Impact of Solution Chemistry and Particle Anisotropy on the Collective

Sep 4, 2018 - The Voiland School of Chemical and Biological Engineering and Department of Chemistry, Washington State University , Pullman , Washingto...
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Impact of Solution Chemistry and Particle Anisotropy on the Collective Dynamics of Oriented Aggregation Elias Nakouzi, Jennifer A Soltis, Benjamin A Legg, Gregory K. Schenter, Xin Zhang, Trent R. Graham, Kevin M. Rosso, Lawrence M. Anovitz, James J. De Yoreo, and Jaehun Chun ACS Nano, Just Accepted Manuscript • DOI: 10.1021/acsnano.8b04909 • Publication Date (Web): 04 Sep 2018 Downloaded from http://pubs.acs.org on September 5, 2018

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Impact of Solution Chemistry and Particle Anisotropy on the Collective Dynamics of Oriented Aggregation Elias Nakouzi1*, Jennifer Soltis1, Benjamin A. Legg1,2, Gregory K. Schenter1, Xin Zhang1, Trent R. Graham3, Kevin M. Rosso1, Lawrence M. Anovitz4, James J. De Yoreo1,2*, Jaehun Chun1*

ABSTRACT Although oriented aggregation (OA) of particles is a widely recognized mechanism of crystal growth, the impact of many fundamental parameters, such as crystallographically distinct interfacial structures, solution composition, and nanoparticle morphology on the governing mechanisms and assembly kinetics are largely unexplored. Thus, the collective dynamics of systems exhibiting OA has not been predicted. In this context, we investigated the structure and dynamics of boehmite aggregation as a function of solution pH and ionic strength. Cryogenic transmission electron microscopy shows that boehmite nanoplatelets assemble by oriented attachment on (010) planes. The coagulation rate constants obtained from dynamic light scattering during the early stages of aggregation span seven orders of magnitude and cross both the reaction-limited and diffusion-limited regimes. Combining a simple scaling analysis with calculations for stability ratios and rotational/translational diffusivities of irregular particle shapes, the effects of orientation for irregular-shaped particles on the early stages of aggregation is understood via angular dependence of van der Waals, electrostatic, and hydrodynamic interactions. Using Monte Carlo simulations, we found that a simple geometric parameter, namely the contact area between two attaching nanoplatelets, presents a useful tool for correlating nanoparticle morphologies to the emerging larger-scale aggregates, hence explaining the unusually high fractal dimensions measured for boehmite aggregates. Our findings on nanocrystal transport and interactions provide insights towards the predictive understanding of nanoparticle growth, assembly, and aggregation, which will address critical challenges in the developing synthesis strategies for nanostructured materials, understanding the evolution of geochemical reservoirs, and addressing many environmental problems.

Keywords: oriented, aggregation, boehmite, attachment, nanoplatelets

1 Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99354, USA.

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2 Department of Materials Science and Engineering, University of Washington, Seattle, WA 98195, USA. 3 The Voiland School of Chemical and Biological Engineering and Department of Chemistry, Washington State University, Pullman, Washington 99164, USA. 4 Chemical Sciences Division, MS 6110, Oak Ridge National Laboratory, Oak Ridge, TN 37831, USA.

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In recent years, exciting observations in biological, biomimetic, and geochemical systems have demonstrated the ubiquity of non-classical pathways of crystal growth and assembly.1,2 One particular mode of assembly is oriented attachment (OA) in which primary particles attach to one another on specific crystal faces with alignment of their crystallographic axes. Although the original discovery of OA was made in the context of mineral systems1, 3 and a number of subsequent investigations have been carried out on geologically relevant materials, particularly iron oxides and oxyhydroxides,4-6 much remains unknown about the conditions and interparticle forces that give rise to OA in minerals. For example, how basic parameters associated with mineral systems, such as particle shape and structural anisotropy, particle concentration, solution ionic strength7-9 and pH,10-12 impact the mechanism and dynamics of this process and, in turn, how the process itself directs the evolution of hierarchical structures via assembly is largely unknown. One of the key unresolved questions in OA is the role of anisotropic crystal morphology on the energetics and dynamics of particle aggregation. Specifically, the effects of structural and chemical anisotropy as well as heterogeneities in charge density distributions on particle transport and interactions are currently difficult to predict.13-15 Underlying these factors is a rich interplay between directional interparticle forces,7, 16-18 hydrodynamic forces, and allowable packing patterns. In principle, these factors can be described within the framework of classical colloidal physics for the case of spherical particles in simple solution chemistries.19 However, many mineral systems present high degrees of structural or morphological anisotropy, sharp-edges, and corners. They exist within extreme conditions of pH and electrolyte concentration that are beyond existing models. For example, layered silicates and aluminates commonly take the form of platelets with large basal planes whose charge state is strongly dependent on pH and ionic strength.20,21 Consequently, assumptions about surface charge and Debye length that enter typical colloidal interaction models can break down in concentrated electrolyte environments. Environmentally significant mineral phases that exhibit structural anisotropy, such as aluminates, are often present in highly alkaline environments with pH values of 10 or more. A case in point are the Hanford nuclear waste tanks, where brines with salt concentrations of over 5M and pH values in excess of 12 are filled with over 15 wt% boehmite, a layered aluminum oxyhydroxide which exhibits a plate-like morphology.22 Previous characterization of these wastes revealed highly aggregated states, extreme viscosities, and non-Newtonian behavior. However, the dynamics and structure of boehmite aggregates and other non-spherical shapes have remained significantly understudied,23 with only a few examples of nanorod aggregation.24-26 As we show here, boehmite aggregation occurs with crystallographic alignment and thus provides a prime example of OA under extreme conditions. The purpose of this study is to use the

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boehmite-water-NaOH-NaNO3 system to understand how extreme morphological anisotropy, pH, and electrolyte concentration each impact the mechanism and kinetics of OA.

RESULTS AND DISCUSSION Shape of primary particle We characterized the morphology of the synthesized boehmite (see SI) by ex-situ TEM, which showed that the crystals exhibit rhombic morphologies with a 105° angle and a dominant (010) basal surface (Figure 1a). The platelets have average lateral dimensions of 29.3 (± 9.4) nm and 22.0 (± 7.3) nm, and a thickness of 6.0 (± 1.3) nm along the [010] direction. A more detailed characterization of this material is provided elsewhere, along with various strategies for hydrothermal boehmite synthesis with tunable dimensions and crystal habits.27

Figure 1. a Ex-situ and b–e cryogenic TEM images of boehmite aggregates. Frame size of e: 20×20 nm2. f Intensity profiles showing lattice fringes, crossover between two platelets at x = 0 nm. g Plot of nth lattice positions shows continuity across two platelets (blue circles and orange squares) for multiple platelet pairs. h Comparison of lattice spacing across platelet border (colored circles) to standard deviation of lattice spacing within platelets (error bars). Black line/marker shows average of 13 platelet pairs. i Distribution of platelet orientations in primary stacks. Colors indicate different stacks.

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The particle agglomerates seen in the ex-situ TEM images (Figure 1a) result from drying after synthesis and do not represent the shapes of boehmite aggregates in solutions. Cryo-TEM images28 of boehmite suspensions in pH 9, [NaNO3] = 0.01 M that have been intensely sonicated show that the loosely-bound clumps are disaggregated by this treatment, but we still observe smaller stacks of nanoparticles that cannot be further separated without fracturing the individual platelets. These primary stacks consist of approximately 11 (± 6) individual platelets, and have average dimensions of 151 (± 90) nm, 87 (± 47) nm, and 65 (± 42) nm (Figures 1b-d, S2). In many cases, the crystal lattice appears continuous across stacked platelets, suggesting that they are directly in contact and fused into single crystals, with no hydration layers in between (Figures 1e, 1f, S3). This observation is validated in Figure 1g which plots the spacing between lattice fringes and shows no apparent discontinuity between two attached platelets. Similarly, Figure 1h compares the lattice spacing at the border between platelet pairs to the d spacing within individual platelets. Several features discerned from the cryo-TEM images further demonstrate that the platelets assemble via OA. Firstly, the boehmite platelets attach preferentially on the basal planes (~95%), with significantly fewer face-to-edge attachments (~5%). By comparison, edge-to-edge attachments are more difficult to quantify from the images because of the relatively low contrast of single platelets. Moreover, the stacks are characterized by a high degree of rotational alignment. Approximately two thirds of platelets in a typical stack are oriented in the [010] plane within 10° of perfect crystallographic co-alignment, while most of the other platelets are also co-aligned along a secondary axis ~30° off of crystallographic co-alignment (Figures 1i, S2). Note that these estimated distributions are not completely accurate, as the image analyses are subject to perspective and contrast bias. Nevertheless, the micrographs show unambiguously that the boehmite platelets in these stacks assemble with well-defined crystallographic alignment. Reaction-limited and diffusion-limited aggregation regimes We utilized the boehmite stacks described above as primary particles in aggregation studies to understand how the mechanism and kinetics of particle assembly via OA depends on conditions of high pH and ionic strength. We attempted to perform these studies at high particle concentrations; however, preliminary experiments demonstrated that 15 wt % boehmite solutions gel immediately upon mixing (Figure S4). Moreover, decreasing the boehmite concentration to 0.5 wt % resulted in the rapid formation of microscale aggregates within seconds (Figure S5). We hence used boehmite concentrations between 0.001–0.3 wt % to obtain measurable kinetics in minutes to hours for each solution condition. This approach allowed us to explore a broad region of pH (neutral–12) and [NaNO3] (0–0.1 M) phase space.

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To quantify the impact of pH and [NaNO3] on the aggregation mechanism and rate of boehmite aggregation by OA, we used dynamic light scattering (DLS) to follow the evolution of average hydrodynamic diameter (d) over time (Figures 2a, b, S6-S9). The initial diameter 134 (± 23) nm determined from DLS is consistent with the result from cryo-TEM (Figure 1b-d). For pH = 7, 9, 11 and [NaNO3] = 0, 0.0001 M, 0.001 M, we observed slow aggregation characterized by exponential scaling of the average particle diameter (Figure 2a). This dependence is typical of a reaction-limited aggregation (RLA) regime.29 By comparison, aggregation in pH 12 solutions diverges significantly from exponential scaling, even without any additional salt (Figure S7). Similar trends are obtained for pH 11, 12 and [NaNO3] = 0.005 M, 0.01 M, which show progressively faster kinetics. As [NaNO3] approaches 0.1 M, the data converge onto a single curve for all the pH conditions, indicating that the regime of diffusion-limited aggregation (DLA) has been reached (Figure 2b). Within this regime, the size evolution is only a function of the initial particle concentration, shape, and diameter. The data are well described by a power-law whose inverse exponent is interpreted as the kinetic fractal dimension of the growing aggregates. Interestingly, we obtain a value of Df = 2.30 (± 0.18), which is significantly higher than the 1.5–1.9 range typically observed for spherical colloids.29 This result highlights the failure of models that consider isotropic spherical particles to predict the collective dynamics and structural outcomes in systems of morphologically anisotropic particles like boehmite, a failure that we further address below. Aggregation rate constants We can use the DLS data to determine coagulation rates according to a second order rate law:



 +    

= −  (1)

where nt is the number of primary particles — or “monomers” — at a given time t and k11 is the aggregation rate constant for dimer formation. This assumption is valid in the early stages of aggregation where collisions between monomers provide the main contribution for size evolution.19, 30 Specifically, we limit this analysis to growth from the initial average particle radius r0 to a value of 1.25 r0. For the cases of fast aggregation, we consider data points up to 1.75 r0, which still produces good agreement with the model. The initial number of particles n0 is obtained from: 

 = ⁄ ( )  

"

(2)

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where m is the mass concentration of the boehmite suspension and ρ is the density of boehmite (3.04 g/mL). We then calculate nt by assuming a lognormal particle size distribution (See SI). Similar assumptions of spherical particles and lognormal size distributions are already implicit in most methods for calculating hydrodynamic diameters from DLS autocorrelation functions.31 Finally, k11 is determined as the slope of 1/nt as a function of time (Figure 2c). This approach facilitates the direct comparison of the kinetics in different solution conditions and boehmite concentrations, and provides a more rigorous measure of the rate constants than simply using the slope of d vs t.

Figure 2. DLS measurements of boehmite suspensions. a Green, circle markers indicate [NaNO3] = 0M, [boehmite] = 0.1wt% (open); 0.0001M, 0.1wt% (filled) at pH 11. Blue, square markers: 0M, 0.1wt% (open); 0.0001M, 0.1wt% (light); 0.001M, 0.05wt% (dark) at pH 9. Red, diamond markers: 0M, 0.3wt% (open); 0.0001M, 0.1wt% (light); 0.001M, 0.1wt% (dark) at pH neutral. b Boehmite 0.01wt%. Orange, triangle markers: 0.01M (open); 0.05M (light); 0.1M (dark) at pH 12. Green, circle markers: 0.01M (open); 0.05M (light); 0.1M (dark) at pH 11. Blue, square markers: 0.05M (open); 0.1M (filled) at pH 9. Red, diamond markers: 0.05M (open); 0.1M (filled) at pH neutral. c Second order kinetics fits for 0.05M, pH 12 (open triangles); 0.05M, pH 12 (filled triangles); 0.05M, pH 11 (open circles); 0.1M, pH 11 (filled circles). d Coagulation rate constants and e normalized stability ratios for pH neutral (red diamonds); pH 9 (blue squares); pH 11 (green circles); pH 12 (orange triangles). Dashed line in d indicates Brownian

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coagulation rate. Cryo-TEM images of f RLA, pH 9, [NaNO3] = 0 M and g DLA, pH 9, [NaNO3] = 1 M aggregates.

As expected, the rate constant k11 increases drastically as pH and ionic strength increase,32 but, surprisingly, spans seven orders of magnitude (Figure 2d). For reference, the dashed line in Figure 2d represents the ideal rate constant of Brownian coagulation for spherical particles, defined as k0 = 8kT/3η, where k is Boltzmann’s constant, T is the temperature, and η is the viscosity of the medium, again highlighting the deviation of boehmite aggregation dynamics from that expected for spherical particles. We also calculated the critical concentration for coagulation, typically expressed in terms of the stability ratio W = k0/k11, and normalized against W∞, which is the value of W obtained for the fastest aggregation conditions (pH 12, [NaNO3] = 0.1 M) (Figure 2e). Our data show that the critical coagulation concentration for boehmite aggregation by OA is 50–100 mM, above which diffusion-limited aggregation dominates regardless of the solution pH. The latter result is comparable to previous reports on spherical particle aggregation in the presence of monovalent ions of similar concentrations.32,33 We show example images of the large-scale aggregates grown under RLA (Figure 2f) and DLA (Figure 2g) conditions. Domains of ordered platelets are obvious, but the structures do not preserve a long-range order over the extent of the whole aggregate. Effect of particle shape on diffusivity The aggregation dynamics of particles depend on their diffusivities. For isotropic spherical particles or random aggregation of anisotropic objects, translational diffusion is rate-determining and rotational dynamics have little or no influence. However, in the case of OA, deviations from sphericity and the introduction of anisotropic interactions, which are clearly evident in the irregular and non-spherical boehmite stacks studied here, rotational and translational diffusive motions can become coupled, depending on their characteristic timescales. Thus both need to be considered to obtain physical insights into the aggregation dynamics. We hence attempted to determine the validity of the spherical assumption regarding particle diffusivity. This component has been significantly understudied in aggregation systems with only few reports showing detailed considerations of morphology on particle transport.34 We calculated the diffusivity of primary structures composed of ten randomly stacked platelets using the BEST software package35 (details in Methods section). Using the average rotational diffusivity Dr of the different stacking configurations, we estimated a characteristic timescale of O(10-4) sec (τr = 1/Dr) required for a platelet stack to sample all possible orientations. For comparison, a characteristic timescale τt to diffuse through a characteristic distance associated with particle collisions — i.e., the

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inverse of the scattering wave number (q) — can be estimated as 1/(Dt·q2).19 We calculate τt ~ O(10-4) sec for the same stacking configurations. Note that a variance of up to 13% is calculated for translational diffusivities along the different principal axes. Moreover, since the two time scales τr and τt have comparable magnitudes, it is clear that both anisotropic rotational and translational diffusion are crucial for understanding the aggregation dynamics. Table S1 compares the diffusivities of stacked platelets to an equivalent sphere and rectangular box (Figure 3a). Our analysis demonstrates that the “coarse-grained” shapes of either spheres or boxes do not provide an accurate description of particle diffusion; the rectangular box shows τr up to five times longer than the particle stacks and τr has no relevance to the spheres.

Figure 3. a Schematics of spherical and box coarse-grain assumptions, as well as more realistic stacked particle geometry. b Comparison of experimental and theoretical stability ratios in pH 9 solutions.

Effect of particle shape and orientation on aggregation In addition to the effect on diffusivity, irregular particle geometry plays a determining role on the interactions that influence aggregation. As described below, a delicate balance between various orientation-dependent interactions will inhibit or enhance the aggregation rates in the RLA or DLA regimes, respectively. Typically, electrostatic

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repulsion between particles becomes appreciable in the RLA regime, while van der Waals attraction dominates in the DLA regime.36,37 Accordingly, it is necessary to understand the scaling behavior of particle interactions with respect to separation and orientation. As a first-order approximation, we calculated the stability ratio based on spherical particle shapes. The stability ratio, W, is a ratio of the number of encounters between non-interacting particles leading to aggregation to encounters between interacting particles leading to aggregation.19 Figure 3b plots the stability calculations as Wexp/Wsp vs. [NaNO3], where the superscripts “exp” and “sp” denote values from the experiments and calculations based on spherical approximation, respectively. We implemented the appropriate formulations using the effective Hamaker constant19 and surface potentials estimated as a function of pH and ionic strength using the triple layer model by Wood et al.38 (see SI for details on calculations). Our results show that the spherical approximation overestimates the stability ratio in the DLA regime, but underestimates it in the RLA regime. The fact that Wsp > 1 for conditions relevant to DLA with spherical particles19 implies that hydrodynamic mobility is important in determining the deviation of Wexp from Wsp (see SI for details). The hydrodynamic mobility at close separations results from a significant pressure build-up at the gap between particles. Thus, the irregular outer boundary of the primary particles (see Figure 1) can effectively reduce such pressure, resulting in a larger mobility. This effect is comparable to spherical particles with rough surface topography, which allow more aggregation events and contribute to lower stability ratios than expected. For conditions relevant to RLA, the significantly large characteristic timescale for aggregation indicates that the orientational correlation for the primary particle is strongly coupled to particle interactions, particularly at close separation (see SI for detailed scaling).39 The primary particle can sample many orientations during approach, suggesting the importance of angular dependence on van der Waals and electrostatic interactions, as well as hydrodynamic mobility. Since formal expressions of this angular dependence do not exist yet in the literature, we consider two characteristic orientations corresponding to “plane-plane” (P-P) and “edge-edge” (E-E) configurations. Our scaling analysis shows that the van der Waals attraction potential increases, whereas hydrodynamic mobility is significantly reduced, particularly for the P-P configuration, which clearly hinders aggregation (see SI for more details).40,41 By comparison, electrostatic repulsion does not depend as radically on sphere-sphere, P-P, or E-E configurations. Our simple scaling argument demonstrates that the coupling between particle orientation and interactions can lead to Wexp/Wsp >>1. Monte Carlo simulations of particle stacking. To test whether the basic concepts of anisotropic morphology and interactions can provide at least a qualitative explanation for the observed dynamics of boehmite aggregation, we performed Monte Carlo simulations that took into account the role of

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particle geometry on the structure, dynamics, and fractal scaling of aggregates for particles that exhibit face-specific binding. The model is analogous to that of WittenSander DLA,42 but particle transport is assumed to be linear and not governed by Brownian diffusion. Starting with a seed platelet, we iteratively introduce more platelets that transport towards and collide with the growing aggregate. The success of an attachment event is determined solely by whether or not the two colliding platelets exhibit a minimum fractional contact area σ. In principle, σ is inversely correlated to the sticking probability used in typical sphere-based simulations (Figure S12), but also imposes a geometric constraint relevant to non-spherical particles. We consider only translational degrees of freedom and face-to-face attachments; recognizing that this is a simplification and that the rotational and translational time constants are of similar order. However, here the intent is to understand the impact of the fractional area required for sticking on morphology and dynamics.

Figure 4. a Simulated aggregates with increasing overlap parameter σ, orange to blue color indicates early to late particles. b Evolution of radius of gyration (rg). c rg of 100-platelet

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aggregates. d Evolution of rx,y/rz for increasing σ (top to bottom, red to blue). e Steady-state rx,y/rz, f steady-state branching probability, and g fractal dimension as a function of σ. Orange circles and blue triangles represent the kinetic and mass fractal dimensions, respectively.

Using this approach, we probed the effect of the collision overlap parameter, σ, on the aggregate shapes (Figure 4a). At the limit of low σ, almost every particle collision leads to an attachment event. Accordingly, the structures branch out and expand rapidly (Figure 4b). At the other limit of σ ≥ 0.50, the attaching particles are physically restricted from branching and hence form wavy, one-dimensional chains. These structures grow at a constant rate of approximately one platelet thickness per added unit. Figure 4c plots the radius of gyration (rg) of 100-unit aggregates as a function of σ. Interestingly, rg decreases slightly, then increases drastically, before approaching a saturated value for σ ≥ 0.50. To understand this non-intuitive growth behavior, we calculated the ratio of the radius of gyration about the lateral and vertical principal axes, namely rx,y/rz. Two key observations are immediately obvious. Firstly, the growth converges very rapidly to a steady-state mode after the addition of approximately ten platelets (Figure 4d). Secondly, the steady state ratio (rx,y/rz (ss)) decays monotonically with increasing σ (Figure 4e). The trends in Figure 4c, e clearly reflect the inherent anisotropy; low σ values favor expansion by aggregate branching while high values favor stacking. The minimum rg is obtained for an intermediate value of σ = 0.25, which produces compact structures that grow at moderate rates in both lateral and vertical directions. We attempted to further characterize the growth dynamics by calculating branching probabilities at different aggregation conditions (Figures S14, 15). The growth behavior approaches a characteristic branching probability (Pss) that decreases with increasing σ (Figure 4f). Interestingly, Pss follows a simple empirical equation: 





#$$ (%) = − % + ; % ≤  &  

#$$ (%) = 0 ; % ≥ 

(3)

Moreover, we determined the fractal dimensions (Df) of the simulated aggregates using two methods: a power-law scaling of rg vs n whose exponent represents 1/Df (Figure 4g, orange circles), and a power-law scaling of the mass autocorrelation function with an exponent of Df – 3 (Figure 4g, blue triangles, Figure S16).43 Note that the latter approach slightly underestimates fractal dimensions, since each platelet in a given aggregate is replaced by its center of mass.44 As expected, the mass fractal dimension approaches a value of one for the linear chains at high σ. This result contrasts sharply with spherical particle systems, which form denser structures at lower sticking probabilities.45 Moreover, we obtained Df values of 2.2–2.6 at low σ, which are

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comparable to the experimentally determined values for boehmite aggregates in the DLA regime (Figure 2b). Despite being based on purely geometric rules, the Monte Carlo simulations provide useful physical insights into the aggregation process. The parameter σ simulates dynamical features of the system that are indirectly related to the balance of interparticle forces. For example, two particles interacting via Brownian motion are in proximity for some average amount of time before diffusing away from one another. If the fluctuations needed to achieve contact do not occur during that time, then there is no attachment event. For platelets, larger cross-sectional overlap upon approach, results in longer the time period over which the two particles will be in proximity, and thus a greater chance that the right set of fluctuations will come about to achieve contact. Consequently, the average value of the contact area is biased towards large values and hence corresponds to the parameter σ in the simulations.

CONCLUSIONS The results presented here provide an excellent opportunity for understanding the effect of particle geometry on the structure and dynamics of oriented aggregation, particularly for boehmite at high pH and ionic strength. Several key observations are comparable to spherical particle aggregation, such as the critical coagulation concentration and the scaling of aggregate size evolution. However, the stability ratios calculated using spherical assumptions are significantly underestimated (overestimated) in the RLA (DLA) regime, which is ascribed to directional dependence of particle interactions that become more prominent for irregular shapes. Moreover, our Monte Carlo simulations showed that the particle shape — even without accounting for rotational dynamics — can give rise to interesting and non-intuitive results. We determined an empirical relationship between a geometric parameter, namely the minimum fractional contact area σ between two colliding platelets, and the aggregate branching probability. This result provides a simple yet powerful tool: knowledge of the nanoscale particle and microscale aggregate shapes can be linked directly to the sticking coefficient and hence provide a measure of the underlying particle interactions. Understanding particle transport, interactions, and aggregation presents a critical challenge for interpreting mineralogical signatures,46 predicting the evolution of geochemical reservoirs,1 and addressing a broad range of environmental problems 47,48. At the atomic scale, uptake and release of nutrients, metals and other impurities, the sequestration of organic compounds, and the fractionation of isotopes should exhibit distinctly different dynamics and spatial distributions in mineral systems for which aggregation-based pathways dominate over classical ion-by-ion growth. At the macroscale, the rheological properties of reservoirs marked by aggregates with large fractal dimensions will differ dramatically from those containing compact particles grown

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by classical mechanisms. However, there currently exists no proven framework for generalizing the basic concepts of particle transport, interaction, and aggregation beyond simple approximations of spherical particles, and the impact of face and orientation-specific binding has not been considered. As shown here, the shape of irregular particles and the impact of pH and ionic strength on their anisotropic interactions can play a determining role in the nanoscale properties, including diffusivity and orientation-specific interactions, as well as macroscale structure of the resulting aggregates. A successful delineation of how these components scale with particle shape, structural anisotropy, and response to extreme chemical environments will be necessary to reach a predictive understanding of particle aggregation and attachment.

METHODS Dynamic light scattering. Boehmite is dispersed in 10 mL of NaNO3 (≥99%, SigmaAldrich) and NaOH (≥98%, Sigma-Aldrich) solutions of the desired concentrations, prepared with nuclease-free, ultrapure water (ThermoFisher Scientific). The mixture was sonicated for 30 minutes using a Fisher Scientific probe sonicator (120 W, 20 kHz, 80% amplitude). For conditions that produce rapid aggregation, we sonicated the boehmite in pure water, and subsequently pipetted the required volume of salt and base. Measurements were conducted using a Brookhaven Instruments 90Plus Nanoparticle Size Analyzer equipped with a 15 mW, 635 nm solid state laser. The acquisition time for each measurement solution was ten seconds and the autocorrelation functions were analyzed based on the cumulants method. We validated the results by measuring gold nanoparticles (30 nm, Sigma-Aldrich) and polystyrene latex beads (100 nm and 300 nm, Sigma-Aldrich). Cryogenic transmission electron microscopy. We placed 3-µL of an intensely sonicated boehmite suspension onto a 200 mesh copper TEM grid coated with lacey carbon film (EMS). Prior to use, all grids were glow discharged for approximately one minute at 15 mA using a Ted Pella EasiGlow. After loading the sample, the grid was placed into an FEI Vitrobot Mark IV operating at ambient room temperature and 70% relative humidity. The specimens were then vitrified by rapid plunging into liquid ethane and stored in liquid nitrogen. Specimens were transferred to a Gatan 626 cryo-TEM holder and inserted into an FEI Titan 80-300 Environmental TEM equipped with a field emission electron gun and operated at 300 kV under low-dose conditions. Micrographs were collected using a US 1000 2k×2k Gatan charge-coupled device (CCD) camera controlled with the DigitalMicrograph interface. The images were analyzed using inhouse MATLAB routines. Monte Carlo simulations. Boehmite platelets modelled as box-shaped particles (300×300×60) were used to perform simulations in MATLAB, starting with a single seed platelet. Iteratively, new platelets followed random linear trajectories across the bounding sphere of the aggregate. The incoming platelets attached successfully to the

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aggregate if the contact area between the two colliding platelets is greater than a defined parameter σ. Particle diffusivity. Hydrodynamic resistivity and diffusivity tensors for particles based on Stokes flow with stick boundary conditions can be calculated using the BEST software package,35 which is based on a boundary element method, utilizing an integral representation of the Stokes flow via a hydrodynamic Green’s function, called the Oseen tensor. We constructed 20 different configurations for the primary particles by stacking 10 individual platelets, each of dimensions: 25.0 nm × 25.0 nm (width) × 6.0 (thickness) nm as shown in Figure 3A. A numerical triangulated mesh of the structure was generated by excluding attached regions using the gmsh software.49 This mesh is then used to calculate the hydrodynamic resistivity and diffusivity tensors of the primary particle based on Cartesian coordinates. The rotational timescale is calculated using τr = 1/Dr. Dt is measured as the average translational diffusivity along the three principal axes (Dxx+Dyy+Dzz)/3. The characteristic timescale τt is obtained from 1/ (Dt·q2) where q = 1.87×10-2 1/nm for the instrument parameters used in this study.

ACKNOWLEDGMENTS This work was supported as part of IDREAM (Interfacial Dynamics in Radiation Environments and Materials), an Energy Frontier Research Center funded by the U.S. Department of Energy, Office of Science, Basic Energy Sciences (BES). Monte Carlo simulations and DLS measurements were supported by the Laboratory Directed Research and Development Program at PNNL through the Linus Pauling Distinguished Postdoctoral Fellowship program. E Nakouzi is grateful for the support of the Linus Pauling Distinguished Postdoctoral Fellowship program. TR Graham acknowledges a graduate fellowship through the Pacific Northwest National Laboratory – Washington State University Distinguished Graduate Research Program (PNNL-WSU DGRP).The authors greatly appreciate Shawn Kathmann for dielectric function data for boehmite. TEM, XRD, DLS and zeta potential measurements were carried out at the Environmental and Molecular Sciences Laboratory (EMSL), a national scientific user facility sponsored by the DOE Office of Biological and Environmental Research and located at Pacific Northwest National Laboratory (PNNL). PNNL is a multiprogram national laboratory operated for DOE by Battelle Memorial Institute under Contract No. DE-AC05-76RL0-1830.

ASSOCIATED CONTENT Supporting Information Supporting Information Available: Further experimental and theoretical details on boehmite synthesis, TEM imaging, zeta potential measurements, powder X-ray diffraction measurements, rate constant calculations, as well as stability ratio theory and

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calculations. This material is available free of charge via the Internet at http://pubs.acs.org. The authors declare no competing financial interest.

AUTHOR INFORMATION Corresponding Authors *E-mail: [email protected] *E-mail: [email protected] *E-mail: [email protected] Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

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