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All sources NASA NTRS DOE OSTI

DOE OSTI2020

Electron Trapping and Ion Leaching at the Li-Modified Quartz–Water Interface

Electrons and ions at metal oxide-water interfaces have a critical role in many phenomena and applications, thus making their properties of considerable interest. We here investigate the behavior of a lithium impurity at the water interface with Li-doped SiO 2 using hybrid density functional based ab initio molecular dynamics simulations. We find that the excess electron donated by the lithium dopant localizes on a surface silicon atom and is partially solvated at the aqueous interface. While the position of the excess electron does not change during our ~60 ps simulation, the lithium cation diffuses from its initial position in the SiO 2 subsurface toward the interface and eventually leaches out of the oxide surface and becomes solvated by four water molecules, forming an aqueous Li+- electron complex at the interface. The degree of interaction between the localized electron and the lithium ion controls not only the energy level of the excess electron but also the extent of structural distortion and hydrogen-bonding at the interface. The results of our study can be relevant for understanding the initial stages of glass corrosion, where alkali ions are leached from the surface region by interactions with water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Maintaining a Flat Li Surface during the Li Stripping Process via Interface Design

Electroplating has been the main focus in mitigating the dendrite growth on the Li-metal electrode; however, the stripping process is equally critical, since the nonsmooth Li surface during stripping will lead to nonuniform local current density, planting the seeds for dendrite growth. In this paper, density functional theory (DFT) and kinetic Monte Carlo (KMC) techniques were combined to investigate the vacancy evolution in Li interfaced with different solid–electrolyte interphase (SEI) materials. It was found that the lithiophilic interface, such as Li/Li 2 O, repels vacancies into the bulk Li, so Li atoms can quickly fill the Li vacancies near the Li/Li 2 O interface and maintain a smooth Li surface. In contrast, the lithiophobic interface, such as Li/LiF, traps Li vacancies toward the interface, and the accumulated Li vacancies form voids and roughen the surface. The predicted critical stripping current density, below which a smooth Li surface will be maintained, is therefore much faster at the lithiophilic interface than that at the lithiophobic interface. It was further revealed that the lithiophilicity at different SEI or coating materials can be ranked as Li/Li 2 O > Li/LiPON > Li/Li 2 CO 3 > Li/LiF based on the calculated interfacial adhesion and accumulation of electron density at the interface. Furthermore, this suggests that interface and coating design at nanoscale can be effective for maintaining a smooth Li surface during the stripping process, solving another challenge to achieving a dendrite-free Li-metal electrode in both liquid and solid electrolytes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2020

Interface structures of inclined ZnO thin film on (0 1 1)-MgO substrate with bulk-like optical properties

Combining different phase structure materials with unique properties to design novel devices plays a significant role in the development of modern electronics. Here, we explore the characteristics of this type of complex interface and epitaxy structures based on the coupling between hexagonal ZnO film and cubic MgO substrate. The ZnO film was prepared by the molecular beam epitaxy technique on the MgO (0 1 1) substrate. The analysis results from the in situ reflection high energy electron diffraction patterns, X-ray diffraction (XRD)-pole figures and high resolution transmission electron microscopy images demonstrate that the film exhibits two-fold symmetry domains with a growth direction deviated from c-axis at about 31º along the [0 1 0] MgO or [0 $\bar{1}$ 0] MgO azimuth. Despite the intertwined diffusion from Zn and Mg atoms in the interface, which is the possible origin of a blue shift of about 0.083 eV in the Photoluminescence (PL) spectrum, the inclined film shows a full width at half maximum value that is close to the reported value from the high quality film. Finally, this work hopefully provides useful insights to the design and exploration of the novel optoelectronic devices that involve the integration of materials with different structure and different properties.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

Pd-promoted reduction and restructuring of an In 2 O 3 -based catalyst for CO 2 hydrogenation at room temperature

An unconventional reaction mechanism in an In 2 O 3 /Pd(1 1 1) inverse model catalyst for the CO 2 hydrogenation reaction has been uncovered: In 2 O 3 is partially reduced at room temperature in a reaction atmosphere as a result of its direct contact with Pd(1 1 1), which is an efficient H 2 splitter. The reduction induces changes in surface free energy, leading to a dynamical restructuring at the In 2 O 3 /Pd(1 1 1) interface via formation of InO x and outward diffusion of Pd, as revealed by ambient pressure X-ray photoelectron spectroscopy, X-ray absorption spectroscopy and density functional theory simulations. This dynamical restructuring eventually promotes the growth of 2D InPd y O x nanodomains as the catalytically active phase and the exclusive formation of methanol upon hydrogenation of CO 2 at room temperature. A comparable high selectivity toward CH 3 OH was found in more realistic bulk catalytic systems (2 wt% Pd/In 2 O 3 catalyst and commercial CZA catalyst). Scanning tunneling microscopy under ultrahigh vacuum and ambient pressure reaction atmospheres further reveals the structural dynamics at the InO x /Pd(1 1 1) interface, where we follow in situ the evolution of the InO x particles on Pd(1 1 1) and the mobility of the InPd y O x nanodomains in a CO 2 + H 2 environment. The present findings of the formation of a mixed oxide phase in a dynamically restructuring metal/reducible-oxide interface indicate further implications for other heterogeneous catalytic systems beyond the present CO 2 hydrogenation example and highlight the importance of in situ investigations.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Improved analytic modeling of the linear Rayleigh–Taylor instability with plasma transport

The Rayleigh–Taylor (R–T) instability with transport effects has long been studied analytically in the neutral fluid regime. How this picture may differ in plasmas has been given less consideration, however. Leveraging previous numerical simulations with plasma viscosity and diffusion of R–T at a binary plasma interface, we show how plasma transport and kinetic effects alter the linear R–T dispersion relation. Our insight informs a much improved analytical dispersion relation, which better matches the simulation data than previously established models. Additionally, we demonstrate the importance of employing asymptotically correct viscosity coefficients in fluid codes for accurately capturing plasma R–T growth.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

The synergistic role of Mn and Zr/Ti in producing θ'/L12 co-precipitates in Al-Cu alloys

Microstructural stability is a critical factor to consider when designing new alloys for high-temperature applications. An Al-Cu alloy with Mn and Zr additions has recently been developed to withstand extended exposures of up to 350 °C. The addition of Mn in combination with Zr and their segregation to precipitate interfaces play a significant role in stabilizing the metastable θ ' precipitates responsible for the alloy's hardness; however, adding Zr and Mn separately only improves the stability to 200 °C and 300 °C, respectively. To this end, the effect of the synergistic additions on interfacial structure and chemistry was studied in detail using atom probe tomography (APT) and scanning transmission electron microscopy (STEM) for Al-Cu-Mn-Zr/Ti-containing alloys subjected to long-term annealing (up to 2,100 h) in the critical temperature range, 300 °C and 350 °C, to investigate the role of Zr/Ti in increasing the θ '-precipitate stability. The APT and STEM results reveal that Mn additions stabilize θ ' long enough for the slower diffusing Zr atoms to segregate to coherent θ ' interfaces that eventually create a θ '/ L1 2 -Al 3 (Zr x ,Ti 1-x ) co-precipitate structure. The co-precipitate is highly stable, as shown by density functional theory calculations, and is a key factor that governs microstructural stability beyond 300 °C. This study reveals how solute additions with different stabilization mechanisms can work in concert to stabilize a desired microstructure, and the results provide insights that can be applied to other high-temperature alloy systems.

36 MATERIALS SCIENCE↗

DOE OSTI2023

A Guideline to Mitigate Interfacial Degradation Processes in Solid‐State Batteries Caused by Cross Diffusion

Abstract Diffusion of transition metals across the cathode–electrolyte interface is identified as a key challenge for the practical realization of solid‐state batteries. This is related to the formation of highly resistive interphases impeding the charge transport across the materials. Herein, the hypothesis that formation of interphases is associated with the incorporation of Co into the Li 7 La 3 Zr 2 O 12 lattice representing the starting point of a cascade of degradation processes is investigated. It is shown that Co incorporates into the garnet structure preferably four‐fold coordinated as Co 2+ or Co 3+ depending on oxygen fugacity. The solubility limit of Co is determined to be around 0.16 per formula unit, whereby concentrations beyond this limit causes a cubic‐to‐tetragonal phase transition. Moreover, the temperature‐dependent Co diffusion coefficient is determined, for example, D 700 °C = 9.46 × 10 −14 cm 2 s −1 and an activation energy E a = 1.65 eV, suggesting that detrimental cross diffusion will take place at any relevant process condition. Additionally, the optimal protective Al 2 O 3 coating thickness for relevant temperatures is studied, which allows to create a process diagram to mitigate any degradation with a minimum compromise on electrochemical performance. This study provides a tool to optimize processing conditions toward developing high energy density solid‐state batteries.

Chemistry↗

NASA NTRS1973

Lidar Measurements of On-Shore Wind Diffusion

The concept to place electric power generating stations on the oceans off the coast of the United States has instilled new efforts in research for improved understanding of the diffusion properties of the atmosphere in the ocean-air interface. The Atomic Energy Commission has instigated a program by the Meteorology Group at Brookhaven National Laboratory to investigate the low level, on-shore wind systems that dominate many of the coastal regions. Analytical techniques and specialized instrumentation from previous studies at Brookhaven are being used in this new program. The Brookhaven Lidar system is used to measure some of the physical properties of the oil-fog plume originating from a portable smoke generator on a boat off the coast. The oil-fog plume is used as a tracer which can be observed, photographed and measured to determine the diffusive power of the atmosphere associated with the ocean-air interface and the discontinuities found in the ocean-land boundary. This paper will describe the program rather briefly and the oil-fog scattering measurements that have been made with the Lidar system.

Brown, R. M.↗

DOE OSTI2026

SAM Code Enhancements for Fission Product Tracking of Noble Gases and Metals in MSRs

This report documents fiscal year 2026 enhancements to the System Analysis Module (SAM) for modeling fission product transport in liquid-fueled molten salt reactors (MSRs). The work advances three principal areas: noble gas transport, noble metal deposition, and user interface improvements. The noble gas transport capability integrates drift-flux gas transport, Henry’s law two-film interphase mass transfer with pressure-based nucleation suppression, Knudsen-regime pore diffusion into porous graphite with a conjugate salt-graphite interface constraint, built-in material properties, five Sherwood-number mass transfer correlations including three derived from high-fidelity NekRS simulations, and xenon-135 reactivity feedback through SAM’s point-kinetics model. This work also presents a comprehensive verification test suite, including new analytically verified cases for pressure-dependent onset of interphase gas transfer in a stagnant vertical pipe, a postulated FLiBe-graphite Xe extraction permeator, a gravity riser with a fission-product source, and a descending pipe with gas redissolution driven by hydrostatic pressure. A machine learning framework for bubble rise velocity prediction in molten salt systems is developed and benchmarked on molten-salt and diverse aqueous bubble datasets. The best-performing fine-tuned transfer-learning networks achieve an 82% reduction in RMSE relative to the Clift correlation, and is implemented directly in SAM. The noble metal transport capability is developed, including a liquid-wall deposition model and a gas-surface flotation mechanism that transfers insoluble particles entrained by sparging gas to wetted structures. Verification tests and demonstration cases cover the surface deposition, flotation efflux, and flotation shedding. Finally, a new [SpeciesTransport] input structure replaces positional global vectors with selfcontained, order-independent, named species blocks, simplifies the specification of multiphase species and decay chains, and remains fully compatible with existing SAM input files. Together, these developments improve the physical fidelity, verification basis, and usability of SAM for system-level analyses of fissionproduct behavior in MSRs.

Mui, Travis (ORCID:0000000303736470)↗

DOE OSTI2020

Insights into Na + Diffusion in Silicon Modules under Operating Conditions: Measuring Low Concentrations by D-SIMS

Sodium induced shunting under an electric field is a challenging reliability issue in crystalline Si solar modules. The source of this Potential-Induced Degradation of the Shunting type (PID-s) is well understood and its influence on power loss has been intensively studied based on phenomenological models on cell or module level relating the experimental power-loss to stressing parameters (time, temperature, voltage). However, little is known about the Na ion migration kinetics, responsible for PID on a microscopic level, and its quantitative relation to the efficiency degradation. In this paper we present our investigations of sodium ion migration in Ethylene-Vinyl Acetate (EVA) and silicon through Dynamic Secondary Ion Mass Spectroscopy (D-SIMS). Each sample was annealed at field relevant temperatures from 60-90 °C to address typical migration mechanisms of common PV installations. Analysis of the SIMS migration profiles revealed a diffusivity constant D 0,EVA = 0.09 ± 0.14 cm 2 /s and an activation energy E A,EVA = 0.85 ± .04 eV for Na in EVA and diffusivities higher than extrapolated literature values in silicon (D 0,Si = (3.03 ± 2.42)x10 -5 cm 2 /s, and E A,Si = 0.98 ± 0.02 eV). The new insight will be included in a drift-diffusion based degradation model accounting for the partition coefficient across all relevant interfaces. This model can assist in predicting PID-failure in the field based on the given model stack and the diffusion of Na + through each material. Furthermore, this tool can be used for process optimization as well as material selection significantly reducing the cost and time to validate a technology.

14 SOLAR ENERGY↗

DOE OSTI2020

Growth and Properties of Vapor Diffused Nb3Sn Coating for Superconducting Radiofrequency Accelerator Cavity Applications

The desire to reduce construction and operating costs of future SRF accelerators motivates the search for higher-performing alternative materials. Nb3Sn (Tc ~ 18.3 K and Hsh ~ 425 mT) is the front runner. The tin vapor diffusion process is currently the technique of choice to produce promising Nb3Sn-coated cavities. Understanding Nb3Sn nucleation and growth in this process is essential to progress. Samples representing different stages of Nb3Sn formation have been produced and studied to elucidate the effects of nucleation, growth, process conditions, and impurities. Nb3Sn films with thickness from a few hundred nm up to ~15 µm were grown and characterized. The microscopic examination of samples suggests the mechanisms of thin film nucleation and growth. Broadly, nucleation deposits tin as a thin surface phase and, under some conditions, a few hundred nanometer sized particles as well. Conditions that impair nucleation promote the formation of defects, such as ?patches?, in subsequent coating growth. Analysis of coated samples is consistent with the model of Nb3Sn grown in which tin diffuses via grain boundaries to Nb3Sn-Nb interface, where the growth Nb3Sn into the niobium bulk takes place. Similar scaling laws are found for grain growth and layer thickness. Non-parabolic layer growth is consistent with significant grain growth, which reduces the number of Sn-transport channels. Examination of patchy region in Nb3Sn coating revealed it to be large single crystalline grains, pointing to impeded Nb3Sn layer growth due to low grain boundary density, resulting in a significantly thin coating in those areas. Examination of RF loss regions from a coated cavity, identified with a thermometry mapping system showed patchy regions and carbonus defects were associated with strong local field-dependent surface resistance. RF measurements of coated cavities were combined with material characterization of witness samples and coated-cavity cutouts to improve the coating process. Understanding obtained and applied to cavity coatings, resulted in single-cell Nb3Sn cavities with a quality factor of ~2 ×1010 up to 15 MV/m accelerating gradient at 4 K, without "Wuppertal" Q-slope. We have also produced Nb3Sn-coated CEBAF 5-cell cavities with accelerating gradients useful for accelerator cryomodules. This dissertation will discuss the genesis of the Nb3Sn coating in a typical tin vapor diffusion process, effects of different process parameters, and its consequences to the coating of single-cell and multi-cell SRF cavities.

Pudasaini, Uttar↗

NASA NTRS2001

The Isothermal Dendritic Growth Experiment (IDGE)

Dendritic solidification is one of the simplest examples of pattern formation where a structureless melt evolves into a ramified crystalline microstructure; it is a common mode of solidification in many materials, but especially so in metals and alloys. There is considerable engineering interest in dendrites because of the role dendrites play in the determination of microstructure, and thereby in influencing the physical properties of cast metals and alloys. Dendritic solidification provides important examples of non-equilibrium physics, pattern formation dynamics, and models for computational condensed matter and material physics. Current theories of dendritic growth generally couple diffusion effects in the melt with the physics introduced by the interface. Unfortunately, in terrestrial based experiments, convective effects in the melt alter the growth process in such a manner as to prevent definitive analysis of convective, diffusive or interfacial effects. Thus, the effective elimination of convection in the melt by operating experiments on orbit were required to produce high-fidelity data needed for achieving further progress. This simple fact comprised the scientific justification for the IDGE.

Glicksman, M. E.↗

DOE OSTI2026

Interfacial Void Formation and Self-Healing in Oxide Scales on Al-containing High-Entropy Alloy

The exceptional high-temperature oxidation resistance of Al-containing high-entropy alloys (HEAs) is often attributed to the formation of a protective α-Al 2 O 3 scale. However, the dynamic, atomic-scale mechanisms governing the stability of this scale—including interfacial void formation and the often-postulated but rarely visualized “self-healing” capacity—remain poorly understood. Herein, we reveal the complex evolution of the triple-layer oxide scale on an Al 10 CoCrFeNi HEA through combined electron microscopy and diffraction study. We show that interfacial voids are an inherent consequence of the scaling process, originating from two distinct mechanisms: the Kirkendall effect at the interface between the γ-Al 2 O 3 /α-Al 2 O 3 and alloy driven by cationic diffusion imbalance and volumetric contraction due to phase transformations at the spinel/Cr 2 O 3 interface. Crucially, we provide microstructural evidence consistent with an intrinsic self-healing response. This process is driven by coupled inward diffusion of oxygen and outward diffusion of metal cations, leading to the in-situ formation of transient θ-Al 2 O 3 and spinel phases that partially fill and seal the voids. Here, these results provide atomic-scale insights into the phase evolution, defect formation, and self-repair of oxide scales in HEAs—highlighting pathways to enhance their oxidation resistance in extreme environments.

High-entropy alloy↗

NASA NTRS2003

Effect of Gravity Level on the Particle Shape and Size During Zeolite Crystal Growth

A microscopic diffusion model is developed to represent solute transport in the boundary layer of a growing zeolite crystal. This model is used to describe the effect of gravity on particle shape and solute distribution. Particle dynamics and crystal growth kinetics serve as the boundary conditions of flow and convection-diffusion equations. A statistical rate theory is used to obtain the rate of solute transport across the growing interface, which is expressed in terms of concentration and velocity of solute species. Microgravity can significantly decrease the solute velocity across the growing interface compared to its earth-based counterpart. The extent of this reduction highly depends on solute diffusion constant in solution. Under gravity, the flow towards the crystal enhances solute transport rate across the growing interface while the flow away from crystals reduces this rate, suggesting a non-uniform growth rate and thus an elliptic final shape. However, microgravity can significantly reduce the influence of flow and obtain a final product with perfect spherical shape. The model predictions compare favorably with the data of space experiment of zeolites grown in space.

Song, Hong-Wei↗

NASA NTRS2019

In Situ Observation of Growth Dynamics in DECLIC Directional Solidification Insert Onboard ISS: DSI-R Flight Campaign

The study of solidification microstructure formation is of utmost importance for materials design and processing, as solid-liquid interface patterns largely govern mechanical and physical properties. Pattern selection occurs under dynamic conditions of growth in which the initial morphological instability evolves nonlinearly and undergoes a reorganization process. The dynamic and nonlinear nature of this instability renders in situ observation of the interface an invaluable tool to gain knowledge on the time-evolution of the interface pattern. Transparent organic analogs, which solidify like metallic alloys, allow direct visualization of interface dynamics. Extensive ground-based studies of both metallic and organic bulk samples have established the presence of significant convection during solidification processes that alters the formation of interfacial microstructures. A reduced-gravity environment is therefore mandatory for fluid flow elimination in bulk samples. In the framework of the CNES project MISOL3D (MIcrostrutures de SOLidification 3D) and the NASA projects DSIP (Dynamical Selection of 3D Interface Patterns), SPADES (SPAtiotemporal Evolution of three-dimensional DEndritic array Structures) and CAMUS (ComputAtional Studies of MicrostrUcture Formation During Alloy Solidification in Microgravity), we participated in the development of the Directional Solidification Insert (DSI) of the DEvice for the study of Critical Liquids and Crystallization (DECLIC). The DECLIC-DSI is dedicated to in situ and real-time characterization of solid-liquid interface patterns during directional solidification of transparent alloys in diffusive transport regime. Between April 2010 and March 2011, the first ISS campaign (DSI) explored the entire range of microstructures resulting in unprecedented observations. A second campaign (DSI-R), performed between October 2017 and December 2018, in which the insert contained an alloy of higher solute concentration, allowed to complete the benchmark database. The increase of solute concentration resulted in well-developed dendritic patterns at lower velocities (lower interface curvature and larger tip radius). The microstructure resulting from dendritic growth is dominant in metallurgy so that it is fundamental to understand the mechanisms of its formation. The main aims of this experimental campaign are to understand: the mechanisms of the cell to dendrite transition, the fundamental mechanisms of sidebranching formation, the dependence of dendrite tip shapes on growth conditions, the interaction of primary array and secondary sidebranches, and the influence of subgrain boundaries on the spatiotemporal organization of the array structure. Preparation, analysis and interpretation of the experiments performed onboard ISS are considerably enhanced by experiments performed on ground using thin-samples (Pr. Trivedi’s group) and phase-field simulations of microstructure formation in a diffuse growth regime (Pr. Karma’s group). In this summary, we will present an initial assessment of the results obtained during the DSI-R campaign. Nomenclature Vp: pulling velocity G: thermal gradient L: solidified length rtip: tip curvature radius Acronyms/Abbreviations CADMOS: Centre d'Aide au Développement des activités en Micro-pesanteur et des Opérations Spatiales CNES: Centre National d’Études Spatiales DECLIC: Device for the study of Critical LIquids and Crystallization DSI: Directional Solidification Insert DSI-R: Directional Solidification Insert - Refurbish ISS: International Space Station NASA: National Aeronautics and Space Administration PF: phase-field SCN: Succinonitrile 3D: three-dimensional

Mota, F.L.↗

NASA NTRS2017

Kinetic Monte Carlo Simulations of Oxygen Diffusion in Environmental Barrier Coating Materials

Ceramic Matrix Composite (CMC) materials are of interest for use in next-generation turbine engine components, offering a number of significant advantages, including reduced weight and high operating temperatures. However, in the hot environment in which such components operate, the presence of water vapor can lead to corrosion and recession, limiting the useful life of the components. Such degradation can be reduced through the use of Environmental Barrier Coatings (EBCs) that limit the amount of oxygen and water vapor reaching the component. Candidate EBC materials include Yttrium and Ytterbium silicates. In this work we present results of kinetic Monte Carlo (kMC) simulations of oxygen diffusion, via the vacancy mechanism, in Yttrium and Ytterbium disilicates, along with a brief discussion of interstitial diffusion. An EBC system typically includes a bond coat located between the EBC and the component surface. Bond coat materials are generally chosen for properties other than low oxygen diffusivity, but low oxygen diffusivity is nevertheless a desirable characteristic, as the bond coat could provide some additional component protection, particularly in the case where cracks in the coating system provide a direct path from the environment to the bond coat interface. We have therefore performed similar kMC simulations of oxygen diffusion in this material.

Good, Brian S.↗

NASA NTRS1988

Diffusional decay of striations

This paper investigates the amount of decay of growth striations in bulk crystals grown from melts and solutions, due to solid-state diffusion during the cooling of the crystal to room temperature. A model is developed based on the assumption of a sinusoidal variation in the solid composition at the interface of a semiinfinite ingot growing at constant velocity, and the damping behavior of this variation is followed as it moves away from the solid-liquid interface. Numerical results are presented showing that an increase in the diffusivity causes the striations to penetrate deeper into the solid and, consequently causes the distance for 99.9 percent decay to increase. Analytical results are also presented for the decay of striations in an isothermal ingot induced by a sinusoidal fluctuation in the rate of crystal growth.

Gray, R. T.↗

DOE OSTI2021

Analytical modeling for redox flow battery design

Deeper market penetration of redox flow batteries requires optimization of the cell performance. Though important for optimization, detailed analytical solutions have not been developed for electrolyte flow, mass and charge transport, and reaction kinetics within redox flow batteries. To this end, here we present analytical solutions to active species concentration and over-potential based on advection-diffusion transport for ions and Bulter-Volmer model for interface reaction kinetics. The solutions were validated with results from a finite element model. These solutions were then applied to investigate the relationship between over-potential and state of charge, current density, reaction rate constant, flow velocity, diffusivity, total active species concentration, and electrode structure. Explicit formulas were identified for minimum activation over-potential and limiting current density as well as their dependence on electrolyte properties, operation conditions, and electrode structure. With our new mathematical formulas, this work provides a theoretical framework for flow battery design.

25 ENERGY STORAGE↗