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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 217 records · Page 12
All sourcesNASA NTRSDOE OSTI
DOE OSTI2016

Multiply Reduced Oligofluorenes: Their Nature and Pairing with THF-Solvated Sodium Ions

Conjugated oligofluorenes are chemically reduced up to five charges in tetrahydrofuran solvent and confirmed with clear spectroscopic evidence. Stimulated by these experimental results, we have conducted a comprehensive computational study of the electronic structure and the solvation structure of representative oligofluorene anions with a focus on the pairing between sodium ions and these multianions. In addition, using density functional theory (DFT) methods and a solvation model of both explicit solvent molecules and implicit polarizable continuum, we first elucidate the structure of tightly solvated free sodium ions, and then explore the pairing of sodium ions either in contact with reduced oligofluorenes or as solvent-separated ion pairs. Computed time-dependent-DFT absorption spectra are compared with experiments to assign the dominant ion pairing structure for each multianion. Computed ion pair binding energies further support our assignment. Lastly, the availability of different length and reducing level of oligofluorenes enables us to investigate the effects of total charge and charge density on the binding with sodium ions, and our results suggest both factors play important roles in ion pairing for small molecules. However, as the oligofluorene size grows, its charge density determines the binding strength with the sodium ion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Preferential Solvation of an Asymmetric Redox Molecule

The fundamental correlations between inter-molecular interactions, solvation structure and functionality of electrolytes are in many cases unknown, particularly for multi-component liquid systems. In this work, we explore such correlations by investigating the complex interplay between solubility and solvation structure for the electrolyte system comprising N-(ferrocenylmethyl)-N,N-dimethyl-N-ethylammonium bistrifluoromethylsulfonimide (Fc1N112-TFSI) dissolved in a ternary carbonate solvent mixture using combined NMR relaxation and computational analyses. Probing the evolution of the solvent-solvent, ion-solvent and ion-ion interactions with an increase in solute concentration provides a molecular level understanding of the solubility limit of the Fc1N112-TFSI system. An increase in solute con-centration leads to pronounced Fc1N112-TFSI contact-ion pair formation by diminishing solvent-solvent and ion-solvent type interactions. At the solubility limit, the precipitation of solute is initiated through agglomeration of contact-ion pairs due to overlapping solvation shells.

Environmental Molecular Sciences Laboratory↗
DOE OSTI2019

Affordable Estimation of Solvation Contributions to the Adsorption Energies of Oxygenates on Metal Nanoparticles

Electrocatalysts are mainly characterized by their intrinsic adsorption properties. However, the observed electrocatalytic activity ultimately results from the interplay between such properties and various additional interactions within the electrified solid–liquid interface. One of such phenomena is solvation, which can substantially affect the stability of adsorbates. The incorporation of solvation in computational electrocatalysis models can be fully implicit (inaccurate for H-bonded adsorbates), fully explicit (challenging computation of free energies), or embedded. Here, we show that without any need for explicit or implicit media, a microsolvation approach with just three water molecules captures the contribution of co-adsorbed water to the adsorption energies of *OH and *OOH (two important adsorbates for oxygen reduction) on platinum nanoparticles of various sizes. The approach enables an accurate yet inexpensive explicit modeling of solvent–adsorbate interactions in nanoparticles and the calculation of solvation corrections, estimated as -0.59 ± 0.14 and -0.47 ± 0.13 eV for *OH and *OOH adsorption on Pt, respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Tuning the Solvation and Solubility Properties of Molecularly Heterogeneous Nonionic Deep Eutectic Solvents via Interface Organization

Common separation techniques, such as liquid− liquid extraction, are usually used for extractions and purifications due to their industrial scalability and affordability. However, these well-established practices are hindered by low selectivity and challenges in recovering solutes and solvents. Deep eutectic solvents (DES), a fairly new type of solvent, have the potential to overcome these issues. DESs are binary mixtures whose physical properties can be tuned by selecting the appropriate precursors to facilitate and/or enhance processes such as extraction. A promising DES for selective separations is formed when lauric acid (LA) is mixed with N-methylacetamide (NMA). This LA-NMA DES has a heterogeneous microscopic structure that can solvate compounds with completely different polarities. This study explores how forming an organized structure on the mesoscale affects the solubility of nonpolar solutes in nonionic DESs. To this end, the molecular and mesoscale structures and their effect on the solubility and solvation properties are evaluated for the LA-NMA DES and two new DESs with slight chemical variations in their precursors. It is observed that the organization of the nonpolar DES domains and, consequently, of their interfaces directly relates to the solubility of nonpolar compounds. Specifically, correctly selecting the DES precursors that form organized nonpolar domains leads to an organized interface in which the nonpolar solutes are solvated, thereby increasing the solubility. Additionally, enhanced dissolution power was observed in a completely different DES with mesoscale order in its molecular structure and composed of menthol and lauric acid. The latter result further validates the proposed tunability of the DES dissolution power through organized interfaces, extending it beyond a specific DES family and opening the possibility of new extraction-tailored designer solvents.

Extraction↗
DOE OSTI2018

Solvate Ionic Liquids at Electrified Interfaces

Solvate ionic liquids (SILs) are a promising electrolyte for Li-ion batteries; thus, their behavior at electrified interfaces is crucial for the operation of these batteries. We report molecular dynamics simulation results for a prototypical SIL of lithium triglyme bis(trifluoro-methanesulfonyl)imide ([Li(G3)][TFSI]) sandwiched between electrified surfaces. At negatively charged as well as neutral electrodes, the electrolyte largely maintains the characteristics of SILs, e.g., a majority of the interfacial Li + ions remains coordinated by the similar number of oxygen atoms on G3 ligands as the bulk Li + ions. The persistence of the complex ions is attributed to the 1:1 Li-G3 ratio in bulk SILs and the fact that G3 molecules readily adapt to the interfacial environment, e.g., by aligning themselves with the surface to ensure good solvation of the interfacial Li + ions. Nevertheless, the interfacial Li + ions also display changes of solvation from that in bulk SIL by deviating from the molecular plane formed by the oxygen atoms on G3 ligands as electrodes become more negatively charged. Using density functional theory along with natural bond orbital calculations, we examine the effects of such structural distortion on the properties of the complex cation. Both the frontier orbital energies of the complex cation and the donor-acceptor interactions between Li + ions and G3 ligands are found to be dependent on the deviation of Li + ions from the molecular plane of the G3 ligands, which suggest that the reduction of Li + ions should be facilitated by the structural distortion. These results bear important implications for the nanostructures and properties of SILs near electrified interfaces during actual operations of Li-ion batteries and serve to provide guidance toward the rational design of new SILs electrolytes.

25 ENERGY STORAGE↗
DOE OSTI2022

Kinetic Model for the Reduction of Cu II Sites by NO + NH 3 and Reoxidation of NH 3 -Solvated Cu I Sites by O 2 and NO in Cu-SSZ-13

In this work, a kinetic model is developed for the reduction of Cu II sites by NO + NH 3 and the reoxidation of NH 3 -solvated Cu I sites by O 2 and NO in Cu-SSZ-13. Fourier transform infrared (FTIR) spectroscopy and spatially resolved capillary inlet mass spectrometry (SpaciMS) measurements during transient reactor experiments are utilized to identify the rate parameters associated with NO + NH 3 RHC (reduction half-cycle), proposed to occur via two distinct pathways involving adsorbed NH 3 and gas-phase NH 3 . The resulting NO + NH 3 RHC model is validated using spatiotemporal N 2 measurements covering a wide range of temperatures (200–450 °C) and space velocities (53,000–640,000 h –1 ). N 2 O formation is observed and modeled during NO + NH 3 RHC, with quantitative validation under standard selective catalytic reduction (SCR) conditions. Experimentally measured enthalpic and entropic changes associated with O 2 adsorption on NH 3 -solvated Cu I (ZCu(NH 3 ) 2 ) complexes [ Kamasamudram, K. Catal. Today 2010 , 151 (3–4), 212-222], along with activation energies estimated computationally for the intercage diffusion of ZCu(NH 3 ) 2 complexes [ Paolucci, C. Science 2017 , 357 (6 354), 898-903], are incorporated into a mean field kinetic model for the low-temperature oxidation half-cycle (OHC). Significant NH 3 release is observed during the isothermal oxidation of Cu I sites, attributed to desorption of NH 3 ligands from NH 3 -solvated Cu II dimers (Z 2 Cu 2 (NH 3 ) 4 O 2 ). Reduction of these dimeric complexes leads to the consumption of one NO/Cu II , contradicting the expected reduction stoichiometry. Inclusion of a global Arrhenius rate for the NO titration of Z 2 Cu 2 (NH 3 ) 4 O 2 complexes provides accurate representations of standard SCR on reduced and oxidized catalysts, predicting transient NO and NH 3 consumption between 150 and 250 °C as a function of hydrothermal aging. Deactivation of low-temperature standard SCR by NH 3 is observed at high NH 3 pressures, modeled via the formation of superoxo amino (ZCu(NH 3 ) 3 OO*) complexes during NH 3 titration of Z 2 Cu 2 (NH 3 ) 4 O 2 complexes [ Negri, C. J. Am. Chem. Soc. 2020 , 142 (37), 15884-15896]. The redox kinetic model presented here provides a foundational description of active site redox during low-temperature standard SCR, combining the recent kinetic, spectroscopic, and computational findings on the mechanism of standard SCR over Cu-SSZ-13.

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

Effect of Building Block Connectivity and Ion Solvation on Electrochemical Stability and Ionic Conductivity in Novel Fluoroether Electrolytes

Novel electrolytes are required for the commercialization of batteries with high energy densities such as lithium metal batteries. Recently, fluoroether solvents have become promising electrolyte candidates because they yield appreciable ionic conductivities, high oxidative stability, and enable high Coulombic efficiencies for lithium metal cycling. However, reported fluoroether electrolytes have similar molecular structures, and the influence of ion solvation in modifying electrolyte properties has not been elucidated. In this work, we synthesize a group of fluoroether compounds with reversed building block connectivity where ether moieties are sandwiched by fluorinated end groups. These compounds can support ionic conductivities as high as 1.3 mS/cm (30 °C, 1 M salt concentration). Remarkably, we report that the oxidative stability of these electrolytes increases with decreasing fluorine content, a phenomenon not observed in other fluoroethers. Using Raman and other spectroscopic techniques, we show that lithium ion solvation is controlled by fluoroether molecular structure, and the oxidative stability correlates with the “free solvent” fraction. Finally, we show that these electrolytes can be cycled repeatedly with lithium metal and other battery chemistries. Understanding the impact of building block connectivity and ionic solvation structure on electrochemical phenomena will facilitate the development of novel electrolytes for next-generation batteries.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Water or Anion? Uncovering the Zn 2+ Solvation Environment in Mixed Zn(TFSI) 2 and LiTFSI Water-in-Salt Electrolytes

Applications of aqueous zinc batteries for grid-scale energy storage are limited by their poor reversibility and the competing water splitting reaction. The recent invention of a water-in-salt (WIS) electrolyte concept provides a new route enabling a stable and highly reversible aqueous zinc battery chemistry. In the present work, a mixed zinc bis(trifluoromethane sulfonyl)imide (Zn(TFSI) 2 ) and LiTFSI WIS electrolyte was studied using X-ray total scattering, X-ray absorption, and Fourier transform infrared spectroscopy in conjunction with classical molecular dynamics simulations. It was found that, in the highly concentrated WIS electrolyte consisting of 1 m Zn(TFSI) 2 and 20 m LiTFSI, Zn 2+ cations are mainly solvated by six waters in their first solvation shell, while the TFSI – anions are completely excluded. This ion solvation picture is fundamentally different from the previous understandings. The results suggest that additional studies are needed to fully understand the unusual stability and reversibility of zinc-WIS electrolyte-based batteries.

25 ENERGY STORAGE↗
DOE OSTI2024

Optimizing Nonaqueous Sodium–Polysulfide Redox-Flow Batteries: The Role of Solvation Effects with Glyme Solvents

Nonaqueous redox-flow batteries (NARFBs) that use economical alkali metals and the corresponding metal polysulfides are highly attractive for grid-scale energy storage. Although sodium–sulfur systems have been recognized as promising candidates and have been the focus of many studies due to their high earth abundance and energy density, an understanding of the role of the solvation chemistry of commonly used glyme solvents is missing. Herein, we report a systematic investigation into the solvation effects of glyme-based Na-S electrolytes through comprehensive physiochemical experiments and Density Functional Theory (DFT) simulations. Our findings revealed, on one hand, that an optimal coordination strength between glymes and Na + could maintain a relatively smooth Na + diffusion. On the other hand, glyme solvents with extended chain lengths shift the reduction potential of S 8 2– negatively to elevate the formation barrier of undesirable short-chain polysulfides (S n 2– , n ≤ 4) that have high membrane permeability. This solvation phenomenon not only mitigates capacity fading but also extends the operational longevity of the Na-S NARFBs. In conclusion, the results underscore the critical roles of balanced solvent–cation interactions and controlled redox potentials in improving the stability and efficiency of Na-S NARFB systems, marking a significant advancement in the development of sustainable energy storage solutions.

25 ENERGY STORAGE↗
DOE OSTI2021

Molecular Level Differences in Ionic Solvation and Transport Behavior in Ethylene Oxide-Based Homopolymer and Block Copolymer Electrolytes

Block copolymer electrolytes (BCE) such as polystyrene-block-poly(ethylene oxide) (SEO) blended with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) and composed of mechanically robust insulating and rubbery conducting nanodomains are promising solid-state electrolytes for Li batteries. Here, we compare ionic solvation, association, distribution, and conductivity in SEO-LiTFSI BCEs and their homopolymer PEO-LiTFSI analogs toward a fundamental understanding of the maximum in conductivity and transport mechanisms as a function of salt concentration. Ionic conductivity measurements reveal that SEO-LiTFSI and PEO-LiTFSI exhibit similar behaviors up to a Li/EO ratio of 1/12, where roughly half of the available solvation sites in the system are filled, and conductivity is maximized. As the Li/EO ratios increase to 1/5 the conductivity, of the PEO-LiTFSI drops nearly 3-fold, while the conductivity of SEO-LiTFSI remains constant. FTIR spectroscopy reveals that additional Li cations in the homopolymer electrolyte are complexed by additional EO units when the Li/EO ratio exceeds 1/12, while in the BCE, the proportion of complexed and uncomplexed EO units remains constant; Raman spectroscopy data at the same concentrations show that Li cations in the SEO-LiTFSI samples tend to coordinate more to their counteranions. Atomistic-scale molecular dynamics simulations corroborate these results and further show that associated ions tend to segregate to the SEO-LiTFSI domain interfaces. The opportunity for "excess" salt to be sequestered at BCE interfaces results in the retention of an optimum ratio of uncompleted and complexed PEO solvation sites in the middle of the conductive nanodomains of the BCE and maximized conductivity over a broad range of salt concentrations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Hydroxide Solvation and Transport in Anion Exchange Membranes

Understanding hydroxide solvation and transport in anion exchange membranes (AEMs) can provide important insight into the design principles of these new membranes. To accurately model hydroxide solvation and transport, we developed a new multiscale reactive molecular dynamics model for hydroxide in aqueous solution, which was then subsequently modified for an AEM material. With this model, we investigated the hydroxide solvation structure and transport mechanism in the membrane. We found that a relatively even separation of the rigid side chains produces a continuous overlapping region for hydroxide transport that is made up of the first hydration shell of the tethered cationic groups. Our results show that hydroxide has a significant preference for this overlapping region, transporting through it and between the AEM side chains with substantial contributions from both vehicular (standard diffusion) and Grotthuss (proton hopping) mechanisms. Comparison of the AEM with common proton exchange membranes (PEMs) showed that the excess charge is less delocalized in the AEM than the PEMs, which is correlated with a higher free energy barrier for proton transfer reactions. The vehicular mechanism also contributes considerably more than the Grotthuss mechanism for hydroxide transport in the AEM, while our previous studies of PEM systems showed a larger contribution from the Grotthuss mechanism than the vehicular mechanism for proton transport. The activation energy barrier for hydroxide diffusion in the AEM is greater than that for proton diffusion in PEMs, implying a more significant enhancement of ion transport in the AEM at elevated temperatures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

Atomistic characterization of the active-site solvation dynamics of a model photocatalyst

The interactions between the reactive excited state of molecular photocatalysts and surrounding solvent dictate reaction mechanisms and pathways, but are not readily accessible to conventional optical spectroscopic techniques. Here we report an investigation of the structural and solvation dynamics following excitation of a model photocatalytic molecular system [Ir 2 (dimen) 4 ] 2+ , where dimen is para-diisocyanomenthane. The time-dependent structural changes in this model photocatalyst, as well as the changes in the solvation shell structure, have been measured with ultrafast diffuse X-ray scattering and simulated with Born-Oppenheimer Molecular Dynamics. Both methods provide direct access to the solute–solvent pair distribution function, enabling the solvation dynamics around the catalytically active iridium sites to be robustly characterized. Our results provide evidence for the coordination of the iridium atoms by the acetonitrile solvent and demonstrate the viability of using diffuse X-ray scattering at free-electron laser sources for studying the dynamics of photocatalysis.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2025

Imaging solvated oxygen atoms with a femtosecond laser

As a powerful oxidant, atomic oxygen (O) holds considerable promise for a variety of biomedical and industrial applications. However, the inability to quantify solvated oxygen atoms has prevented the determination of the fundamental parameters governing its behaviour in relevant aqueous environments. Here, we directly image ground-state oxygen atoms in water using femtosecond two-photon absorption laser-induced fluorescence. Measurements show that oxygen atoms persist for tens of microseconds in water, penetrating hundreds of micrometres into the liquid. This observed longevity has significant implications, suggesting a need to re-evaluate existing models of solvated atomic oxygen reactivity and transport. Beyond atomic oxygen, this technique is broadly applicable to other solvated atomic species of interest, including nitrogen (N) and hydrogen (H). This work establishes that radical atomic species can be quantified in liquid with ultrafast laser spectroscopy, providing the basis for the determination of key properties including reaction rates, chemical lifetimes, and Henry’s law constants.

Fluorescence spectroscopy↗
DOE OSTI2026

Aqueous electrolyte solutions with anion-bridged secondary solvation sheaths for highly efficient zinc metal batteries

Aqueous zinc metal batteries are low-cost electrochemical devices suitable for safe grid energy storage. However, water decomposition and Zn dendrite formation detrimentally affect their coulombic efficiency. Conventional aqueous electrolyte solutions, with a concentration around 1 M, are cost-effective and exhibit high bulk ionic conductivity but cannot form a stable solid electrolyte interphase. Water-in-salt and aqueous-organic hybrid electrolyte solutions can form robust solid electrolyte interphases, but they are not kinetically efficient and cost-effective. Here, to circumvent these issues, we design variously concentrated aqueous electrolyte solutions using several salts with different donor numbers to extend anion coordination into the secondary solvation sheath. We show that salt-derived anions with donor number > 18 enter the Zn2+ first solvation sheath, and ensure a strong binding energy between the Zn2+(H2O)5-anion nanometric clusters and water molecules in the secondary solvation sheath. In particular, 2 M aqueous electrolyte solutions containing fluorinated anions exhibit bulk ionic conductivities of 26-35 mS cm−1 at 25 °C and form a ZnF2-rich solid electrolyte interphase. When tested in Zn||NaV3O8·1.5H2O Swagelok cells, the best-performing electrolyte solution enables an average coulombic efficiency of 99.99% for 1,000 cycles at 1.5 mA cm−2, corresponding to an initial specific energy of 130 Wh kg−1 (based on the combined weight of the positive and negative electrodes).

25 ENERGY STORAGE↗
DOE OSTI2020

Dependency of solvation effects on metal identity in surface reactions

Solvent interactions with adsorbed moieties involved in surface reactions are often believed to be similar for different metal surfaces. However, solvents alter the electronic structures of surface atoms, which in turn affects their interaction with adsorbed moieties. To reveal the importance of metal identity on aqueous solvent effects in heterogeneous catalysis, we studied solvent effects on the activation free energies of the O–H and C–H bond cleavages of ethylene glycol over the (111) facet of six transition metals (Ni, Pd, Pt, Cu, Ag, Au) using an explicit solvation approach based on a hybrid quantum mechanical/molecular mechanical (QM/MM) description of the potential energy surface. A significant metal dependence on aqueous solvation effects was observed that suggests solvation effects must be studied in detail for every reaction system. The main reason for this dependence could be traced back to a different amount of charge-transfer between the adsorbed moieties and metals in the reactant and transition states for the different metal surfaces.

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

On the relationship between the structural and volumetric properties of solvated metal ions in O -donor solvents using new structural data in amide solvents

The structures of the N , N -dimethylformamide (dmf), N , N -dimethylacetamide (dma), and N , N -dimethylpropionamide (dmp) solvated strontium and barium ions have been determined in solution using large angle X-ray scattering and EXAFS spectroscopy. The strontium ion has a mean coordination number (CN) between 6.2 and 6.8, and the barium ion has a mean CN between 7.1 and 7.8 in these amide solvents. The non-integer numbers indicates that equilibria between different coordination numbers and geometries exist in these systems. Structural information of the alkali, alkaline earth, and selected transition metal and lanthanoid( III ) ions, and the halide ions in water, methanol, ethanol, dimethylsulfoxide, formamide, dmf and dma has been combined with previously reported standard partial molar volumes, V 0 . The ionic radii and charge densities (charge/ionic volume), and corresponding V 0 values have been used to gain information on the relationship between structural and volumetric properties. For the structure-breaking ions, i.e. the alkali metal and halide ions, there is an almost linear relationship between the ionic radius and V 0 . On the other hand, for the structure-making ions, here the alkaline earth, transition metal and lanthanoid( III ) ions, a linear relationship is observed between the charge density and V 0 . Solvents with a well-defined bulk structure through hydrogen bonding, specifically, water, methanol and ethanol, will be more contracted through solvation than aprotic solvents, as the space between the solvent molecules is lost as a result of the hydrogen bonding. In this respect, methanol stands out as the most compressed solvent participating in solvation compared to its bulk structure.

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

Aqueous solvation of the chloride ion revisited with density functional theory: impact of correlation and exchange approximations

The specificity of aqueous halide solvation is fundamental to a wide range of bulk and interfacial phenomena spanning from biology to materials science. Halide polarizability is thought to drive the ion specificity, and if so, it is essential to have an accurate description of the electronic properties of halide ions in water. To this end, the solvation of the chloride anion, Cl - has been reinvestigated with state-of-the-art density functional theory. Specifically, the PBE-D3, PBE0-D3, and SCAN functionals have been employed to probe the impact of correlation and exchange approximations. Anticipating the findings, adding exact exchange improves the electronic structure, but simultaneously significantly reduces the Cl - polarizability, resulting in an over-structured Cl–O radial distribution function (RDF) and longer water H-bond lifetimes to Cl - . SCAN does not yield as much improvement in the energetics of Cl - relative to bulk water, but does result in a smaller reduction of the polarizability and thus a less structured Cl–O RDF, which agrees better with experiment. Special consideration is therefore warranted in assessing the impact of exchange on the energy, charge density, and the charge density response when designing and testing hybrid functionals for aqueous halide solvation.

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

Solvation vs. surface charge transfer: an interfacial chemistry game drives cation motion

Electrolyte structure and ion solvation dynamics determine ionic conductivities, and ion (de)solvation processes dominate interfacial chemistry and electrodeposition barriers. In this work, we elucidate electrolyte effects facilitating or impeding Li + diffusion and deposition, and evaluate structural and energetic changes during the solvation complex pathway from the bulk to the anode surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗