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At least 1,081 records · Page 60

Thermal Model of the Promoted Combustion Test

Flammability of metals in high pressure, pure oxygen environments, such as rocket engine turbopumps, is commonly evaluated using the Promoted Combustion Test (PCT). The PCT emphasizes the ability of an ignited material to sustain combustion, as opposed to evaluating the sample's propensity to ignite in the first place. A common arrangement is a rod of the sample material hanging in a chamber in which a high pressure, pure oxygen environment is maintained. An igniter of some energetically combusting material is fixed to the bottom of the rod and fired. This initiates combustion, and the sample burns and melts at its bottom tip. A ball of molten material forms, and this ball detaches when it grows too large to be supported by surface tension with the rod. In materials which do not sustain combustion, the combustion then extinguishes. In materials which do sustain combustion, combustion re-initiates from molten residue left on the bottom of the rod, and the melt ball burns and grows until it detaches again. The purpose of this work is development of a PCT thermal simulation model, detailing phase change, melt detachment, and the several heat transfer modes. Combustion is modeled by a summary rate equation, whose parameters are identified by comparison to PCT results. The sensitivity of PCT results to various physical and geometrical parameters is evaluated. The identified combustion parameters may be used in design of new PCT arrangements, as might be used for flammability assessment in flow-dominated environments. The Haynes 214 nickel-based superalloy, whose PCT results are applied here, burns heterogeneously (fuel and oxidizer are of different phases; combustion takes place on the fuel surface). Heterogeneous combustion is not well understood. (In homogeneous combustion, the metal vaporizes, and combustion takes place in an analytically treatable cloud above the surface). Thermal modeling in heterogeneous combustion settings provides a means for linking test results more directly to detailed combustion mechanics, leading to improved data analysis, and improved understanding of heterogeneous combustion phenomena.

Jones, Peter D.↗

Detection of Foreign Materials on Broiler Breast Meat Using a Fusion of Visible Near-Infrared and Short-Wave Infrared Hyperspectral Imaging

Foreign material (FM) found on a poultry product lowers the quality and safety of the product. We developed a fusion method combining two hyperspectral imaging (HSI) modalities in the visible-near infrared (VNIR) range of 400–1000 nm and the short-wave infrared (SWIR) range of 1000–2500 nm for the detection of FMs on the surface of fresh raw broiler breast fillets. Thirty different types of FMs that could be commonly found in poultry processing plants were used as samples and prepared in two different sizes (5 × 5 mm 2 and 2 × 2 mm 2 ). The accuracies of the developed Fusion model for detecting 2 × 2 mm 2 pieces of polymer, wood, and metal were 95%, 95%, and 81%, respectively, while the detection accuracies of the Fusion model for detecting 5 × 5 mm 2 pieces of polymer, wood, and metal were all 100%. The performance of the Fusion model was higher than the VNIR- and SWIR-based detection models by 18% and 5%, respectively, when F1 scores were compared, and by 38% and 5%, when average detection rates were compared. The study results suggested that the fusion of two HSI modalities could detect FMs more effectively than a single HSI modality.

36 MATERIALS SCIENCE↗

Accelerating charge estimation in molecular dynamics simulations using physics-informed neural networks: corrosion applications

Molecular Dynamics (MD) simulations are used to understand the effects of corrosion on metallic materials in salt brine. Reactive force fields in classical MD enable accurate modeling of bond formation and breakage in the aqueous medium and at the metal-electrolyte interface, while also facilitating dynamic partial charge equilibration. However, MD simulations are computationally intensive and unsuitable for modeling the long time scales characteristic of corrosive phenomena. To address this, we develop reduced-order machine learning models that provide accurate and efficient predictions of charge density in corrosive environments. Specifically, we use Long Short-Term Memory (LSTM) networks to forecast charge density evolution based on atomic environments represented by Smooth Overlap of Atomic Positions (SOAP) descriptors. A physics-informed loss function enforces charge neutrality and electronegativity equivalence. The atomic charges predicted by the deep learning model trained on this work were obtained two orders of magnitude faster than those from molecular dynamics (MD) simulations, with an error of less than 3% compared to the MD-obtained charges, even in extrapolative scenarios, while adhering to physical constraints. This demonstrates the excellent accuracy, computational efficiency, and validity of the developed model. Lastly, even though developed for corrosion, these protocols are formulated in a phenomenon-agnostic manner, allowing application to various variable-charge interatomic potentials and related fields.

Atomistic models↗

Thermodynamics of Minerals Stable near Earth's Surface

Project “Thermodynamics of Minerals Stable Near the Earth’s Surface” uses specialized calorimetric techniques to obtain new thermochemical data for solid phases of interest in the Earth’s “critical zone”, the near surface regions of the planet most directly affecting and affected by human activity. Major activity was in three areas: manganese oxide materials, aluminum clusters which are precursors to aluminum oxyhydroxide precipitates, and zeolites. All these classes of minerals are potential carriers of heavy metals and radionuclides in the environment, both within their crystal structures and as adsorbed layers or colloids. Their thermodynamic stability, as well as the sequence of stability of competing phases, governs the aqueous solubility of contaminants (and nutrients) in soil, groundwater, and sediments. The thermodynamics of these phases is strongly affected by particle size and crystallinity, since they often occur as very fine particles which do not coarsen in the near-surface environment. Many of these materials exhibit extensive polymorphism, multicomponent solid solution, and variable hydration states. Thus, one must define and systematize important thermodynamic variables, since one cannot make measurements on each and every possible phase, particle size, and composition. A major finding of the work on manganese oxides was labile water-induced oxidation-reduction reactions. These will be studied further by a combination of thermodynamic and synchrotron-based spectroscopic methods, the latter in collaboration with Peggy O’Day at UC Merced. The adsorption of other species, including simple organics, on such redox-active surfaces will also be investigated by a combination of thermochemical and spectroscopic studies. Studies of the energetics of water adsorption on mineral surfaces will be expanded to emphasize the adsorption of CO2 and small organic molecules, relevant to soil, groundwater, and the subsurface environment. Gas adsorption calorimetry, immersion calorimetry, and solution calorimetry will be combined with appropriate analytical and spectroscopic techniques to obtain a comprehensive picture of the interactions and their energetics. The evolution of aqueous aluminum clusters to form aluminum oxyhydroxide precipitates will be studied in detail by a combination of calorimetric and structural methods applied to aqueous samples aged at room temperature. The energetics of new classes of clusters will be explored. The project addresses several common themes relevant to the broad mission of the Department of Energy. Thermochemical data for minerals stable near the Earth’s surface, though still incomplete, are essential for understanding both natural and anthropogenic processes that affect our very existence on this planet. Such data contribute to the fundamental underpinning for mitigation and management strategies for the extraction and use of energy. Fundamental thermodynamic and mechanistic understanding is required to model processes ranging from heavy metal pollution to nuclear waste disposal to climate change.

58 GEOSCIENCES↗

Electromagnetic wave energy conversion research

Known electromagnetic wave absorbing structures found in nature were first studied for clues of how one might later design large area man-made radiant-electric converters. This led to the study of the electro-optics of insect dielectric antennae. Insights were achieved into how these antennae probably operate in the infrared 7-14um range. EWEC theoretical models and relevant cases were concisely formulated and justified for metal and dielectric absorber materials. Finding the electromagnetic field solutions to these models is a problem not yet solved. A rough estimate of losses in metal, solid dielectric, and hollow dielectric waveguides indicates future radiant-electric EWEC research should aim toward dielectric materials for maximum conversion efficiency. It was also found that the absorber bandwidth is a theoretical limitation on radiant-electric conversion efficiency. Ideally, the absorbers' wavelength would be centered on the irradiating spectrum and have the same bandwith as the irradiating wave. The EWEC concept appears to have a valid scientific basis, but considerable more research is needed before it is thoroughly understood, especially for the complex randomly polarized, wide band, phase incoherent spectrum of the sun. Specific recommended research areas are identified.

Bailey, R. L.↗

Experimental observation of electrochemical rate limitations affecting sodium ion-electron recombination at electrodes of the alkali metal thermoelectric converter at T about 1200 K

This paper considers a model of the internal impedances of thin porous Mo and W alkali metal thermoelectric converter (AMTEC), in which the kinetic parameters associated with the reaction of the beta-double-prime alumina solid electrolite (BASE)/porous metal/gas three-phase boundary can be evaluated. Impedance data in the frequency range 0.01-100,000 Hz were collected over a range of AMTEC cell operating voltages for small-area thin porous Mo and W electrodes, yielding apparent charge transfer resistances at a series of cell potentials/currents. The ohmic resistance in the AMTEC cell could be broken down and characterized with three parameters: the BASE ionic resistance, the electrode film sheet resistance, and the contact/lead resistance, all of which could be calculated or measured independently and used to calculate power curves in good agreement with observed power curves. It is shown that these calculations can be used to predict the properties of electrodes with optimized parameters or to detect enhanced transport modes.

Williams, R. M.↗

Chemical model for Viking biology experiments - Implications for the composition of the Martian regolith

The labelled-release and the gas-exchange experiments of the 1976 Mars Viking biology experiment program detected, respectively, C-14 labelled gases and O2 gas. A chemical model is proposed here for these experiments in which the reactants are an inorganic nitrate salt which has been partly photolyzed by ultraviolet light and a sparingly soluble metal carbonate such as calcite. The model reproduces the main effects seen, indicating that nitrates are present in the Martian regolith as well as calcite (or some other carbonate with similar solubility).

Plumb, Robert C.↗

COOL-LAMPS. I. An Extraordinarily Bright Lensed Galaxy at Redshift 5.04

In this paper, we report the discovery of COOL J1241+2219, a strongly lensed galaxy at redshift z = 5.043 ± 0.002 with observed magnitude z AB = 20.47, lensed by a moderate-mass galaxy cluster at z = 1.001 ± 0.001. COOL J1241+2219 is the brightest lensed galaxy currently known at optical and near-infrared wavelengths at z $\gtrsim$ 5; it is ~5 times brighter than the prior record-holder lensed galaxy, and several magnitudes brighter than the brightest unlensed galaxies known at these redshifts. It was discovered as part of COOL-LAMPS, a collaboration initiated to find strongly lensed systems in recent public optical imaging data. We characterize the lensed galaxy, as well as the central galaxy of the lensing cluster using ground-based grizJH imaging and optical spectroscopy. We report model-based magnitudes, and derive stellar masses, dust content, metallicity, and star-formation rates via stellar-population synthesis modeling. Our lens mass modeling, based on ground-based imaging, implies a median source magnification of ~30, which puts the stellar mass and star-formation rate (in the youngest age bin, closest to the epoch of observation) at logM* = ${10.11}_{-0.26}^{+0.21}$ and SFR = ${27}_{-9}^{+13} M_⊙$ yr –1 , respectively. We constrain a star-formation history for COOL J1241+2219 consistent with constant star formation across ~1 Gyr of cosmic time, and that places this galaxy on the high-mass end of the star-forming main sequence. COOL J1241+2219 is two to four times more luminous than a galaxy with the characteristic UV luminosity at these redshifts. The UV continuum slope β = –2.2 ± 0.2 places this galaxy on the blue side of the observed distribution of galaxies at z = 5, although the lack of Lyα emission indicates dust sufficient to suppress this emission.

79 ASTRONOMY AND ASTROPHYSICS↗

The Binary Fraction of Stars in the Dwarf Galaxy Ursa Minor via Dark Energy Spectroscopic Instrument

We utilize multi-epoch line-of-sight velocity measurements from the Milky Way Survey of the Dark Energy Spectroscopic Instrument to estimate the binary fraction for member stars in the dwarf spheroidal galaxy Ursa Minor. Our dataset comprises 670 distinct member stars, with a total of more than 2,000 observations collected over approximately one year. We constrain the binary fraction for UMi to be $0.61^{+0.16}_{-0.20}$ and $0.69^{+0.19}_{-0.17}$, with the binary orbital parameter distributions based on solar neighborhood observation from Duquennoy & Mayor (1991) and Moe & Di Stefano (2017), respectively. Furthermore, by dividing our data into two subsamples at the median metallicity, we identify that the binary fraction for the metal-rich ([Fe/H]>-2.14) population is slightly higher than that of the metal-poor ([Fe/H]<-2.14) population. Based on the Moe & Di Stefano model, the best-constrained binary fractions for metal-rich and metal-poor populations in UMi are $0.86^{+0.14}_{-0.24}$ and $0.48^{+0.26}_{-0.19}$, respectively. After a thorough examination, we find that this offset cannot be attributed to sample selection effects. We also divide our data into two subsamples according to their projected radius to the center of UMi, and find that the more centrally concentrated population in a denser environment has a lower binary fraction of $0.33^{+0.30}_{-0.20}$, compared with $1.00^{+0.00}_{-0.32}$ for the subsample in more outskirts.

Qiu, Tian [Shanghai Jiao Tong Univ. (China); DESI ↗

A line-blanketed model stellar atmosphere of Sirius

The method of artificial absorption edges is applied to a grid of model atmospheres to include the effects of hydrogen and metal line blanketing on the atmospheric structure. A best-fit model of Sirius is obtained which is free of the discrepancies inherent in unblanketed or partially blanketed models. All major spectral features calculated from the model agree with the corresponding observed features to within the observational uncertainty. Some additional properties of the models are discussed.

Fowler, J. W.↗

Photocatalytic Semiconductor–Metal Hybrid Nanoparticles: Single-Atom Catalyst Regime Surpasses Metal Tips

Semiconductor–metal hybrid nanoparticles (HNPs) are promising materials for photocatalytic applications, such as water splitting for green hydrogen generation. While most studies have focused on Cd containing HNPs, the realization of actual applications will require environmentally compatible systems. Using heavy-metal free ZnSe-Au HNPs as a model, we investigate the dependence of their functionality and efficiency on the cocatalyst metal domain characteristics ranging from the single-atom catalyst (SAC) regime to metal-tipped systems. The SAC regime was achieved via the deposition of individual atomic cocatalysts on the semiconductor nanocrystals in solution. Utilizing a combination of electron microscopy, X-ray absorption spectroscopy, and X-ray photoelectron spectroscopy, we established the presence of single Au atoms on the ZnSe nanorod surface. Upon increased Au concentration, this transitions to metal tip growth. Photocatalytic hydrogen generation measurements reveal a strong dependence on the cocatalyst loading with a sharp response maximum in the SAC regime. Ultrafast dynamics studies show similar electron decay kinetics for the pristine ZnSe nanorods and the ZnSe-Au HNPs in either SAC or tipped systems. This indicates that electron transfer is not the rate-limiting step for the photocatalytic process. Combined with the structural-chemical characterization, we conclude that the enhanced photocatalytic activity is due to the higher reactivity of the single-atom sites. This holistic view establishes the significance of SAC-HNPs, setting the stage for designing efficient and sustainable heavy-metal-free photocatalyst nanoparticles for numerous applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Local Ultrasonic Resonance Spectroscopy of Lithium Metal Batteries for Aerospace Applications

As next-generation aircraft and vehicles continue to develop, so do their associated energy demands. Lithium metal batteries are a leading candidate to fulfill this energy requirement, but these batteries are prone to internal dendrite defects that can lead to catastrophic thermal runaway events. Current battery management systems are capable of mitigating such risks, but are unable to detect such defects until thermal runaway has already begun. Various nondestructive evaluation (NDE) techniques, particularly ultrasonic NDE, can directly monitor internal battery parameters giving them the potential to detect critical defects prior to catastrophic failure. However, most of the current battery NDE research has focused on improved battery state-of-charge (SOC) and stateof- health (SOH) monitoring with little emphasis on critical defect detection. Thus, a measurement technique sensitive to subtle battery defects is needed. In addition, the complex mechanics of ultrasound in porous, thin, multilayered batteries prompt the use of physics-based simulation to guide inspections. In this work, an ultrasonic NDE technique has been developed utilizing frequency domain analysis of local battery resonances to detect the presence of battery defects. This technique is a practical extension of local ultrasonic resonance spectroscopy (LURS) – which previously required non-contact laser ultrasonics – to measurements with piezoelectric contact and immersion scan transducers. To extend the technique to work with piezoelectric transducers, ultrasonic battery measurements were compared to a sans-battery calibration measurement. Then, a linear systems deconvolution was used to eliminate the transfer functions of extraneous factors such as the transducer and electronics, leaving only the frequency-dependent battery reflection coefficient. The LURS technique was first validated on stainless steel and aluminum plates, producing reflection coefficients in line with analytical and numerical finite element modeling (FEM) results. Functioning Li-metal pouch cells were then seeded with lithium chip defects prior to LURS measurements. The presence of these defects is shown to cause a measurable shift in the battery’s through-thickness local resonances. 2D, frequency-domain poroelastic models of ultrasonic propagation in a single-cell lithium metal pouch battery were created and corroborated these findings. Thus, this work has both extended and proven the feasibility of the LURS technique in the detection of local battery defects.

Ultrasound↗

Material analysis of metal hydrides for bulk hydrogen storage

The United States Department of Energy (DOE) Hydrogen Storage Engineering Center of Excellence (HSECoE), 2009–2014, was established to evaluate the viability of material-based hydrogen storage for light duty vehicles. The HSECoE concluded that there were no metal hydrides that simultaneously met the DOE targets for gravimetric and volumetric capacity, and rate of onboard refueling. However, it was noted by the DOE that potential applications existed for stationary hydrogen storage systems. An application of particular interest is using a metal-hydride to store a hydrogen supply for fuel cell backup power to a 5 MWe data center. A generalized numerical model that coupled mass and energy conservation, chemical kinetics and thermodynamics was developed to simulate the discharge process for a given metal-hydride. The model was applied to an interstitial and a complex metal-hydride. In conclusion, it was found that the interstitial metal-hydride, which is discharged by a pressure swing is preferrable in a practical sense to the complex metal-hydride, which requires a temperature swing discharge process.

08 HYDROGEN↗

Split representation of adaptively compressed polarizability operator

The polarizability operator plays a central role in density functional perturbation theory and other perturbative treatment of first principle electronic structure theories. The cost of computing the polarizability operator generally scales as O(Ne4) where Ne is the number of electrons in the system. The recently developed adaptively compressed polarizability operator (ACP) formulation [L. Lin, Z. Xu and L. Ying, Multiscale Model. Simul. 2017] reduces such complexity to O(Ne 3 ) in the context of phonon calculations with a large basis set for the first time, and demonstrates its effectiveness for model problems. In this paper, we improve the performance of the ACP formulation by splitting the polarizability into a near singular component that is statically compressed, and a smooth component that is adaptively compressed. The new split representation maintains the O(Ne 3 ) complexity, and accelerates nearly all components of the ACP formulation, including Chebyshev interpolation of energy levels, iterative solution of Sternheimer equations, and convergence of the Dyson equations. For simulation of real materials, we discuss how to incorporate nonlocal pseudopotentials and finite temperature effects. In this work, we demonstrate the effectiveness of our method using one-dimensional model problem in insulating and metallic regimes, as well as its accuracy for real molecules and solids.

97 MATHEMATICS AND COMPUTING↗

First-principles study of grain-boundary wetting in Fe-Σ5(013)[100] tilt boundary

Here, we report an ab-initio study of grain-boundary wetting (GBW) in three systems (Fe/Zn, Fe/Pb & Fe/Bi) on a Σ5(013)[100] tilt grain boundary. An energy-based approach is pursued and adapted to the study of liquid-metal/solid-metal interfaces. We provide a sound calculation of the wettability parameter S (i.e., defined as the minimum energy difference between the unbroken initial state and final state with liquid-metal/solid-metal interfaces). Solid/liquid interfaces are modelled by ab-initio molecular dynamics, also allowing a study of structural effects in the liquid phase near the solid interface. We show how surface energies for solid-metal/liquid-metal interfaces need a special treatment for the liquid-metal chemical potential due to the change in crystallinity near the interface. The computation of the wettability criterion for the three systems correctly predicts the GBW trend known experimentally for these systems. The computations are compared with small-scale TEM experiments on GBW of two systems (Fe/Pb and Fe/Bi) and it is shown to provide reasonable results. This approach offers new perspectives in predicting GBW trends across various systems.

36 MATERIALS SCIENCE↗

Hydrogen Localization and Cluster Formation in α-Zr from First-Principles Investigations

We report alpha-zirconium (α-Zr) is a hydrogen atom host material used in nuclear energy and semiconducting applications due to Zr's excellent properties such as corrosion resistance, low thermal neutrons cross-section, and thermodynamically favorable interstitial sequestering of H atoms. Herein we use density functional theory simulations to systematically analyze the initial stages of H insertion in the Zr matrix, and determine optimal hydrogen localization, distribution, and clustering tendencies from a thermodynamics and kinetics perspective. Our results suggest that H occupation of tetrahedral sites is strongly favored, consistent with previous experimental and theoretical studies. Further, a cooperative effect in H localization is shown where H atoms favor clustering. The H pair is found to be the most stable by occupying tetrahedral sites with pairs at second nearest-neighbor positions (TTn2). Among the four H atom clusters, the most favorable configuration has two TTn2 pairs forming "box " or "zig-zag" shaped-cluster with the pairs separated by 3.03 or 3.25 Å, respectively. Nudged elastic band simulations suggest that the formation of TTn2 is facile and is limited by the small diffusion barrier of the monomer of less than 0.1 eV. Further, the formation routes for the 4H atom clusters are also presented. The current study can serve as a foundation to systematically model H atom clustering in metals and alloys.

36 MATERIALS SCIENCE↗

TEM characterization of two variants of fuel cladding chemical interaction in a HT-9 Clad U-10Zr Fuel. Variant 1: FCCI with a Zr Rind

Here, this study investigated the fuel cladding chemical interaction (FCCI), a key factor that limits operational temperature and burnup, in an HT-9 clad U-10Zr nuclear fuel sample irradiated to a high burnup of 13.1 at.% at a time-averaged peak inner cladding temperature (PICT) of 530 °C. Previous results showed this fuel sample exhibited two distinct levels of FCCI at d. This paper analyzed the FCCI at an azimuthal position showing an interdiffusion layer of <10 µm using transmission electron microscopy to examine chemical and crystallographic nature of phases at the fuel-cladding interface at the nanoscale level. A ZrC layer and a Zr 3 Si phase were identified at the interface; these, along with the relatively low local temperature, potentially contributed to limit interdiffusion, behaving as inhibitors for deleterious interactions. Lanthanides (Ln) partially consumed the ZrC layer and interacted with Fe, forming a Zr-Ln compound and a (Zr,Ce)Fe 2+x phase while also infiltrating up to 4 µm into the cladding. Neither U nor Zr were observed in the cladding, whereas Fe diffused up to 3–5 µm in the fuel. Fe infiltration formed a ternary U-Zr-Fe ε-phase and likely promoted the precipitation of a Cr-rich α’ phase on the cladding interface. Additionally, a Cr-rich χ-phase, likely formed by the dissociation of pre-existing M 23 C 6 carbide precipitates, was identified about 2–5 µm from the fuel-cladding interface. Irradiation-induced nano-voids were also observed in the HT-9 bulk. These findings provide critical insights into FCCI mechanisms at representative irradiation conditions, essential for developing models simulating in-pile metallic fuel behaviors for next-generation reactors.

36 - MATERIALS SCIENCE↗

Impact of Pendent Ammonium Groups on Solubility and Cycling Charge Carrier Performance in Nonaqueous Redox Flow Batteries

The synthesis, characterization, electrochemical performance, and theoretical modeling of two base-metal charge carrier complexes incorporating a pendent quaternary ammonium group, [Ni(bppn-Me3)][BF4], 3′, and [Fe(PyTRENMe)][OTf]3, 4’, are described. Both complexes were produced in high yield and fully characterized using NMR, IR, and UV–vis spectroscopies as well as elemental analysis and single-crystal X-ray crystallography. The solubility of 3′ in acetonitrile showed a 283% improvement over its neutral precursor, whereas the solubility of complex 4’ was effectively unchanged. Cyclic voltammetry indicates an ∼0.1 V positive shift for all waves, with some changes in reversibility depending on the wave. Bulk electrochemical cycling demonstrates that both 3′ and 4’ can utilize the second more negative wave to a degree, whereas 4’ ceases to have a reversible positive wave. Flow cell testing of 3′ and 4’ with Fc as the posolyte reveals little improvement to the cycling performance of 3′ compared with its parent complex, whereas 4’ exhibits reductions in capacity decay when cycling either negative wave. Postcycling CVs indicate that crossover is the likely source of capacity loss in complexes 3, 3′, and 4’ because there is little change in the CV trace. Density functional theory calculations indicate that the ammonium group lowers the HOMO energy in 3′ and 4’, which may impart stability to cycling negative waves while making positive waves less accessible. The incorporation of a positively charged species can improve solubility, stored electron density, and capacity decay depending on the complex, features critical to high energy density redox flow battery performance.

25 ENERGY STORAGE↗