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Estimating reaction parameters in mechanism-enabled population balance models of nanoparticle size distributions: A Bayesian inverse problem approach
In order to quantitatively predict nano- as well as other particle-size distributions, one needs to have both a mathematical model and estimates of the parameters that appear in these models. Here, we show how one can use Bayesian inversion to obtain statistical estimates for the parameters that appear in recently derived mechanism-enabled population balance models (ME-PBM) of nanoparticle growth. The Bayesian approach addresses the question of “how well do we know our parameters, along with their uncertainties?.” The results reveal that Bayesian inversion statistical analysis on an example, prototype $\mathrm{lr(0)_n}$ nanoparticle formation system allows one to estimate not just the most likely rate constants and other parameter values, but also their SDs, confidence intervals, and other statistical information. Moreover, knowing the reliability of the mechanistic model's parameters in turn helps inform one about the reliability of the proposed mechanism, as well as the reliability of its predictions. Importantly, the paper can also be seen as a tutorial with the additional goal of achieving a “Gold Standard” Bayesian inversion ME-PBM benchmark that others can use as a control to check their own use of this methodology for other systems of interest throughout nature. Overall, the results provide strong support for the hypothesis that there is substantial value in using a Bayesian inversion methodology for parameter estimation in particle formation systems.
Higher Harmonics in Multipactor Induced Plasma Ionization Breakdown near a Dielectric Surface
In this Letter, the novel physics of higher harmonic (HH) generation of the normal electric field near a dielectric surface is reported in multipactor induced plasma ionization breakdown, as determined by kinetic particle-in-cell simulations. The observed HH frequency is around ten times the fundamental rf driving frequency, but lower than the electron plasma frequency. A theory is constructed which indicates that stream plasma interaction-induced instability is the mechanism of HH generation in the collisional regime. The HH frequency and its corresponding growth rate of the HH oscillation amplitude from the theory are in good agreement with kinetic particle-in-cell simulations.
Oxide evolution on the SiC layer of TRISO particles during extended air oxidation
Tristructural isotropic (TRISO) fuel particles have been primarily developed for high-temperature gas-cooled nuclear reactors and can be subjected to oxidizing environments for extended periods in an off-normal accident scenario. Surrogate TRISO fuel particles were oxidized in air at 1,000 or 1,100 °C for up to 120 h. Here, the oxide scale morphology and thickness were studied via scanning electron microscopy, focused ion beam, and atomic force microscopy. TRISO particles oxidized at 1,100 °C exhibited a highly crystalline oxide scale, which led to significant cracking and irregularly shaped closed porosity, whereas those oxidized at 1,000 °C possessed a primarily amorphous oxide scale, which contained small, rounded internal pores and no larger defects. The observed phenomena deviated from the expected behavior based on models for oxide growth on flat-plate and fiber SiC. The oxidation kinetics of TRISO fuel particles in high-temperature air were investigated without mechanically deforming the surface and were analyzed with respect to oxide morphology.
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 effect of both on van der Waals forces and torques has not been adequately investigated. Here, in this study, we develop a numerical scheme and 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 motion for various materials systems and conditions. The effect of surface roughness increases this shape effect, resulting in stronger van der Waals interactions ascribed to protrusions in the rough 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.
Complex Fluorine Chemical Potential Effects on the Shape and Compositional Heterogeneity of KTa 1– x Nb x O 3 Nanoparticles
When kinetic conditions dominate and dictate the growth in a nanoparticle synthesis, properties of the synthesis environment can have considerable effects on the properties of the products. Such effects were studied here, where the solution environment was changed via the addition of KF to the hydrothermal syntheses of KTa 1– x Nb x O 3 and KTaO 3 . One result demonstrated the straightforward cause-and-effect relationship between the solution and reaction kinetics: KF directly increased the solution stability of the Ta species and therefore decreased its reaction rate, resulting in a change in composition heterogeneity of Ta and Nb in the KTa 1– x Nb x O 3 particles. However, not all effects are so simple; changing the chemical potential of the solution with KF can also promote the formation of particles with anisotropic defect enhanced kinetic Wulff shapes instead of cuboidal shapes. The increased F chemical potential in the solution enabled the formation of planar defects in the bulk, which accelerated growth in-plane to form particles characterized by flat rectangular flake geometries. In this work, thermodynamic modeling with density functional theory calculations confirmed that sufficient KF concentrations can drive the formation of a defect phase K n +1 Ta n O 3 n F.
Towards understanding particle rigid-body motion during solid-state sintering
A quantitative understanding of particle rigid body (RB) motion that inherently accompanies grain boundary (GB) diffusion is highly desirable to understand and control the dynamic interplay between coarsening and densification during solid state sintering. In this work, by computer simulation using a multi-phase-field approach, we analyze systematically the roles played by each of these processes at different stages of the shrinkage of the internal pore in a three-particle green body as a function of particle size as well as thermodynamic and kinetic factors of interfaces. We demonstrate that particle RB translation promotes both neck growth, and pore rounding and shrinkage. Moreover, the forces acting at GBs and pulling neighboring particles towards one another dynamically evolve as particles fuse. In contrast, particle RB rotation has no contribution to pore shrinkage. The translational force acting on an individual particle varies with not only its size, but also the number and sizes of its neighboring particles.
Peptoid-Directed Formation of Five-Fold Twinned Au Nanostars through Particle Attachment and Facet Stabilization
While bio-inspired synthesis offers great potential for controlling nucleation and growth of inorganic particles, precisely tuning biomolecule-particle interactions is a long-standing challenge. Herein, we used variations in peptoid sequence to manipulate peptoid-Au interaction, leading to synthesis of concave five-fold twinned, five-pointed Au nanostars via a process of repeated particle attachment and facet stabilization. Ex situ and liquid-phase TEM observations show that a balance between particle attachment biased to occur near the star points, preferential growth along the [100] direction, and stabilization of (111) facets is critical to forming star-shaped particles. Molecular simulations predict that interaction strengths between peptoids and distinct Au facets differ significantly and thus can alter attachment kinetics and surface energies to form the stars. This work provides new insights into how sequence-defined ligands affect particle growth to regulate crystal morphology.
A Model of Grain Boundary Complexion Transitions and Grain Growth in Yttria-Doped Alumina
In this work, we present a physically-parameterized microstructure evolution model for the Yttria-doped alumina system. Yttria-doped alumina is a well-known ceramic system which undergoes first-order phase-like transitions at grain boundaries, which can radically alter interface properties. The change in interfacial properties in turn can radically change microstructure outcomes during processing, including the induction of abnormal grain growth modes. In this work, we develop a simulation that evolves alumina microstructure as a function of yttria concentration and temperature. In the window studied, we achieve strong agreement with reviewed experimental results in identifying the windows for large grains, small grains, abnormal grain growth, and complexion transition kinetics. We then apply the model to study and demonstrate how the possible inclusion of second-phase particles or uneven solute distribution profiles will impact microstructure evolution. It is found that particles do not significantly affect abnormal grain growth in the window studied (but do lead to reduced grain size through pinning effects). It is found that even modest amounts of solute inhomogeneity will result in substantial changes in microstructure outcomes, frequently leading to clusters of abnormal grains. This model largely corroborates the expectations and hypotheses made from recent experimental studies in oxide-doped alumina systems. Further, it is found that there exists a peak transition fraction for the system at which abnormal grain size tends to be maximized.
Toward Rational Design of Nickel Catalysts for Thermocatalytic Decomposition of Methane for Carbon Dioxide-Free Hydrogen and Value-Added Carbon Co-Product: A Review
Thermocatalytic decomposition of methane provides opportunities for hydrogen (H2) production with no emission of carbon dioxide. However, high-value carbon products need to be produced for economic deployment of thermocatalytic decomposition and to achieve a minimum H 2 selling price below the U.S, Department of Energy target of $ 1/kg H 2 . In this review, we re-evaluate data on catalyst development reported in the literature and propose correlations between catalyst characteristics, catalytic stability, and properties of carbon co-products. In the first part of the review, growth mechanisms for carbon nanotubes using state-of-the-art chemical vapor deposition are reviewed to catalog the effects of catalyst characteristics, the influence of carbon sources, interactions between metal particles and supports, and metal particle sizes on carbon growth. In the second part, representative developments in mono-, bi-, and tri-metallic nickel catalysts are highlighted. We present kinetic analysis of reactions catalyzed by mono-metallic nickel catalysts, which generates a correlation between metal particle size and catalyst stability. Rational design of Ni-based catalysts for TCD of methane requires attention to the size of the metal particle and effective normalization of the reaction rates. Further attention to the distribution of the metal particle sizes may help identify catalyst properties that contribute longevity and selectivity to processes that use them. While it is tempting to focus on the highest valued carbon products (e.g., CNTs and CFs), analysis of the markets for other carbon products suggests that a more flexible approach may generate comparable returns without the risk associated with specialization.
Theoretical studies of chemical reactions related to the formation and growth of polycyclic aromatic hydrocarbons (PAH) and molecular properties of their key intermediates (Final Progress Report)
The formation mechanisms of polycyclic aromatic hydrocarbons, (PAHs) – organic molecules carrying fused benzene rings – are of great interest to scientists and engineers due to their importance in combustion chemistry and astrochemistry. On Earth, PAHs are largely produced in incomplete combustion of fossil fuel and are considered as critical precursors to unwanted soot particles leading to combustion inefficiency and causing air pollution along with detrimental health effects. Simple PAH molecules initially formed in the gas phase, are further involved in a build-up process in combustion flames leading to larger PAH, bowl-shaped nanostructures, fullerenes, and solid-phase species including carbonaceous dust, graphene particles, and soot. In deep space, PAH and their derivatives are potential key intermediates and nucleation sites leading eventually to carbonaceous nanoparticles (“interstellar grains”). Therefore, the understanding of the key processes in the synthesis of PAHs along with their precursors and their degradation mechanisms in combustion systems and in interstellar, circumstellar, and planetary atmospheric environments will provide critical insights into how complex aromatic structures, carbonaceous nanoparticles, and fullerenes are formed and destroyed. Achieving this understanding is an important step in the development of the efficient combustion processes and of the ecofriendly devices with reduced environmental pollution as well as technological strategies for the production of hydrogen and solid carbon through thermal or plasma-assisted pyrolysis of natural gas and biomass. Also, the understanding of the key processes of PAH and soot growth will help in our comprehension of chemical evolution in the universe. Detailed information on the mechanisms and reliable rate constants of the key elementary chemical reactions involved in PAH formation and destruction processes and in inception of soot particles is often missing, with the main deficiencies being the absence of temperature- and pressure-dependent rate constants for the broad range of conditions occurring in various terrestrial and interstellar processes and the lack of data on the reaction products and their branching ratios. Complementary to experimental studies, these gaps in knowledge can be filled by using quantum chemical calculations of reaction potential energy surfaces providing us with accurate energies of reaction products, intermediates, and transition states, revealing the reaction mechanism, and giving the molecular properties required to compute rate constants for relevant reaction steps and product branching ratios using the RRKM-Master Equation (ME) method. Molecular dynamics (MD) simulations can be used in cases when a reaction rate cannot be properly described by statistical theories. During the terminal renewal project period we employed these ab initio/RRKM-ME and MD approaches to complete our studies on several key reactions relevant to the formation/growth of PAH and inception of soot particles including (1) the reaction mechanism and kinetics of the resonance stabilized fulvenallenyl radical with propargyl and C 3 H 4 isomers; (2) the reaction mechanism and kinetics for the C + indene and C 2 + styrene reactions producing naphthyl or azulenyl radicals in low-temperature environments; (3) the MD study of non-equilibrium dimerization of acepyrene and coronene and its radical. The information derived from our theoretical calculations contributed to a better fundamental understanding of the reaction mechanisms and provide missing critical kinetic data to improve combustion models of hydrocarbon fuels and astrochemical models of the growth of carbonaceous molecules and particles in cold molecular clouds, circumstellar envelopes, and planetary atmospheres.
Effect of kinetic ions on the toroidal double-tearing modes
We investigate the effects of kinetic ions on double-tearing modes (DTMs) using the gyrokinetic particle-in-cell simulation code GEM with a gyrokinetic ion/fluid electron hybrid model. It is found that the ion kinetic effects can decrease the growth rate of the DTMs. This effect is more significant for stronger coupling of DTMs with smaller distance between the rational surfaces. Kinetic ions can also enhance the coupling effect between the two rational surfaces. Energy transfer analyses between particles and wave fields show that the stabilizing effect of kinetic ions comes mainly from the perpendicular magnetic drift of ions in the coupling region and around the outer rational surface.
Employing Machine Learning for New Particle Formation Identification and Mechanistic Analysis: Insights From a Six‐Year Observational Study in the Southern Great Plains
We present a supervised machine learning (ML) framework to automatically identify new particle formation (NPF) events and analyze key atmospheric factors associated with their occurrence and growth. We applied ML to detect NPF events using start time and particle concentrations across size ranges, while identifying atmospheric variables including ambient temperature, relative humidity, solar radiation intensity (SRI), wind speed, wind direction, boundary layer height, total organics, sulfate, nitrate, total surface area concentration, sulfur dioxide, and turbulent kinetic energy (TKE). We analyzed a 6-year data set from the Atmospheric Radiation Measurement at the Southern Great Plains (SGP) site in Oklahoma, USA. Using long-term ground-based measurements, we identified NPF events and applied Random Forest Classifiers, which achieved 90%–95% prediction accuracy. Feature importance analysis highlighted SRI, relative humidity, and ambient temperature as the most influential variables, contributing normalized importances of 28%, 17%, and 10%. Partial Dependence Plots (PDPs) indicated that higher SRI and lower relative humidity were critical in promoting NPF formation at SGP. Seasonally, NPF events were more frequent in winter (42.1%) and spring (35.5%), and least in summer (4.0%). Particle growth rates also exhibited a seasonal variation, with the lowest in winter (below 2 nm hr −1 ) and highest in late spring and early summer (exceeding 5 nm hr −1 ). Temperature, turbulent kinetic energy, and aerosol properties were the primary factors of growth rate variability. This study advances predictive modeling of NPF, offers insights for future campaign deployments, and demonstrates the effectiveness of ML in understanding the formation and growth of atmospheric aerosols.
An Analysis of the Impact of Particle Growth on Transport Losses in Polymer-Electrolyte Fuel Cells
Voltage cycling causes catalyst nanoparticles in polymer-electrolyte fuel cells to grow. The concomitant loss of interfacial area results in larger kinetic, transport, and possibly ohmic overpotentials. This paper uses recently published experimental data and mathematical models to investigate the evolutions of transport and ohmic resistances to platinum nanoparticles located on the surface and inside the micropores of carbon black supports. Resistance to oxygen transport rises as surface area declines primarily because the flux to each remaining larger platinum particle increases. The path lengths governing oxygen diffusion to surface and buried platinum sites also increase as nanoparticles grow. Platinum nanoparticles on the surface become relatively less favorable as voltage cycling proceeds because they grow faster than platinum in micropores. Because voltage cycling causes total interfacial area to decline, and the fraction located inside micropores to increase, nanoscale ohmic losses increase as a catalyst layer decays. The practical importance of this effect is difficult to discern because proton conductivity in carbon micropores is not well characterized.
Hydrodynamic and frictional modulation of deformations in switchable colloidal crystallites
Displacive transformations in colloidal crystals may offer a pathway for increasing the diversity of accessible configurations without the need to engineer particle shape or interaction complexity. To date, binary crystals composed of spherically symmetric particles at specific size ratios have been formed that exhibit floppiness and facile routes for transformation into more rigid structures that are otherwise not accessible by direct nucleation and growth. There is evidence that such transformations, at least at the micrometer scale, are kinetically influenced by concomitant solvent motion that effectively induces hydrodynamic correlations between particles. Here, we study quantitatively the impact of such interactions on the transformation of binary bcc-CsCl analog crystals into close-packed configurations. We first employ principal-component analysis to stratify the explorations of a bcc-CsCl crystallite into orthogonal directions according to displacement. We then compute diffusion coefficients along the different directions using several dynamical models and find that hydrodynamic correlations, depending on their range, can either enhance or dampen collective particle motions. These two distinct effects work synergistically to bias crystallite deformations toward a subset of the available outcomes.
Electrolyzer Performance Loss from Accelerated Stress Tests and Corresponding Changes to Catalyst Layers and Interfaces
Stress tests are developed for proton exchange membrane electrolyzers that utilize low catalyst loading, elevated potential, and frequent cycling with square- and triangle-waves to accelerate anode catalyst layer degradation during intermittent operation. Kinetics drive performance losses (ohmic/transport secondary) and are accompanied by decreasing exchange current density, decreasing cyclic voltammetric capacitance, and increasing polarization resistance. Decreased kinetics are likely due to a combination of iridium (Ir) migration into electrochemically inaccessible locations in the anode or membrane, Ir particle growth (supported by X-ray scattering), changes in the extent of the Ir oxidation state (supported by X-ray absorption spectroscopy), and anode catalyst layer reordering. Decreasing catalyst/transport layer contact and catalyst/membrane interfacial tearing may add contact resistances and account for increasing ohmic losses. Performance losses for low and moderate catalyst loading, as well as from accelerated and model wind/solar cycling protocols, were likewise dominated by kinetics but vary in severity. Additionally, accelerated cycling (1 cycle per minute) appears to reasonably accelerate relevant loss mechanisms and can be used to project electrolyzer lifetime from anode deterioration. Ongoing accelerated stress test development and studies into performance loss mechanisms will continue to be critical as electrolysis shifts to intermittent power and low-cost applications.
Tuning Stoichiometry to Promote Formation of Binary Colloidal Superlattices
The self-assembly of binary nanoparticle superlattices from colloidal mixtures is a promising method for the fabrication of complex colloidal cocrystal structures. However, binary mixtures often form amorphous or metastable phases instead of the thermodynamically stable phase. Here we show that in binary mixtures of differently sized spherical particles, an excess of the smaller component can promote—and, in some cases, may be necessary for—the self-assembly of a binary cocrystal. Using computer simulations, we identify two mechanisms responsible for this phenomenon. First, excess small particles act like plasticizers and enable systems to reach a greater supersaturation before kinetic arrest occurs. Second, they can disfavor competing structures that may interfere with the growth of the target structure. We find the phase behavior of simulated mixtures of nearly hard spheres closely matches published experimental results. We demonstrate the generality of our findings for mixtures of particles of arbitrary shape by presenting a binary mixture of hard shapes that only self-assembles with an excess of the smaller component.
Modeling of Lithium Nucleation and Plating Kinetics Under Fast Charge Conditions
The onset of lithium nucleation and subsequent plating on the graphite particles is a challenging problem in the design of fast charging batteries. Here, a variational phase field formulation has been developed to initiate the nucleation of lithium particles based on the local plating overpotential conditions and allowing to predict the lithium plating under fast charge conditions. The model demonstrates that (1) at small charging current density, there is no nucleation and plating of metallic lithium, and no effect on the intercalation kinetics; (2) at intermediate charging current densities, initially a stagnated growth from isolated lithium nuclei is observed followed by a continuous growth of metallic lithium; (3) at large charging current densities, a continuous growth of metallic lithium resulting from coalescence of small nuclei into large nuclei decreases the excess interfacial energy, which in turn slows down the intercalation kinetics. The formulation sets the stage for predicting and evaluating the influence of various electrolyte compositions, graphite particle morphologies and electrode loadings on the nucleation and plating dynamics under fast charge conditions.