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.

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.

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.

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.

Visualization of Aluminum Ions at the Mica Water Interface Links Hydrolysis State-to-Surface Potential and Particle Adhesion.

When hydrolyzable cations such as aluminum interact with solid-water interfaces, macroscopic interfacial properties (e.g., surface charge and potential) and interfacial phenomena (e.g., particle adhesion) become tightly linked with the microscopic details of ion adsorption and speciation. We use in situ atomic force microscopy to directly image individual aluminum ions at a mica-water interface and show how adsorbate populations change with pH and aluminum activity. Complementary streaming potential measurements then allow us to build a triple layer model (TLM) that links surface potentials to adsorbate populations, via equilibrium binding constants. Our model predicts that hydrolyzed species dominate the mica-water interface, even when unhydrolyzed species dominate the solution. Ab initio molecular dynamics (AIMD) simulations confirm that aluminum hydrolysis is strongly promoted at the interface. The TLM indicates that hydrolyzed adsorbates are responsible for surface-potential inversions, and we find strong correlations between hydrolyzed adsorbates and particle-adhesion forces, suggesting that these species mediate adhesion by chemical bridging.

Direct Observation of the Orientational Anisotropy of Buried Hydroxyl Groups inside Muscovite Mica.

Muscovite mica (001) is a widely used model surface for controlling molecular assembly and a common substrate for environmental adsorption processes. The mica (001) surface displays near-trigonal symmetry, but many molecular adsorbates-including water-exhibit unequal probabilities of alignment along its three nominally equivalent lattice directions. Buried hydroxyl groups within the muscovite structure are speculated to be responsible, but direct evidence is lacking. Here, we utilize vibrational sum frequency generation spectroscopy (vSFG) to characterize the orientation and hydrogen-bonding environment of near-surface hydroxyls inside mica. Multiple distinct peaks are detected in the O-H stretch region, which we attribute to Si/Al substitution in the SiO4 tetrahedron and K+ ion adsorption above the hydroxyls based on density functional theory simulations. Our findings demonstrate that vSFG can identify the absolute orientation of -OH groups and, hence, the surface termination at a mica surface, providing a means to investigate how -OH groups influence molecular adsorption and better understand mica stacking-sequences and physical behavior.

The energetics of prenucleation clusters in lattice solutions.

According to classical nucleation theory, nucleation from solution involves the formation of small atomic clusters. Most formulations of classical nucleation use continuum "droplet" approximations to describe the properties of these clusters. However, the discrete atomic nature of very small clusters may cause deviations from these approximations. Here, we present a self-consistent framework for describing the nature of these deviations. We use our framework to investigate the formation of "polycube" atomic clusters on a cubic lattice, for which we have used combinatoric data to calculate the thermodynamic properties of clusters with 17 atoms or less. We show that the classical continuum droplet model emerges as a natural approach to describe the free energy of small clusters, but with a size-dependent surface tension. However, this formulation only arises if an appropriate "site-normalized" definition is adopted for the free energy of formation. These results are independently confirmed through the use of Monte Carlo calculations. Our results show that clusters formed from sparingly soluble materials (µM solubility range) tend to adopt compact configurations that minimize the solvent-solute interaction energy. As a consequence, there are distinct minima in the cluster-size-energy landscape that correspond to especially compact configurations. Conversely, highly soluble materials (1M) form clusters with expanded configurations that maximize configurational entropy. The effective surface tension of these clusters tends to smoothly and systematically decrease as the cluster size increases. However, materials with intermediate solubility (1 mM) are found to have a balanced behavior, with cluster energies that follow the classical "droplet" scaling laws remarkably well.

Determination of the three-dimensional structure of ferrihydrite nanoparticle aggregates.

Aggregation impacts the reactivity, colloidal stability, and transport behavior of nanomaterials, yet methods to characterize basic structural features of aggregates are limited. Here, cryo-transmission electron microscope (cryo-TEM) based tomography is utilized as a method for directly imaging fragile aggregates of nanoparticles in aqueous suspension and an approach for extracting quantitative fractal dimensions from the resulting three-dimensional structural models is introduced. The structural quantification approach is based upon the mass autocorrelation function, and is directly comparable with small-angle X-ray scattering (SAXS) models. This enables accurate characterization of aggregate structure, even in suspensions where the aggregate cluster size is highly polydisperse and traditional SAXS modeling is not reliable. This technique is applied to study real suspensions of ferrihydrite nanoparticles. By comparing tomographic measurements with SAXS-based measurements, we infer that certain suspensions contain polydisperse aggregate size distributions. In other suspensions, fractal-type structures are identified with low intrinsic fractal dimensions. The fractal dimensions are lower than would be predicted by simple models of particle aggregation, and this low dimensionality enables large, low-density aggregates to exist in stable colloidal suspension.

Impacts of ionic strength on three-dimensional nanoparticle aggregate structure and consequences for environmental transport and deposition.

The transport of nanoparticles through aqueous systems is a complex process with important environmental policy ramifications. Ferrihydrite nanoparticles commonly form aggregates, with structures that depend upon solution chemistry. The impact of aggregation state on transport and deposition is not fully understood. In this study, small-angle X-ray scattering (SAXS) and cryogenic transmission electron microscopy (cryo-TEM) were used to directly observe the aggregate structure of ferrihydrite nanoparticles and show how the aggregate structure responds to changing ionic strength. These results were correlated with complementary studies on ferrihydrite transport through saturated quartz sand columns. Within deionized water, nanoparticles form stable suspensions of low-density fractal aggregates that are resistant to collapse. The particles subsequently show limited deposition on sand grain surfaces. Within sodium nitrate solutions the aggregates collapse into denser clusters, and nanoparticle deposition increases dramatically by forming thick, localized, and mechanically unstable deposits. Such deposits limit nanoparticle transport and make transport less predictable. The action of ionic strength is distinct from simpler models of colloidal stability and transport, in that salt not only drives aggregation or attachment but also alters the behavior of preexisting aggregates by triggering their collapse.

Ion Correlations Decrease Particle Aggregation Rate by Increasing Hydration Forces at Interfaces.

The connection between solution structure, particle forces, and emergent phenomena at solid-liquid interfaces remains ambiguous. In this case study on boehmite aggregation, we established a connection between interfacial solution structure, emerging hydration forces between two approaching particles, and the resulting structure and kinetics of particle aggregation. In contrast to expectations from continuum-based theories, we observed a nonmonotonic dependence of the aggregation rate on the concentration of sodium chloride, nitrate, or nitrite, decreasing by 15-fold in 4 molal compared to 1 molal solutions. These results are accompanied by an increase in repulsive hydration forces and interfacial oscillatory features from 0.27-0.31 nm in 0.01 molal to 0.38-0.52 nm in 2 molal. Moreover, molecular dynamics (MD) simulations indicated that these changes correspond to enhanced ion correlations near the interface and produced loosely bound aggregates that retain electrolyte between the particles. We anticipate that these results will enable the prediction of particle aggregation, attachment, and assembly, with broad relevance to interfacial phenomena.

Uptake of Pb and the Formation of Mixed (Ba,Pb)SO4 Monolayers on Barite During Cyclic Exposure to Lead-Containing Sulfuric Acid.

Barite (BaSO4) is a common additive in lead-acid batteries, where it acts as a nucleating agent to promote the reversible formation and dissolution of PbSO4 during battery cycling. However, little is known about the molecular-scale mechanisms that control the nucleation and cyclic evolution of PbSO4 over a battery's lifetime. In this study, we explore the responses of a barite (001) surface to cycles of high and low lead concentrations in 100 mM sulfuric acid solution using in situ atomic force microscopy and high-resolution X-ray reflectivity. We find that PbSO4 epitaxial films readily nucleate on the barite surface, even from solutions that are undersaturated relative to bulk PbSO4. Despite this, barite (001) proves to be an ineffective nucleator of bulk PbSO4, as multilayer growth is suppressed even in highly supersaturated solutions. Instead, we find evidence that Pb2+ ions can directly exchange with Ba2+ to create mixed (Ba,Pb)SO4 surfaces. These chemically mixed surfaces do not host PbSO4 monolayers as readily as pristine barite, and the original reactivity is not regained until a fresh surface is re-established by aggressive etching. Our results can be partly explained by traditional models of thin-film growth, which predict a Stranski-Krastanov (S-K) growth mode, where monolayer films are stabilized by a reduction in surface energy, but multilayer growth is inhibited by epitaxial strain. Complementary density functional theory calculations confirm the basic energetic terms of the model but also show evidence for thickness-dependent energetics that are more complex than would be predicted from traditional models. The experimental results are better understood by extending the model to consider the formation of mixed surfaces and films, which have reduced strain and interfacial energies relative to pure films while also being stabilized by entropy of mixing. These insights into nonstoichiometric heteroepitaxy will enable better predictions of how barite affects PbSO4 nucleation in battery environments.

Effects of particle shape and surface roughness on van der Waals interactions and coupling to dynamics in nanocrystals.

The van der Waals interaction between colloids and nanoparticles is one of the key components to understanding particle aggregation, attachment, and assembly. While the ubiquity of anisotropic particle shapes and surface roughness is well-recognized in nanocrystalline materials, the effects of both on van der Waals forces and torques have not been adequately investigated. In this study, we develop a numerical scheme to determine the van der Waals forces and torques between cubic particles with multiple configurations and relative orientations. Our results show that the van der Waals torque due to anisotropic particle shapes is appreciable at nearly all configurations and mutual angles, outcompeting Brownian torque for various materials systems and conditions. Surface roughness enhances this particle shape effect, resulting in stronger van der Waals interactions ascribed to protrusions on the surfaces. Moreover, a scaling analysis indicates that the surface roughness alters the separation dependence of the van der Waals force and, more importantly, significantly influences the dynamics of two approaching particles. Our results clearly demonstrate that surface roughness and anisotropic shape play a crucial role in the energetics and kinetics of various particle-scale and emergent phenomena, such as crystal growth by oriented attachment, nanomaterials synthesis and assembly, mud flow rheology, as well as the deposition of natural nanocrystals within the subsurface.

Crystal dissolution by particle detachment.

Crystal dissolution, which is a fundamental process in both natural and technological settings, has been predominately viewed as a process of ion-by-ion detachment into a surrounding solvent. Here we report a mechanism of dissolution by particle detachment (DPD) that dominates in mesocrystals formed via crystallization by particle attachment (CPA). Using liquid phase electron microscopy to directly observe dissolution of hematite crystals - both compact rhombohedra and mesocrystals of coaligned nanoparticles - we find that the mesocrystals evolve into branched structures, which disintegrate as individual sub-particles detach. The resulting dissolution rates far exceed those for equivalent masses of compact single crystals. Applying a numerical generalization of the Gibbs-Thomson effect, we show that the physical drivers of DPD are curvature and strain inherently tied to the original CPA process. Based on the generality of the model, we anticipate that DPD is widespread for both natural minerals and synthetic crystals formed via CPA.

Predicting Outcomes of Nanoparticle Attachment by Connecting Atomistic, Interfacial, Particle, and Aggregate Scales.

Predicting nanoparticle aggregation and attachment phenomena requires a rigorous understanding of the interplay among crystal structure, particle morphology, surface chemistry, solution conditions, and interparticle forces, yet no comprehensive picture exists. We used an integrated suite of experimental, theoretical, and simulation methods to resolve the effect of solution pH on the aggregation of boehmite nanoplatelets, a case study with important implications for the environmental management of legacy nuclear waste. Real-time observations showed that the particles attach preferentially along the (010) planes at pH 8.5 and the (101) planes at pH 11. To rationalize these results, we established the connection between key physicochemical phenomena across the relevant length scales. Starting from molecular-scale simulations of surface hydroxyl reactivity, we developed an interfacial-scale model of the corresponding electrostatic potentials, with subsequent particle-scale calculations of the resulting driving forces allowing successful prediction of the attachment modes. Finally, we scaled these phenomena to understand the collective structure at the aggregate-scale. Our results indicate that facet-specific differences in surface chemistry produce heterogeneous surface charge distributions that are coupled to particle anisotropy and shape-dependent hydrodynamic forces, to play a key role in controlling aggregation behavior.

Hydroxide films on mica form charge-stabilized microphases that circumvent nucleation barriers.

Crystal nucleation is facilitated by transient, nanoscale fluctuations that are extraordinarily difficult to observe. Here, we use high-speed atomic force microscopy to directly observe the growth of an aluminum hydroxide film from an aqueous solution and characterize the dynamically fluctuating nanostructures that precede its formation. Nanoscale cluster distributions and fluctuation dynamics show many similarities to the predictions of classical nucleation theory, but the cluster energy landscape deviates from classical expectations. Kinetic Monte Carlo simulations show that these deviations can arise from electrostatic interactions between the clusters and the underlying substrate, which drive microphase separation to create a nanostructured surface phase. This phase can evolve seamlessly from a low-coverage state of fluctuating clusters into a high-coverage nanostructured network, allowing the film to grow without having to overcome classical nucleation barriers.

Visualizing Solution Structure at Solid-Liquid Interfaces using Three-Dimensional Fast Force Mapping.

Amongst the challenges for a variety of research fields are the visualization of solid-liquid interfaces and understanding how they are affected by the solution conditions such as ion concentrations, pH, ligands, and trace additives, as well as the underlying crystallography and chemistry. In this context, three-dimensional fast force mapping (3D FFM) has emerged as a promising tool for investigating solution structure at interfaces. This capability is based on atomic force microscopy (AFM) and allows the direct visualization of interfacial regions in three spatial dimensions with sub-nanometer resolution. Here we provide a detailed description of the experimental protocol for acquiring 3D FFM data. The main considerations for optimizing the operating parameters depending on the sample and application are discussed. Moreover, the basic methods for data processing and analysis are discussed, including the transformation of the measured instrument observables into tip-sample force maps that can be linked to the local solution structure. Finally, we shed light on some of the outstanding questions related to 3D FFM data interpretation and how this technique can become a central tool in the repertoire of surface science.

Direct observation of anisotropic growth of water films on minerals driven by defects and surface tension.

Knowledge of the occurrences of water films on minerals is critical for global biogeochemical and atmospheric processes, including element cycling and ice nucleation. The underlying mechanisms controlling water film growth are, however, misunderstood. Using infrared nanospectroscopy, amplitude-modulated atomic force microscopy, and molecular simulations, we show how water films grow from water vapor on hydrophilic mineral nanoparticles. We imaged films with up to four water layers that grow anisotropically over a single face. Growth usually begins from the near edges of a face where defects preferentially capture water vapor. Thicker films produced by condensation cooling completely engulf nanoparticles and form thicker menisci over defects. The high surface tension of water smooths film surfaces and produces films of inhomogeneous thickness. Nanoscale topography and film surface energy thereby control anisotropic distributions and thicknesses of water films on hydrophilic mineral nanoparticles.

In situ characterization of kinetics and mass transport of PbSe nanowire growth via LS and VLS mechanisms.

We grew binary PbSe nanowires in an in situ gas-heating cell in a transmission electron microscope and elucidated species dependent mass transport pathways and key correlations among supersaturation, nucleation, and growth kinetics, thereby enabling morphological and compositional control of nanowires with tailored properties.

Hydrogen bonding and molecular orientations across thin water films on sapphire.

HYPOTHESIS: Water vapor binding to metal oxide surfaces produces thin water films with properties controlled by interactions with surface hydroxo sites. Hydrogen bonding populations vary across films and induce different molecular orientations than at the surface of liquid water. Identifying these differences can open possibilities for tailoring film-mediated catalytic reactions by choice of the supporting metal oxide substrate. EXPERIMENTS: The (0001) face of a single sapphire (α-Al2O3) sample exposed to water vapor and the surface of liquid water were probed by polarization dependent Sum Frequency Generation-Vibration Spectroscopy (SFG-VS). Molecular dynamics (MD) provided insight into the hydrogen bond populations and molecular orientations across films and liquid water. FINDINGS: SFG-VS revealed a submonolayer film on sapphire exposed to 43% relative humidity (R.H.), and a multilayer film at 78% R.H. Polarization dependent SFG-VS spectra showed that median tilt angles of free OH bonds on the top of films are at ∼43° from the normal of the (0001) face but at 38° on neat liquid water. These values align with MD simulations, which also show that up to 36% of all OH bonds on films are free. This offers new means for understanding how interfacial reactions on sapphire-supported water films could contrast with those involving liquid water.

Near surface nucleation and particle mediated growth of colloidal Au nanocrystals.

During non-classical growth of nanostructures via assembly of primary nuclei, nucleation and assembly are assumed to be distinct processes: nanoparticles nucleate randomly and aggregate to form extended structures through Brownian motion in the presence of long-range attractive interactions. Here we investigate the relationship between these two processes by using in situ AFM, in situ, ex situ and cryo TEM and UV-Vis spectroscopy to observe growth of colloidal gold and simulations to develop a mechanistic model of the process. Our results reveal an inexorable link between nucleation and assembly with nuclei forming almost exclusively within a ∼1 nm interfacial region of existing particles. The new particles immediately close the gap either through a diffusive jump or via growth of a neck between the seed and new particle, generating aggregates exhibiting features commonly attributed to oriented attachment of independently nucleated particles. The results demonstrate that creation of initial particle interfaces leads to local environments that redirect growth towards non-classical processes.