Concentrated Solution Theory Research Articles

Aspects of Reduced Performance of Proton-Exchange-Membrane Water Electrolysis Via Continuum Modeling

Proton-exchange-membrane water electrolysis (PEMWE) is a technology, where hydrogen is electrochemically produced from water. Efficient industrial-scale production of hydrogen via PEMWE is contingent upon developing systems that are sufficiently resilient to operate under non-ideal operating conditions. Mathematical models can provide insight into the underlying physical mechanisms and inform the development of mitigating strategies. In the current work, a cell-level non-isothermal continuum model that is based on concentrated-solution theory that accounts for multiple ionic mobile species in the membrane and ionomer, energy transport, and fluid flow through porous media, was used to investigate two challenges to PEMWE becoming a viable technology, specifically contamination and hydrogen crossover. In cationic contamination, dissolved salts in the reactant water supplant protons in the membrane and ionomer and significantly increase the applied potentials required for operation. Hydrogen crossover is a concern especially in low-current operational modes, which can arise due to PEMWE powered by variable and cyclical renewable energy sources and can result in the production of combustible gas mixtures.For cation-contaminated cells, simulation results suggest that the uptake of the contaminant cation increased as a function of current density until local conditions in the cathode catalyst layer (cCL) allowed the contaminant desorption to occur. The model suggests that the increased cell potential is primarily due to proton activity losses in the hydrogen evolution reaction within the cCL and that ionic conductivity losses are insufficient to cause the performance losses observed experimentally. Agreement with experimental data lends the model as a possible method or predictive models for PEMWE cell recovery methods. Observations of hydrogen crossover simulations suggest several aspects of hydrogen crossover, which include that localized pressures within the catalyst layers can enhance crossover, bubble-nucleation kinetics limit the exhaust of product gases, and convective fluxes due to electroomostic drag are negligible. An improved understanding of the crossover mechanisms can inform the development of low-crossover designs and mitigation strategies. Figure 1

Accurate Ionic Conductivity Calculations of Battery Electrolytes at High Salt Concentration Using Molecular Dynamics Simulations

The ionic conductivity of an electrolyte formulation is a crucial property influencing battery performance. The dependence of ionic conductivity on multiple parameters, such as salt and solvent type, concentration, and temperature complicates the design of next-generation electrolytes. Efficient design of superior electrolytes requires methods capable of accurately and rapidly predicting ionic conductivity. Such methods would enable high-throughput screening of electrolyte chemistries to establish structure-property relationships.The simple Nernst-Einstein approximation is widely used in the literature to estimate ionic conductivity of electrolytes using the measured self-diffusivity. However, the failure of this approximation for concentrated solutions due to stronger intermolecular interactions requires incorporating a rigorous concentrated solution theory, such as Maxwell-Stefan (MS) diffusivity. Here, we present a molecular dynamics (MD) simulation workflow for calculating the ionic conductivity of liquid electrolytes utilizing the ion-correlated MS diffusion approach. We explore the sensitivity of calculated ionic conductivity to various simulation parameters and various methods in the literature to guide a standardized simulation protocol. Through rigorous benchmarking across a diverse range of electrolyte systems, we validate the model's accuracy by directly comparing the calculated ionic conductivities against experiments and existing literature. This work is a significant step toward a more unified and comprehensive evaluation procedure for ionic conductivity, accelerating the development of advanced electrolytes for improved battery performance.

Ion Transport in Polymer Electrolytes: Building New Bridges between Experiment and Molecular Simulation.

ConspectusPolymer electrolytes constitute a promising type of material for solid-state batteries. However, one of the bottlenecks for their practical implementation lies in the transport properties, often including restricted Li+ self-diffusion and conductivity and low cationic transference numbers. This calls for a molecular understanding of ion transport in polymer electrolytes in which molecular dynamics (MD) simulation can provide both new physical insights and quantitative predictions. Although efforts have been made in this area and qualitative pictures have emerged, direct and quantitative comparisons between experiment and simulation remain challenging because of the lack of a unified theoretical framework to connect them.In our work, we show that by computing the glass transition temperature (Tg) of the model system and using the normalized inverse temperature 1000/(T - Tg + 50), the Li+ self-diffusion coefficient can be compared quantitatively between MD simulations and experiments. This allows us to disentangle the effects of Tg and the polymer dielectric environment on ion conduction in polymer electrolytes, giving rise to the identification of an optimal solvating environment for fast ion conduction.Unlike Li+ self-diffusion coefficients and ionic conductivity, the transference number, which describes the fraction of current carried by Li+ ions, depends on the boundary conditions or the reference frame (RF). This creates a non-negligible gap when comparing experiment and simulation because the fluxes in the experimental measurements and in the linear response theory used in MD simulation are defined in different RFs. We show that by employing the Onsager theory of ion transport and applying a proper RF transformation, a much better agreement between experiment and simulation can be achieved for the PEO-LiTFSI system. This further allows us to derive the theoretical expression for the Bruce-Vincent transference number in terms of the Onsager coefficients and make a direct comparison to experiments. Since the Bruce-Vincent method is widely used to extract transference numbers from experimental data, this opens the door to calibrating MD simulations via reproducing the Bruce-Vincent transference number and using MD simulations to predict the true transference number.In addition, we also address several open questions here such as the time-scale effects on the ion-pairing phenomenon, the consistency check between different types of experiments, the need for more accurate force fields used in MD simulations, and the extension to multicomponent systems. Overall, this Account focuses on building new bridges between experiment and simulation for quantitative comparison, warnings of pitfalls when comparing apples and oranges, and clarifying misconceptions. From a physical chemistry point of view, it connects to concentrated solution theory and provides a unified theoretical framework that can maximize the power of MD simulations. Therefore, this Account will be useful for the electrochemical energy storage community at large and set examples of how to approach experiments from theory and simulation (and vice versa).

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.

Comparing Experimentally-Measured Sand’s Times with Concentrated Solution Theory Predictions in a Polymer Electrolyte

We compare the electrochemically measured Sand’s time, the time required for the cell potential to diverge when the applied current density exceeds the limiting current, with theoretical predictions for a 0.47 M poly(ethylene oxide) (5 kg mol−1)/LiTFSI electrolyte. The theoretical predictions are made using concentrated solution theory which accounts for both concentration polarization and polymer motion, using independently measured parameters that depend on concentration, c: conductivity (κ), salt diffusion coefficient (D), cationic transference number with respect to the solvent velocity (), thermodynamic factor and partial molar volume of the salt (); is the mean molar activity coefficient of the salt. We find quantitative agreement between experimental data and theoretical predictions. We derive a generalized analytical expression for Sand’s time for electrolytes based on dilute solution theory. This expression correctly predicts the divergence of the Sand’s time at the limiting current, in agreement with experimental data and concentrated solution theory predictions. When the applied current is large compared to the limiting current, the analytical expression approaches the standard expression for Sand’s time used in the literature.

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 ()), 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.

Warburg Conductivity for Binary Electrolyte for Enabling Electrolyte Screening and Efficient Battery Operations

Estimating the potential drop in a separator and an electrode is crucial for efficient battery operations and electrolyte screening. Currently, calculating the potential drop in the electrolyte phase for Li-ion batteries requires numerical simulation of coupled partial differential equations resulting from concentrated solution theory. In this study, we introduce the concept of Warburg conductivity to represent the potential drop due to concentration gradient in a binary electrolyte to simplify the theoretical treatment. Accurate quantification of this potential drop can facilitate the development of fast charging algorithms by allowing a higher voltage cutoff during battery charging. To express the potential drop in the binary electrolyte, four parameters are necessary: conductivity, diffusivity, transference number, and thermodynamic factor. While the effect of the conductivity on the potential drop in the electrolyte is straightforward (representing ionic resistance), this work introduces the concept of Warburg conductivity to combine the remaining three parameters and derive the expression of the Warburg resistance. By considering both ionic and Warburg resistances, a comprehensive understanding of the total potential drop in the electrolyte phase is achieved, which is essential for analyzing battery performance and electrolyte screening.

Overlimiting Currents and Sand’s Time Behaviors in Solid Polymer Electrolytes

Dendrite growth in solid polymer electrolytes has been frequently analyzed since it was the critical issue that limited its applications. For the liquid electrolyte systems, the dilute solution theory and the classic Nernst-Planck equation have been proven to be useful tools for analysis of ion transport dynamics and especially the dendrite initiation at Sand’s time. However, characterization of the Sand’s time in solid polymer electrolyte systems is challenging and also seldomly performed. From the experimental perspective, operando observations have been done, but the true local current density was different from the geometrical average current density since there was always heterogeneous current distribution for millimeter-scale electrolytes. From the theoretical perspective, the dendrite initiation time followed the trend predicted by Sand’s equation, but discrepancies were found such as dendrites observed at under-limiting currents or the order-of-magnitude extended Sand’s time compared to theoretical predictions. Here, we use transparent microcapillary cells for solid polymer electrolyte systems to overcome these challenges. These specialized cells allow direct operando optical observations, while the micron-scale cross-sectional area minimizes the discrepancy between true local and averaged geometrical current densities. Comparison between operando image and voltage response during constant current polarization shows that, unlike liquid electrolyte cases, the dendrite initiation for solid polymer electrolytes doesn’t always trigger a voltage spike. We also derived transport parameters from the measured Sand’s time, limiting current density, and conductivity and the cross-validated transport parameters were used to calculate theoretical Sand’s time that can be compared with the experimental values. Using the analytical solution from the Nernst-Planck equation and numerical calculations using Newman’s concentrated solution model and COMSOL Multiphysics, the predicted Sand’s time for the dilute and concentrated solution theory both matched closely with our experimental values. This work demonstrates that while the polarization process and the onset of lithium dendritic growths in solid polymer electrolytes can be still accurately predicted by the dilute solution theory, it may not always result in voltage responses similar to that of the liquid electrolyte cases. It’s also suggested that ensuring the homogenous distribution of lithium flux and avoiding the localized overlimiting current density is the key to realizing the dendrite-free polymer electrolytes.

Investigating Nafion Responsiveness Via Coupled Transport-Mechanical Network Modelling

Perfluorosulfonated (PFSA) ionomer membranes owe their high conductivity and durability, which make them popular as proton-exchange membranes for fuel cells and electrolyzers, to their characteristic phase-separated morphology. The hydrophilic domains connecting the ionic moieties form the transport network for ions and water, while the hydrophobic polymeric backbone affords them the much-needed mechanical stability. Interactions between these domains constitute the structure-property relationship. PFSAs such as Nafion can be reimagined as responsive materials by leveraging this structure-property relationship, integral to their functionality, as a stimuli-response dynamic.Modelling, in tandem with morphological, mechanical, and transport experimental evidence, can be a powerful tool to deconstruct how different stimuli can be designed to elicit a desired response from an ionomer. A large majority of relevant models have dealt with transport in and mechanics of Nafion membranes as isolated behaviors. Transport models, which are usually continuum scale, use dilute solution (Nernst–Planck) or concentrated solution (Onsager–Stefan–Maxwell) theory depending on the scale and complexity of the phenomena in focus. Mechanical models range from statistical-mechanics-led molecular scale formulations to macroscopic phenomenological approaches. Whereas the continuum models lose out on details regarding morphological changes, molecular models are simply too expensive to scale up. Mesoscale models can offer an elegant solution for this problem by incorporating phenomenon inseparable from structural details of the material while remaining computationally tenable.In this work, the hydrophilic and hydrophobic domains in the ionomer will be modelled as two-way coupled mesoscale networks. Whereas the transport network will share characteristics with a pore-network-like configuration, the polymeric backbone will be visualized as a network of non-Hookean springs. The interspersed networks will be configured using the dual-cubic as well as the Delaunay–Voronoi conformations. The mathematical frameworks for each phase will also be modified to include mass-momentum coupling, as implemented by a few continuum models. The network nature of the topology will allow for local flux and deformation changes to organically propagate beyond the nearest neighbors, capturing the core of the ionomer’s responsiveness. Deeper insights into the stimuli-response behavior will allow for more nuanced control of operating conditions for fuel cells and electrolyzers to obtain a tailored performance from existing ionomers as well as enable development of better customized materials for the future.

Finite-Element Simulation for Ion Co-Intercalation Chemistry on Si Anode at Lithium-Ion Half-Cell

The increasing demand for higher capacity energy storage technologies is rapidly becoming an important consideration in the development of EV and related energy storage devices. Silicon is one promising solution as an earth-abundant element with a higher capacity than the more commonly used graphite anode of a lithium-ion battery. However, silicon anodes face unique challenges with volume expansion, notable during lithium ion intercalation and the stability of the SEI layer. To solve this problem, some recent research efforts discovered introducing a co-intercalation ion in the traditional lithium electrolyte Gen2 increases the coulombic efficiency, capacity, and stability of the silicon anode, but its mechanism of action remains unclear.In this work, in combination with experimental measurements we demonstrate the use of Newman's P2D Lithium Model in COMSOL together with the Butler-Volmer equation and concentrated solution theory to describe cation co-intercalation into the porous silicon anode material. Experimental data indicates that phase formation and transformation coincide with ion insertion, as reflected in the current response signal. Both the original ion intercalation and the foreign ion intercalation are reflected by CV generated by our model under the influence of model parameters, such as the variable speed of potential changed per second. As designed, our model can be extended towards general application in the cointercalation system and understanding of the foreign ion effect.

Electrochemical Characterization of PEO/LiTFSI Electrolytes Near the Solubility Limit

Polymer electrolytes are commonly studied as potential solid replacements for conventional liquid electrolytes to enable the design of rechargeable batteries with a lithium metal anode. Poly(ethylene oxide) (PEO)/lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) has been studied extensively and serves as the foundation for advanced systems. We present the first full electrochemical characterization of this system at high salt concentrations above r = 0.30, where r is the molar ratio of lithium ions to ethylene oxide in the electrolyte. Above r = 0.28, we observe two coexisting phases: an amorphous phase with r = 0.28 and a crystalline phase with r = 0.50. We measure the limiting current, the maximum current that can be applied to an electrolyte before the time-dependent potential diverges exponentially, and find that at r = 0.50, the limiting current is essentially zero. This indicates that r = 0.50 is the solubility limit for PEO/LiTFSI. Based on this solubility limit, we use concentrated solution theory to predict the limiting current below r = 0.50. The theory and experiments agree qualitatively but not quantitatively because the theory was developed for single-phase systems.

Influence of Mesoscale Interactions on Proton, Water, and Electrokinetic Transport in Solvent-Filled Membranes: Theory and Simulation.

Transport of protons and water through water-filled, phase-separated cation-exchange membranes occurs through a network of interconnected nanoscale hydrophilic aqueous domains. This paper uses numerical simulations and theory to explore the role of the mesoscale network on water, proton, and electrokinetic transport in perfluorinated sulfonic acid (PFSA) membranes, pertinent to electrochemical energy-conversion devices. Concentrated-solution theory describes microscale transport. Network simulations model mesoscale effects and ascertain macroscopic properties. An experimentally consistent 3D Voronoi-network topology characterizes the interconnected channels in the membrane. Measured water, proton, and electrokinetic transport properties from literature validate calculations of macroscopic properties from network simulations and from effective-medium theory. The results demonstrate that the hydrophilic domain size affects the various microscale, domain-level transport modes dissimilarly, resulting in different distributions of microscale coefficients for each mode of transport. As a result, the network mediates the transport of species nonuniformly with dissimilar calculated tortuosities for water, proton, and electrokinetic transport coefficients (i.e., 4.7, 3.0, and 6.1, respectively, at a water content of 8 H2O molecules per polymer charge equivalent). The dominant water-transport pathways across the membrane are different than those taken by the proton cation. Finally, the distribution of transport properties across the network induces local electrokinetic flows that couple water and proton transport; specifically, local electrokinetic transport induces water chemical-potential gradients that decrease macroscopic conductivity by up to a factor of 3. Macroscopic proton, water, and electrokinetic transport coefficients depend on the collective microscale transport properties of all modes of transport and their distribution across the hydrophilic domain network.

(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. 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.In this talk, different modeling approaches, governing equations, and constitutive relationships will be described, including the benefits and limits of modeling. While focus will be on continuum equations and macroscale effects, detailed submodels and approaches for scaling to full cells and specific components, respectively, will be introduced. For example, as shown in Figure 1, one can perform an applied voltage breakdown and describe the different mechanisms resulting in the necessary applied overpotentials, which is useful in identifying opportunities for improving cell performance by quantifying the potential losses associated with a specific mechanism. In the talk, the generation of such analysis will be discussed including various approaches. Also shown in Figure 1 is how modeling can be used to elucidate safety concerns and identify issues to be resolved, in this case, nonlinear hydrogen crossover. Finally, future directions for multiscale modeling and multi-model coupling will be discussed. Figure 1

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.

Toward Bottom-Up Understanding of Transport in Concentrated Battery Electrolytes.

Bottom-up understanding of transport describes how molecular changes alter species concentrations and electrolyte voltage drops in operating batteries. Such an understanding is essential to predictively design electrolytes for desired transport behavior. We herein advocate building a structure–property–performance relationship as a systematic approach to accurate bottom-up understanding. To ensure generalization across salt concentrations as well as different electrolyte types and cell configurations, the property–performance relation must be described using Newman’s concentrated solution theory. It uses Stefan–Maxwell diffusivity, ij, to describe the role of molecular motions at the continuum scale. The key challenge is to connect ij to the structure. We discuss existing methods for making such a connection, their peculiarities, and future directions to advance our understanding of electrolyte transport.

Overlimiting ion transport dynamic toward Sand's time in solid polymer electrolytes

The ion transport dynamics in solid polymer electrolytes can be well captured by the classic Nernst-Planck equation under the dilute solution assumption. However, investigations on the characteristic Sand's time under various overlimiting currents are quite limited, partly due to the difficulties of determining the true current density and the accurate starting time of dendritic growths. Here, transparent microcapillary cells are fabricated to overcome these challenges. Our specialty cells not only minimize the possible discrepancy between the geometric current density and the true local current density by reducing the cross-sectional area, but also allow reliable determination of the Sand's time via direct operando optical observation. Sand's time simulations using both the dilute solution theory and the concentrated solution theory, with the parameters cross-validated by independent measurements, match closely with the experimental Sand's time. Our work demonstrates that the onset of lithium dendritic growths in solid polymer electrolytes may not always yield the familiar Sand's time voltage spike. Avoiding the localized overlimiting current density is the key to developing penetration-free polymer electrolytes.

Parameter Identification of Lithium-Ion Batteries by Coupling Electrochemical Impedance Spectroscopy with a Physics-Based Model

Nondestructive, quick, and accurate diagnosis of Lithium-ion batteries are critical tools to extend battery lifetime and ensure safe operation under complicated real-time power demand conditions. In this study, an electrochemical characterization approach coupling impedance spectroscopy with a physics-based model (EIS-Physical) has been demonstrated to accurately identify key transport and kinetic parameters for an in-house assembled Li(Ni0.5Mn0.3Co0.2)O2/Li-metal half-cell. The parameter identification process has been realized by a nonlinear optimization algorithm, along with proper sensitivity and dependence analyses on initial guesses. The parameters obtained using this approach have been compared with those determined from the benchmark Galvanostatic Intermittent Titration Technique (GITT). Equivalent circuit method as an important state-of-the-art modeling approach to interpret EIS has also been compared against the proposed method. The results show that: i) cathode Li-ion diffusivity and cathode/electrolyte exchange current density are quadratic functions of x Li, which indicates cathode is the capacity limiting electrode and operates in a wide SOC range. Therefore, cathode must be simulated using the concentrated solution theory. ii) EIS-Physical method can provide consistent and unique parameters with clear physical meanings compared to its equivalent circuit counterpart. iii) EIS-Physical method is as precise as GITT but less time consuming (i.e., <2.5 h vs > 200 h). Consequently, the proposed method is found to be more practical to implement as a Lithium-ion battery diagnostic tool.

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.

Comparison of Electrolyte Transport Modelling in Lithium-ion Batteries: Concentrated Solution Theory Vs Generalized Nernst-Planck Model

Mathematical modelling is widely used to provide insights into lithium-ion battery operation, mainly by using Doyle-Fuller-Newman (DFN) porous electrode theory. A key aspect of thermo-electrochemical models is the description of electrolyte transport phenomena and their implications on thermal effects, which are the subject of this study. We show that the so-called generalized Poisson-Nernst-Planck approach (here re-named generalized Nernst-Planck, gNP) for electrolyte transport is equivalent to DFN concentrated solution theory only if the electrolyte thermodynamic factor obeys a specific gNP expression as a function of three electrolyte parameters. However, such an expression does not capture accurately the experimental dependence of the thermodynamic factor for concentrations lower than 0.5 mol l−1 or higher than 1.5 mol l−1 in a common LiPF6-based electrolyte, causing discrepancies between model predictions. The deviation between simulation results of the DFN and gNP models is negligible at low C-rates and ambient temperature. However, as the operative conditions get more challenging as for C-rate > 1 and/or extreme temperatures, detectable deviations are shown in terms of predicted voltage, maximum temperature, and accessible/restored capacity. Furthermore, the electrolyte transport models predict different onsets of lithium plating upon charge, showing moderate deviations in the estimated penetration depth of plating.

Complete Electrochemical Characterization and Limiting Current of Polyacetal Electrolytes

We investigate a polyacetal-based electrolyte, poly(1,3,6-trioxocane) (P(2EO-MO)) mixed with lithium bis(trifluoromethanesulfonyl)imide (LiTFSI) salt, and report full electrochemical characterization of the transport parameters and a thermodynamic property in comparison to the previously reported poly(ethylene oxide) (PEO) electrolyte data [D. Gribble et al., J. Electrochem. Soc., 166, A3228 (2019)]. While the steady-state current fraction (ρ +) of P(2EO-MO) electrolyte is greater than that of PEO electrolyte in the entire salt concentration window we explored, the rigorously defined transference number using Newman’s concentrated solution theory () appears to be similar to that of PEO electrolyte. On the basis of full electrochemical characterization, we calculate the salt concentration profile as a function of position in the cell and predict limiting current density (i L L) as a function of salt concentration. Experimental data were compared to the predicted values. The non-monotonic behaviors were observed both in prediction and experimental results with offset peak positions. We find that the limiting current density of P(2EO-MO) electrolyte is systematically lower than that of PEO electrolyte in most of the salt concentrations with the exception of r av = 0.05. It is noteworthy that even though one measure of electrolyte efficacy (κρ +) is superior in P(2EO-MO) electrolyte, the limiting current density, which is another metric of electrolyte efficacy at high currents, is not greater in P(2EO-MO).