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At least 1,081 records · Page 60

Hubbard-corrected oxide formation enthalpies without adjustable parameters

A density functional theory (DFT) approach to computing transition metal oxide heat of formation without adjustable parameters is presented. Different degrees of d-electron localization in oxides are treated within the DFT+U approach with site-dependent, first-principles Hubbard U-parameters obtained from linear response theory, and delocalized states in the metallic phases are treated without Hubbard corrections. Comparison of relative stabilities of these differently treated phases is enabled by a local d-electron density matrix-dependent model, which was found by genetic programming against experimental reference formation enthalpies. This mathematically simple model does not explicitly depend on the Hubbard-corrected ionic species and is shown to reproduce the heats of formation of the Mott insulators Ca 2 RuO 4 and Y 2 Ru 2 O 7 within ~3% of experimental results, where the experimental training data did not contain Ru oxides. This newly developed method thus absolves from the need for element-specific corrections fitted to experiments in existing Hubbard-corrected approaches to the prediction of reaction energies of transition metal oxides and metals. The absence of fitting parameters opens up here the possibility to predict relative thermodynamic stabilities and reaction energies involving d-states of varying degree of localization at transition metal oxide interfaces and defects, where site-dependent U-parameters will be particularly important and devising a fitting scheme against experimental data with predictive power would be exceedingly difficult.

transition metal oxides↗

Ensemble Simulations and Experimental Free Energy Distributions: Evaluation and Characterization of Isoxazole Amides as SMYD3 Inhibitors

Optimization of binding affinities for ligands to their target protein is a primary objective in rational drug discovery. Herein, we report on a collaborative study that evaluates various compounds designed to bind to the SET and MYND domain-containing protein 3 (SMYD3). SMYD3 is a histone methyltransferase and plays an important role in transcriptional regulation in cell proliferation, cell cycle, and human carcinogenesis. Experimental measurements using the scintillation proximity assay show that the distributions of binding free energies from a large number of independent measurements exhibit non-normal properties. We use ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent) and TIES (thermodynamic integration with enhanced sampling) protocols to predict the binding free energies and to provide a detailed chemical insight into the nature of ligand-protein binding. Our results show that the 1-trajectory ESMACS protocol works well for the set of ligands studied here. Although one unexplained outlier exists, we obtain excellent statistical ranking across the set of compounds from the ESMACS protocol and good agreement between calculations and experiments for the relative binding free energies from the TIES protocol. ESMACS and TIES are again found to be powerful protocols for the accurate comparison of the binding free energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Thermodynamic and Kinetic Roles of H2 in Structure Evolution of Urchin-like Co: A density functional theory study

Small gas molecules working as good capping agents play important roles in controlling the morphologies and surface structures of the metal nanocrystals. In present work, the thermodynamic and kinetic roles of H2 molecule played on the morphology of Co nanocrystal were systematically studied based on density functional theory (DFT). The Gibbs surface free energies (?) of Co(100), Co(110) and Co(111) under different hydrogen surface coverages were investigated by ab initio thermodynamics, based on which i) the phase diagrams of stable H coverage on each plane were obtained; ii) the morphology evolutions of the Co nanocrystals with various surface hydrogen coverages were further predicted by Wulff construction. It was revealed that addition of H2 could change the facet stability generating diverse morphological Co nucleus. The kinetic role of H2 was further explored by DFT during adatom Co surface diffusions under different H coverages (?H), which suggested that except for Co(100) at ?H of 0.56 ML, the surface H would hinder Co surface diffusions. The projected density of state (PDOS) gave a deeper insight that the electronic structures of the Co adatom could be alerted by addition of the surface H, which thereby affected its surface diffusion ability. X. Wang, N. Liu, Q. Zhang, X. Liang, and B. Chen were financially supported by the National Natural Science Foundation of China (No. 21476012, 21571012, and 91534201). D. Mei was supported by the US Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences & Biosciences. Pacific Northwest National Laboratory (PNNL) is a multiprogram national laboratory operated for DOE by Battelle. Computing time was granted by the facility user proposal grand challenge of computational catalysis of the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL). EMSL is a national scientific user facility located at Pacific Northwest National Laboratory (PNNL) and sponsored by DOE’s Office of Biological and Environmental Research.

Nanocrystal Co, Surface free energy, Surface diffu↗

Thermodynamic Stability and Site‐Specific Distribution of Graphitic and Pyridinic Nitrogen in Graphene Moiré on Ru(0001)

Abstract Graphene‐like materials are of interest for large‐scale hydrogen storage applications due to their lightweight, durable, and scalable properties. Nitrogen‐doping minimizes kinetic limitations in diffusion and recombination on surfaces, however, the role of graphitic nitrogen (GN) and pyridinic nitrogen (PN) is not well understood. Nitrogen‐doped graphene is synthesized on Ru(0001) using chemical vapor deposition (CVD) of pyridine and ion irradiation. Scanning tunneling microscopy (STM), x‐ray photoelectron spectroscopy (XPS), and density functional theory (DFT) are used to identify the structure, location, and thermodynamic stability of nitrogen species within the graphene moiré. CVD of pyridine results in a low nitrogen concentration (<0.1at%), while the post‐growth nitrogen ion irradiation allows us to increase the concentration further. The concentration of GN and PN is controlled by varying the ion dose and annealing temperature. Comparison of measured and simulated STM images of GN and PN yield an excellent agreement, allowing us to confidently establish that GN is preferentially located near the center of the Atop region, while PN is located in the valley region of the graphene moiré. This report explicitly confirms the site assignments and provides a foundation for the site synthesis and analysis of structural and electronic properties that drive the reactivity of N‐doped graphene.

Gedara, Buddhika S. A. [Physical and Computational↗

An MPMD approach coupling electromagnetic continuum mechanics approximations in ALEGRA

In this work, two complementary approximations for describing aspects of continuum electromagnetics in moving media are discussed: electroquasistatic and magnetoquasistatic. Each has been implemented in the finite element shock code ALEGRA for modeling dynamic electromechanical phenomena on typical engineering time scales, with fully integrated circuit coupling. The approximations can be obtained by consistent asymptotic balancing of Maxwell’s equations relative to timescales associated with magnetic diffusion, charge relaxation, and electromagnetic wave propagation. In ALEGRA, the electroquasistatic approximation is used for ferroelectric (FE) modeling, while the magnetoquasistatic approximation is used for magnetohydrodynamic (MHD) modeling. In this paper we introduce for the first time a detailed derivation of a useful quasi-steady “low-R m ” variant of the MHD approximation applicable for cases, such as with detonators, where the thermodynamic pressure arising from Joule heating dominates over magnetic forces. An additional purpose of this paper is to present a coupling mode using Multiple Program-Multiple Data (MPMD) message passing communication that allows the user to run 3D FE problems together with 2D and/or 3D MHD problems with the respective simulation domains coupled through a common circuit equation. The MPMD coupling capability is used here to model the dynamic coupling of a notional ferroelectric generator with an RP-87 exploding bridgewire detonator. The simulated bridgewire heats up and bursts under current generated by simulated depoling of the ferroelectric generator, as a demonstration of the MPMD capability.

42 ENGINEERING↗

Demonstrating non-isothermal vacuum membrane air dehumidification for efficient next-generation air conditioning

Vacuum membrane air dehumidification has gained significant interest in recent years as a highly efficient means of air dehumidification. Prior theoretical modeling work by the authors introduced the Active Membrane Energy Exchanger (AMX) concept, which combines active heat exchange and vacuum membrane dehumidification into one non-isothermal system, and found that it could outperform other air conditioning technologies under many conditions. However, no experimental literature exists on combining active heat exchangers and vacuum membrane dehumidification. Here, the goal of the present study is to evaluate the dehumidification (mass transfer) performance of the AMX concept relative to isothermal membrane dehumidification through three main methodologies: (1) membrane material-level characterization, (2) experimental prototype development and testing, and (3) computational fluid dynamics (CFD) simulations. The dense membranes used in this work showed up to a 40% increase in water vapor permeance at cooler temperatures, and the prototype system showed up to a 6% increase in humidity removal when the air was simultaneously cooled. Furthermore, the membrane module-integrated heat exchange tubes provided additional mixing and turbulence, leading to a 4–8% increase in humidity removal. The upper limit coefficient of performance was equal to approximately 2.2, necessitating advanced system designs to improve efficiency. This study is the first to highlight that combining the cooling and vacuum dehumidification processes can improve dehumidification performance.

30 DIRECT ENERGY CONVERSION↗

Coupling solidification kinetics with phase-behavior computations in hydrodynamic simulations of high-pressure, dynamic-compression processes

In this study, we report a numerical scheme to integrate models for the kinetics of solidification processes together with phase-behavior computations in the context of continuum-scale hydrodynamic simulations. The objective of the phase-behavior computations is to determine the pressure and temperature, given the following three sets of inputs: (1) an appropriate equation of state to describe our system, (2) the phase fraction(s) produced by the kinetic models, (3) and the volume and internal energy obtained by solving the conservation equations that govern the hydrodynamic behavior. The kinetics are assumed to be governed by the Kolmogorov–Johnson–Mehl–Avrami equation, and the nucleation and growth rates that enter into that equation are functions of the pressure and temperature produced by the phase-behavior computations. Our formulation allows for the fluid and solid phases to be at different temperatures (thermal nonequilibrium) and pressures (arising from surface-tension-induced Laplace contributions). The formulation is presented in a fairly general setting that is independent of any particular material, although we demonstrate it in some examples related to high-energy-density science applications where materials are rapidly compressed to pressures exceeding several gigapascals in less than a microsecond. We conclude with a critical evaluation of our approach and provide suggestions for future work to improve the predictive capabilities and generality of the models.

42 ENGINEERING↗

Characterizing Structure-Dependent TiS 2 /Water Interfaces Using Deep-Neural-Network-Assisted Molecular Dynamics

As a promising layered electrode material, TiS 2 -based capacitive deionization (CDI) devices for water desalination have attracted significant attention. However, TiS 2 /H 2 O interfacial features, potentially important for device optimization, remain unidentified. Using Deep Potential Molecular Dynamics (DPMD), we characterized distinct aqueous interfaces introduced by four TiS 2 terminations expected to be present as water intercalates into TiS 2 , namely, Armchair, Zigzag, Zigzag-L, and Zigzag-R. First, we assessed important representative physical properties of the system to validate the deep potentials (DPs). DPMD simulations agree well with experiments and first-principles simulations, suggesting the DPs are accurate and reliable. Subsequent simulations of these TiS 2 /water interfaces revealed how TiS 2 surface termination influences the structure of interfacial water. This effect is most evident in the first and second water layers close to the TiS 2 surface, and more pronounced when spontaneous dissociative adsorption of water occurs. The extent of water dissociation on each surface was evaluated using enhanced sampling. Zigzag-L is the only interface where proton transfer from adsorbed water to TiS 2 surface S atoms is thermodynamically and kinetically favored. The coexistence of surface four-fold-coordinated Ti (Ti 4c ) and one-fold-coordinated S (S 1c ) is found to be essential to making proton transfer feasible on the Zigzag-L surface. Furthermore, remaining unprotonated S 1c atoms can act as good proton acceptors after water dissociation. Thus, TiS 2 with Zigzag-L termination may be a surface to avoid in CDI device construction, given that pH fluctuations adversely affect performance. Furthermore, this work provides new understanding of TiS 2 /H 2 O interfacial features that could aid future design and optimization of TiS 2 -based CDI devices for water desalination.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Iron-Catalyzed Cross-[2 + 2] Cycloaddition of Butadiene and α,ω-Dienes for Ductile and Chemically Recyclable Poly(oligocyclobutanes)

Poly(divinyloligocyclobutanes) (pDVOCBs) are a distinct class of butadiene-derived, chemically recyclable polyolefins prepared from iron-catalyzed [2 + 2] cycloaddition followed by ruthenium-catalyzed ADMET polymerization. These polymers are highly crystalline, with high melting temperatures and unique rotator phases. The high degree of crystallinity in these materials not only leads to high stiffness over a broad temperature range but also results in brittle failure for polymers of modest molecular weights. Iron-catalyzed cross-[2 + 2] cycloaddition of butadiene and α,ω-dienes was accomplished, where the number of methylene units between the four-membered rings was systematically varied. Subsequent ADMET polymerization of the resulting telechelic oligomers provided a new class of chemically recyclable polyolefins that exhibit distinct thermomechanical properties. Specifically, methylene units induce changes in crystallinity that, in combination with the increased molecular weight, favored the formation of stable necks upon tensile deformation, with ∼10× enhanced ductility and improved toughness compared to pDVOCB. Through combined experimental and computational studies, the effects of methylene spacers on the crystal-to-rotator transition of the cyclobutane polymers were established. Ultimately, these methylene-modified cyclobutane polymers expand the range of properties and potential applications of this class of recyclable polyolefins.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hyperelastic nature of the Hoek–Brown criterion

In this article, we propose a nonlinear elasto-plastic model, for which a specific class of hyperbolic elasticity arises as a straight consequence of the yield criterion invariance on the plasticity level. We superimpose this nonlinear elastic (or hyperelastic) behavior with plasticity obeying the associated flow rule. Interestingly, we find that a linear yield criterion on the thermodynamical force associated with plasticity results in a quadratic yield criterion in the stress space. This suggests a specific hyperelastic connection between Mohr–Coulomb and Hoek–Brown (or alternatively between Drucker–Prager and Pan–Hudson) yield criteria. We compare the elasto-plastic responses of standard tests for the Drucker–Prager yield criterion using either linear or the suggested hyperbolic elasticity. Notably, the nonlinear case stands out due to dilatancy saturation observed during cyclic loading in the triaxial compression test. We conclude this study with structural finite element simulations that clearly demonstrate the numerical applicability of the proposed model.

97 MATHEMATICS AND COMPUTING↗

A Thermogravimetric Temperature-Programmed Thermal Redox Protocol for Rapid Screening of Metal Oxides for Solar Thermochemical Hydrogen Production

As combinatorial and computational methods accelerate the identification of potentially suitable thermochemically-active oxides for use in solar thermochemical hydrogen production (STCH), the onus shifts to quickly evaluating predicted performance. Traditionally, this has required an experimental setup capable of directly carrying out a two-stage thermochemical water-splitting process. But this can be a difficult endeavor, as most off-the-shelf equipment cannot adequately deal simultaneously with the high temperatures, varying oxygen partial pressures, and high H 2 O partial pressures required; achieving sufficient temporal sensitivity to accurately quantify the kinetics is also a major challenge. However, as proposed here, a less complicated experiment can be used as a first screening for thermochemical water splitting potential. Temperature-Programmed Thermal Redox (TPTR) using thermogravimetry evaluates the thermal reduction behavior of materials. This technique does not require water splitting or CO 2 -splitting analogs but can nonetheless predict water-splitting performance. Three figures of merit are obtained from the TPTR experiment: reduction onset temperature, extent of reduction, and extent of recovery upon reoxidation. These metrics can collectively be used to determine if a material is capable of thermochemical water-splitting, and, to good approximation, predict whether the thermodynamics are favorable for use under more challenging high-conversion conditions. This paper discusses the pros and cons of using TPTR and proposes a protocol for use within the STCH community.

08 HYDROGEN↗

G4Boost: a machine learning-based tool for quadruplex identification and stability prediction

Background: G-quadruplexes (G4s), formed within guanine-rich nucleic acids, are secondary structures involved in important biological processes. Although every G4 motif has the potential to form a stable G4 structure, not every G4 motif would, and accurate energy-based methods are needed to assess their structural stability. Here, we present a decision tree-based prediction tool, G4Boost, to identify G4 motifs and predict their secondary structure folding probability and thermodynamic stability based on their sequences, nucleotide compositions, and estimated structural topologies. Results: G4Boost predicted the quadruplex folding state with an accuracy greater then 93% and an F1-score of 0.96, and the folding energy with an RMSE of 4.28 and R 2 of 0.95 only by the means of sequence intrinsic feature. G4Boost was successfully applied and validated to predict the stability of experimentally-determined G4 structures, including for plants and humans. Conclusion: G4Boost outperformed the three machine-learning based prediction tools, DeepG4, Quadron, and G4RNA Screener, in terms of both accuracy and F1-score, and can be highly useful for G4 prediction to understand gene regulation across species including plants and humans.

59 BASIC BIOLOGICAL SCIENCES↗

L-SCIE and SUPCRTNE model and database development

This progress report (Level 3 Milestone Number M3SF-25LL010301052) summarizes research conducted at Lawrence Livermore National Laboratory (LLNL) within the Argillite Host Rock Properties & Processes Work Package SF-25LL01030105. The focus of this milestone is to create an initial SUPCRTNE database and extensively test the SUPCRTNE code. We prepared a draft manuscript describing our workflow and approach for developing a next-generation thermodynamic database for the Spent Fuel and High Level Waste Disposition campaign. The goal is to ease any future formal software qualification effort as was done on the Yucca Mountain Project for codes including SUPCRT92 and EQ3/6. We are attempting to extend the SUPCRTNE database to include more species, mainly from the NEA volumes. We can also take advantage of thermodynamic database activities that are ongoing at Thermochimie and as part of the EURADII program. However, our effort is limited by the funds available and the changes to program scope that was initiated in mid-FY25.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

CHARMM-GUI Nanomaterial Modeler for Modeling and Simulation of Nanomaterial Systems

Molecular modeling and simulation are invaluable tools for nanoscience that predict mechanical, physicochemical, and thermodynamic properties of nanomaterials and provide molecular-level insight into underlying mechanisms. However, building nanomaterial-containing systems remains challenging due to the lack of reliable and integrated cyberinfrastructures. Here we present Nanomaterial Modeler in CHARMM-GUI, a web-based cyberinfrastructure that provides an automated process to generate various nanomaterial models, associated topologies, and configuration files to perform state-of- the-art molecular dynamics simulations using most simulation packages. The nanomaterial models are based on the interface force field, one of the most reliable force fields (FFs). The transferability of nanomaterial models among the simulation programs was assessed by single-point energy calculations, which yielded 0.01% relative absolute energy differences for various surface models and equilibrium nanoparticle shapes. Three widely used Lennard-Jones (LJ) cutoff methods are employed to evaluate the compatibility of nanomaterial models with respect to conventional biomolecular FFs: simple truncation at r = 12 Å (12 cutoff), force-based switching over 10 to 12 Å (10-12 fsw), and LJ particle mesh Ewald with no cutoff (LJPME). The FF parameters with these LJ cutoff methods are extensively validated by reproducing structural, interfacial, and mechanical properties. As a result, we find that the computed density and surface energies are in good agreement with reported experimental results, although the simulation results increase in the following order: 10-12 fsw <12 cutoff < LJPME. Nanomaterials in which LJ interactions are a major component show relatively higher deviations (up to 4% in density and 8% in surface energy differences) compared with the experiment. Nanomaterial Modeler's capability is also demonstrated by generating complex systems of nanomaterial-biomolecule and nanomaterial-polymer interfaces with a combination of existing CHARMM-GUI modules. We hope that Nanomaterial Modeler can be used to carry out innovative nanomaterial modeling and simulations to acquire insight into the structure, dynamics, and underlying mechanisms of complex nanomaterial-containing systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Development of a Reactive Force Field for Simulating Photoinitiated Acrylate Polymerization

Light-driven and photo-curable polymer based additive manufacturing (AM) has enormous potential due to its excellent resolution and precision. Acrylated radical chain-growth polymerized resins are widely used in photopolymer AM due to their fast kinetics, and often serve as a departure point for developing other resin materials for photopolymer-based AM technologies. For successful control of the photopolymer resins, the molecular basis of the acrylate free-radical polymerization has to be understood in detail. We present an optimized reactive force field (ReaxFF) for molecular dynamics (MD) simulations of acrylate polymer resins that captures radical polymerization thermodynamics and kinetics. The force field is trained against an extensive training set including density functional theory (DFT) calculations of reaction pathways along the radical polymerization from methyl acrylate to methyl butyrate, bond dissociation energies, and structures and partial charges of several molecules and radicals. We also found that it was critical to train the force field against an incorrect, nonphysical reaction pathway observed in simulations that used parameters not optimized for acrylate polymerization. As a result, the parameterization process utilizes a parallelized search algorithm, and the resulting model can describe polymer resin formation, crosslinking density, conversion rate, and residual monomers of the complex acrylate mixtures.

36 MATERIALS SCIENCE↗

A Molecular View of Methane Activation on Ni(111) through Enhanced Sampling and Machine Learning

A combination of machine learned interatomic potentials (MLIPs) and enhanced sampling simulations is used to investigate the activation of methane on a Ni(111) surface. The work entails the development and iterative refinement of MLIPs, initially trained on a dataset constructed via ab initio molecular dynamics (AIMD) simulations, supplemented by adaptive biasing forces, to enrich the sampling of catalytically relevant configurations. Our results reveal that by incorporating collective variables that capture the behavior of the reactant molecule, as well as additional frames that describe the dynamic response of the catalytic surface, it is possible to enhance considerably the accuracy of predicted energies and forces. By employing enhanced sampling schemes in the refinement of the MLIP, we systematically explore the potential energy surface, leading to a refined MLIP capable of predicting DFT-level energies and forces and replicating key geometric characteristics of the catalytic system. The resulting free energy landscapes at several temperatures provide a detailed view of the thermodynamics and dynamics of methane activation. Specifically, as methane approaches and dissociates on the catalytic surface, the process involves the dynamic interplay of CH 4 and the Ni catalyst that includes both enthalpic and entropic contributions. The progression towards the transition state involves an CH 4 moiety that is increasingly restrained in its ability to rotate or translate, while the stage following the transition state is characterized by a notable rise of the Ni atom that interacts with the cleaved C–H bond. Furthermore, this leads to an increase in the mobility of the adsorbed species, a feature that becomes more pronounced at higher temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Radiation driven diffusion in γU-Mo

A monolithic fuel design based on a U-Mo alloy has been selected as the fuel type for conversion of the United States High-Performance Research Reactors (HPRRs). A critical phenomenon of interest with U-Mo monolithic fuel is the large amount of swelling that takes place during operation, particularly at high fission densities. The accurate prediction of fuel evolution under irradiation requires implementation of correct thermodynamic and kinetic properties into mesoscale and continuum level fuel performance modeling codes. One such property where there exists incomplete data is the diffusion of relevant species under irradiation. Fuel performance swelling predictions rely on an accurate representation of diffusion in order to determine the rate of fission gas swelling and the local microstructural evolution. In this work, we present molecular dynamics simulations of the radiation driven diffusion of U, Mo and Xe in U-Mo nuclear fuels. Diffusion coefficients for each species are determined over a range of temperatures and compositions. In this work, updated diffusion coefficients are presented that are applicable under irradiation that incorporate both intrinsic and radiation driven diffusion.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Evaluation of the Rapid Refresh Numerical Weather Prediction Model over Arctic Alaska

Abstract Despite a need for accurate weather forecasts for societal and economic interests in the U.S. Arctic, thorough evaluations of operational numerical weather prediction in the region have been limited. In particular, the Rapid Refresh Model (RAP), which plays a key role in short-term forecasting and decision-making, has seen very limited assessment in northern Alaska, with most evaluation efforts focused on lower latitudes. In the present study, we verify forecasts from version 4 of the RAP against radiosonde, surface meteorological, and radiative flux observations from two Arctic sites on the northern Alaskan coastline, with a focus on boundary layer thermodynamic and dynamic biases, model representation of surface inversions, and cloud characteristics. We find persistent seasonal thermodynamic biases near the surface that vary with wind direction, and may be related to the RAP’s handling of sea ice and ocean interactions. These biases seem to have diminished in the latest version of the RAP (version 5), which includes refined handling of sea ice, among other improvements. In addition, we find that despite capturing boundary layer temperature profiles well overall, the RAP struggles to consistently represent strong, shallow surface inversions. Further, while the RAP seems to forecast the presence of clouds accurately in most cases, there are errors in the simulated characteristics of these clouds, which we hypothesize may be related to the RAP’s treatment of mixed-phase clouds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗