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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 1,027 records · Page 57
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Iodine Immobilization by Materials through Sorption and Redox-Driven Processes: A Literature Review

Radioiodine-129 (129I) in the subsurface is mobile and limited information is available on treatment technologies. Scientific literature was reviewed to compile information on materials that could potentially be used to immobilize 129I through sorption and redox-driven processes, with an emphasis on ex-situ processes. Candidate materials to immobilize 129I include iron minerals, sulfur-based materials, silver-based materials, bismuth-based materials, ion exchange resins, activated carbon, modified clays, and tailored materials (metal organic frameworks (MOFS), layered double hydroxides (LDHs) and aerogels). Where available, compiled information includes material performance in terms of (i) capacity for 129I uptake; (ii) long-term performance (i.e., solubility of a precipitated phase); (iii) technology maturity; (iv) cost; (v) available quantity; (vi) environmental impact; (vii) ability to emplace the technology for in situ use at the field-scale; and (viii) ex situ treatment (for media extracted from the subsurface or secondary waste streams). Because it can be difficult to compare materials due to differences in experimental conditions applied in the literature, Part II of this review describes results of laboratory studies for selected materials using a standardized batch loading test.

Moore, Robert C.↗
DOE OSTI2019

Technetium immobilization by materials through sorption and redox-driven processes: A literature review

The purpose of this review is to evaluate materials for use as a barrier or other deployed technology to treat technetium-99 (Tc) in the subsurface. To achieve this, Tc interactions with different materials are considered within the context of remediation strategies. Several naturally occurring materials are considered for Tc immobilization, including iron oxides and low solubility sulfide phases. Synthetic materials are also considered, and include tin-based materials, sorbents (resins, activated carbon, modified clays), layered double hydroxides, metal organic frameworks, cationic polymeric networks and aerogels. All of the materials were evaluated for their potential in-situ and ex-situ performance with respect to long-term Tc uptake and immobilization, environmental impacts and deployability. Other factors such as the technology maturity, cost and availability were also considered. Given the difficulty of evaluating materials under different experimental conditions (e.g., solution chemistry, redox conditions, solution to solid ratio, Tc concentration etc.), a subset of these materials will be selected, on the basis of this review, for subsequent standardized batch loading tests.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Zinc speciation and desorption kinetics in a mining waste impacted tropical soil amended with phosphate

Mining is an important component of the Brazilian economy. However, it may also contribute to environmental problems such as the pollution of soils with zinc and other potentially toxic metals. Our objective was to evaluate changes in the chemical speciation and mobility of Zn in a soil amended with phosphate. Soil samples were collected from a deactivated mining area in the state of Minas Gerais, Brazil, and amended with NH 4 H 2 PO 4 saturated with deionized water to 70 % of maximum water retention and incubated at 25 ± 2 °C in open containers for 60 days. The soil was chemically and mineralogically characterized, and sequential extraction, desorption kinetics, and speciation were carried out using synchrotron bulk-sample and micro–X-ray Absorption Near-Edge Structure (XANES/μ-XANES) spectroscopy at the Zn K-edge, and X-ray fluorescence microprobe analysis (μ-XRF). The combination of μ-XRF and μ-XANES techniques made it possible to identify Zn hotspots in the main species formed after phosphate remediation. The best fit combination for bulk XANES and μ-XANES was observed in Zn-montmorillonite, Zn-kerolite, Zn-ferrihydrite, and gahnite. In the course of phosphate treatment, gahnite, Zn layered double hydroxides (Zn-LDH), Zn3(PO4), and ZnO were identified by bulk XANES, while Zn-ferrihydrite, Zn-montmorillonite, and scholzite were identified by μ-XANES. Zinc in the phosphate-amended soil had the strongest partial correlations (r' > 0.05) with Ni, Co, Fe, Cr, Mn, Si, P, Cd, Pb, and Cd, while the unamended soil showed the strongest correlation with Cu, Pb, Fe, and Si. The application of NH 4 H 2 PO 4 altered Zn speciation and favored an increase in Zn desorption. Here, the most available Zn contents after phosphate amendment were correlated with the release of exchangeable Zn fractions, associated with carbonate and organic matter.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Grain boundary slip transfer classification and metric selection with artificial neural networks

An artificial neural network is used to evaluate the effectiveness of six metrics and their combinations to assess whether slip transfers across grain boundaries in coarse-grained oligocrystalline Al foils. This approach extends the one- or two-dimensional projections formerly applied to analyze slip transfer. The accuracy of this binary classification reaches around 87% for the best single metric and around 90% when considering two or more metrics simultaneously. Here, the results suggest slip transfer mostly depends on the geometric relationship between grains. Training a double-layer network having 10 nodes per hidden layer with 40 measurements is sufficient to render the maximum accuracy.

36 MATERIALS SCIENCE↗
DOE OSTI2018

A high-precision miniaturized rotating coil transducer for magnetic measurements

A miniaturized Printed Circuit Board (PCB) sensing coil, jointly developed by CERN and Fermilab for measuring the field of small-gap (less than 10 mm) accelerator magnets, is illustrated. A sensing coil array, with a scheme for compensating the main field when measuring the harmonic error components, hosted on a synthetic sapphire-based transducer, is presented. Key innovating features are (i) very-small size, both for the sensing coil array (thickness of 1.380 mm) and for the transducer (overall diameter of 7.350 mm), (ii) metrological performance, namely accuracy (more than five times better than state of the art), and 1-sigma repeatability (ten times better on harmonics with amplitude less than 100 ppm), and (iii) manufacturing technology of both the coil array (13 double layers aligned within 10 μm), and the sapphire support (concentricity, the most important uncertainty source for rotating coils, 3 μm of uncertainty, namely one order of magnitude better than fiberglass support). After stating the measurement problem, the design of the transducer and a case study of a two-layer PCB sensor array are also illustrated. Then, the prototyping and quality control of both the sensor and the transducer are discussed. Furthermore, the calibration and the results obtained with a prototype setup at Fermilab are presented. Finally, in the appendix, the theory of the rotating coil, the sensor geometry, and the harmonic compensation are briefly reviewed for the reader easiness.

06.20.fb/calibration↗
DOE OSTI2025

Zeta potential measurements of SiO 2 and TiO 2 particles in anionic and cationic surfactant solutions

Zeta potential measurements can provide valuable insights into colloidal stability and may reflect changes in the electrochemical double layer that influence electrocatalysis. In this study, we used zeta potential measurements to monitor and investigate the adsorption behavior of anionic sodium dodecyl sulfate (SDS), cationic dodecyl trimethyl ammonium bromide (DTAB), and cationic cetyl trimethyl ammonium bromide (CTAB) surfactants on SiO 2 and TiO 2 particles in DI water. The zeta potentials of SiO 2 and TiO 2 particles were measured as a function of particle concentration in 1.0 mM, 5.0 mM, and 10.0 mM surfactant solutions. Results indicate that there is no significant adsorption of DS - ions on SiO 2 particles across all SDS concentrations investigated in this study. The zeta potential of TiO 2 particles shifts from negative to positive as particle concentration increases at 1.0 mM SDS, indicating a decrease in DS - ions adsorption per TiO 2 particle. Adsorption plateaus at 5.0 mM SDS for all TiO 2 concentrations studied. In contrast, DTA + and CTA + ions showed clear adsorption on SiO 2 particles, but DTA + exhibited no apparent adsorption on TiO 2 particles. Interestingly, CTA + adsorption on TiO 2 was only evident at higher surfactant concentrations. This study presents a systematic investigation of zeta potential behavior as a function of particle and surfactant concentration, highlighting adsorption saturation and electrostatic reversal. Unlike prior work that was limited to single particle concentration measurements, our approach reveals how surfactant adsorption per particle decreases with increasing surface area. Despite the structural similarity between DTAB and CTAB, this study captured the different adsorption behaviors of both surfactants on SiO 2 and TiO 2 , emphasizing the role of the overall structure of the surfactant on surfactant adsorption behavior. These insights refine the interpretation of zeta potential data and advance understanding of surfactant adsorption on oxide particles. The insight provided in this study about surfactant adsorption on SiO 2 and TiO 2 particles could have important implications for the design of more effective colloidal and catalytic systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Self similarities in desalination dynamics and performance using capacitive deionization

Charge transfer and mass transport are two underlying mechanisms which are coupled in desalination dynamics using capacitive deionization (CDI). We developed simple reduced-order models based on a mixed reactor volume principle which capture the coupled dynamics of CDI operation using closed-form semi-analytical and analytical solutions. We use the models to identify and explore self-similarities in the dynamics among flow rate, current, and voltage for CDI cell operation including both charging and discharging cycles. The similarity approach identifies the specific combination of cell (e.g. capacitance, resistance) and operational parameters (e.g. flow rate, current) which determine a unique effluent dynamic response. We here demonstrate self-similarity using a conventional flow between CDI (fbCDI) architecture, and we hypothesize that our similarity approach has potential application to a wide range of designs. We performed an experimental study of these dynamics and used well-controlled experiments of CDI cell operation to validate and explore limits of the model. For experiments, we used a CDI cell with five electrode pairs and a standard flow between (electrodes) architecture. Guided by the model, we performed a series of experiments that demonstrate natural response of the CDI system. We also identify cell parameters and operation conditions which lead to self-similar dynamics under a constant current forcing function and perform a series of experiments by varying flowrate, currents, and voltage thresholds to demonstrate self-similarity. Based on this study, we hypothesize that the average differential electric double layer (EDL) efficiency (a measure of ion adsorption rate to EDL charging rate) is mainly dependent on user-defined voltage thresholds, whereas flow efficiency (measure of how well desalinated water is recovered from inside the cell) depends on cell volumes flowed during charging, which is determined by flowrate, current and voltage thresholds. Results of experiments strongly support this hypothesis. Results show that cycle efficiency and salt removal for a given flowrate and current are maximum when average EDL and flow efficiencies are approximately equal. We further explored a range of CC operations with varying flowrates, currents, and voltage thresholds using our similarity variables to highlight trade-offs among salt removal, energy, and throughput performance.

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

Process design tools and techno-economic analysis for capacitive deionization

Capacitive deionization (CDI) devices use cyclical electrosorption on porous electrode surfaces to achieve water desalination. Process modeling and design of CDI systems requires accurate treatment of the coupling among input electrical forcing, input flow rates, and system responses including salt removal dynamics, water recovery, energy storage, and dissipation. Techno-economic analyses of CDI further require a method to calculate and compare between a produced commodity (e.g. desalted water) versus capital and operational costs of the system. In this work, we demonstrate a new modeling and analysis tool for CDI developed as an installable Matlab program that allows direct numerical simulation of CDI dynamics and calculation of key performance and cost parameters. The program is provided for free and is used to run open-source Simulink models. The Simulink environment sends information to the program and allows for a drag and drop design space where users can connect CDI cells to relevant periphery blocks such as grid energy, battery, solar panel, waste disposal, and maintenance/labor cost streams. The program allows for simulation of arbitrary current forcing and arbitrary flow rate forcing of one or more CDI cells. We employ validated well-mixed reactor formulations together with a non-linear circuit model formulation that can accommodate a variety of electric double layer sub-models (e.g. for charge efficiency). The program includes a graphical user interface (GUI) to specify CDI plant parameters, specify operating conditions, run individual tests or parameter batch-mode simulations, and plot relevant results. The techno-economic models convert among dimensional streams of species (e.g. feed, desalted water, and brine), energy, and cost and enable a variety of economic estimates including levelized water costs.

42 ENGINEERING↗
DOE OSTI2024

A two-dimensional numerical study of ion-acoustic turbulence

We investigate the linear and nonlinear evolution of the current-driven ion-acoustic instability in a collisionless plasma via two-dimensional (2-D) Vlasov–Poisson numerical simulations. We initialise the system in a stable state and gradually drive it towards instability with an imposed, weak external electric field, thus avoiding physically unrealisable super-critical initial conditions. A comprehensive analysis of the nonlinear evolution of ion-acoustic turbulence (IAT) is presented, including the detailed characteristics of the evolution of the particles’ distribution functions, (2-D) wave spectrum and the resulting anomalous resistivity. Our findings reveal the dominance of 2-D quasi-linear effects around saturation, with nonlinear effects, such as particle trapping and nonlinear frequency shifts, becoming pronounced during the later stages of the system's nonlinear evolution. Remarkably, the Kadomtsev–Petviashvili (KP) spectrum is observed immediately after the saturation of the instability. Another crucial and noteworthy result is that no steady saturated nonlinear state is ever reached: strong ion heating suppresses the instability, which implies that the anomalous resistivity associated with IAT is transient and short-lived, challenging earlier theoretical results. Towards the conclusion of the simulation, electron-acoustic waves are triggered by the formation of a double layer and strong modifications to the particle distribution induced by IAT.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Crystal structure of meglumine diatrizoate, (C 7 H 18 NO 5 )(C 11 H 8 I 3 N 2 O 4 )

The crystal structure of meglumine diatrizoate has been solved and refined using synchrotron X-ray powder diffraction data and optimized using density functional theory techniques. Meglumine diatrizoate crystallizes in space group P2 1 (#4) with a = 10.74697(4), b = 6.49364(2), c = 18.52774(7) Å, β = 90.2263(3), V = 1292.985(5) Å 3 , and Z = 2. Two different crystal structures, which yielded essentially identical refinement residuals and positions of the non-H atoms, were obtained. The differences were in the H atom positions and the hydrogen bonding. One structure was 123.0 kJ/mol/cell lower in energy than the other and was adopted for the final description. The crystal structure consists of alternating double layers of cations and anions along the c-axis. The hydrogen bonds link the cations and anions into a three-dimensional framework. Each of the hydrogen atoms on the ammonium nitrogen of the cation acts as a donor in a strong N–H∙∙∙O hydrogen bond. One of these is to a hydroxyl group of another cation, and the other is to the carboxylate group of the anion. Each of the amide nitrogen atoms of the anion forms a strong N–H∙∙∙O intermolecular hydrogen bond, one to a carbonyl and the other to a carboxylate group. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®).

36 MATERIALS SCIENCE↗
DOE OSTI2022

Engineering Catalyst–Electrolyte Microenvironments to Optimize the Activity and Selectivity for the Electrochemical Reduction of CO 2 on Cu and Ag

We report the electrochemical reduction of carbon dioxide (CO 2 R) driven by renewably generated electricity (e.g., solar and wind) offers a promising means for reusing the CO 2 released during the production of cement, steel, and aluminum as well as the production of ammonia and methanol. If CO 2 could be removed from the atmosphere at acceptable costs (i.e., <$100/t of CO 2 ), then CO 2 R could be used to produce carbon-containing chemicals and fuels in a fully sustainable manner. Economic considerations dictate that CO 2 R current densities must be in the range of 0.1 to 1 A/cm 2 and selectivity toward the targeted product must be high in order to minimize separation costs. Industrially relevant operating conditions can be achieved by using gas diffusion electrodes (GDEs) to maximize the transport of species to and from the cathode and combining such electrodes with a solid-electrolyte membrane by eliminating the ohmic losses associated with liquid electrolytes. Additionally, high product selectivity can be attained by careful tuning of the microenvironment near the catalyst surface (e.g., the pH, the concentrations of CO 2 and H 2 O, and the identities of the cations in the double layer adjacent to the catalyst surface).

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

Anomalous mobility of highly charged particles in pores

Single micropores in resistive-pulse technique were used to understand a complex dependence of particle mobility on its surface charge density. We show that the mobility of highly charged carboxylated particles decreases with the increase of the solution pH due to an interplay of three effects: (i) ion condensation, (ii) formation of an asymmetric electrical double layer around the particle, and (iii) electroosmotic flow induced by the charges on the pore walls and the particle surfaces. The results are important for applying resistive-pulse technique to determine surface charge density and zeta potential of the particles. As a result, the experiments also indicate the presence of condensed ions, which contribute to the measured current if a sufficiently high electric field is applied across the pore.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

In Situ Mass Spectrometric Monitoring of the Dynamic Electrochemical Process at the Electrode–Electrolyte Interface: a SIMS Approach

The in situ molecular characterization of reaction intermediates and products at electrode-electrolyte interfaces is central to mechanistic studies of complex electrochemical processes, yet a great challenge. The coupling of electrochemistry (EC) and mass spectrometry (MS) has seen rapid development and found broad applicability in tackling challenges in analytical and bioanalytical chemistry. However, few truly in situ and real-time EC-MS studies have been reported at electrode-electrolyte interfaces. An innovative EC-MS coupling method named in situ liquid secondary ion mass spectrometry (SIMS) was recently developed by combining SIMS with a vacuum compatible microfluidic electrochemical device. Using this novel capability we report the first in situ elucidation of the electro-oxidation mechanism of a biologically significant organic compound, ascorbic acid (AA), at the electrode-electrolyte interface. The short-lived radical intermediate was successfully captured, which had not been detected directly before. Moreover, we demonstrated the power of this new technique in real-time monitoring of the formation and dynamic evolution of electrical double layers at the electrode-electrolyte interface. This work suggests further promising applications of in situ liquid SIMS in studying more complex chemical and biological events at the electrode-electrolyte interface.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2025

NiAl–MoO 2 S 2 Nanoparticles: Structural Evolution and Mechanistic Insights into High-Performance Selenium Oxyanion Removal across Diverse pH Conditions

Advancing sorbent materials for the selective removal of toxic oxyanions from water requires synthetic control, tunable chemistry, and an atomic-level understanding of structure–function relationships. Here, we report the synthesis and detailed characterization of NiAl–MoO 2 S 2 , a novel layered double hydroxide (LDH) nanomaterial designed for the efficient sequestration of selenium oxoanions (SeO 3 2– and SeO 4 2– ) from complex aqueous environments. The material is synthesized through a room-temperature ion-exchange process, wherein interlayer NO 3 – anions in NiAl–LDH are replaced with MoO 2 S 2 2– clusters, forming high-surface-area, flower-like nanoparticles. Comprehensive structural analysis using the synchrotron X-ray pair distribution function, X-ray absorption spectroscopy, and X-ray photoelectron spectroscopy reveals a distinct chemical transformation of intercalated [MoO 2 S 2 ] 2– into [Mo 2 O 2 S 6 ] 2– -like clusters, generating redox-active interlayers that drive selenium capture. This tailored interfacial chemistry underpins the material’s exceptional sorption performance, achieving distribution coefficients (K d ) ≥ 10 6 mL/g and maximum capacities of 343 mg/g for SeO 4 2– and 514 mg/g for SeO 3 2– , outperforming state-of-the-art inorganic sorbents. Importantly, NiAl–MoO 2 S 2 maintains high selectivity and capacity across acidic, neutral, and alkaline pH, efficiently removing selenium from ppm to sub-10 ppb trace levels, even in the presence of competing ions typical of natural and industrial waters. The selenium uptake proceeds via reductive precipitation coupled with the oxidation of molybdenum and sulfide within the LDH framework. This study highlights the power of strategic synthetic modification and interlayer functionalization in LDHs to unlock new structural motifs and redox chemistries, offering a scalable route to advanced materials for environmental remediation.

Adsorption↗
DOE OSTI2016

Tuning the Reversibility of Mg Anodes via Controlled Surface Passivation by H 2 O/Cl – in Organic Electrolytes

Developing a new generation of battery chemistries is a critical challenge to moving beyond current Li-ion technologies. In this work, we introduce a surface-science-based approach for understanding the complex phenomena controlling the reversibility of Mg anodes for Mg-ion batteries. In addition, we identify the profound impact of trace levels of H 2 O (≤3 ppm) on the kinetics of Mg deposition and determine that passive films of MgO and Mg(OH) 2 are formed only after Mg deposition ceases, rather than continuously during Mg reduction. We also find that Cl – inhibits passivation through the formation of adsorbed Cl – (Mg–Cl(ad)) and/or MgCl 2 on the surface, as well as through a dynamic competition with H 2 O in the double layer. In conclusion, this surface-science-based approach goes well beyond Mg anodes, highlighting the need for more in-depth understanding of electrolyte chemistries before a new generation of efficient and reversible battery technologies can be realized.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Function of Tetrahedral ZnS 3 O Building Blocks in the Formation of SrZn 2 S 2 O: A Phase Matchable Polar Oxysulfide with a Large Second Harmonic Generation Response

Single crystals of a new zinc oxysulfide SrZn 2 S2O were grown in a eutectic KF-KCl flux and the structure was determined by single-crystal X-ray diffraction. SrZn 2 S 2 O crystallizes in the non-centrosymmetric polar space group Pmn2 1 with lattice parameters of a = 3.87440(10) Å, b = 9.9847(3) Å, and c = 6.0916(2) Å. In the crystal structure, close-packed corrugated double layers of ZnS3O tetrahedra, which are derived from the wurtzite structure, are vertically separated by Sr 2+ ions. In addition, the O/S anion ordered arrangement in each close-packed layer yields two distinct orientations of the Zn-centered tetrahedra. The crystals of SrZn 2 S 2 O are colorless and transparent and the oxysulfide has a band gap of 3.86 eV, based on UV-vis-NIR diffuse reflectance measurements. Thermogravimetric measurements showed that SrZn 2 S 2 O is stable up to 650 °C in O 2 gas atmosphere. First-principle calculations indicate that the valence band maximum is mainly composed of O-2p and S-3p states, whereas the conduction band minimum is derived from Zn-4s, Zn-4p, and Sr-4d states. The calculated band dispersion reveals a direct band gap corresponding to a transition between S-3p and Zn-4s energy levels. Second harmonic generation (SHG) measurements determined that SrZn 2 S 2 O is phase matchable with twice the SHG intensity of potassium dihydrogen phosphate (KDP) in contrast to CaZnSO with similar ZnS 3 O building units, which exhibits non-phase matching behavior.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Real Space Visualization of Competing Phases in La 0.6 Sr 2.4 Mn 2 O 7 Single Crystals

We report that correlated quantum materials are expected to provide the foundation for the next generation of information or energy technologies. A key feature of these materials is the proximity of multiple ground states close in energy, which results in the ability to tune properties with small changes in an external parameter such as magnetic field, composition, or temperature. For example, the colossal magnetoresistance exhibited by manganites is related to charge and orbital ordering and results from a metallic ferromagnetic phase in proximity to a paramagnetic insulating phase. The presence of competing ground states, at the heart of the physics and functionality of these materials, often results in nanoscale phase separation. Probing nanoscale phase separation with conventional diffraction techniques alone is not adequate, particularly when the domains are small or nanosized. In the present work we use a scanning transmission electron microscopy image-based technique of picometer precision strain maps (PPSM) to directly visualize the competing nanoscale phases with charge and orbital ordering in a double-layer manganite. Finally, this work underscores the role of subtle structural distortions in determining the electron physics in correlated quantum materials and provides insights into designing new functionalities via spatially tuning multiple competing ground states.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Pseudocapacitance: From Fundamental Understanding to High Power Energy Storage Materials

There is an urgent global need for electrochemical energy storage that includes materials that can provide simultaneous high power and high energy density. One strategy to achieve this goal is with pseudocapacitive materials that take advantage of reversible surface or near-surface Faradaic reactions to store charge, surpassing the capacity limitations of electrical double-layer capacitors and mass transfer limitations of batteries. The past decade has seen tremendous growth in the understanding of pseudocapacitance as well as materials that exhibit this phenomenon. The purpose of this study is to examine the fundamental development of the concept of pseudocapacitance and how it came to prominence in electrochemical energy storage as well as to describe new classes of materials whose electrochemical energy storage behavior can be described as pseudocapacitive.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗