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At least 163 records · Page 9

Facilitating Ionic and Electronic Conduction in Radical Polymers through Controlled Assembly

The major objectives, research performed, and significant results associated with this effort agree with the originally proposed work. That is, we have made significant advances in terms of both the experimental and computational thrusts of this effort, and these key results have allowed for us to have significant impact in the materials chemistry community. As is usual, this has led to even greater tangible product generation in the final year of the work relative to the first two years. Importantly, we have observed that the materials created under this effort have promising electronic and ionic conductivity properties along these lines, and we have developed the initial structure-property-performance relationships that offer future promise for these open-shell materials in advanced energy applications. One metric that represents this success is the number of publications that appear in notable journals regarding the work performed. Additionally, the team has been invited to present at many conferences of leading societies and at top academic institutions due to the work associated with this award. Finally, we anticipate that this will be of interest to multiple communities in the materials chemistry realm, and they will have broader impact into related technologies as well.

36 MATERIALS SCIENCE↗

Secondary electron emission measurements from imidazolium-based ionic liquids

The electron-induced secondary electron emission (SEE) yields of imidazolium-based ionic liquids are presented for primary electron beam energies between 30 and 1000 eV. These results are important for understanding plasma synthesis of nanoparticles in plasma discharges with an ionic liquid electrode. Due to their low vapor pressure and high conductivity, ionic liquids can produce metal nanoparticles in low-pressure plasmas through reduction of dissolved metal salts. In this work, the low vapor pressure of ionic liquids is exploited to directly measure SEE yields by bombarding the liquid with electrons and measuring the resulting currents. The ionic liquids studied are [BMIM][Ac], [EMIM][Ac], and [BMIM][BF 4 ]. The SEE yields vary significantly over the energy range, with maximum yields of around 2 at 200 eV for [BMIM][Ac] and [EMIM][Ac], and 1.8 at 250 eV for [BMIM][BF 4 ]. Molecular orbital calculations indicate that the acetate anion is the likely electron donor for [BMIM][Ac] and [EMIM][Ac], while in [BMIM][BF 4 ], the electrons likely originate from the [BMIM] + cation. The differences in SEE yields are attributed to varying ionization potentials and molecular structures of the ionic liquids. These findings are essential for accurate modeling of plasma discharges and understanding SEE mechanisms in ionic liquids.

ionic liquids↗

Tailoring the structural durability and proton conductivity of electrolytes for highly fuel-flexible and reversible ceramic cells

A durable and high ionic conducting electrolyte is critical for achieving fuel-flexible and reversible protonic ceramic cells (PCCs) at reduced temperatures since the developed electrolyte materials are vulnerable to steam, CO 2 , or coking deterioration. Here, we report a fast-conducting electrolyte material BaZr 0.06 Ce 0.7 Y 0.06 Yb 0.06 Hf 0.06 Gd 0.06 O 3−δ (BZCYYbHG), demonstrating excellent durability against CO 2 and H 2 O under the realistic electrolysis operations, and a high conductivity of 0.017 S cm −1 at 550 °C for lowering the PCC operating temperature. Further, density functional theory calculations indicate that the higher configurational entropy of mixing at the B-site cations slightly reduces the hydrogen adsorption energy, suggesting a higher incorporation rate of protons or hydrogen atoms into the electrolyte bulk. Ultimately, single cells with the BZCYYbHG electrolyte deliver peak power densities of 1.39, 1.12, and 0.7 W cm −2 in H 2 , NH 3 , and wet CH 4 at 550 °C with promising durability. In addition, the PCCs achieve a current density of −1.61 A cm −2 at 1.3 V and 550 °C with a high faradaic efficiency of 91.3% at −0.5 A cm −2 , enabling stable operations in steam electrolysis mode under humid air (30% H 2 O), wet air containing CO 2 (up to 10%), and reversible cycling.

25 ENERGY STORAGE↗

Critical role of polymer-ceramic ion exchange for high conductivity composite electrolytes

Polymer-ceramic composites offer a path to enhance the transport and mechanical properties of solid electrolytes. However, an in-depth understanding of the extent and role of ion transport along and across polymer-ceramic interfaces in these systems is lacking. We have recently shown that Li-conducting Li 0.11 Na 0.24 K 0.02 La 0.43 TiO 2.82 (LMTO) nanorods can be prepared by a molten flux method, and the addition of 30–50 weight (wt.)% LMTO to a bis[(trifluoromethyl)sulfonyl]imide-vinyl ethylene carbonate-based single-ion conducting (SIC) polymer electrolyte leads to a two-fold enhancement in Li-ion conductivity, from 1.4 to 3.0 × 10 −5 S/cm at 30 °C. In the present study, we use NMR methods to identify the Li-ion transport pathways and determine the timescale of chemical exchange between the SIC polymer and LMTO ceramic components. Tracer exchange NMR indicates preferential transport through the polymer or polymer-interfacial regions, and exchange spectroscopy (EXSY) and a new isotope exchange method reveal negligible Li exchange between the SIC polymer and LMTO ceramic up to several days. Here, LMTO nanorods act as a passive filler. Our results further highlight that significant (e.g., 10- or 100-fold) conductivity enhancements in composite electrolytes can only be achieved 1) with ionically-conductive fillers, and 2) when both the ceramic and polymer components actively participate in long-range transport. For this, fast interfacial ion exchange is needed. In conclusion, this leads us to introduce a critical interfacial ion exchange time to evaluate whether a filler actively contributes to conduction in a composite electrolyte, and screen for promising polymer-ceramic pairings to accelerate the development of high conductivity solid electrolytes.

Battery, Solid electrolyte↗

Li-Ion Cells Employing Electrolytes With Methyl Propionate and Ethyl Butyrate Co-Solvents

Future NASA missions aimed at exploring Mars and the outer planets require rechargeable batteries that can operate at low temperatures to satisfy the requirements of such applications as landers, rovers, and penetrators. A number of terrestrial applications, such as hybrid electric vehicles (HEVs) and electric vehicles (EVs) also require energy storage devices that can operate over a wide temperature range (i.e., -40 to +70 C), while still providing high power capability and long life. Currently, the state-of-the-art lithium-ion system has been demonstrated to operate over a wide range of temperatures (-30 to +40 C); however, the rate capability at the lower temperatures is very poor. These limitations at very low temperatures are due to poor electrolyte conductivity, poor lithium intercalation kinetics over the electrode surface layers, and poor ionic diffusion in the electrode bulk. Two wide-operating-temperature-range electrolytes have been developed based on advances involving lithium hexafluorophosphate-based solutions in carbonate and carbonate + ester solvent blends, which have been further optimized in the context of the technology and targeted applications. The approaches employed include further optimization of electrolytes containing methyl propionate (MP) and ethyl butyrate (EB), which are effective co-solvents, to widen the operating temperature range beyond the baseline systems. Attention was focused on further optimizing ester-based electrolyte formulations that have exhibited the best performance at temperatures ranging from -60 to +60 C, with an emphasis upon improving the rate capability at -20 to -40 C. This was accomplished by increasing electrolyte salt concentration to 1.20M and increasing the ester content to 60 percent by volume to increase the ionic conductivity at low temperatures. Two JPL-developed electrolytes 1.20M LiPF6 in EC+EMC+MP (20:20:60 v/v %) and 1.20M LiPF6 in EC+EMC+EB (20:20:60 v/v %) operate effectively over a wide temperature range in MCMB-LiNiCoAlO2 and Li4Ti5O12-LiNi-CoAlO2 prototype cells. These electrolytes have enabled high rate performance at low temperature (i.e., up to 2.0C rates at -50 C and 5.0C rates at -40 C), and good cycling performance over a wide temperature range (i.e., from -40 to +70 C). Current efforts are focused upon improving the high temperature resilience of the methyl propionatebased system through the use of electrolyte additives, which are envisioned to improve the nature of the solid electrolyte interphase (SEI) layers.

Smart, Marshall C.↗

New Polymer Electrolyte Cell Systems

PAPERS PUBLISHED: 1. Pappenfus, Ted M.; Henderson, Wesley A.; Owens, Boone B.; Mann, Kent R.; Smyrl, William H. Complexes of Lithium Imide Salts with Tetraglyme and Their Polyelectrolyte Composite Materials. Journal of the Electrochemical Society (2004), 15 1 (2), A209-A2 15. 2. Pappenfus, Ted M.; Henderson, Wesley A.; Owens, Boone B.; Mann, Kent R.; Smyrl, William H. Ionic-liquidlpolymer electrolyte composite materials for electrochemical device applications. Polymeric Materials Science and Engineering (2003), 88 302. 3. Pappenfus, Ted R.; Henderson, Wesley A.; Owens, Boone B.; Mann, Kent R.; and Smyrl, William H. Ionic Conductivity of a poly(vinylpyridinium)/Silver Iodide Solid Polymer Electrolyte System. Solid State Ionics (in press 2004). 4. Pappenfus Ted M.; Mann, Kent R; Smyrl, William H. Polyelectrolyte Composite Materials with LiPFs and Tetraglyme. Electrochemical and Solid State Letters, (2004), 7(8), A254.

Smyrl, William H.↗

Preliminary study: Moisture-polymer interaction. Stuby objectives

The problems associated with mathematically modeling water-module interaction phenomena, including sorption and desorption, diffusion, and permeation are discussed. With reliable analytical models, an extensive materials data base, and solar radiation surface meteorological observations (SOLMET) weather data, predicting module lifetimes in realistic environments can become a practical reality. The status of the present techniques of simulating the various transport mechanisms was reported. The Dent model (a modified Brunauer-Emmet-Teller) approach represented polyvinyl butyral (PVB) sorption data. A 100-layer material model and Fick's diffusion model gave diffusivity values exhibiting adequate agreement with those measured for PVB. Diffusivity of PVB is concentration dependent, decreasing as the water content in PVB increases. The temperature dependence of diffusion in PVB is well modeled by the Arrhenius rate equation. Equilibrium conductivity and leakage current data are well represented by Hearle's model for bulk ionic conductivity. A nodal network analysis using the Systems Improved Numerical Differencing Analyzer (SINDA) Thermal Analyzer gave reasonable correlation with measurable data. It is concluded that realistic lifetime predictions seem to be feasible.

Wen, L. C.↗

High temperature conductivity of potassium-beta(double prime)-alumina

Potassium beta(double prime)-alumina (BDPA) single crystals have been reported by several groups to leave higher ionic conductivity than sodium BDPA crystals at room temperature, and similar conductivities are obtained at temperatures up to 600-700 K. Potassium BDPA ceramics have been reported to have significantly poorer conductivities than those of sodium BDPA ceramics, but conductivity measurements at temperatures above 625 K have not been reported. In this study, K(+)-BDPA ceramics were prepared from Na(+)-BDPA ceramic using a modified version of the exchange reaction with KCl vapor reported by Crosbie and Tennenhouse (1982), and the conductivity has been measured in K vapor at temperatures up to 1223 K, using the method of Cole et al. (1979). The results indicate reasonable agreement with earlier data on K(+)-BDPA ceramic measured in a liquid K cell, but show that the K(+)-BDPA ceramic's conductivity approaches that of Na(+)-BDPA ceramic at higher temperatures, being within a factor of four at 700 K and 60 percent of the conductivity of Na(+)-BDPA at T over 1000 K. Both four-probe dc conductivity and four probe ac impedance measurements were used to characterize the conductivity. A rather abrupt change in the grain boundary resistance suggesting a possible phase change in the intergranular material, potassium aluminate, is seen in the ac impedance behavior.

Williams, R. M.↗

Framework Short-Range Order Observed in a Spinel-Type Li Superionic Conductor

Solid-state superionic conductors are characterized by rich structural disorders. Though structural complexities are central to their functionalities, they often give rise to short-range order that eludes detection by conventional diffraction-based techniques and is thus overlooked in establishing precise structure-property relationships. In this work, we synthesized single crystals of a recently discovered lithium (Li) superionic conductor Li16.2(1)In9.00(2)Sn1.10(1)O23.8 (LISO) for in-depth characterizations of structural subtleties. LISO exhibits an unusual spinel-like phase with significant Li overstoichiometry and a face-sharing Li network. Single-crystal neutron diffraction confirms significant Li disorder, as manifested in Li site splitting and partial occupancy. More importantly, synchrotron diffuse scattering combined with 3D-ΔPDF analysis and Monte Carlo simulations reveal short-range order in the nonalkali framework that might contribute to the phase stability and ionic conductivity. This work showcases an example in which subtle local energetics can be directly visualized in structurally disordered ionic conductors.

Chen, Yu↗

Probing the potential of type V Deep eutectic solvents as sustainable electrolytes

The increasing interest within the scientific community in environmentally friendly solvents has led to a focus on Deep Eutectic Solvents (DES), which have natural components. DES are viewed as alternatives to traditional organic solvents and have the potential to be used as electrolytes. For the first time, transport properties of four Type V Deep Eutectic Salt Solutions (DESS) were accessed to investigate the potential of this technology, selecting precursors ranked as excellent in Eco-Scale metrics. The DESS were composed of terpene and trioctylphosphine oxide (TOPO), and varying concentrations of lithium bis(trifluoromethane)sulfonimide (LiTFSI), and their properties were assessed through self-diffusion, viscosity, density, and conductivity measurements. While Type V DESS are capable of dissolving significant amounts of LiTFSI (up to 30 % molar), their ionic conductivity is low, with values ranging from 3.6·10 –3 to 9.3·10 –2 mS·cm –1 at 25 °C, thus limiting their suitability as electrolytes, for instance, for lithium-ions batteries applications. Similar diffusion coefficients for Li + and TFSI – ions suggest the formation of long-lived ion pairs moving as a neutral species. As a result, future research aims to introduce additives to disrupt contact ion pairs and enhance transport properties, leveraging the sustainable appeal of DES and their use in advanced energy storage technologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Polycarbonate‐Based Solid‐Polymer Electrolytes for Solid‐State Sodium Batteries

Solid-polymer electrolytes comprised of polypropylene carbonate (PPC) and varied sodium bis(fluorosulfonyl)imide (NaFSI) salt concentrations are investigated for implementation as a conductive solid polymer electrolyte into solid-state cathode composites utilizing a sodium-layered oxide active material. The ionic conductivity generally increases with NaFSI salt content, reaching ≈1 mS cm −1 at 80 °C at the highest salt concentration (PPC:NaFSI = 0.5:1). Through an all-in-one slurry casting method, Na 2/3 Ni 1/3 Mn 2/3 O 2 cathode composites are fabricated in which the dispersed PPC electrolyte acts as the primary binder. Enabled by a bilayer polymer electrolyte system, cycling performance with the PPC cathode electrolyte is optimized with respect to salt concentration and anode material. The best cyclability is achieved with a moderate salt concentration electrolyte (PPC:NaFSI = 5:1), showcasing an initial capacity of 83 mA h g −1 with a remarkable 80% capacity retention after 150 cycles at C/5 rate and 60 °C. The superior performance of the lower salt concentration electrolyte is attributed to better electrochemical stability, as confirmed by linear sweep voltammetry and online electrochemical mass spectrometry measurements. In conclusion, these results underscore the potential of carbonate-based polymer electrolytes and the importance of balancing electrolyte conductivity and stability in cell design.

25 ENERGY STORAGE↗

Infiltrated electrodes for metal supported solid oxide electrolysis cells

Metal-supported solid oxide cells (MSOCs) are an alternative to conventional solid oxide cells (SOCs) based on ceramic cermets, offering lower material costs and higher operational flexibility. In this study symmetric MSOCs with infiltrated electrodes are explored for steam electrolysis operation to understand the underlying operation and degradation principles and suggest a direction for future MSOCs development. Two different fuel electrode backbones are used: an electronically-conductive lanthanum strontium co-doped iron nickel titanate (LSFNT) infiltrated with cerium-gadolinium oxide (CGO), or an ionic conductive zirconia based backbone (10ScYSZ) infiltrated with Ni:CGO. At the oxygen side, the backbone is 10ScYSZ, which is infiltrated with lanthanum-strontium co-doped cobalt oxide (LSC), or praseodymium oxide as cobalt-free alternative for comparison. This study suggests that the backbone electronic conductivity is key for good electrochemical performance as well as for boosting cell durability. Highly electronically conductive nanoparticles, especially nickel, were observed to irreversibly agglomerate driven by thermal conditions, whereas CGO proved to be a very stable electrocatalyst. At the fuel side, CGO (LSFNT) electrode showed lower ASR and degradation rate than Ni:CGO(ScYSZ) configuration with measured values of 0.50 Ω cm2 and 11 %/1000 h (at 0.60 A/cm2), and 0.70 Ω cm2 and 26 %/1000 h (at 0.50 A/cm2) at 1.30 V, respectively (700 °C, 50 % steam in hydrogen at the fuel side and air at the oxygen electrode side, LSC(ScYSZ) oxygen electrode).

25 ENERGY STORAGE↗

Norbornene-Based Polymer Electrolytes for Lithium Cells

Norbornene-based polymers have shown promise as solid electrolytes for lithium-based rechargeable electrochemical cells. These polymers are characterized as single-ion conductors. Single-ion-conducting polymers that can be used in lithium cells have long been sought. Single-ion conductors are preferred to multiple-ion conductors as solid electrolytes because concentration gradients associated with multiple-ion conduction lead to concentration polarization. By minimizing concentration polarization, one can enhance charge and discharge rates. Norbornene sulfonic acid esters have been synthesized by a ring-opening metathesis polymerization technique, using ruthenium-based catalysts. The resulting polymer structures (see figure) include sulfonate ionomers attached to the backbones of the polymer molecules. These molecules are single-ion conductors in that they conduct mobile Li+ ions only; the SO3 anions in these polymers, being tethered to the backbones, do not contribute to ionic conduction. This molecular system is especially attractive in that it is highly amenable to modification through functionalization of the backbone or copolymerization with various monomers. Polymers of this type have been blended with poly(ethylene oxide) to lend mechanical integrity to free-standing films, and the films have been fabricated into solid polymer electrolytes. These electrolytes have been demonstrated to exhibit conductivity of 2 10(exp -5)S/cm (which is high, relative to the conductivities of other solid electrolytes) at ambient temperature, plus acceptably high stability. This type of norbornene-based polymeric solid electrolyte is in the early stages of development. Inasmuch as the method of synthesis of these polymers is inherently flexible and techniques for the fabrication of the polymers into solid electrolytes are amenable to optimization, there is reason to anticipate further improvements.

Cheung, Iris↗

In-situ polymerized and crosslinked electrolytes with interchangeable Li/Na transport for battery applications

The next generation of batteries requires electrolytes with high conductivity, mechanical stability, good adhesion with electrodes, wide electrochemical windows, and scalability. The present study introduces a concept of doped quasi single-ion conducting copolymers based on methacrylate-(trifluoromethanesulfonyl)imide (TFSI) and vinyl ethylene carbonate which at room temperature are mechanically robust and display ionic conductivities of ~0.1 mS/cm. These electrolytes can be polymerized/crosslinked in-situ, making them easily implementable in current battery manufacturing technologies. They also allow for switching between Li + and Na + transport using simple chemistry procedures. To demonstrate their potential for battery applications, the newly developed Li conductors have been tested in symmetric cells, exhibiting overall impedance below 350 Ohm and plating/stripping stability up to 1 mA/cm 2 . Moreover, lithium metal batteries incorporating this electrolyte and high-voltage Lithium Nickel Manganese Cobalt Oxide (NMC) cathodes show good capacity retention (~79%) during charging and discharging for 80 cycles at C/10 rate and a Coulombic efficiency close to 100% in the entire measurement range. The compositional, mechanical and electrochemical versatility of these electrolytes opens new venues for the design of polymer-based batteries capable of fast charging and extended cycle life, aligning with the current global green energy storage strategies.

Polymer electrolytes↗

Structuring, stochastic behavior, and charge storage capacity of redox-active microemulsions formulated with mixtures of toluene and ionic liquid as oil phase

Oil/water microemulsions (µEs) are promising electrolytes for redox flow batteries (RFBs) as they simultaneously improve charge capacity and ionic conductivity. Here, we report the successful formulation of bicontinuous µEs where the oil phase is a solution of trihexyltetradecylphosphonium bis(trifluoromethylsulfonyl)amide ionic liquid in toluene with redox-active ferrocene. We examined the effect of supporting electrolyte anion (NO 3 – , Cl – , ClO 4 – ) on the structure, reactivity, transport, and electrolytic performance of redox-active µEs. Neutron scattering and nuclear magnetic resonance showed that the domain size increased as Cl – > NO 3 – > ClO 4 – while the ferrocene diffusion coefficient increased as NO 3 – > Cl – > ClO 4 – . Scanning electrochemical microscopy indicated anion-dependent current fluctuations during electrolysis, with ClO 4 – exhibiting the least high-frequency oscillations, which correlate to the highest charge and discharge capacity and reversibility. All ionic liquid containing systems improved the performance of toluene-based µEs, highlighting new design principles for these electrolytes.

diffusion↗

Nanoconfined Grain Boundaries Increase the Conductivity of Polycrystalline Molecular Crystals

Soft-solid molecular crystals consist of crystalline grains and fluid grain boundaries (GBs) that enhance the grain binding and transport of Li + ions between the grains. The total ionic conductivity consists of ion migration in both the grains and GBs. To unravel these contributions in adiponitrile (Adpn):LiPF 6 molecular crystals, the GB volume fraction was varied by changing the size of the crystals and the Adpn:LiPF 6 molar ratio. Molecular dynamics (MD) simulations indicate that ion motion was subdiffusive in the grains and “well-diffusive” in the GBs, with GBs characterized as disordered nanoconfined regions of higher charge carrier concentration (∼1 M) than in saturated Adpn:LiPF 6 solutions (0.04 M), and Li + ions predominantly solvated by cyano groups with few contact ion pairs. The diffusivity in the GBs is at least an order of magnitude higher than that in the crystalline grains. The emergent picture is the grains as a reservoir of ions that migrate to faster-conducting GBs.

Crystals↗

Mechanically activated and deactivated ion transport across nanopores with heterogeneous surface charge distributions

To mimic the intricate and adaptive functionalities of biological ion channels, electrohydrodynamic ion transport has been studied extensively, albeit mostly, across uniformly charged nanochannels. Here, we analyze the ion transport under coupled electric field and pressure across heterogeneously charged nanopores with oppositely charged sections on their lateral surface. We only consider such pores with symmetric hourglass-like and cylindrical shapes to focus on the effects of the non-uniform surface charge distribution. Finite-element simulations of a continuum model demonstrate that a pressure applied in either direction of the pore-axis equally suppresses or amplifies the ionic conductance, depending on the electric field polarity, by distorting the quasi-static distribution of ions in the pore. The resulting anomalous mechanical deactivation and activation of ionic current under opposite voltage biases exhibit the functional modularity of our setup, while their intensities are highly tunable, substantially greater than those of analogous behaviors in other nanochannels, and fundamentally correlated to ionic current rectification (ICR) in our pores. A detailed study of ICR subsequently reveals its counterintuitive non-monotonous variations, in the pores, with the magnitude of applied voltage and the pore length, that can help optimize their diode-like behavior. We further illustrate that while the hourglass-shaped nanopores yield the more efficient mechanical suppressors of ion transport, their cylindrical analogs are the superior rectifiers and mechanical amplifiers of ion conduction. Therefore, this article provides a blueprint for the strategic design of nanofluidic circuits to attain a robust, modular, and tunable control of ion transport under external electrical and mechanical stimuli.

Physics↗

Effect of H + Exchange and Surface Impurities on Bulk and Interfacial Electrochemistry of Garnet Solid Electrolytes

Contact loss and current constriction pose significant challenges at the Li metal interface of solid-state batteries. For garnet-structured Li 7 La 3 Zr 2 O 12 (LLZO), these effects are amplified by Li + /H + exchange and surface contamination reactions, which lead to conductivity losses and poor Li wetting. In this study, we utilize a variety of surface treatment processes across 37 cells to selectively induce proton exchange and contamination reactions in LLZO. The resulting bulk and surface chemistry is systematically characterized and correlated to changes in electrochemical properties. Additionally, we combine impedance analysis and finite element method modeling to deconvolute sources of impedance contributions at the Li metal interface. Specifically, we show that constriction impedance at the Li metal interface arises not solely from voids, but also from ionically-resistive surface contaminants. Further, these findings emphasize the connection between ionic conductivity and constriction, demonstrating that micron-scale ionically-resistive components increase constriction even with identical contact geometries. Finally, we leverage our comprehensive dataset to highlight unstable overpotential growth as a failure mechanism, additionally showing that the phase of a cell’s impedance is a sensitive indicator for the onset of interfacial instability. Overall, this study clarifies the impacts of proton exchange and surface contamination on electrochemical properties at the Li|solid electrolyte interface and elucidates insights that are generalizable to other solid-state battery systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗