Self-similar mesocrystals form via interface-driven nucleation and assembly.

Crystallization by particle attachment (CPA) is a frequently occurring mechanism of colloidal crystallization that results in hierarchical morphologies1-4. CPA has been exploited to create nanomaterials with unusual properties4-6 and is implicated in the development of complex mineral textures1,7. Oriented attachment7,8-a form of CPA in which particles align along specific crystallographic directions-produces mesocrystals that diffract as single crystals do, although the constituent particles are still discernible2,9. The conventional view of CPA is that nucleation provides a supply of particles that aggregate via Brownian motion biased by attractive interparticle potentials1,9-12. However, mesocrystals often exhibit regular morphologies and uniform sizes. Although many crystal systems form mesocrystals1-9 and individual attachment events have been directly visualized10, how random attachment events lead to well defined, self-similar morphologies remains unknown, as does the role of surface-bound ligands, which are ubiquitous in nanoparticle systems3,9,11. Attempts to understand mesocrystal formation are further complicated in many systems by the presence of precursor nanoparticles with a phase distinct from that of the bulk1,13,14. Some studies propose that such particles convert before attachment15, whereas others attribute conversion to the attachment process itself16 and yet others conclude that transformation occurs after the mesocrystals exceed a characteristic size14,17. Here we investigate mesocrystal formation by iron oxides, which are important colloidal phases in natural environments18,19 and classic examples of systems forming ubiquitous precursor phases and undergoing CPA accompanied by phase transformations15,19-21. Combining in situ transmission electron microscopy (TEM) at 80 degrees Celsius with 'freeze-and-look' TEM, we tracked the formation of haematite (Hm) mesocrystals in the presence of oxalate (Ox), which is abundant in soils, where iron oxides are common. We find that isolated Hm particles rarely appear, but once formed, interfacial gradients at the Ox-covered surfaces drive Hm particles to nucleate repeatedly about two nanometres from the surfaces, to which they then attach, thereby generating mesocrystals. Comparison to natural and synthetic systems suggests that interface-driven pathways are widespread.

Design of biologically active binary protein 2D materials.

Ordered two-dimensional arrays such as S-layers1,2 and designed analogues3-5 have intrigued bioengineers6,7, but with the exception of a single lattice formed with flexible linkers8, they are constituted from just one protein component. Materials composed of two components have considerable potential advantages for modulating assembly dynamics and incorporating more complex functionality9-12. Here we describe a computational method to generate co-assembling binary layers by designing rigid interfaces between pairs of dihedral protein building blocks, and use it to design a p6m lattice. The designed array components are soluble at millimolar concentrations, but when combined at nanomolar concentrations, they rapidly assemble into nearly crystalline micrometre-scale arrays nearly identical to the computational design model in vitro and in cells without the need for a two-dimensional support. Because the material is designed from the ground up, the components can be readily functionalized and their symmetry reconfigured, enabling formation of ligand arrays with distinguishable surfaces, which we demonstrate can drive extensive receptor clustering, downstream protein recruitment and signalling. Using atomic force microscopy on supported bilayers and quantitative microscopy on living cells, we show that arrays assembled on membranes have component stoichiometry and structure similar to arrays formed in vitro, and that our material can therefore impose order onto fundamentally disordered substrates such as cell membranes. In contrast to previously characterized cell surface receptor binding assemblies such as antibodies and nanocages, which are rapidly endocytosed, we find that large arrays assembled at the cell surface suppress endocytosis in a tunable manner, with potential therapeutic relevance for extending receptor engagement and immune evasion. Our work provides a foundation for a synthetic cell biology in which multi-protein macroscale materials are designed to modulate cell responses and reshape synthetic and living systems.

A molecular view of peptoid-induced acceleration of calcite growth.

The extensive deposits of calcium carbonate (CaCO3) generated by marine organisms constitute the largest and oldest carbon dioxide (CO2) reservoir. These organisms utilize macromolecules like peptides and proteins to facilitate the nucleation and growth of carbonate minerals, serving as an effective method for CO2 sequestration. However, the precise mechanisms behind this process remain elusive. In this study, we report the use of sequence-defined peptoids, a class of peptidomimetics, to achieve the accelerated calcite step growth kinetics with the molecular level mechanistic understanding. By designing peptoids with hydrophilic and hydrophobic blocks, we systematically investigated the acceleration in step growth rate of calcite crystals using in situ atomic force microscopy (AFM), varying peptoid sequences and concentrations, CaCO3 supersaturations, and the ratio of Ca2+/ HCO3-. Mechanistic studies using NMR, three-dimensional fast force mapping (3D FFM), and isothermal titration calorimetry (ITC) were conducted to reveal the interactions of peptoids with Ca2+ and HCO3- ions in solution, as well as the effect of peptoids on solvation and energetics of calcite crystal surface. Our results indicate the multiple roles of peptoid in facilitating HCO3- deprotonation, Ca2+ desolvation, and the disruption of interfacial hydration layers of the calcite surface, which collectively contribute to a peptoid-induced acceleration of calcite growth. These findings provide guidelines for future design of sequence-specific biomimetic polymers as crystallization promoters, offering potential applications in environmental remediation (such as CO2 sequestration), biomedical engineering, and energy storage where fast crystallization is preferred.

Understanding the mechanisms of anisotropic dissolution in metal oxides by applying radiolysis simulations to liquid-phase TEM.

Iron-based redox-active minerals are ubiquitous in soils, sediments, and aquatic systems. Their dissolution is of great importance for microbial impacts on carbon cycling and the biogeochemistry of the lithosphere and hydrosphere. Despite its widespread significance and extensive prior study, the atomic-to-nanoscale mechanisms of dissolution remain poorly understood, particularly the interplay between acidic and reductive processes. Here, we use in situ liquid-phase-transmission electron microscopy (LP-TEM) and simulations of radiolysis to probe and control acidic versus reductive dissolution of akaganeite (ß-FeOOH) nanorods. Informed by crystal structure and surface chemistry, the balance between acidic dissolution at rod tips and reductive dissolution at rod sides was systematically varied using pH buffers, background chloride anions, and electron beam dose. We find that buffers, such as bis-tris, effectively inhibited dissolution by consuming radiolytic acidic and reducing species such as superoxides and aqueous electrons. In contrast, chloride anions simultaneously suppressed dissolution at rod tips by stabilizing structural elements while promoting dissolution at rod sides through surface complexation. Dissolution behaviors were systematically varied by shifting the balance between acidic and reductive attacks. The findings show LP-TEM combined with simulations of radiolysis effects can provide a unique and versatile platform for quantitatively investigating dissolution mechanisms, with implications for understanding metal cycling in natural environments and the development of tailored nanomaterials.

Formation, chemical evolution and solidification of the dense liquid phase of calcium (bi)carbonate.

Metal carbonates, which are ubiquitous in the near-surface mineral record, are a major product of biomineralizing organisms and serve as important targets for capturing anthropogenic CO2 emissions. However, pathways of carbonate mineralization typically diverge from classical predictions due to the involvement of disordered precursors, such as the dense liquid phase (DLP), yet little is known about DLP formation or solidification processes. Using in situ methods we report that a highly hydrated bicarbonate DLP forms via liquid-liquid phase separation and transforms into hollow hydrated amorphous CaCO3 particles. Acidic proteins and polymers extend DLP lifetimes while leaving the pathway and chemistry unchanged. Molecular simulations suggest that the DLP forms via direct condensation of solvated Ca²+⋅(HCO3-)2 complexes that react due to proximity effects in the confined DLP droplets. Our findings provide insight into CaCO3 nucleation that is mediated by liquid-liquid phase separation, advancing the ability to direct carbonate mineralization and elucidating an often-proposed complex pathway of biomineralization.

Controlling protein assembly on inorganic crystals through designed protein interfaces.

The ability of proteins and other macromolecules to interact with inorganic surfaces is essential to biological function. The proteins involved in these interactions are highly charged and often rich in carboxylic acid side chains1-5, but the structures of most protein-inorganic interfaces are unknown. We explored the possibility of systematically designing structured protein-mineral interfaces, guided by the example of ice-binding proteins, which present arrays of threonine residues (matched to the ice lattice) that order clathrate waters into an ice-like structure6. Here we design proteins displaying arrays of up to 54 carboxylate residues geometrically matched to the potassium ion (K+) sublattice on muscovite mica (001). At low K+ concentration, individual molecules bind independently to mica in the designed orientations, whereas at high K+ concentration, the designs form two-dimensional liquid-crystal phases, which accentuate the inherent structural bias in the muscovite lattice to produce protein arrays ordered over tens of millimetres. Incorporation of designed protein-protein interactions preserving the match between the proteins and the K+ lattice led to extended self-assembled structures on mica: designed end-to-end interactions produced micrometre-long single-protein-diameter wires and a designed trimeric interface yielded extensive honeycomb arrays. The nearest-neighbour distances in these hexagonal arrays could be set digitally between 7.5 and 15.9 nanometres with 2.1-nanometre selectivity by changing the number of repeat units in the monomer. These results demonstrate that protein-inorganic lattice interactions can be systematically programmed and set the stage for designing protein-inorganic hybrid materials.

Amyloid-like amelogenin nanoribbons template mineralization via a low-energy interface of ion binding sites.

Protein scaffolds direct the organization of amorphous precursors that transform into mineralized tissues, but the templating mechanism remains elusive. Motivated by models for the biomineralization of tooth enamel, wherein amyloid-like amelogenin nanoribbons guide the mineralization of apatite filaments, we investigated the impact of nanoribbon structure, sequence, and chemistry on amorphous calcium phosphate (ACP) nucleation. Using full-length human amelogenin and peptide analogs with an amyloid-like domain, films of ß-sheet nanoribbons were self-assembled on graphite and characterized by in situ atomic force microscopy and molecular dynamics simulations. All sequences substantially reduce nucleation barriers for ACP by creating low-energy interfaces, while phosphoserines along the length of the nanoribbons dramatically enhance kinetic factors associated with ion binding. Furthermore, the distribution of negatively charged residues along the nanoribbons presents a potential match to the Ca­Ca distances of the multi-ion complexes that constitute ACP. These findings show that amyloid-like amelogenin nanoribbons provide potent scaffolds for ACP mineralization by presenting energetically and stereochemically favorable templates of calcium phosphate ion binding and suggest enhanced surface wetting toward calcium phosphates in general.

Rotational dynamics and transition mechanisms of surface-adsorbed proteins.

Assembly of biomolecules at solid­water interfaces requires molecules to traverse complex orientation-dependent energy landscapes through processes that are poorly understood, largely due to the dearth of in situ single-molecule measurements and statistical analyses of the rotational dynamics that define directional selection. Emerging capabilities in high-speed atomic force microscopy and machine learning have allowed us to directly determine the orientational energy landscape and observe and quantify the rotational dynamics for protein nanorods on the surface of muscovite mica under a variety of conditions. Comparisons with kinetic Monte Carlo simulations show that the transition rates between adjacent orientation-specific energetic minima can largely be understood through traditional models of in-plane Brownian rotation across a biased energy landscape, with resulting transition rates that are exponential in the energy barriers between states. However, transitions between more distant angular states are decoupled from barrier height, with jump-size distributions showing a power law decay that is characteristic of a nonclassical Levy-flight random walk, indicating that large jumps are enabled by alternative modes of motion via activated states. The findings provide insights into the dynamics of biomolecules at solid­liquid interfaces that lead to self-assembly, epitaxial matching, and other orientationally anisotropic outcomes and define a general procedure for exploring such dynamics with implications for hybrid biomolecular­inorganic materials design.

Particle-based hematite crystallization is invariant to initial particle morphology.

SignificanceMany crystallization processes occurring in nature produce highly ordered hierarchical architectures. Their formation cannot be explained using classical models of monomer-by-monomer growth. One of the possible pathways involves crystallization through the attachment of oriented nanocrystals. Thus, it requires detailed understanding of the mechanism of particle dynamics that leads to their precise crystallographic alignment along specific faces. In this study, we discover a particle-morphology-independent oriented attachment mechanism for hematite nanocrystals. Independent of crystal morphology, particles always align along the [001] direction driven by aligning interactions between (001) faces and repulsive interactions between other pairs of hematite faces. These results highlight that strong face specificity along one crystallographic direction can render oriented attachment to be independent of initial particle morphology.

Oriented Assembly of Lead Halide Perovskite Nanocrystals.

Cesium lead halide nanostructures have highly tunable optical and optoelectronic properties. Establishing precise control in forming perovskite single-crystal nanostructures is key to unlocking the full potential of these materials. However, studying the growth kinetics of colloidal cesium lead halides is challenging due to their sensitivity to light, electron beam, and environmental factors like humidity. In this study, in situ observations of CsPbBr3-particle dynamics were made possible through extremely low dose liquid cell transmission electron microscopy, showing that oriented attachment is the dominant pathway for the growth of single-crystal CsPbBr3 architectures from primary nanocubes. In addition, oriented assembly and fusion of ligand-stabilized cubic CsPbBr3 nanocrystals are promoted by electron beam irradiation or introduction of polar additives that both induce partial desorption of the original ligands and polarize the nanocube surfaces. These findings advance our understanding of cesium lead halide growth mechanisms, aiding the controlled synthesis of other perovskite nanostructures.

Uncovering the Size-Dependent Thermal Solid Transformation of Akaganéite.

Investigating the structural evolution and phase transformation of iron oxides is crucial for gaining a deeper understanding of geological changes on diverse planets and preparing oxide materials suitable for industrial applications. In this study, in-situ heating techniques are employed in conjunction with transmission electron microscopy (TEM) observations and ex-situ characterization to thoroughly analyze the thermal solid-phase transformation of akaganéite 1D nanostructures with varying diameters. These findings offer compelling evidence for a size-dependent morphology evolution in akaganéite 1D nanostructures, which can be attributed to the transformation from akaganéite to maghemite (γ-Fe2O3) and subsequent crystal growth. Specifically, it is observed that akaganéite nanorods with a diameter of ∼50 nm transformed into hollow polycrystalline maghemite nanorods, which demonstrated remarkable stability without arresting crystal growth under continuous heating. In contrast, smaller akaganéite nanoneedles or nanowires with a diameter ranging from 20 to 8 nm displayed a propensity for forming single-crystal nanoneedles or nanowires through phase transformation and densification. By manipulating the size of the precursors, a straightforward method is developed for the synthesis of single-crystal and polycrystalline maghemite nanowires through solid-phase transformation. These significant findings provide new insights into the size-dependent structural evolution and phase transformation of iron oxides at the nanoscale.

Molecular Mechanisms of Sorbed Ion Effects during Boehmite Particle Aggregation.

Classical theories of particle aggregation, such as Derjaguin-Landau-Verwey-Overbeek (DLVO), do not explain recent observations of ion-specific effects or the complex concentration dependence for aggregation. Thus, here, we probe the molecular mechanisms by which selected alkali nitrate ions (Na+, K+, and NO3-) influence aggregation of the mineral boehmite (γ-AlOOH) nanoparticles. Nanoparticle aggregation was analyzed using classical molecular dynamics (CMD) simulations coupled with the metadynamics rare event approach for stoichiometric surface terminations of two boehmite crystal faces. Calculated free energy landscapes reveal how electrolyte ions alter aggregation on different crystal faces relative to pure water. Consistent with experimental observations, we find that adding an electrolyte significantly reduces the energy barrier for particle aggregation (∼3-4×). However, in this work, we show this is due to the ions disrupting interstitial water networks, and that aggregation between stoichiometric (010) basal-basal surfaces is more favorable than between (001) edge-edge surfaces (∼5-6×) due to the higher interfacial water densities on edge surfaces. The interfacial distances in the interlayer between aggregated particles with electrolytes (∼5-10 Å) are larger than those in pure water (a few Ångströms). Together, aggregation/disaggregation in salt solutions is predicted to be more reversible due to these lower energy barriers, but there is uncertainty on the magnitudes of the energies that lead to aggregation at the molecular scale. By analyzing the peak water densities of the first monolayer of interstitial water as a proxy for solvent ordering, we find that the extent of solvent ordering likely determines the structures of aggregated states as well as the energy barriers to move between them. The results suggest a path for developing a molecular-level basis to predict the synergies between ions and crystal faces that facilitate aggregation under given solution conditions. Such fundamental understanding could be applied extensively to the aggregation and precipitation utilization in the biological, pharmaceutical, materials design, environmental remediation, and geological regimes.

Cerium Nanophases from Cerium Ammonium Nitrate.

Ceria nanomaterials with facile CeIII/IV redox behavior are used in sensing, catalytic, and therapeutic applications, where inclusion of CeIII has been correlated with reactivity. Understanding assembly pathways of CeO2 nanoparticles (NC-CeO2) in water has been challenged by "blind" synthesis, including rapid assembly/precipitation promoted by heat or strong base. Here, we identify a layered phase denoted Ce-I with a proposed formula CeIV(OH)3(NO3)·xH2O (x ≈ 2.5), obtained by adding electrolytes to aqueous cerium ammonium nitrate (CAN) to force precipitation. Ce-I represents intermediate hydrolysis species between dissolved CAN and NC-CeO2, where CAN is a commonly used CeIV compound that exhibits unusual aqueous and organic solubility. Ce-I features Ce-(OH)2-Ce units, representing the first step of hydrolysis toward NC-CeO2 formation, challenging prior assertions about CeIV hydrolysis. Structure/composition of poorly crystalline Ce-I was corroborated by a pair distribution function, Ce-L3 XAS (X-ray absorption spectroscopy), compositional analysis, and 17O nuclear magnetic resonance spectroscopy. Formation of Ce-I and its transformation to NC-CeO2 is documented in solution by small-angle X-ray scattering (SAXS) and in the solid-state by transmission electron microscopy (TEM) and powder X-ray diffraction. Morphologies identified by TEM support form factor models for SAXS analysis, evidencing the incipient assembly of Ce-I. Finally, two morphologies of NC-CeO2 are identified. Sequentially, spherical NC-CeO2 particles coexist with Ce-I, and asymmetric NC-CeO2 with up to 35% CeIII forms at the expense of Ce-I, suggesting direct replacement.

Hierarchical Materials from High Information Content Macromolecular Building Blocks: Construction, Dynamic Interventions, and Prediction.

Hierarchical materials that exhibit order over multiple length scales are ubiquitous in nature. Because hierarchy gives rise to unique properties and functions, many have sought inspiration from nature when designing and fabricating hierarchical matter. More and more, however, nature's own high-information content building blocks, proteins, peptides, and peptidomimetics, are being coopted to build hierarchy because the information that determines structure, function, and interfacial interactions can be readily encoded in these versatile macromolecules. Here, we take stock of recent progress in the rational design and characterization of hierarchical materials produced from high-information content blocks with a focus on stimuli-responsive and "smart" architectures. We also review advances in the use of computational simulations and data-driven predictions to shed light on how the side chain chemistry and conformational flexibility of macromolecular blocks drive the emergence of order and the acquisition of hierarchy and also on how ionic, solvent, and surface effects influence the outcomes of assembly. Continued progress in the above areas will ultimately usher in an era where an understanding of designed interactions, surface effects, and solution conditions can be harnessed to achieve predictive materials synthesis across scale and drive emergent phenomena in the self-assembly and reconfiguration of high-information content building blocks.

Ion-dependent protein-surface interactions from intrinsic solvent response.

The phyllosilicate mineral muscovite mica is widely used as a surface template for the patterning of macromolecules, yet a molecular understanding of its surface chemistry under varying solution conditions, required to predict and control the self-assembly of adsorbed species, is lacking. We utilize all-atom molecular dynamics simulations in conjunction with an electrostatic analysis based in local molecular field theory that affords a clean separation of long-range and short-range electrostatics. Using water polarization response as a measure of the electric fields that arise from patterned, surface-bound ions that direct the adsorption of charged macromolecules, we apply a Landau theory of forces induced by asymmetrically polarized surfaces to compute protein-surface interactions for two muscovite-binding proteins (DHR10-mica6 and C98RhuA). Comparison of the pressure between surface and protein in high-concentration KCl and NaCl aqueous solutions reveals ion-specific differences in far-field protein-surface interactions, neatly capturing the ability of ions to modulate the surface charge of muscovite that in turn selectively attracts one binding face of each protein over all others.

Biomimetic Mineral Synthesis by Nanopatterned Supramolecular-Block Copolymer Templates.

Supramolecular structures of matrix proteins in mineralizing tissues are known to direct the crystallization of inorganic materials. Here we demonstrate how such structures can be synthetically directed into predetermined patterns for which functionality is maintained. The study employs block copolymer lamellar patterns with alternating hydrophilic and hydrophobic regions to direct the assembly of amelogenin-derived peptide nanoribbons that template calcium phosphate nucleation by creating a low-energy interface. Results show that the patterned nanoribbons retain their ß-sheet structure and function and direct the formation of filamentous and plate-shaped calcium phosphate with high fidelity, where the phase, amorphous or crystalline, depends on the choice of mineral precursor and the fidelity depends on peptide sequence. The common ability of supramolecular systems to assemble on surfaces with appropriate chemistry combined with the tendency of many templates to mineralize multiple inorganic materials implies this approach defines a general platform for bottom-up-patterning of hybrid organic-inorganic materials.

Luminescence and Covalency in Ytterbium-Doped CrX3 (X = Cl, Br, I) van der Waals Compounds.

The layered 2D van der Waals ferromagnets CrX3 (X = Cl, Br, I) show broad d-d photoluminescence (PL). Here we report preparation, structural characterization, and spectroscopic studies of all three CrX3 compounds doped with the optical impurity, Yb3+. EXAFS measurements show very similar Cr K-edge and Yb L-edge data for each doped compound, and good fits of the latter are obtained for structures having Yb3+ occupying substitutional octahedral sites. Yb-X bond lengths are systematically ∼0.25 Å larger than their Cr-X counterparts. 4 K PL measurements show efficient sensitization of Yb3+ luminescence upon photoexcitation into lattice absorption bands [Cr3+ d-d and ligand-to-metal charge-transfer (LMCT)] for all three compounds, converting their nondescript broadband d-d PL into sharp f-f emission. The PL of CrCl3:Yb3+ and CrBr3:Yb3+ occurs at energies typical for [YbX6]3- with these halides, with PL decay times of 0.5-1.0 ms at 4 K, but CrI3:Yb3+ displays anomalously low-energy Yb3+ emission and an unusually short PL decay time of only 8 µs at 4 K. Data analysis and angular overlap model (AOM) calculations show that Yb3+ in CrI3:Yb3+ has a lower spin-orbit splitting energy than reported for any other Yb3+ in any other compound. We attribute these observations to exceptionally high covalency of the Yb3+ f orbitals in CrI3:Yb3+ stemming primarily from the shallow valence-shell ionization potentials of the iodide anions.

Co-Assembly of Carbon Nanotube Porins into Biomimetic Peptoid Membranes.

Robust and cost-effective membrane-based separations are essential to solving many global crises, such as the lack of clean water. Even though the current polymer-based membranes are widely used for separations, their performance and precision can be enhanced by using a biomimetic membrane architecture that consists of highly permeable and selective channels embedded in a universal membrane matrix. Researchers have shown that artificial water and ion channels, such as carbon nanotube porins (CNTPs), embedded in lipid membranes can deliver strong separation performance. However, their applications are limited by the relative fragility and low stability of the lipid matrix. In this work, we demonstrate that CNTPs can co-assemble into two dimension (2D) peptoid membrane nanosheets, opening up a way to produce highly programmable synthetic membranes with superior crystallinity and robustness. A combination of molecular dynamics (MD) simulations, Raman spectroscopy, X-ray diffraction (XRD), and atomic force microscopy (AFM) measurements to verify the co-assembly of CNTP and peptoids are used and show that it does not disrupt peptoid monomer packing within the membrane. These results provide a new option for designing affordable artificial membranes and highly robust nanoporous solids.

In situ imaging of amorphous intermediates during brucite carbonation in supercritical CO2.

Progress in understanding crystallization pathways depends on the ability to unravel relationships between intermediates and final crystalline products at the nanoscale, which is a particular challenge at elevated pressure and temperature. Here we exploit a high-pressure atomic force microscope to directly visualize brucite carbonation in water-bearing supercritical carbon dioxide (scCO2) at 90 bar and 50 °C. On introduction of water-saturated scCO2, in situ visualization revealed initial dissolution followed by nanoparticle nucleation consistent with amorphous magnesium carbonate (AMC) on the surface. This is followed by growth of nesquehonite (MgCO3·3H2O) crystallites. In situ imaging provided direct evidence that the AMC intermediate acts as a seed for crystallization of nesquehonite. In situ infrared and thermogravimetric-mass spectrometry indicate that the stoichiometry of AMC is MgCO3·xH2O (x = 0.5-1.0), while its structure is indicated to be hydromagnesite-like according to density functional theory and X-ray pair distribution function analysis. Our findings thus provide insight for understanding the stability, lifetime and role of amorphous intermediates in natural and synthetic systems.

Effects of Size and Shape on the Tolerances for Misalignment and Probabilities for Successful Oriented Attachment of Nanoparticles.

Oriented attachment (OA) of nanoparticles is an important pathway of crystal growth, but there is a lack of tools to model OA. Here, we present several simple models that relate the probability of achieving OA to basic geometric parameters, such as particle size, shape, and lattice periodicity. A Moiré-domain model is applied to understand twist misorientations between parallel surfaces, and it predicts that the range of twist angles yielding perfect OA is inversely related to the width of the contact area. This idea is explored further through a surface functional model, which investigates how patterns of crystallographic registration can drive the emergence of complex orientational energy landscapes. The energy landscapes are predicted to possess multiple local minima that can trap particles in imperfect alignments, and these local minima become deeper and more numerous as the contact area increases, which makes OA more challenging for large particles. A second set of models is presented to understand the sequence of events by which two crystallographic faces become coplanar after the collision. We use a central force approximation to predict the odds that two particle faces will attain coalignment when the particles collide with random misalignments, and we show that in the absence of special biasing forces, the probability of attaining alignment on a given face is roughly proportional to its solid angle as viewed from the center of the particle. The model thus predicts that OA is most favorable between well-faceted particles and becomes exceedingly unlikely for large spherical particles that express many microfacets.