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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Effect of Solvent Motion on Ion Transport in Electrolytes

We use concentrated solution theory to derive an equation governing solvent velocity in a binary electrolyte when a current passes through it. This equation, in combination with the material balance equation, enables the prediction of electrolyte concentration profiles and species velocities as a function of space and time. This framework is used to predict ion velocities in Li-Li symmetric cells containing a mixture of lithium bis(trifluoromethanesulfonyl)imide and poly(ethylene oxide) (LiTFSI/PEO), for which the cation transference number relative to the solvent velocity, ${t}_{+}^{0},$ can be either positive or negative, depending on salt concentration. Accounting for the solvent motion is increasingly important at higher concentrations. Especially for negative ${t}_{+}^{0},$ if solvent velocity is set to zero, the cation velocity, based on the electrode-electrolyte interface reference frame, is pointed opposite to the current flow. However, when solvent motion is taken into account, the cation velocity, based on the same reference frame, is in the same direction as the current. This analysis demonstrates the importance of accounting for solvent velocity rigorously in seemingly simple systems such as symmetric cells.

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

The Importance of a Moving Boundary Approach for Modeling the SEI Layer Growth to Predict Capacity Fade

One of the contributing factors to the aging of lithium-ion batteries is the growth of the solid-electrolyte interphase (SEI) layer. The growth of the SEI layer leads to the irreversible loss of lithium available for cycling and increases the resistance of the battery. Physics-based models in literature model the kinetically limited or solvent diffusion-limited growth. In such models, the interface resistance is a constant, and the contribution to the overpotential of the intercalation reaction from the SEI layer is considered to be ohmic. In this study, we propose a model that describes the growth of the SEI layer on the electrode surface as a moving interface. The transport of lithium ions and the solvent in the electrolyte are affected by this moving interface. The equations that govern the species transport and the potential drop across the SEI layer are derived from dilute solution theory and solved by transforming the coordinates of the moving boundary. The ion transport induces changes in the conductivity across the SEI layer, which affects the potential drop that arises due to its growth. The effects of this potential on capacity fade are studied over cycling the battery.

25 ENERGY STORAGE↗
DOE OSTI2022

Divergence of Velocity Fields in Electrochemical Systems

The passage of current through electrochemical systems results in the development of concentration gradients in the electrolytic phase that can be modeled using concentrated solution theory. Application of this theory requires knowledge of three concentration-dependent transport coefficients, which are often taken to be conductivity, diffusion coefficient, and the cation transference number with respect to the solvent velocity. The governing diffusion equation for molar concentration contains two additional terms - the thermodynamic factor which is related to activity of the electrolytic species and the solvent velocity. The main advance in this paper is the derivation of an expression for the divergence of the solvent velocity. Solving this equation requires knowledge of the partial molar volume of the electrolyte. Analogous expressions are derived for the mass average and molar average velocities. These velocities occur naturally in the diffusion equation if concentration is expressed as weight fraction and mole fraction of the electrolytic species, respectively.

diffusion↗
DOE OSTI2023

Comparing Theoretical Salt Concentration Profiles in a Polymer Electrolyte with Experimental Measurements using Operando Raman Spectroscopy

Concentrated solution theory has furthered our understanding of ion transport in electrolytes. This theory can be used to predict salt concentration profiles under an applied current if the transport properties of the electrolyte (conductivity ( κ ), restricted diffusion coefficient ( D ), and the cation transference number with respect to the solvent velocity ( t + 0 )), and the thermodynamic factor ( T f ) are known. In this work, we provide the first study comparing the predicted salt concentration profiles with measurements based on operando Raman spectroscopy. Concentration polarization is asymmetrical; the increase in salt concentration near the positive electrode is a factor of two greater than the decrease in salt concentration near the negative electrode. We find qualitative agreement between theory and experiment. Further work is needed to resolve the quantitative differences.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Low-Temperature Characterization of a Nonaqueous Liquid Electrolyte for Lithium Batteries

Rechargeable batteries exhibit poor performance at low temperatures due to sluggish ion transport through the electrolytic phase. Ion transport is governed by three transport parameters—conductivity, diffusion coefficient, and the cation transference number with respect to the solvent velocity—and the thermodynamic factor. Understanding how these parameters change with temperature is necessary for designing improved electrolytes. In this work, we combine electrochemical techniques with electrophoretic NMR to determine the temperature dependence of these parameters for a liquid electrolyte, LiTFSI salt dissolved in tetraglyme between −20 and 45 °C. At colder temperatures, all species in the electrolyte tend to move more slowly due to increasing viscosity, which translates to a monotonic decrease in conductivity and diffusion coefficient with decreasing temperature. Surprisingly, we find that the field-induced velocity of solvent molecules at a particular salt concentration is a nonmonotonic function of temperature. The cation transference number with respect to the solvent velocity thus exhibits a complex dependence on temperature and salt concentration. The measured thermodynamic and transport properties are used to predict concentration gradients that will form in a lithium-lithium symmetric cell under a constant applied potential as a function of temperature using concentrated solution theory. The calculated steady current at −20 °C is lower than that at 45 °C by roughly two orders of magnitude.

25 ENERGY STORAGE↗
DOE OSTI2025

Mapping Spatiotemporal Solvent Velocity from Measured Concentration Gradients in a Polarized Electrolyte

The electric-field induced motion of neutral species impedes the efficacy of electrochemical devices. By combining operando X-ray transmission measurements with continuum mechanics, we have developed a methodology for determining the velocity of neutral solvent molecules under an applied field. The X-ray transmission experiments were used to determine ion concentration profiles as a function of space and time in a polymer electrolyte. The unsteady state solvent mass balance equation was solved numerically with experimental concentration profiles to map spatiotemporal solvent velocities. We compare our experimentally derived results with predictions made with concentrated solution theory. We use the cation transference number as the only adjustable parameter to match experimental measurements of both concentration and solvent velocity. Our approach may be used to determine solvent velocity with any operando technique used to measure time-dependent ion concentration profiles.

Abdo, Emily E↗
DOE OSTI2025

Toward Establishing Uniqueness of Experimentally Determined Transference Numbers

The passage of current through a battery results in the development of concentration gradients in the electrolytic phase. For a fully characterized binary electrolyte, where the conductivity, salt diffusion coefficient, cation transference number, and the thermodynamic factor are known, concentration and potential gradients in the electrolytic phase can be modeled using Newman’s concentrated solution theory. We report two methods for measuring the transference number: the standard method based on electrochemical measurements ( t + , echem 0 ) and electrophoretic NMR ( t + , eNMR 0 ). The electrochemical approach requires combining measurements from multiple experiments; the equations used to determine the cation transference number and the thermodynamic factor are coupled, nonlinear algebraic equations. In the electrophoretic-NMR-based approach, however, the equations used to determine the cation transference number and the thermodynamic factor are decoupled. We find for a liquid electrolyte comprised of a lithium salt dissolved in tetraglyme, the values of the transference numbers obtained by these two methods are distinct. For example, at 30 °C, t + , echem 0 = −1.02 ± 1.11 and t + , eNMR 0 = 0.25 ± 0.04. The corresponding thermodynamic factors are also different. While the magnitude of the predicted concentration gradients based on the two sets of parameters are different, the predicted current-voltage relationships are similar.

Hickson, Darby T. (ORCID:0000000251339755)↗
DOE OSTI2025

Ion Transport in Concentrated Crosslinked Solid Polymer Electrolytes

Crosslinking polymers is a common approach to create mechanically stable solid materials such as polymer electrolytes for lithium batteries. In conventional liquid electrolytes, the solvent molecules move freely to accommodate the field-induced motion of ions. However, in crosslinked polymer electrolytes, the rearrangement of polymer segments is constrained by the deformation limits of the network. Herein, we develop a new transport model that accounts for both the formation of concentration gradients and the elasticity of the electrolyte. The elasticity is incorporated by adding an additional term related to the entropy of crosslinked strands to the electrochemical potential of the salt. The resulting Crosslink Model contains two adjustable parameters: $\mathcal{N}$, the average number of monomers in a strand, and λ crit , the maximum strain the network can sustain. These solid-like constraints produce singularities in the governing transport equations, fundamentally altering the concentration profiles. Plateaus in salt concentrations emerge near the electrodes, and network elasticity introduces a strain overpotential. When compared to a Baseline Model ($\mathcal{N}$ → ∞, equivalent to concentrated solution theory), which predicts steepest gradients near the electrodes, both models yield similar current–voltage relationships. Model predictions are compared to electrochemical data for a poly(ethylene oxide)-based crosslinked polymer electrolyte.

Patel, Vivaan [University of California, Berkeley,↗
DOE OSTI2020

Modeling Synergistic Fuel Cell Membrane Degradation with Mitigating Effects of Cerium

During operation, polymer-electrolyte-membrane (PEM) fuel cells undergo mechanical and chemical degradation mechanisms, which behave synergistically and lead to accelerated membrane degradation over time. This study builds upon previous modeling work on mechanical degradation as described by a pinhole in the membrane and the effects of cerium on chemical degradation.1 By combining these two models, analysis can be carried out on the coupled degradation methods and how the mitigation effects of cerium disrupt the degradation cycle. The mechanical model represents a pinhole in the membrane using an effective void fraction, which allows for increased gas crossover through the membrane and impacts the membrane transport and mechanical properties. A microkinetic model for the chemical degradation is included in the model, including attack of the membrane polymer by hydroxyl radicals as well as the mitigation reaction for quenching of hydroxyl radicals with cerium. A concentrated solution theory approach is used to model the transport of cerium ions throughout the cell.2 The model results show how the location of cerium in the cell can be used to prevent chemical degradation. In addition, the model shows how cerium slows down the rate of pinhole growth by reducing the gas crossover and membrane thinning rate. Finally, the model can be used to optimize the distribution of cerium in the membrane and catalyst layers by balancing trade-offs between lowering degradation rates and decreasing fuel cell performance.

25 ENERGY STORAGE↗
DOE OSTI2022

(Invited) Continuum Mathematical Modeling of Water Electrolysis: A Tutorial

Widespread use of hydrogen energy is contingent on the development of reliable and economical sources of hydrogen. Electrolysis from renewably-derived low-carbon electricity is a potentially viable method of hydrogen generation. Prime among the electrolysis technologies are those utilizing ion-conducting polymers (ionomers) including proton-exchange-membrane water electrolyzer (PEMWE). However, these technologies need to exhibit increased efficiency, performance, and durability to become commercially viable. Like most electrochemical devices, PEMWEs involve multiple components (e.g., catalyst, ionomer, transport layers, membrane, plates) and multiple phases, with phenomena occurring across different time and length scales. Furthermore, it is difficult to experimentally probe many of the species and phenomena during operation. Thus, mathematical modeling at the continuum level has been an invaluable aid in exploring, understanding, and optimizing PEMWE cell and components. Furthermore, this is especially true in the highly coupled and complex physics and chemistries that occur with the membrane-electrode assembly (MEA). The physics in a typical volume-averaged non-isothermal model include multiphase transport in porous media, concentrated-solution theory, Ohm's Law, and Butler-Volmer kinetics, and ion, gas, and water transport in the ionomer.

Dizon, Arthur↗
NASA NTRS1976

Determination of optimum planforms for control surfaces

A theoretical analysis is made to determine the optimum chord distribution, location, and extent of control surfaces, with the ratio of hinge moment to effectiveness as the criterion. Expressions for the effectiveness - for ailerons, the rolling moment, and for tail surfaces, the change of lift on the tail due to deflection of the surface-were derived from lifting line theory. Solutions found for a range of airfoil planforms indicate that, regardless of the characteristics of the tail surface, the chord of the rudder or the elevator should be very nearly constant over its span. The optimum ailerons are also of a characteristics shape, varying little with the planform of the wing.

Jones, R. T.↗
NASA NTRS1979

Advanced methods for preparation and characterization of infrared detector materials

Crystal growth of Hg sub 1-x Cd sub x Te and density measurements of ingot slices are discussed. Radial compositional variations are evaluated from the results of infrared transmission edge mapping. The pseudo-binary HgTe-CdTe phase diagram is examined with reference to differential thermal analysis measurements. The phase equilibria calculations, based on the 'regular association solution' theory (R.A.S.) are explained and, using the obtained R.A.S. parameters, the activities of Hg, Cd, and Te vapors and their partial pressures over the pseudo-binary melt are calculated.

Lehoczy, S. L.↗
NASA NTRS1982

Solubility of Sulfur Dioxide in Sulfuric Acid

The solubility of sulfur dioxide in 50% (wt./wt.) sulfuric acid was evaluated by regular solution theory, and the results verified by experimental measurements in the temperature range of 25 C to 70 C at pressures of 60 to 200 PSIA. The percent (wt./wt.) of sulfur dioxide in 50% (wt./wt.) sulfuric acid is given by the equation %SO2 = 2.2350 + 0.0903P - 0.00026P 10 to the 2nd power with P in PSIA.

Chang, K. K.↗
NASA NTRS1987

Recursive Robot-Arm Dynamics via Filtering and Smoothing

Forward and inverse dynamics solved using Kalman filtering and Bryson-Frazier smoothing. Dynamics of serial-link robot arm solved by using recursive techniques from linear filtering and smoothing theory. Solutions of dynamical equations give forces, moments, and accelerations at joints between links, and multilink inertia matrix and its inverse. Theoretical developments lay foundation for use of filtering and smoothing techniques in design of robot controls.

Rodriguez, Guillermo↗
NASA NTRS1989

Calculation of steady and unsteady pressures at supersonic speeds with CAP-TSD

A finite difference technique is used to solve the transonic small disturbance flow equation making use of shock capturing to treat wave discontinuities. Thus the nonlinear effects of thickness and angle of attack are considered. Such an approach is made feasible by the development of a new code called CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance), and is based on a fully implicit approximate factorization (AF) finite difference method to solve the time dependent transonic small disturbance equation. The application of the CAP-TSD code to the calculation of low to moderate supersonic steady and unsteady flows is presented. In particular, comparisons with exact linear theory solutions are made for steady and unsteady cases to evaluate shock capturing and other features of the current method. In addition, steady solutions obtained from an Euler code are used to evaluate the small disturbance aspects of the code. Steady and unsteady pressure comparisons are made with measurements for an F-15 wing model and for the RAE tailplane model.

Bennett, Robert M.↗
NASA NTRS1988

Smooth indentation of a composite laminate

Finite difference method is used to analyze the problem of smooth contact between a rigid indenter and a laminated circular plate clamped at the edges. The plate consists of transversely isotropic layers. The interlaminar shear stresses in the contact region are found to be much different from the laminate plate theory solutions. It has been found that low-modulus interlayers cause significant reduction in the maximum interlaminar shear stresses.

Sankar, B. V.↗
NASA NTRS1989

Computation of hypersonic flow fields

The present discussion of the theory, solution methods, and development status of chemically reactive flow CFD codes pertaining to the flow field around a hypersonic vehicle encompasses the formulation of multicomponent viscous equations, grid-generation techniques, and finite-difference algorithms. The Navier-Stokes equations presented focus on such particularities of high speed vehicles as their aerodynamic configuration, lee and wake flow, bow shock, and chemistry and low density effects. Issues for which further development is desirable encompass boundary treatments, grid quality, shock capturing, and the decoupling of chemistry from flow variables.

Li, Chien-Peng↗
NASA NTRS1991

Calculation of Gallium-metal-Arsenic phase diagrams

Electrical contacts and metallization to GaAs solar cells must survive at high temperatures for several minutes under specific mission scenarios. The determination of which metallizations or alloy systems that are able to withstand extreme thermal excursions with minimum degradation to solar cell performance can be predicted by properly calculated temperature constitution phase diagrams. A method for calculating a ternary diagram and its three constituent binary phase diagrams is briefly outlined and ternary phase diagrams for three Ga-As-X alloy systems are presented. Free energy functions of the liquid and solid phase are approximated by the regular solution theory. Phase diagrams calculated using this method are presented for the Ga-As-Ge and Ga-As-Ag systems.

Scofield, J. D.↗