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At least 541 records · Page 30

Catalyst: Fast and flexible modeling of reaction networks

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst’s broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.

59 BASIC BIOLOGICAL SCIENCES↗

Bayesian analysis of the 86 Sr ⁢(𝛼,𝛼) reaction to constrain the 86 Sr ⁢(𝛼,𝑛) cross section at astrophysical energies

The alpha optical model potential (𝛼-OMP ) is a phenomenological approach used to describe elastic scattering where multiple reaction channels are open. It is one of the most critical inputs for the calculation of thermonuclear reaction rates in explosive stellar environments, but uncertainties within the 𝛼-OMP lead to imprecise predictions hindering comparisons between calculations and observations. In order to improve the precision of the 𝛼-OMP, additional nuclear physics data are required. In this paper, a measurement of the 86 Sr (𝛼, 𝛼) elastic scattering cross section at multiple energies is reported. Here, a local optical potential is constructed via a fully Bayesian analysis of the elastic scattering data. The resulting uncertainties on the low-energy cross sections relevant to nuclear astrophysics are then calculated and shown to be on the order of 50%.

59 ≤ A ≤ 89↗

Synthesis and Structural Study of Substituted Ternary Nitrides for Ammonia Production

Over the past few decades, inorganic nitride materials have grown in importance in part due to their potential as catalysts for the synthesis of NH 3 , a key ingredient in fertilizer and precursor to industrial chemicals. Of particular interest are the ternary (ABN) or higher-order nitrides with high metal-to-nitrogen ratios that show promise in enhancing NH 3 synthesis reaction rates and yields via heterogeneous catalysis or chemical looping. Although metal nitrides are predicted to be numerous, the stability of nitrogen triple bonds found in N 2 , especially in comparison to the metal–nitrogen bonds, has considerably hindered synthetic efforts to produce complex nitride compounds. In this study, we present an exhaustive down-selection process to identify ternary nitrides for a promising chemical looping NH 3 production mechanism. We also report on a facile and efficient two-step synthesis method that can produce well-characterized η-carbide Co 3 Mo 3 N/Fe 3 Mo 3 N or filled β-manganese Ni 2 Mo 3 N ternaries, as well as their associated quaternary, (Co,Fe) 3 Mo 3 N, (Fe,Ni) 2 Mo 3 N, and (Co,Ni) 2 Mo 3 N, solid solutions. To further explore the quaternary space, syntheses of (Co,Ni) 3 Mo 3 N (Ni ≤ 10 mol %) and Co 3 (Mo,W) 3 N (W ≤ 10 mol %) were also investigated. The structures of the nitrides were characterized via X-ray powder diffraction. The morphology and compositions were characterized with scanning electron microscopy. In conclusion, the multitude of chemically unique, but structurally related, nitrides suggests that properties such as nitrogen activity may be tunable, making the materials of great interest for NH 3 synthesis schemes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Translating Fundamental Insights into Ag-Based Bimetallic Electrocatalysts to Anion-Exchange Membrane Fuel Cells

To address challenges of high costs and scalability for fuel cells, it is essential to develop af-fordable and earth-abundant materials that are Pt-group-metal (PGM)-free. Recent advance-ments in PGM-free electrocatalysis for the oxygen reduction reaction (ORR) in alkaline media show that high catalyst loadings are needed to achieve high reaction rates; however, there are associated mass transport limitations. To address this issue, we develop low-loading ionomer-less Ag-bimetallic thin films by alloying with 3d block elements or Sn. We bridge knowledge from fundamental rotating disk electrode (RDE) studies to gas-diffusion cathodes in high-temperature anion-exchange membrane fuel cells (HT-AEMFCs), resulting in high-activity ORR catalysis and peak power densities up to 1.2 W cm-² geo for the Ag-Sn and Ag-Co alloys. Here, experimental post-characterization and theoretical calculations reveal small Co or Sn oxide nano-islands on Ag as likely active sites enhancing ORR activity, ultimately offering these low-loading PGM-free ORR materials as a viable path towards sustainable energy conversion.

Catalysts↗

Modeling the Impact of the Organic Aerosol Phase State on Multiphase OH Reactive Uptake Kinetics and the Resultant Heterogeneous Oxidation Timescale of Organic Aerosol in the Amazon Rainforest

Accurate predictions of chemical lifetime, i.e., oxidation timescale and change in the mass of organic aerosols (OAs) in atmospheric models, are critical to quantify the impacts of OA on aerosol–cloud interactions, radiative forcing, and air quality. The heterogeneous oxidation of OA by hydroxyl (OH) radicals is a key process governing OA mass changes during their oxidation. Recently, laboratory observations of the OH uptake coefficient (γ OH ) and heterogeneous reaction rate (k het,OH ) for different OA systems with varying phase states have been combined to develop a new parameterization of γ OH and k het,OH as a function of the OA phase state, i.e., viscosity (η OA ). Here, in this work, we use a recently published viscosity prediction framework to analyze the new γ OH and k het,OH parameterization with a box model. Subsequently, we implement this box model to predict γ OH and k het,OH over the Amazon rainforest in the dry-to-wet transition season with both significant biomass burning and biogenic influences. Relevant parameters within our box model are specified based on detailed regional model simulations over the Amazon using the Weather Research and Forecasting model coupled with Chemistry (WRF-Chem). η OA is predicted as a function of species volatility, OA composition (including water uptake) along with ambient relative humidity (RH), and temperature. Based on ambient conditions simulated by WRF-Chem over the entire atmospheric column, we use the box model to predict the upper bounds of the heterogeneous oxidation timescale of OA. Based on previous laboratory measurements, we assume that this heterogeneous OH oxidation causes fragmentation (carbon loss) of OA, followed by the evaporation of the fragmented molecules that results in the exponential decay of OA. We predict that the oxidation timescale of OA is ~1 month near the Earth’s surface in the pristine Amazonian background because of low OH concentrations. But OA is oxidized more rapidly within urban and wildfire plumes near the Earth’s surface with an order of magnitude higher OH concentrations compared to the pristine background, causing the simulated oxidation timescale of OA to be much shorter, ~3–4 days. At 3–5 km altitudes where biomass burning OA is predicted to be semisolid, the heterogeneous oxidation timescale is estimated as ~6 days to 3 weeks and decreases with increasing OH concentrations within plumes. We show that the simulated mass loss of OA is strongly size-dependent, where smaller particles oxidize more rapidly compared to larger particles due to their greater per-particle surface area-to-volume ratio. Increasing urbanization and deforestation in the Amazon in the future might increase OH concentrations in the background Amazon, causing faster oxidation of OA. At higher altitudes above liquid clouds, especially in the upper troposphere where temperatures approach ~250 K, future measurements are needed to reduce the uncertainties related to the mass loss of OA at colder temperatures and low relative humidity conditions due to its heterogeneous OH oxidation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Monolayer Support Control and Precise Colloidal Nanocrystals Demonstrate Metal-Support Interactions in Heterogeneous Catalysts

We report that electronic and geometric interactions between active and support phases are critical in determining the activity of heterogeneous catalysts, but metal-support interactions are challenging to study. Here, it is demonstrated how the combination of the monolayer-controlled formation using atomic layer deposition (ALD) and colloidal nanocrystal synthesis methods leads to catalysts with sub-nanometer precision of active and support phases, thus allowing for the study of the metal-support inter-actions in detail. The use of this approach in developing a fundamental understanding of support effects in Pd-catalyzed methane combustion is demonstrated. Uniform Pd nanocrystals are deposited onto Al2O 3 /SiO 2 spherical supports prepared with control over morphology and Al 2 O 3 layer thicknesses ranging from sub-monolayer to a ≈4 nm thick uniform coating. Dramatic changes in catalytic activity depending on the coverage and structure of Al 2 O 3 situated at the Pd/Al 2 O 3 interface are observed, with even a single monolayer of alumina contributing an order of magnitude increase in reaction rate. By building the Pd/Al 2 O 3 interface up layer-by-layer and using uniform Pd nanocrystals, this work demonstrates the importance of controlled and tunable materials in determining metal-support interactions and catalyst activity.

36 MATERIALS SCIENCE↗

Understanding Operando Water Management in Hydroxide‐Exchange‐Membrane Fuel Cells

The water balance in hydroxide-exchange-membrane fuel cells (HEMFCs) is a key challenge for improved performance and durability, intimately linked with the various interfaces and coupled phenomena. For every 4 electrons produced, 4 water molecules are generated in the anode and 2 consumed in the cathode, while electroosmosis transports water across the HEM from the cathode to the anode. Consequently, a concentration gradient drives water back, from anode to cathode. Ineffective water management could lead to cathode dry-out, limiting reaction rate and causing ionomer degradation, or to anode flooding. To address these concerns, it is critical to measure the water transport operando . Herein, a home-built water-flux station is used to measure total water flux during cell operation with different inlet relative humidities and back pressures. Increasing the HEM thickness fourfold decreases the water flux at high current density, and utilizing microporous layers on both the anode and cathode decreases the water flux from the anode to the cathode. However, the most significant variable in changing the water flux was found by increasing the anode back pressure. Furthermore, humidity cycling significantly changed electrochemical performance without affecting the overall water fluxes. These findings can be translated to other devices utilizing an HEM.

AEMFC↗

An Active‐Site Sulfonate Group Creates a Fast Water Oxidation Electrocatalyst That Exhibits High Activity in Acid

Abstract The storage of solar energy in chemical bonds will depend on pH‐universal catalysts that are not only impervious to acid, but actually thrive in it. Whereas other homogeneous water oxidation catalysts are less active in acid, we report a catalyst that maintained high electrocatalytic turnover frequency at pH values as low as 1.1 and 0.43 ( k cat =1501±608 s −1 and 831±254 s −1 , respectively). Moreover, current densities, related to catalytic reaction rates, ranged from 15 to 50 mA cm −2 mM −1 comparable to those reported for state‐of‐the‐art heterogeneous catalysts and 30 to 100 times greater than those measured for two prominent literature homogeneous catalysts at pH 1.1 and 0.43. The catalyst also exhibited excellent durability when a chemical oxidant was used (Ce IV , 7400 turnovers, TOF 0.88 s −1 ). Preliminary computational studies suggest that the unusual active‐site sulfonate group acts a proton relay even in strong acid, as intended.

Nash, Aaron G.↗

An Active–Site Sulfonate Group Creates a Fast Water Oxidation Electrocatalyst That Exhibits High Activity in Acid

The storage of solar energy in chemical bonds will depend on pH–universal catalysts that are not only impervious to acid, but actually thrive in it. Whereas other homogeneous water oxidation catalysts are less active in acid, we report a catalyst that maintained high electrocatalytic turnover frequency at pH values as low as 1.1 and 0.43 (k cat = 1501±608 s –1 and 831±254 s –1 , respectively). Moreover, current densities, related to catalytic reaction rates, ranged from 15 to 50 mA cm –2 mM –1 comparable to those reported for state–of–the–art heterogeneous catalysts and 30 to 100 times greater than those measured for two prominent literature homogeneous catalysts at pH 1.1 and 0.43. The catalyst also exhibited excellent durability when a chemical oxidant was used (Ce IV , 7400 turnovers, TOF 0.88 s –1 ). Here, preliminary computational studies suggest that the unusual active–site sulfonate group acts a proton relay even in strong acid, as intended.

14 SOLAR ENERGY↗

Surface Density Dependent Catalytic Activity of Single Palladium Atoms Supported on Ceria

The analogy between single-atom catalysts (SACs) and molecular catalysts predicts that the specific catalytic activity of these systems is constant. Here we provide evidence that this prediction is not necessarily true. As a case in point, we show that the specific activity over ceria-supported single Pd atoms linearly increases with metal atom density, originating from the cumulative enhancement of CeO 2 reducibility. The long-range electrostatic footprints (≈1.5 nm) around each Pd site overlap with each other as surface Pd density increases, resulting in an observed deviation from constant specific activity. These cooperative effects exhaust previously active O atoms above a certain Pd density, leading to their permanent removal and a consequent drop in reaction rate. The findings of our combined experimental and computational study show that the specific catalytic activity of reducible oxide-supported single-atom catalysts can be tuned by varying the surface density of single metal atoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Mechanistic Insights into Adsorptive and Catalytic Reactions from Controllable Distributions of Metal Cations (Pd, Pt, Ni, Cr, Cu) as [M‐OH] +1 /1Al or M +2 /2Al in Zeolites

Anchoring divalent metal ions in the same zeolite framework with similar Si/Al ratio selectively as zeolite-bound M +2 or [M +2 -OH] +1 cationic species enables critical comparison of the species’ intrinsic reactivity for industrially and fundamentally relevant reactions. H-BEA zeolites with similar Si/Al ratios but differing framework Al siting were used to anchored multiple divalent metal cations (Ni, Pd, Pt, Cr, Cu) in the zeolite micropores. State-of-the-art infrared (IR) spectroscopy, electron paramagnetic resonance (EPR) measurements, including two-dimensional pulsed HYSCORE EPR, extended X-ray absorption fine structure (EXAFS), and density functional theory (DFT) calculations together provide unambiguous evidence for the selective formation of divalent metal cations as M +2 /2Al species (for H-BEA prepared in the conventional hydroxide media), and [M +2 OH] +1 /1Al species for H-BEA prepared in HF. Solid-state proton-decoupled triple-quantum magic-angle spinning (3Q MAS) NMR measurements confirmed contrasting Al distributions in the two H-BEA zeolites, which led to a contrasting divalent cation speciation. The reactivities of the two cationic species were explored for catalytic and adsorptive applications in both organometallic homogeneous and heterogeneous catalysis. This work demonstrates their divergent reactivity in ethylene dimerization, ethylene oxidation (Wacker process), selective catalytic reduction (SCR) of NO, NO adsorption, and methane oxidation. Both M +2 /2Al and [M +2 OH] +1 /1Al cations are both active for ethylene dimerization, but [M +2 OH] +1 /1Al species show higher reaction rates for each Pd, Ni, Pt. [M +2 OH] +1 /1Al is active for acetaldehyde formation in Wacker ethylene oxidation. A new active site for ethylene oligomerization is proposed that possesses a terminal OH group (Cr-OH) in Phillips catalysts evident by a nearly inactive isolated Cr +2 /2Al species that contrast an active Cr─OH motif.

Divalent metal cations in a zeolite↗

Model validation and selection in metabolic flux analysis and flux balance analysis

13C-Metabolic Flux Analysis (13C-MFA) and Flux Balance Analysis (FBA) are widely used to investigate the operation of biochemical networks in both biological and biotechnological research. Both methods use metabolic reaction network models of metabolism operating at steady state so that reaction rates (fluxes) and the levels of metabolic intermediates are constrained to be invariant. They provide estimated (MFA) or predicted (FBA) values of the fluxes through the network in vivo, which cannot be measured directly. These fluxes can shed light on basic biology and have been successfully used to inform metabolic engineering strategies. Several approaches have been taken to test the reliability of estimates and predictions from constraint-based methods and to compare alternative model architectures. Despite advances in other areas of the statistical evaluation of metabolic models, such as the quantification of flux estimate uncertainty, validation and model selection methods have been underappreciated and underexplored. We review the history and state-of-the-art in constraint-based metabolic model validation and model selection. Applications and limitations of the χ 2 -test of goodness-of-fit, the most widely used quantitative validation and selection approach in 13C-MFA, are discussed, and complementary and alternative forms of validation and selection are proposed. A combined model validation and selection framework for 13C-MFA incorporating metabolite pool size information that leverages new developments in the field is presented and advocated for. Finally, we discuss how adopting robust validation and selection procedures can enhance confidence in constraint-based modeling as a whole and ultimately facilitate more widespread use of FBA in biotechnology.

59 BASIC BIOLOGICAL SCIENCES↗

Enhancing 2‐Pyrone Synthase Efficiency by High‐Throughput Mass‐Spectrometric Quantification and In Vitro/In Vivo Catalytic Performance Correlation

Abstract Engineering efficient biocatalysts is essential for metabolic engineering to produce valuable bioproducts from renewable resources. However, due to the complexity of cellular metabolic networks, it is challenging to translate success in vitro into high performance in cells. To meet such a challenge, an accurate and efficient quantification method is necessary to screen a large set of mutants from complex cell culture and a careful correlation between the catalysis parameters in vitro and performance in cells is required. In this study, we employed a mass‐spectrometry based high‐throughput quantitative method to screen new mutants of 2‐pyrone synthase (2PS) for triacetic acid lactone (TAL) biosynthesis through directed evolution in E. coli . From the process, we discovered two mutants with the highest improvement (46 fold) in titer and the fastest k cat (44 fold) over the wild type 2PS, respectively, among those reported in the literature. A careful examination of the correlation between intracellular substrate concentration, Michaelis‐Menten parameters and TAL titer for these two mutants reveals that a fast reaction rate under limiting intracellular substrate concentrations is important for in‐cell biocatalysis. Such properties can be tuned by protein engineering and synthetic biology to adopt these engineered proteins for the maximum activities in different intracellular environments.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Heterogeneous Nature of Electrocatalytic CO/CO 2 Reduction by Cobalt Phthalocyanines

Molecular catalysts for electrochemical CO 2 reduction have traditionally been studied in their dissolved states. However, the heterogenization of molecular catalysts has the potential to deliver much higher reaction rates and enable the reduction of CO 2 by more than two electrons. In light of the recently discovered reactivity of heterogenized cobalt phthalocyanine molecules to catalyze CO 2 reduction into methanol, direct comparison is needed to uncover the distinct catalytic activity and selectivity in homogeneous catalysis versus heterogeneous catalysis. In this work, soluble cobalt phthalocyanine derivatives were synthesized, and their catalytic activities in the homogeneous solutions were evaluated. The results show that the observed catalytic activities for both CO 2 -to-CO and CO-to-methanol conversions in aqueous solutions of the cobalt phthalocyanines are predominantly heterogeneous in nature through the adsorbed species on the electrode.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Simulation of mineral dissolution at the pore scale with evolving fluid-solid interfaces: review of approaches and benchmark problem set

This manuscript presents a benchmark problem for the simulation of single-phase flow, reactive transport, and solid geometry evolution at the pore scale. The problem is organized in three parts that focus on specific aspects: flow and reactive transport (part I), dissolution-driven geometry evolution in two dimensions (part II), and an experimental validation of three-dimensional dissolution-driven geometry evolution (part III). Five codes are used to obtain the solution to this benchmark problem, including Chombo-Crunch, OpenFOAM-DBS, a lattice Boltzman code, Vortex, and dissolFoam. These codes cover a good portion of the wide range of approaches typically employed for solving pore-scale problems in the literature, including discretization methods, characterization of the fluid-solid interfaces, and methods to move these interfaces as a result of fluid-solid reactions. A short review of these approaches is given in relation to selected published studies. Results from the simulations performed by the five codes show remarkable agreement both quantitatively--based on upscaled parameters such as surface area, solid volume, and effective reaction rate--and qualitatively--based on comparisons of shape evolution. This outcome is especially notable given the disparity of approaches used by the codes. Therefore, these results establish a strong benchmark for the validation and testing of pore-scale codes developed for the simulation of flow and reactive transport with evolving geometries. They also underscore the significant advances seen in the last decade in tools and approaches for simulating this type of problem.

58 GEOSCIENCES↗

Breakthrough innovations in carbon dioxide mineralization for a sustainable future

Greenhouse gas emissions and climate change concerns have prompted worldwide initiatives to lower carbon dioxide (CO 2 ) levels and prevent them from rising in the atmosphere, thereby controlling global warming. Effective CO 2 management through carbon capture and storage is essential for safe and permanent storage, as well as synchronically meeting carbon reduction targets. Lowering CO 2 emissions through carbon utilization can develop a wide range of new businesses for energy security, material production, and sustainability. CO 2 mineralization is one of the most promising strategies for producing thermodynamically stable solid calcium or magnesium carbonates for long-term sequestration using simple chemical reactions. Current advancements in CO 2 mineralization technologies, focusing on pathways and mechanisms using different industrial solid wastes, including natural minerals as feedstocks, are briefly discussed. However, the operating costs, energy consumption, reaction rates, and material management are major barriers to the application of these technologies in CO 2 mineralization. Further, the optimization of operating parameters, tailor-made equipment, and smooth supply of waste feedstocks require more attention to make the carbon mineralization process economically and commercially viable. Here, carbonation mechanisms, technological options to expedite mineral carbonation, environmental impacts, and prospects of CO 2 mineralization technologies are critically evaluated to suggest a pathway for mitigating climate change in the future. The integration of industrial wastes and brine with the CO 2 mineralization process can unlock its potential for the development of novel chemical pathways for the synthesis of calcium or magnesium carbonates, valuable metal recovery, and contribution to sustainability goals while reducing the impact of global warming.

54 ENVIRONMENTAL SCIENCES↗

Simulations of n -dodecane/oxygen/nitrogen cellular detonations

In this work, two-dimensional n-dodecane/air/nitrogen cellular detonations are simulated with various equivalence ratios (ERs). A skeletal mechanism consisting of 54 species and 269 reactions is used. The lower and upper equivalence ratio boundaries for self-sustained detonation are 0.3 and 2.2, respectively. Detonation with different regimes characterized by the detonation cell patterns is observed, which aligns well with the category based on the stability parameter, i.e., weakly and highly unstable detonations, and extinction. Further, in terms of the frontal structure, non-negligible effect of diffusion on the cellular detonation is revealed, especially in the vicinity of the leading shock front. In highly unstable and quenched detonations, the alternation in reaction pathway within the induction zone accounts for the changes of detonation dynamics, such as the absence or extended sequence of important radical formation, e.g., OH. In addition, the composition of the unburned pockets depends on both pocket location from the leading shock front and the ER in the fresh mixture, because the former determines the residence time, whilst the latter affects the pocket reaction rate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗