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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Differences in Mechanism and Rate of Zeolite-Catalyzed Cyclohexanol Dehydration in Apolar and Aqueous Phase

The rate of acid-base catalyzed dehydration of alcohols strongly depends on the solvent and the environment of the acid sites. In this work, we find that Brønsted acidic sites in large-pore zeolites, but not in medium-pore zeolites, catalyze cyclohexanol dehydration in decalin at significantly higher rates than hydrated hydronium ions in aqueous phase. Specifically, the difference in turnover rates between the two solvents amounts to two to three orders of magnitude on H-BEA and H-FAU, while being very modest (within a factor of 2) for H-MFI. Combining kinetic, isotopic tracer and 2H NMR measurements, it is established that cyclohexanol dehydration generally follows an E1-elimination pathway in decalin. A notable exception is the monomer dehydration route on H-MFI, which exhibits a much lower activation energy and a substantially negative activation entropy that appear to be associated with an E2-type mechanism. The C-O bond cleavage displays a dominant degree of rate control in decalin, which stands in contrast to deprotonation (C-H cleavage) being rate-limiting in aqueous-phase dehydration.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Experimental Protocols for Studying Organic Non-aqueous Redox Flow Batteries

We report that Redox flow batteries (RFBs) are promising devices for grid-scale energy storage due to the decoupling of power and energy, which can be independently scaled by the electrode area and storage tank size, respectively. To date, only aqueous RFBs, such as the vanadium RFB, have been implemented commercially. Nevertheless, the limited energy densities and high-cost materials may preclude their wider market penetration. Organic non-aqueous redox-flow batteries (O-NRFBs), which utilize redox-active organic molecules (ROMs), have been offered as an attractive alternative. Many possible advantages include the use of earth-abundant elements (C, H, N, O, S, F), wherein the ROMs can be prepared from low-cost and sustainable materials. Additionally, a large variety of electroactive moieties are accessible as building blocks, providing a synthetic platform to tune the properties of ROMs through rational design. As a consequence, the development of novel ROMs has attracted researchers with diverse backgrounds, prompting remarkable innovations in the past decade. However, consistency in experimental protocols (e.g., electrochemical methods, cycling stability, experimental conditions) has not coincided with this uptick in research, leading to sometimes ambiguous and incomparable results. This is further convoluted by the complexity innate to battery development, such as cell design, detection, and characterization of reactions and active components. The O-NRFB application imposes stringent requirements on the physical or/and chemical processes involved in electrochemical cycling. Yet such considerations are often overlooked. Further, while quantum mechanical calculations provide a convenient tool for evaluating and selecting ROM candidates, this simulation is not always performed. Thus, in this Energy Focus, we detail a means to standardize experimental protocols for studies of O-NRFBs and suggest practices to facilitate fundamental understanding and development of ROMs.

25 ENERGY STORAGE↗
DOE OSTI2022

High-Performance InZn Alloy Anodes toward Practical Aqueous Zinc Batteries

Aqueous Zn batteries have high safety, low-cost and potential of delivering comparable energy density to alkali-ion batteries. However, its practical application is largely hampered by the limited cycle life associated with Zn anodes under conditions of high depth of discharge and high plating current densities. In this work, we report on electrodeposited indium-zinc alloy anodes that have well-dispersed zinc-domains surrounding indium domains that form a porous structure after dealloying which greatly improves tolerance to Zn dendrite formation. The InZn anodes exhibit low polarization of ~5 to 25 mV and demonstrate 700 cycles at a current density of ~10 mA cm -2 with a capacity of 5 mAh cm-2 capacity (45% depth-of-discharge). Full cells with an InZn anode, dibenzo[b,i]thianthrene-5,7,12,14-tetraone (DTT) cathode, in 2M ZnSO 4 deliver a capacity of ~ 110 mAh g -1 and good stability over 40 cycles. Finally, the work reveals a rational design of Zn-based anodes towards practical battery applications and opens the curtain for future development of aqueous Zn batteries.

25 ENERGY STORAGE↗
DOE OSTI2022

High Energy Density Aqueous Flow Battery Utilizing Extremely Stable, Branching-Induced High-Solubility Anthraquinone near Neutral pH

An anthraquinone featuring a chiral carboxylate-capped methyl-branched side chain with an ether linkage, 2,2'-((9,10-dioxo-9,10-dihydroanthracene-2,6-diyl)bis(oxy))dipropionic acid (2,6-D2PEAQ), was synthesized and evaluated for use in aqueous redox flow batteries. It was found to have an extraordinary solubility of 2 M (4 M electrons), corresponding to a theoretical volumetric capacity of 107.2 Ah/L for the negative electrolyte, which is 10 times that of its unbranched counterpart. The 2,6-D2PEAQ molecule demonstrated stability against thermal 2 decomposition and was extremely stable under cell cycling conditions. Here, a capacity fade rate of 0.02% day over 14 days was demonstrated in a 1.1 M 2,6-D2PEAQ nearly capacity-balanced cell when paired with a ferro-/ferricyanide posolyte at pH 7. Compared to other aqueous redoxactive organic molecules, its demonstrated fade rate is lower than that of any molecule with a demonstrated volumetric capacity of ≥55 Ah/L, and its volumetric capacity is greater than that of any molecule with a demonstrated fade rate of ≤0.5%/day.

25 ENERGY STORAGE↗
DOE OSTI2023

Fluorinated Interphase Enables Reversible Zn 2+ Storage in Aqueous ZnSO 4 Electrolytes

Aqueous zinc-ion batteries (AZIBs) using ZnSO 4 aqueous electrolytes complement Li-ion batteries and offer high safety, low cost, and scalability. However, an inferior cycle life, attributed to the generation of basic layered double hydroxides (LDHs) on the cathode during cycling, hampers the development of AZIBs. Although Zn(CF 3 SO 3 ) 2 (Zn(OTf) 2 ) electrolytes demonstrate exceptional performance, their higher cost in comparison to ZnSO 4 offsets their electrochemical stability benefits. Toward this end, we propose a fluorinated interphase strategy to achieve a stable battery with ZnSO 4 electrolytes by in situ pre-constructing the cathode-electrolyte interphase (CEI) of ZnOTf-LDH on the cathode surface. Unlike ZnSO 4 - LDH, which obstructs the diffusion channel of zinc ions, ZnOTf-LDH facilitates the desolvation of zinc ions, thereby enhancing the cycling stability (over 50 cycles at a low current density of 200 mA g -1 ). Further, this work offers valuable insights into the degradation mechanism of AZIBs and provides an effective approach for developing stable and low-cost AZIBs.

25 ENERGY STORAGE↗
DOE OSTI2017

Controlling Solid–Liquid Conversion Reactions for a Highly Reversible Aqueous Zinc–Iodine Battery

Aqueous rechargeable batteries are desirable for many energy storage applications due to their low cost and high safety. However, low capacity and short cycle life are the significant obstacles to their practical applications. Here, we demonstrate a highly reversible aqueous zinc-iodine battery using encapsulated iodine in microporous active carbon fibers (ACFs) as cathode materials through the rational control of solid-liquid conversion reactions. The experiments and density function theory (DFT) calculations were employed to investigate the effects of solvents and properties of carbon hosts, e.g. pore size, surface chemistries, on the adsorption of iodine species. The rational manipulation of the competition between the adsorption in carbon and solvation in electrolytes for iodine species is responsible for the high reversibility and cycling stability. The zinc-iodine batteries deliver a high capacity of 180 mAh g-1 at 1C and a stable cycle life over 3000 cycles with ~90% capacity retention as well as negligible self-discharge. We believe the principles for stabilizing the zinc-iodine system could provide new insight into conversion systems such as Li-S systems.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2015

Real-Time Observation of Water-Soluble Mineral Precipitation in Aqueous Solution by In Situ High-Resolution Electron Microscopy

The precipitation and dissolution of water-soluble minerals in aqueous systems is a familiar process occurring commonly in nature. Understanding mineral nucleation and growth during its precipitation is highly desirable, but past in situ techniques have suffered from limited spatial and temporal resolution. In this paper, by using in situ graphene liquid cell electron microscopy, mineral nucleation and growth processes are demonstrated in high spatial and temporal resolution. We precipitate the mineral thenardite (Na 2 SO 4 ) from aqueous solution with electron-beam-induced radiolysis of water. We demonstrate that minerals nucleate with a two-dimensional island structure on the graphene surfaces. We further reveal that mineral grains grow by grain boundary migration and grain rotation. Finally, our findings provide a direct observation of the dynamics of crystal growth from ionic solutions.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Spin State Modulation via Magnetic Fields in Fe Single Atom Catalysts for High-Performance Aqueous Zinc–Sulfur Batteries

Aqueous zinc–sulfur battery has garnered significant attention as a high-energy, low-cost, and safe energy storage system. However, the multielectron transfer kinetics of sulfur cathodes are relatively slow, presenting challenges such as limited sulfur utilization and lower discharge voltage, which significantly hinder their practical applications. Here, in this study, we explored a comprehensive design approach for high-performance, long-cycle aqueous zinc–sulfur batteries. The simultaneous introduction of ZnI 2 and Fe single atoms (Fe-SAs) as catalytically active agents decouples the redox reactions, effectively facilitating ZnS oxidation and S reduction separately. The application of an external magnetic field regulates the spin state of Fe-SAs, further enhancing their catalytic activity and electron transfer capability. Electrochemical tests demonstrate that the S@Fe-NC HS/ZnI 2 cathode assembled under a magnetic field exhibits excellent rate performance, achieving an impressive specific capacity of 1399 mAh g –1 at a high current density of 5 A g –1 and good cycling stability over 300 cycles, representing the highest reported high-current discharge capacity to date. This study provides a comprehensive design framework for optimizing zinc–sulfur (Zn–S) battery performance and elucidates the influence of magnetic field-induced spin state modulation on catalytic behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2012

Thermodynamic Oxidation and Reduction Potentials of Photocatalytic Semiconductors in Aqueous Solution

An approach is introduced to calculate the thermodynamic oxidation and reduction potentials of semiconductors in aqueous solution. Here, by combining a newly developed ab initio calculation method for compound formation energy and band alignment with electrochemistry experimental data, this approach can be used to predict the stability of almost any compound semiconductor in aqueous solution. Thirty photocatalytic semiconductors have been studied, and a graph (a simplified Pourbaix diagram) showing their valence/conduction band edges and oxidation/reduction potentials relative to the water redox potentials is produced. On the basis of this graph, the thermodynamic stabilities and trends against the oxidative and reductive photocorrosion for compound semiconductors are analyzed, which shows the following: (i) some metal oxides can be resistant against the oxidation by the photogenerated holes when used as the n-type photoanodes; (ii) all the nonoxide semiconductors are susceptible to oxidation, but they are resistant to the reduction by the photogenerated electrons and thus can be used as the p-type photocathodes if protected from the oxidation; (iii) doping or alloying the metal oxide with less electronegative anions can decrease the band gap but also degrade the stability against oxidation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Changing Hafnium Speciation in Aqueous Sulfate Solutions: A High-Energy X-ray Scattering Study

The relationship of solution speciation and the structures of corresponding precipitates is examined for an aqueous Hf4+ . sulfate series. High-energy X-ray scattering (HEXS) and Raman spectroscopy data are used to probe atomic correlations in solutions. Hf4+ in acidic perchlorate solution shows no evidence of a mononuclear metal species but instead has a peak in the pair-distribution function (PDF), generated from the HEXS data, at 3.55 angstrom, indicating Hf4+- Hf4+ solution correlations. The peak intensity is consistent with clusters that are, on average, larger than the tetramic unit [M-4(OH)(8)(H2O)(16)](8+) usually attributed to Zr4+ and Hf4+ solution speciation under these conditions. Addition of sulfate results in a breakup of hydroxo-bridged oligomers into sulfate-capped dimers and, for higher concentrations, Hf-sulfate monomers. The bidentate coordination mode of sulfate dominates the dissolved precursors, although it is not found in the structure of the final crystallized product, which instead is comprised of bridging-bidentate sulfate ligation. Neither the PDF patterns nor the Raman spectra show any evidence of the larger oligomers, such as the octadecameric metal clusters, found in similar Zr4+ solutions. The oligomeric units found in solution provide insights into possible assembly routes for crystallization. In addition to expanding our understanding of synthesis science this study also reveals differences in the aqueous chemistries between Hf and Zr, two elements with ostensibly very similar chemical behavior.

hafnium sulfate solutions↗
DOE OSTI2014

EXAFS Study of the Speciation of Protactinium(V) in Aqueous Hydrofluoric Acid Solutions

The speciation of protactinium(V) in hydrofluoric acid (HF) solutions was studied using X-ray absorption spectroscopy. Extended X-ray absorption fine structure measurements were performed on an aqueous solution of 0.05 M protactinium(V) with various HF concentrations ranging from 0.5 to 27 M in order to probe the protactinium coordination sphere with respect to the identity and number of coordinating ligands. The resulting fits to the spectra suggest the presence of an eight-coordinate homoleptic fluoro complex in highly concentrated fluoride solutions (27 M), with equilibrium between seven- and eight-coordinate fluoro complexes at moderate acidities, and in more dilute solutions, results indicate that one water molecule is likely to replace a fluoride in the first coordination sphere, at a distance of 2.54-2.57 angstrom. Comparisons of this chemistry with group V metals, niobium and tantalum, are presented, and the potential implications for these results on the hydrolytic behavior of protactinium in aqueous systems are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Mechanistic studies of hydrogen evolution in aqueous solution catalyzed by a tertpyridine-amine cobalt complex

The ability of cobalt-based transition metal complexes to catalyze electrochemical proton reduction to produce molecular hydrogen has resulted in a large number of mechanistic studies involving various cobalt complexes. In addition, while the basic mechanism of proton reduction promoted by cobalt species is well understood, the reactivity of certain reaction intermediates, such as Co I and Co III –H, is still relatively unknown owing to their transient nature, especially in aqueous media. In this work we investigate the properties of intermediates produced during catalytic proton reduction in aqueous solutions promoted by the [(DPA-Bpy)Co(OH₂)] n+ (DPA-Bpy = N,N -bis(2-pyridinylmethyl)-2,20-bipyridine-6-methanamine) complex ([Co(L)(OH₂)] n+ where L is the pentadentate DPA-Bpy ligand or [ Co (OH₂)] n+ as a shorthand). Experimental results based on transient pulse radiolysis and laser flash photolysis methods, together with electrochemical studies and supported by DFT calculations indicate that, while the water ligand is strongly coordinated to the metal center in the oxidation state 3+, one-electron reduction of the complex to form a Co II species results in weakening the Co–O bond. The further reduction to a Co I species leads to the loss of the aqua ligand and the formation of [ Co I –VS)]⁺ (VS = vacant site). Interestingly, DFT calculations also predict the existence of a [Co I (κ⁴-L)(OH₂)]⁺ species at least transiently, and its formation is consistent with the experimental Pourbaix diagram. Both electrochemical and kinetics results indicate that the Co I species must undergo some structural change prior to accepting the proton, and this transformation represents the rate-determining step (RDS) in the overall formation of [ Co III –H]⁺. We propose that this RDS may originate from the slow removal of a solvent ligand in the intermediate [Co I (κ⁴-L)(OH₂)]⁺ in addition to the significant structural reorganization of the metal complex and surrounding solvent resulting in a high free energy of activation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Architecting a Stable High-Energy Aqueous Al-Ion Battery

Aqueous Al-ion batteries (AAIBs) are the subject of great interest due to the inherent safety and high theoretical capacity of aluminum. The high abundancy and easy accessibility of aluminum raw materials further make AAIBs appealing for grid-scale energy storage. However, the passivating oxide film formation and hydrogen side reactions at the aluminum anode as well as limited availability of the cathode lead to low discharge voltage and poor cycling stability. Here, we proposed a new AAIB system consisting of an Al x MnO 2 cathode, a zinc substrate-supported Zn-Al alloy anode, and an Al(OTF) 3 aqueous electrolyte. Through the in situ electrochemical activation of MnO, the cathode was synthesized to incorporate a two-electron reaction, thus enabling its high theoretical capacity. The anode was realized by a simple deposition process of Al 3+ onto Zn foil substrate. The featured alloy interface layer can effectively alleviate the passivation and suppress the dendrite growth, ensuring ultralong-term stable aluminum stripping/plating. The architected cell delivers a record-high discharge voltage plateau near 1.6 V and specific capacity of 460 mAh g -1 for over 80 cycles. Finally, this work provides new opportunities for the development of high-performance and low-cost AAIBs for practical applications.

25 ENERGY STORAGE↗
DOE OSTI2025

Electrocatalytic Reductive Amination of Aldehydes and Ketones with Aqueous Nitrite

The electrocatalytic utilization of oxidized nitrogen waste for C–N coupling chemistry is an exciting research area with great potential to be adopted as a sustainable method for generation of organonitrogen molecules. The most widely used C–N coupling reaction is reductive amination. In this work, we develop an alternative electrochemical reductive amination reaction that can proceed in neutral aqueous electrolyte with nitrite as the nitrogenous reactant and via an oxime intermediate. We develop a selection criterion for nitrite reduction electrocatalysts suited for oxime electrosynthesis and, in doing so, find Pd to be a highly efficient catalyst for this reaction, reaching an oxime Faradaic efficiency of 82% at −0.21 V vs the reversible hydrogen electrode. The aliphatic or aromatic structure of the carbonyl reactant impacts the efficacy of the catalyst, with aromatic substrates leading to suppressed oxime formation and detrimental reduction of the carbonyl to the alcohol. We developed a Pb/PbO electrocatalyst that selectively performs oxime reduction in the neutral aqueous electrolyte. With acetone as a model substrate, we demonstrate an efficient one-pot, two-step electrochemical reaction for the conversion of acetone to isopropyl amine with 85% yield and 50% global Faradaic efficiency.

catalysts↗
DOE OSTI2015

Titania-catalyzed radiofluorination of tosylated precursors in highly aqueous medium

Nucleophilic radiofluorination is an efficient synthetic route to many positron-emission tomography (PET) probes, but removal of water to activate the cyclotron-produced [ 18 F]fluoride has to be performed prior to reaction, which significantly increases overall radiolabeling time and causes radioactivity loss. In this paper, we demonstrate the possibility of 18 F-radiofluorination in highly aqueous medium. The method utilizes titania nanoparticles, 1:1 (v/v) acetonitrile–thexyl alcohol solvent mixture, and tetra-n-butylammonium bicarbonate as a phase-transfer agent. Efficient radiolabeling is directly performed with aqueous [ 18 F]fluoride without the need for a drying/azeotroping step to significantly reduce radiosynthesis time. High radiochemical purity of the target compound is also achieved. Finally, the substrate scope of the synthetic strategy is demonstrated with a range of aromatic, aliphatic, and cycloaliphatic tosylated precursors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Electrodepositing Textured Sn Film as a Highly Reversible Anode for Aqueous Batteries

Electrodepositing metal materials in large capacity, at low potential, and with high reversibility serves as the foundation for any aqueous rechargeable battery chemistry to realize the promises of high energy, low cost, and high safety. However, such a foundation is not solid because of the natural tendency of metals to form irregular, nonplanar, and often dendritic morphologies during electrochemical crystallization, which is further amplified in an acidic environment due to the faster kinetics of the coupled proton and mass-transport processes between hydrated metal ions and free metal atoms. As a typical representative, tin metal (Sn 0 ) has potential to achieve high energy in acidic batteries, but its nonuniform large-particle morphology, obtained from traditional electrodeposition, leads to dead Sn 0 formation and deteriorating reversibility, accompanied by the sustained hydrogen evolution reaction (HER) and active Sn 0 loss. Here, in this study, we report quaternary onium salts as effective interfacial cocations that, via selective adsorption, steadily texturize Sn 0 deposition along the (211) plane, which is intrinsically inert to the HER, thus regulating the film deposition process by favoring the formation of planar Sn 0 film. Such Sn 0 film brings exceptional reversibility in acidic electrolytes, which translates into sustained cycling stability at applicable areal capacities in both anode-half cells (similar to 1500 deposition/dissolution cycles at 5 mAh cm -2 ) and full cells (350 charge/discharge cycles at 5 mAh cm -2 ). Textured electrodeposition with intrinsic HER-suppression capability provides a universal solution for diverse metal anode materials in rechargeable energy-dense aqueous batteries.

Sn metal↗
DOE OSTI2025

Probing the Mechanism of Selective Phosphate Adsorption from Wastewater Using Aqueous and Synchrotron X-ray Characterization

Ion exchange shows promise for recovering phosphate from wastewater as value-added products, but requires high phosphate selectivity to compete with conventional treatment. Hybrid anion exchange (HAIX) resins, which contain non-selective basic functional groups and selective iron oxide nanoparticles (FeOnp), can effectively remove phosphate from wastewater. However, knowledge gaps remain regarding the mechanisms of phosphate selectivity and influence of competing ions, hindering needed efforts to model adsorption dynamics and design scalable adsorption processes for varying wastewaters. To address these gaps, we integrated aqueous-phase adsorption analysis with solid-phase, synchrotron-based X-ray characterization; this integration facilitated elucidation of the distribution and speciation of iron, phosphate, and competing anions on HAIX resins. We compared a quaternary ammonium-functionalized HAIX resin (SBA) to a tertiary amine version (WBA) to determine the role of functional groups. X-ray radiography revealed differences in FeOnp speciation (goethite vs. ferrihydrite) and distribution (peripheral vs. homogeneous) between the resins, resulting in varied phosphate affinity and intraparticle diffusion resistance. Using micro-X-ray fluorescence (μ-XRF) and micro-X-ray absorption near-edge structure (μ-XANES) spectroscopy, we identified differences in where and how phosphate binds across resin types and wastewaters. Across wastewater compositions, FeOnp sites in WBA contribute more to phosphate adsorption than in SBA, possibly due to variations in Fe distribution and speciation. Phosphate adsorption densities calculated from quantitative μ-XRF maps matched those from aqueous analysis, demonstrating the effectiveness of this integrated approach. Altogether, results demonstrate the use of synchrotron-based X-ray characterization for investigating adsorption mechanisms and advance HAIX as a phosphate recovery technology from complex wastewaters.

Nutrient recovery↗
DOE OSTI2018

Carbon Dioxide Dimer Radical Anion as Surface Intermediate of Photoinduced CO 2 Reduction at Aqueous Cu and CdSe Nanoparticle Catalysts by Rapid-Scan FT-IR Spectroscopy

Monitoring of visible light sensitized reduction of CO 2 at Cu nanoparticles in aqueous solution by rapid-scan ATR FT-IR spectroscopy on the time scale of seconds allowed structural identification of a one-electron intermediate and demonstrated its kinetic relevancy for the first time. Isotopic labeling ( 12 C: 1632, 1358, 1346 cm -1 ; 13 C: 1588, 1326, 1316 cm -1 ) revealed a species of carbon dioxide dimer radical anion structure, most likely bound to the catalyst surface through carbon. Intermediacy of Cu—C(═O)OCO 2 - surface species is in agreement with a recently proposed mechanism for electrocatalytic CO 2 reduction at Cu metal nanoparticles based on Tafel slope analysis. Spontaneous decrease of the intermediate after termination of the photosensitization pulse (Sn porphyrin excited at 405 nm) was accompanied by the growth of HCO 3 - . CO was produced as well, but sensitive detection required photolysis for tens of minutes. A direct kinetic link between a C 2 O 4 - surface intermediate and the CO product was also demonstrated for photocatalyzed CO 2 reduction at aqueous CdSe nanoparticles, where first order growth of a Cd—C(═O)OCO 2 - species was accompanied by rise of CO (monitored by a fast Ni complex trap) and HCO 3 - showing a distinct induction period. The detection of the one-electron surface intermediate and confirmation of its catalytic relevancy was enabled by the delivery of electrons one-by-one by the photosensitization method. The observation of carbon dioxide dimer radical anion points to approaches for rate enhancements of heterogeneous CO 2 reduction by creating catalytic environments that favor formation of this intermediate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗