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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Cryogenic and Temperature-Dependent Photoelectron Spectroscopy of Metal Complexes

Negative ion photoelectron spectroscopy (NIPES) coupled with electrospray ionization (ESI) has been proved to be a powerful gas-phase spectroscopic tool for characterizing electronic structures and chemical bonding of a variety of cluster anions and corresponding neutral radicals involved in the condensed phase reactions and transformations. Since the acquisition of cryogenic and temperature-controlling capabilities, broader range of research scope has been covered. This review summarizes our recent investigations on metal complexes employing cryogenic ESI-NIPES that provide us essential information towards understanding complicated condensed phase reactions including hydrocarbon activations and electron transfer reactions, and afford us spectroscopic probe of highly reactive transient species and intimate redox pairs. Special attention has been drawn to connect gas phase photodetachment processes with solution phase redox reactions. Photodetachment of transition metal-EDTA complexes has been systematically investigated to model the sequential oxidation reactions of these species in solutions. The obtained gas phase electron affinity (EA) is compared with the solution redox potential (E1/2) and the metal ionization potential (IP) for several series of homologous metal complexes to emphasize their intrinsic correlations with deviations being largely modulated by different degrees of ligand participations.

Yuan, Qinqin↗
DOE OSTI2020

Anomalously high elastic modulus of a poly(ethylene oxide)-based composite electrolyte

The practical use of lithium metal anodes in solid-state batteries requires a polymer membrane with high lithium-ion conductivity, thermal/electrochemical stability, and mechanical strength. The primary challenge is to effectively decouple the ionic conductivity and mechanical strength of the polymer electrolytes. We report a remarkably facile single step synthetic strategy based on in-situ crosslinking of poly(ethylene oxide) (xPEO) in the presence of a woven glass fiber (GF). Such a simple method yields composite polymer electrolytes (CPE) of anomalously high elastic modulus up to 2.5 GPa over a broad temperature range (20 °C – 245 °C) that has never been previously documented. An unsupervised machine learning algorithm, K-mean clustering analysis, was implemented on the hyperspectral Raman mapping at the xPEO/GF interface. Using such a unique means, we show for the first time that the promoted mechanical strength originates from xPEO and GF interactions through dynamic hydrogen and ionic bonding. High ionic conductivity is achieved by the addition plasticizer (e.g. tetraglyme), where trifluoromethanesulfonate anions are tethered to the xPEO matrix and Li + cations are favorably transported through coordination with the plasticizer. Further, stringent galvanostatic cycling tests indicates the CPE can be stably cycled for >3000 h in a Li-metal symmetric cell at a moderate temperature (nearly 1500 Coulombs/cm 2 Li equivalents), outperforming most of the PEO-based electrolytes. The GF reinforced CPE reported here has multifunctional uses, such as solid electrolytes for all solid-state batteries and membranes for redox-flow batteries. Although the focus of this study is on lithium-based batteries, the results are equally promising for other alkali metal based batteries such as sodium and potassium.

25 ENERGY STORAGE↗
DOE OSTI2024

Controlling Ion Uptake in Carboxylated Mixed Conductors

Organic mixed ionic‐electronic conductors (OMIECs) have garnered significant attention due to their capacity to transport both ions and electrons, making them ideal for applications in energy storage, neuromorphics, and bioelectronics. However, charge compensation mechanisms during the polymer redox process remain poorly understood, and are often oversimplified as single‐ion injection with little attention to counterion effects. To advance understanding and design strategies toward next‐generation OMIEC systems, a series of p‐channel carboxylated mixed conductors is investigated. Varying side‐chain functionality, distinctive swelling character is uncovered during electrochemical doping/dedoping with model chao‐/kosmotropic electrolytes. Carboxylic acid functionalized polymers demonstrate strong deswelling and mass reduction during doping, indicating cation expulsion, while ethoxycarbonyl counterparts exhibit prominent mass increase, pointing to an anion‐driven doping mechanism. By employing operando grazing incidence X‐ray fluorescence (GIXRF), it is revealed that the carboxyl functionalized polymer engages in robust cation interaction, whereas ester functionalization shifts the mechanism towards no cation involvement. It is demonstrated that cations are pivotal in mitigating swelling by counterbalancing anions, enabling efficient anion uptake without compromising performance. These findings underscore the transformative influence of functionality‐driven factors and side‐chain chemistry in governing ion dynamics and conduction, providing new frameworks for designing OMIECs with enhanced performance and reduced swelling.

carboxylated polythiophenes↗
DOE OSTI2026

Ozonolysis of selenium: an alternative oxidation method for radiochemical separations of arsenic and selenium

Many arsenic and selenium radiochemical separation methods use hydrogen peroxide (H 2 O 2 ) to oxidize selenite (Se(IV)) to selenate (Se(VI)), but this reaction is challenging to control and replicate. Here, this study introduces a simple ozonolysis apparatus with an in-line oxygen-ozone generator and impinger system for rapid selenium oxidation in aqueous samples as an alternative to H 2 O 2 . The system quickly converts Se(IV) to Se(VI), enabling successful separations of arsenic-73 and selenium-75 with high recoveries using ion-exchange chromatography (1-X8). Compared to traditional H 2 O2 treatment, ozone oxidation is a faster and more easily controlled method for selenium redox chemistry.

and nuclear chemistry↗
DOE OSTI2023

Electronic Rearrangement in Steps of Reductive Elimination of Polar Electrophiles Leads to Refinement of Redox Events

The oxidative addition/reductive elimination of polar molecules such as methyl iodide at late metal centers has a strongly supported $S_{N^2}$ mechanism for many key organometallic complexes, including important industrial catalysts. In the reductive elimination direction, it is proposed that a ligand initially dissociates, typically a halide, followed by subsequent nucleophilic attack at the ligand trans to the now vacant site. The prevailing view is the metal reduction occurs upon transferring the electrophile in the $S_{N^2}$ step. Herein, we report the use of an ensemble of computational techniques to characterize the electronic structure of the reactants and intermediates along this reductive elimination pathway. These calculations demonstrate, unexpectedly, that the initiating loss of an anionic ligand from the octahedral highly oxidized structure leads to an electronic rearrangement that shifts electron density from the apical ligand back toward the metal resulting in an inversion of the electron flow between the metal and apical ligand. The anisotropic shift in electron density to the metal disproportionately affects the apical position, which is best described as a Pt → Me dative bond. With this Pt → Me bonding description, our interpretation of the IUPAC oxidation state formalism would assign the intermediate as Pt ΙΙ . Although counterintuitive, the formal and functional reduction of the metal thus occurs upon halide dissociation.

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

Sulfur-functionalized solid-phase materials for the selective separation of arsenic and selenium

Radioactive arsenic (As) isotopes are of growing interest for applications in nuclear medicine, national security, and environmental research. Recent efforts at the Facility for Rare Isotope Beams (FRIB) have focused on aqueous harvesting of selenium-72,73 ( 72,73 Se) and their daughter isotopes, arsenic-72,73 ( 72,73 As), which are particularly valuable for medical applications and nuclear data studies, respectively. Both conventional isotope production and harvesting methods require chemical separations to purify radioactive As from parent and co-produced Se radioisotopes. While several solid-phase separation methods for As and Se exist, many depend on complex oxidation state control or highly acidic conditions. This study presents results for sulfur-based solid-phase materials selected to enable uptake at lower acidity and eliminate the need for intricate redox chemistry. Specifically, the performance of three covalently bound sulfur-based ligands were evaluated: (1) thiophenol-polystyrene, (2) propanethiol-silica, and (3) thiourea-silica. Uptake characteristics—including distribution coefficients (Dw), kinetics, and column separation behavior—were assessed using 75 Se and 73 As in hydrochloric (HCl) acid and nitric (HNO 3 ) solutions. The resins demonstrated high-yield (>95%) and high-purity As recovery across a range of HCl concentrations. Comparable results in HNO 3 were achieved when combined with anion exchange chromatography. Furthermore, the potential application of these materials for medical isotope generators was also investigated through ligand stability and repeated elution studies. Overall, sulfur leaching from the resins was negligible at the concentrations relevant for these separations but increased with higher acid concentrations.

Arsenic↗
DOE OSTI2021

Measuring Electronic Structure of Multiply Charged Anions to Understand their Chemistry: A Case Study on Gaseous Polyhedral closo-Borate Dianions

Research on multiply charged anions (MCAs) in the gas phase has been intensively performed during the last decades, mainly to understand fundamental molecular physics phenomena, e.g., intramolecular Coulomb repulsion and existence of the repulsive Coulomb barrier. However, the relevance of these investigations with respect to understanding MCAs’ chemistry appears often vague. Here, we discuss how insights on the electronic structure obtained from negative ion photoelectron spectroscopy (NIPES) combined with theoretical calculations and collision induced dissociation can provide fundamental understanding on the intrinsic chemical reactivity of MCAs and their fragments. This is exemplified on our studies on polyhedral closo-borate dianions [BnXn]2- (n = 6, 10, 11, 12; X = H, F-I, CN) and their fragment ions. For example, the rational design of closo-borate dianions with specific electronic properties is described, which leads to generating highly reactive fragments. Depending on the dianionic precursor, these fragments are either tuned to bind noble gases effectively or to activate small molecules like CO and N2. The intrinsic electronic properties of closo-borate dianions are further compared to their electrochemistry in solutions, revealing solvent effects on the redox potentials. Neutral host molecules such as cyclodextrins are found to bind strongly to [BnXn]2-, and gas phase NIPES provides insights on the intrinsic host-guest interactions. Finally, outlooks including the direct NIPES of molecular fragment ions which cannot be generated in the condensed phase and their utilization in preparative mass spectrometry are discussed. J.W is grateful to the Volkswagen foundation for a Freigeist Fellowship. X. B. W acknowledges support from the U.S. Department of Energy (DOE), Office of Science, Office of Basic Energy Sciences, the Division of Chemical Sciences, Geosciences and Biosciences. We are grateful to our colleagues who support our work on gas phase ion chemistry for many years. In particular we acknowledge the members of our groups, the Asmis group (Leipzig), Laskin Group (West Lafayette), the Jenne group (Wuppertal), the Finze group (Würzburg), the Grabowsky group (Bern), and the Sun group (Shanghai). We are grateful to Edoardo Apra for the many theoretical investigations on closo-borate anions. JW acknowledges support of Harald Knorke and Markus Rohdenburg with the preparation of graphical material, and XBW thanks Qinqin Yuan for the help in organizing references.

Warneke, Jonas↗
DOE OSTI2021

A low-cost sulfate-based all iron redox flow battery

Redox flow batteries (RFBs) are promising choices for stationary electric energy storage. Nevertheless, commercialization is impeded by high-cost electrolyte and membrane materials. Here, we report a low-cost all-iron RFB that features inexpensive FeSO 4 electrolytes, microporous membrane along with a glass fiber separator. The addition of 0.1 м 1-ethyl-3-methylimidazolium chloride (EMIC) overcomes the low solubility of FeSO 4 in water which is raised to 2.2 м. DFT calculations demonstrate that EMI + can strengthen the interaction between sulfate anions and water molecules. This electrolyte composition also allows both anode and cathode reactions to operate without actively maintaining a pH gradient between them, thus eliminating the need for expensive ion exchange membranes. The all-iron RFB demonstrates stable operation at a current density of 20 mA cm –2 for more than 800 cycles via a simple, periodic regeneration process. Furthermore, the system cost of FeSO 4 /EMIC RFBs is projected to be $ 50 per kWh due to its low-cost active materials and the inexpensive microporous membrane. Finally, this low-cost, high-concentration all-iron RFB is a promising stationary energy–storage system for storing renewable energy.

25 ENERGY STORAGE↗
DOE OSTI2025

Lewis Acidity of the SbCl 3 / o ‐chloranil System

Abstract While SbCl 3 is typically inert toward oxidation by ortho ‐quinones, we use o ‐chloranil to show that the outcome of such reactions may be altered by the presence of a donor such as triphenylphosphine oxide, which readily traps the SbCl 3 (cat Cl ) synthon (cat Cl = tetrachlorocatecholate) in the form of the corresponding adduct Ph 3 PO→SbCl 3 (cat Cl ). The same reaction in the presence of a chloride salt affords the corresponding antimonate anion [Cl 4 Sb(cat Cl )] − . Computational studies indicate that the putative SbCl 3 (cat Cl ) synthon has a higher chloride ion affinity than SbCl 5 , suggesting significant Lewis acidity. This property is further demonstrated by the use of the SbCl 3 / o ‐chloranil system for both THF polymerization and a Friedel–Crafts‐type alkylation of benzene using 1‐fluorooctane. Finally, the reaction of E ‐stilbene with o ‐chloranil in the presence of SbCl 3 affords the corresponding benzodioxene, suggesting that SbCl 3 may also operate as a redox‐active catalyst.

Şit, Ferit [Department of Chemistry Texas A&amp,M ↗
DOE OSTI2021

Realizing continuous cation order-to-disorder tuning in a class of high-energy spinel-type Li-ion cathodes

Conventional Li-ion cathode materials are dominated by well-ordered structures, in which Li and transition metals occupy distinct crystallographic sites. Here, we show in this paper that profoundly new degrees of freedom for the optimization of electrochemical properties may be accessed if controllable cation disorder is introduced. In a class of high-capacity spinel-type cathode materials, we identify cation to anion ratio in synthesis as a key parameter for tuning the structure continuously from a well-ordered spinel, through a partially ordered spinel, to rocksalt. We find that the varying degree of cation disorder modifies the voltage profile, rate capability, and charge-compensation mechanism in a rational and predictable way. Our results indicate that spinel-type order is most beneficial for achieving high-rate performance as long as the cooperative 8a to 16c phase transition is suppressed, while more rocksalt-like disorder facilitates O redox, which can increase capacity. Our findings reveal an important tuning handle for achieving high energy and power in the vast space of partially ordered cathode materials.

25 ENERGY STORAGE↗
DOE OSTI2020

A Single Small-Scale Plutonium Redox Reaction System Yields Three Crystallographically-Characterizable Organoplutonium Complexes

Here, an approach to obtaining substantial amounts of data from a hazardous starting material that can only be obtained and handled in small quantities is demonstrated by the investigation of a single small-scale reaction of cyclooctatetraene, C 8 H 8 , with a solution obtained from the reduction of Cp' 3 Pu (Cp' = C 5 H 4 SiMe 3 ) with potassium graphite. This one reaction coupled with oxidation of a product has provided single-crystal X-ray structural data on three organoplutonium compounds as well as information on redox chemistry thereby demonstrating an efficient route to new reactivity and structural information on this highly radioactive element. The crystal structures were obtained from the reduction of C 8 H 8 by a putative Pu(II) complex, (Cp' 3 Pu II ) 1– , generated in situ, to form the Pu(III) cyclooctatetraenide complex, [K(crypt)][(C 8 H 8 ) 2 Pu III ], 1-Pu , and the tetra(cyclopentadienyl) Pu(III) complex, [K(crypt)][Cp' 4 Pu III ], 2-Pu . Oxidation of the sample of 1-Pu with Ag(I) afforded a third organoplutonium complex that has been structurally characterized for the first time, (C 8 H 8 ) 2 Pu IV , 3-Pu . Complexes 1-Pu and 3-Pu contain Pu sandwiched between parallel (C 8 H 8 ) 2– rings. The (Cp' 4 Pu III ) – anion in 2-Pu features three η 5 -Cp' rings and one η 1 -Cp' ring, which is a rare example of a formal Pu–C η 1 -bond. In addition, this study addresses the challenge of small-scale synthesis imparted by radiological and material availability of transuranium isotopes, in particular that of pure metal samples. A route to an anhydrous Pu(III) starting material from the more readily available Pu IV O 2 was developed to facilitate reproducible syntheses and allow complete spectroscopic analysis of 1-Pu and 2-Pu . Pu IV O 2 was converted to Pu III Br 3 (DME) 2 (DME = CH 3 OCH 2 CH 2 OCH 3 ) and subsequently Pu III Br 3 (THF) x , which was used to independently synthesize 1-Pu , 2-Pu , and 3-Pu .

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2022

Fluorination‐Enhanced Surface Stability of Disordered Rocksalt Cathodes

Abstract Cation‐disordered rocksalt (DRX) oxides are a promising new class of high‐energy‐density cathode materials for next‐generation Li‐ion batteries. However, their capacity fade presents a major challenge. Partial fluorine (F) substitution into the oxygen (O) lattice appears to be an effective strategy for improving the cycling stability, but the underlying atomistic mechanism remains elusive. Here, using a combination of advanced transmission electron microscopy based imaging and spectroscopy techniques, the structural and chemical evolution upon cycling of Mn‐based DRX cathodes with an increasing F content (Li–Mn–Nb–O–F x , x = 0, 0.05, 0.2) are probed. The atomic origin behind the beneficial effect of high‐level fluorination for enhancing the surface stability of the DRX is revealed. It is discovered that, due to the reduced O redox activity while with increasing F concentration, F in the DRX lattice mitigates the formation of an O‐deficient surface layer upon cycling. For low F‐substituted DRX, the O loss near the surface results in the formation of an amorphous cathode–electrolyte interphase layer and nanoscale voids after extended cycling. Increased F concentration in the DRX lattice minimizes both O loss and the interfacial reactions between DRX and the liquid electrolyte, enhancing the surface stability of DRX. These results provide guidance on the development of next‐generation cathode materials through anion substitution.

Li, Linze↗
DOE OSTI2025

Lewis Acidity of the SbCl 3 /o-chloranil System

While SbCl 3 is typically inert toward oxidation by ortho-quinones, we use o-chloranil to show that the outcome of such reactions may be altered by the presence of a donor such as triphenylphosphine oxide, which readily traps the SbCl 3 (cat Cl ) synthon (cat Cl = tetrachlorocatecholate) in the form of the corresponding adduct Ph 3 PO→SbCl 3 (cat Cl ). The same reaction in the presence of a chloride salt affords the corresponding antimonate anion [Cl 4 Sb(cat Cl )] − . Computational studies indicate that the putative SbCl 3 (cat Cl ) synthon has a higher chloride ion affinity than SbCl 5 , suggesting significant Lewis acidity. This property is further demonstrated by the use of the SbCl 3 /o-chloranil system for both THF polymerization and a Friedel–Crafts-type alkylation of benzene using 1-fluorooctane. Finally, the reaction of E-stilbene with o-chloranil in the presence of SbCl 3 affords the corresponding benzodioxene, suggesting that SbCl 3 may also operate as a redox-active catalyst.

Antimony↗
DOE OSTI2021

Long-Term Structural and Chemical Stability of Carbon Electrodes in Vanadium Redox Flow Battery

Predicting the performance decay in carbon electrodes is critical to maximizing the longevity of redox flow battery (RFB) systems. This study investigates the effect of long-term cycling (over 8000 cycles) on the structural and chemical evolution of carbon electrodes. We find that the microstructural aspects such as graphitic stacking order and interlayer spacing along with overall morphological construct remains largely unchanged even after the prolonged cycling process. Conversely, significant changes in surface chemistry such as evolution of functional groups and point defects are evident from our combined multimodal spectroscopic and computational analysis. The XPS and FTIR analysis reveals chemical absorption of chloride counter anions at point defects within graphitic surface. Additionally, our results suggest that vanadium cation plays an important role in counter anion-carbon surface interaction and subsequently the surface chemistry evolutions. Our findings provide insights about surface chemical evolution that is critical for predicting electrode performance and longevity of RFB.

Modachur Sivakumar, Bhuvaneswari↗
DOE OSTI2022

Effective Storage of Electrons in Water by the Formation of Highly Reduced Polyoxometalate Clusters

Aqueous solutions of polyoxometalates (POMs) have been shown to have potential as high-capacity energy storage materials due to their potential for multi-electron redox processes, yet the mechanism of reduction and practical limits are currently unknown. Herein, we explore the mechanism of multi-electron redox processes that allow the highly reduced POM clusters of the form {MO 3 } y to absorb y electrons in aqueous solution, focusing mechanistically on the Wells-Dawson structure X 6 [P 2 W 18 O 62 ], which comprises 18 metal centers and can uptake up to 18 electrons reversibly (y = 18) per cluster in aqueous solution when the countercations are lithium. This unconventional redox activity is rationalized by density functional theory, molecular dynamics simulations, UV-vis, electron paramagnetic resonance spectroscopy, and small-angle X-ray scattering spectra. These data point to a new phenomenon showing that cluster protonation and aggregation allow the formation of highly electron-rich meta-stable systems in aqueous solution, which produce H 2 when the solution is diluted. Finally, we show that this understanding is transferrable to other salts of [P 5 W 30 O 110 ] 15- and [P 8 W 48 O 184 ] 40- anions, which can be charged to 23 and 27 electrons per cluster, respectively.

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

The influence of protein electrostatics on potential inversion in flavoproteins

Biology uses relatively few electron-transfer cofactors, tuning their potentials, electronic couplings, and reorganization energies to carry out the required chemistry. It is remarkable that the potential ordering of two-electron transfer active flavins can be normal (first oxidation at low potential and second oxidation at high potential) or inverted, and the gap between the potentials can be as large as one volt. Analysis based on structural bioinformatics and electrostatics indicates that the ordering of the flavin redox potential is influenced by protein electrostatics. In all 36 flavoproteins examined, the introduction of a negative charge near the flavin in silico increases the extent of potential inversion (by lowering the electrochemical potential of the second electron-transfer step); the introduction of a positive charge near the flavin favors normally ordered potentials. We also find that the addition of positive charges increases the electrochemical potential for the naturally occurring one-electron transition in flavodoxins (between deprotonated hydroquinone and neutral semiquinone) and also increases the second one-electron transition in bifurcating flavins (between anionic semiquinone and fully oxidized flavin). Finally, we find that proximity of a proton acceptor, notably conserved arginine, supports proton-coupled electron transfer because it may act as a proton acceptor, promoting potential inversion. This key arginine residue may enable two-electron transfer chemistry by promoting the proton-coupled electron transfer process over the pure electron transfer process, suggesting how a protein's flavin environment may influence one- or two-electron chemistry in flavoproteins.

Singh, Niven [Duke Univ., Durham, NC (United State↗
DOE OSTI2020

Effect of TiO x Substrate Interactions on the Electrocatalytic Oxygen Reduction Reaction at Au Nanoparticles

Here, we report a robust model for studying electrocatalytic reactions at metal nanoparticles (NPs) in contact with metal oxide surfaces. The metal oxide layer (TiO x ) is prepared by atomic layer deposition, and it is sufficiently thin that it does not hinder electron transfer from the underlying conductive electrode to the supported AuNP electrocatalysts. In advance of the experiments, density functional theory (DFT) predicted that direct contact between AuNPs and TiO x would lead to enhanced activity for the oxygen reduction reaction (ORR). DFT attributes the observed ORR enhancement to partial charge transfer from oxygen vacancies within the TiO x film to the supported AuNPs and hence formation of anionic Au species. The experimental findings are in near quantitative agreement with the DFT results. Specifically, compared to isolated AuNPs, decreases of ~ 100 and ~ 50 mV in the ORR onset potential are observed experimentally for AuNPs supported on TiO 1.9 and TiO 2.0 films, respectively.

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

Treyson Ricks - Intern Showcase Poster

Quinone-based sorbents offer a tunable, energy-efficient route to electrochemical CO2 capture, but systematic guidance for molecular design is lacking. Here, we report a high-throughput computational workflow that combines density functional theory (DFT) screening with machine-learning (ML) modeling to evaluate CO2 binding thermodynamics across several quinone derivatives, spanning benzoquinones, naphthoquinones, and anthraquinones. In addition to using solvents to stabilize the quinone anion and dianion, we studied the effect of ion-pairing on the reduction potentials and the CO2 binding energy. Automated Python scripts handled geometry optimizations and adduct-formation energies on an HPC cluster, reducing manual effort significantly. This integrated platform can uncover structure–property relationships and enables rapid in silico evaluation of untested candidates. We present one example from our workflow to showcase the capability of using quinones with ion-pairing to effectively capture CO2. Our approach paves the way for the rational selection of optimal quinone sorbents and can be extended with experimental thermochemical and kinetic data, alternative redox cycles, and stability assessments to accelerate development of next-generation electrochemical CO2 capture materials.

37 - INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL C↗