor of coupled, collective resonances, (iii) improving quality factors of SLRs from selfassembled periodic plasmonic arrays, (iv) use of chiral SLRs in advanced biodetection, (v) manipulating SLRs by external parameters such as mechanic deformation of the lattice and (reversible) changes of the refractive index in the dielectric environment (substrate or superstrate), and (vi) coupling of\n\nFigure 16. Superfluorescence in NC assemblies. (a) Collective superfluorescence is achieved when NC properties fulfill criteria for identical and coherent emitters. (b -e) Relevant degrees of freedom for superfluorescence. (b) Timescales of radiative decay, T 1 , first-order coherence, T 2 , and accelerated decay, T SF , are of correct relative order to favor superfluorescence, for example, T SF &lt; T 1 , T SF &lt; T 2 . (c) Dipole-dipole interactions between close-packed NCs contribute to radiative coupling, where 1 and 2 are unit vectors of transition electric dipole, and \u03b4 12 is the orientation-dependent interaction energy. (d) Disorder leading to energetic inhomogeneity shall be minimized as it leads to excitation localization as opposed to the collective state. For example, size dispersion results in the energy transfer between NCs with different E g . (e) Mixing NC building blocks is a strategy to tune cooperative emission.\n\n<!-- image -->\n\nSLRs to gain media (emitter) to produce plasmonic nanolasers or sources of chiral light in the case of chiral SLRs.\n\n7.5. Superradiance and Superfluorescence. The fast pace of improvements in the synthesis and optimization of highly luminescent and uniform colloidal NCs 615,616 permits the engineering of cooperative light emission in NC assemblies. Photoluminescence of NCs in an ensemble is typically expected to add up. However, N identical NCs tightly packed in a volume \u03bb 3 (where \u03bb is the emission wavelength) can create a macroscopic polarization after photo-excitation, in the absence of decoherence (such as in low-temperature experiments). This macroscopic polarization decays with a peak intensity proportional to N 2 and an accelerated radiative lifetime (Figure 16a). Such collective phenomena have been theoretically considered for ensembles of two-level systems and are known as (i) superradiance , an accelerated radiative 
        "Identifying ways to enhance the clearance of fibrils or develop interventions that promote their disaggregation is an ongoing challenge.\n\n7.7.2. Nanocrystalline Complexes of Innate Immune Ligands. As discussed in the previous section, pathological self-assembly is a concept that has been associated with amyloids, such as amyloid\u03b2 (A ) in Alzheimer's disease and \u03b2 \u03b1 -synuclein in Parkinson's disease. While the oligomeric forms of amyloids are thought to be responsible for their cytotoxicity via membrane permeation, their fibrillar forms have been known to interact with the innate immune system to induce inflammation. Furthermore, both eukaryotic and prokaryotic amyloids can self-assemble and organize nucleic acids into nanocrystalline complexes, thereby enabling amplification of toll-like receptor (TLR) signaling from the innate immune system. In a more general compass, recent work has shown that antimicrobial peptides (AMPs) from the host innate immune system follow a strikingly similar pattern. AMPs have historically been considered essential components of the host innate immune system and play critical roles in defense against microbes, such as preferential permeation of microbial membranes rather than eukaryotic membranes, and sound the proverbial alarm to activate cellular-mediated immune responses. 646,647 Consistent with this perspective, many AMPs are facially amphiphilic and can facilitate membrane remodeling processes such as pore formation. In fact, in the last ten years, the lines of demarcation between amyloids and AMPs have blurred drastically. Like amyloids, it turns out that AMPs are low symmetry objects that can assemble into protofibrils that organize nucleic acids into nanocrystalline structures that amplify TLR mediated immune responses. 648 -651 Like AMPs, amyloids have recently been shown capable of antimicrobial activity in addition to their cytotoxic properties, suggesting a function in host defense. 652,653\n\nOne question is why the assembly of innate immune ligands like dsDNA or dsRNA into a nanocrystalline organization by AMPs or amyloids leads to amplified immune activation in the host. To answer this question, it is helpful to assess how the innate immune system functions. The innate immune system is capable of fast decision-making because it works via a form of molecular profiling. TLRs do not sense and respond to chemical individuality. Rather, the innate immune system goes through a more streamlined decision-making process to recognize and respond to a relatively small number of the so-called pathogen-associated molecular patterns (PAMPs), conserved molecular ligands derived from microbes. In microbial defense, AMPs can permeate microbial membranes and co-assemble with free microbial ligands from lysed microbes into nanocrystalline complexes that differentially activate TLRs.",
        "Depending on the precise assembled supramolecular crystalline structure of the complex, the TLR response from immune cells can vary from nonactivation up to massively amplified activation at about 100 times basal levels. 648 This system is fast and efficient, but the profiling can go wrong. For example, nonmicrobial self-nucleic acids can erroneously activate TLRs (TLR9 for dsDNA, TLR3 for dsRNA) via this AMP-based multivalent amplification mechanism in autoimmune diseases such as lupus, rheumatoid arthritis, and psoriasis. 648,649,651 The reason for this drastic\n\namplification is a statistical mechanical effect known as superselectivity , which was originally formulated to understand the assembly of multivalent NCs. 654 The crystalline face of an NC with the right lattice spacing commensurate with the steric size of TLRs can mediate successful multivalent binding between immune ligands and immune receptors. 648 More importantly, the system presents a vulnerability that allows innate immune machinery to be exploited by microbes, such as enterotoxins from Clostridioides difficile , 655 and coronaviruses such as SARS-CoV-2, the causative agent for COVID-19. 656 ## 8. CONCLUSIONS AND PERSPECTIVES\n\nAlthough NC-based materials have been used (inadvertently) for more than 3 millennia, 657 the subject, as a field, was basically nonexistent three decades ago. Recent spectacular progress in chemical synthesis and characterization, coupled with rapid advancements in theoretical understanding of fundamental processes, is what motivated the KITP workshop and conference in Santa Barbara entitled 'Nanoparticle Assemblies: A New Form of Matter with Classical Structure and Quantum Function'. This paper is a result of this event and attempts to categorize and summarize the most promising directions as identified by the workshop participants. Several challenges were elucidated in this study, and it is our expectation that their accomplishment will push the boundaries of the field.\n\nThe ability to assemble more complex and diverse structures will continue to be a major area of interest. Increasingly, the effort will be driven by the goal of assembling materials with given functions. Here, it should be expected that theory will increasingly play a leading role. Yet, many important functions are related to electronic properties, so general methods that combine the assembly part, which is more often described by classical statistical mechanics, and the electronic component, which almost entirely requires quantum calculations, will need to be further developed. Nonequilibrium effects have been arguably under-investigated but present ways of controlling equilibrium and metastable assembly, as well as in developing nanoscale active systems. Furthermore, the ability to design materials that perform many different functions requires a precise understanding of nonequilibrium effects. Insights from biological self-assembly, where complex structures are made from a shared set of building blocks (for example, a variety of protein structures arising from the same set of amino acids), have given rise to the growing field of multifarious self-assembly. An apparently unrelated but equally intriguing question pertains to the dynamic nature of structures. If a structure is constantly changing over time, can it break free from kinetic traps that have long hindered the more widespread adoption of selfassembly processes? Recent advancements hold great promise, offering not only potential applications within the self-assembly field but also insights into the statistical mechanics of systems characterized by rugged landscapes. 658\n\nThe exploration and engineering of optical and electronic interactions between NCs suggest potential avenues for practical applications. QD-OLED TVs, which utilize the NC photoluminescence, are a promising step in this direction. In this example, a fundamental discovery \ue0d5 the synthesis of quantum dots (QD), for which the Nobel Prize in Chemistry 2023 was awarded to Moungi G. Bawendi, Louis E. Brus, and Aleksei Y
        "## AUTHOR INFORMATION ## Corresponding Author\n\nAlex Travesset -Iowa State University and Ames Lab, Ames, Iowa 50011, USA; orcid.org/0000-0001-7030-9570; Email: trvsst@ameslab.gov ## Authors\n\n\u0308 - Carlos L. Bassani -Institute for Multiscale Simulation, Friedrich-Alexander-Universit \u00e4 t\n\nErlangen-Nurnberg, 91058 Erlangen, Germany; orcid.org/0000-0003-2451-2476 - Greg van Anders -Department of Physics, Engineering Physics, and Astronomy, Queen's University, Kingston, Ontario K7L 3N6, Canada; orcid.org/0000-0002-97462484\n- Uri Banin -Institute of Chemistry and the Center for Nanoscience and Nanotechnology, The Hebrew University of Jerusalem, Jerusalem 91904, Israel; orcid.org/0000-00031698-2128\n- Dmitry Baranov -Division of Chemical Physics, Department of Chemistry, Lund University, SE-221 00 Lund, Sweden; orcid.org/0000-0001-6439-8132\n- Qian Chen -University of Illinois, Urbana, Illinois 61801, USA; orcid.org/0000-0002-1968-441X\n- Marjolein Dijkstra -Soft Condensed Matter &amp; Biophysics, Debye Institute for Nanomaterials Science, Utrecht University, 3584 CC Utrecht, The Netherlands; orcid.org/0000-0002-9166-6478\n- Michael S. Dimitriyev -Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA; Department of Materials Science and Engineering, Texas A &amp; M University, College Station, Texas 77843, USA; orcid.org/0000-0001-6384-3644\n- Efi Efrati -Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel; James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA\n- Jordi Faraudo -Institut de Ciencia de Materials de Barcelona (ICMAB-CSIC), E-08193 Bellaterra, Barcelona, Spain; orcid.org/0000-0002-6315-4993\n- Oleg Gang -Department of Chemical Engineering and Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA; Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA; orcid.org/ 0000-0001-5534-3121\n\nNicola Gaston -The MacDiarmid Institute for Advanced Materials and Nanotechnology, Department of Physics, The University of Auckland, Auckland 1142, New Zealand; orcid.org/0000-0001-8049-3295\n\nRamin Golestanian -Max Planck Institute for Dynamics and Self-Organization (MPI-DS), 37077 G ttingen, Germany; \u00f6 Rudolf Peierls Centre for Theoretical Physics, University of - Oxford, Oxford OX1 3PU, UK; orcid.org/0000-00023149-4002\n- G. Ivan Guerrero-Garcia -Facultad de Ciencias de la Universidad Aut \u00f3 noma de San Luis Potos , 78295 San Luis \u00ed Potos , M xico; \u00ed \u00e9 orcid.org/0000-0002-3174-2643\n- Michael Gruenwald -Department of Chemistry, University of Utah, Salt Lake City, Utah 84112, USA; orcid.org/00000003-2186-1662\n- Amir Haji-Akbari -Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06511, USA; orcid.org/0000-0002-22286957\n\n\u0303 - Maria Ib\u00e1nez -Institute of Science and Technology Austria (ISTA), 3400 Klosterneuburg, Austria; orcid.org/00000001-5013-2843\n\n\u0308\n\n\u0308 - Matthias Karg -Heinrich-Heine-Universit \u00e4 t Dusseldorf, 40225 Dusseldorf, Germany; orcid.org/0000-0002-62473976\n\n\u0308\n\n\u0308 - Tobias Kraus -INM -Leibniz-Institute for New Materials, 66123 Saarbrucken, Germany; Saarland University, Colloid and Interface Chemistry, 66123 Saarbrucken, Germany; orcid.org/0000-0003-2951-1704\n- Byeongdu Lee -X-ray Science Division, Argonne National Laboratory, Lemont, Illinois 60439, USA; orcid.org/ 0000-0003-2514-8805\n- Reid C. Van Lehn -Department of Chemical and Biological Engineering, University of Wisconsin-Madison, Madison, Wisconsin 53717, USA; orcid.org/0000-0003-48856599\n- Robert J. Macfarlane -Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, USA; orcid.org/00000001-9449-2680\n- Bortolo M. Mognetti -Center for Nonlinear Phenomena and Complex Systems, Universit \u00e9 Libre de Bruxelles, 1050 Brussels, Belgium; orcid.org/0000-000
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}