Table of contents

Numerical physics-based models are useful in understanding battery performance and developing optimal battery design architectures. Data science developments have enabled software algorithms to perform data analysis and decision making that traditionally could only be performed by technical experts. Traditional workflows of model development - manual parameter estimation through visual comparison of simulations to experimental observations, and model discrimination through expert intuition - are time-consuming, and difficult to justify. This paper compares the conclusions derived from computationally scalable algorithms to conclusions developed by expert researchers. This paper illustrates how data science techniques, such as cross-validation and lasso regression, can be used to augment physics-based simulations to perform data analysis such as parameter estimation, model selection, variable selection, and model-guided design of experiment. The validation of these algorithms is that they produce results similar to those of the expert modeler. The algorithms outlined are well-established and the approaches are general, so can be applied to a variety of battery chemistries and architectures. The conclusions reached using these approaches are in agreement with expert analysis (literature results), were reached with minimal human intervention, and provide quantitative justification. By minimizing the amount of expert time, and providing rigorous quantitative justifications, these methods may accelerate battery development.

Transition metal dissolution from high-voltage Li-ion battery cathodes disrupts the formation and performance of the solid-electrolyte interphase (SEI). SEI contamination by transition metals results in continual Li loss and severe capacity fade. Fundamental understanding of how metals undermine SEI passivation is necessary to mitigate this degradation. This two-part study interrogates the mechanisms by which transition metals facilitate through-film charge-transfer and SEI failure. Part I presents experimental results in which we intentionally contaminate SEIs with Mn, Ni, and Co. Rotating disk electrode voltammetry of a redox mediator quantifies how each metal impacts the charge-transfer characteristics of the SEI. A physics-based model finds that all three metals disrupt the electronic properties of the SEI more than the morphology. Surprisingly, the Butler-Volmer kinetics of charge-transfer through a Mn-contaminated SEI are an order of magnitude faster than for a Co-contaminated SEI, even with similar embedded metal concentrations. Such trends between metals are inconsistent with bandgap predictions from density functional theory, implying an alternative redox-cycling mechanism, which is mathematically developed and compared to experiment in Part II.

At high operating voltages, metals like Mn, Ni, and Co dissolve from Li-ion cathodes, deposit at the anode, and interfere with the performance of the solid-electrolyte interphase (SEI) to cause constant Li loss. The mechanism by which these metals disrupt SEI processes at the anode remains poorly understood. Experiments from Part I of this work demonstrate that Mn, Ni, and Co all affect the electronic properties of the SEI much more than the morphology, and that Mn is the most aggressively disruptive of the three metals. In this work we determine how a proposed electrocatalytic mechanism can explain why Mn contamination is uniquely detrimental to SEI passivation. We develop a microkinetic model of the redox cycling mechanism and apply it to experiments from Part I. The results show that the thermodynamic metal reduction potential does not explain why Mn is the most active of the three metals. Instead, kinetic differences between the three metals are more likely to govern their reactivity in the SEI. Our results emphasize the importance of local coordination environment and proximity to the anode within the SEI for controlling electron transfer and resulting capacity fade.

We derive and implement a set of equations that can be used to describe overcharge of a lithium ion cell, which can result in lithium (Li) plating on the graphite electrode. Graphite electrodes are the current material of the choice for the negative electrode (anode on discharge). We add two theoretical developments to published models to address Li plating. First, the existing models are not well-posed in terms of handling the Li deposition and dissolution electrochemical reactions. Second, the plated Li can interact directly with vacant sites in the graphite, which has not been treated in the literature, and which impacts the system response. With the inclusion of these new theoretical developments, and the use of our recently developed multi-site, multi-reaction (MSMR) formulation, we demonstrate the utility of the overcharge model and simulate relatively fast charging and discharging of a graphite electrode (i.e., at the 1C rate, yielding about 1 hour to fully charge or discharge the electrode) with a single-particle representation.

Localized corrosion of carbon steel in CO₂-H₂O environment is a long-standing challenge faced by the oil and gas industry, because of its unfeasible detection and high propagation rate. Numerical modelling can overcome the limitations of the spatial and temporal scales in the experimental studies, thus becoming a valuable complement. A multi-physics coupling model is established to investigate the evolution of localized corrosion of carbon steel in CO₂ aqueous environment. The complex interactions among the kinetics of electrode reactions, multicomponent reactions, mass transfer and the deposition of corrosion products are coupled into the model, achieving a comprehensive and physically realistic description of the actual corrosion process. The arbitrary Lagrangian-Eulerian method is implemented to track the moving metal/solution interface. Special emphasis is put on the coupling mechanism among the underlying processes at different time and length scales. This study characterizes quantitatively the time-dependent corrosion behavior, including the distributions of potential and species concentration within the corroding pit, corrosion current density and pit morphology. The inherent relationship between the corrosion behavior and the local corrosive environment within the pit is revealed. The results indicate that the competition between the chemical effect and electrical effect determines the trend and distribution of corrosion current density. The pit shape and cathode/anode area ratio have a great influence on the corrosion behavior due to the coupled role of local solution chemistry and electrical field.

The energy density of lithium-ion batteries can be enhanced by using thicker and denser electrodes, which leads to transport limitations in the electrolyte within the porous structures. A pore morphology modification of the electrodes can counteract this limitation mechanism and provide higher rate capabilities of the cells. In this work, graphite anodes are structured with a picosecond laser in order to create transport pathways for the lithium-ions and allow for enhanced penetration of the electrodes. Experimental data from graphite/NMC-111 coin cells with varying areal capacities are used for the development and parameterization of an electrochemical model. The modified pore morphology of the structured electrodes is represented in the model by an adapted tortuosity, which results in lower lithium-ion concentration gradients and reduced diffusion polarization in the electrolyte. The effect of electrode thickness and tortuosity on limiting mechanisms is analyzed via simulation studies in order to derive the impact of structured electrodes. As a result, improved discharge as well as charge rate capability appears beside enhanced safety features such as increased tolerance versus hazardous lithium-plating during fast charging scenarios.

Recent advancements in micro-scale additive manufacturing techniques have created opportunities for design of novel electrode geometries that improve battery performance by deviating from the traditional layered battery design. These 3D batteries typically exhibit interpenetrating anode and cathode materials throughout the design space, but the existing well-established porous electrode theory models assume only one type of electrode is present in each battery layer. We therefore develop and demonstrate a multi-electrode volume-averaged electrochemical transport model to simulate transient discharge performance of these new interpenetrating electrode architectures. We implement the new reduced-order model in the PETSc framework and asses its accuracy by comparing predictions to corresponding mesoscale-resolved simulations that are orders of magnitude more computationally-intensive. For simple electrode designs such as alternating plates or cylinders, the volume-averaged model predicts performance within ∼2% for electrode feature sizes comparable to traditional particle sizes (5-10μm) at discharge rates up to 3C. When considering more complex geometries such as minimal surface designs (i.e. gyroid, Schwarz P), we show that using calibrated characteristic diffusion lengths for each design results in errors below 3% for discharge rates up to 3C. These comparisons verify that this novel model has made reliable cell-scale simulations of interpenetrating electrode designs possible.

The morphology and ionomer distribution in the polymer electrolyte membrane fuel cell (PEMFC) cathode electrode (used in Toyota Mirai) are quantified with nano-scale resolution X-ray computed tomography (nano-CT). Using the nano-CT data, different shapes, sizes and compositions of agglomerates are extracted. Statistical information from multiple techniques, including transmission electron microscopy (TEM), ultra-small angle X-ray scattering (USAXS), and Brunauer-Emmett-Teller (BET) gas adsorption porosimetry are combined to reconstruct the high surface-area porous carbon (HSC) support, exterior (on the surface of carbon) and interior (inside carbon pores) catalysts, ionomer, and primary pores in the extracted agglomerates. Application of capillary condensation theory to the reconstructed agglomerate structure is shown to accurately represent the experimentally-observed relative humidity (RH) dependence of the electrochemically-active surface area (ECA). Direct numerical simulations (DNS) show that the high local O₂ transport resistance () under dry conditions is mainly associated with the reduced ECA. We demonstrate that the agglomerate shape and size affect only if the primary pores are poorly accessible (i.e., capillary-condensed water filled primary pores result in lower for lower aspect ratio agglomerates). We also estimate associated with the location of catalyst (whether inside or on the surface of HSC).

An approach to simulate multiphysics phenomena in the cathode catalyst layer of the proton exchange membrane fuel cell (PEMFC) at the resolution of pore scale is presented. Within the framework of pore-scale simulation, a method to couple water generation by oxygen reduction reactions with liquid water transport and mass transport loss in pores and the ionomer is proposed. The multiscale decomposition method that reduces the computational cost of pore-scale simulation is applied to the proposed multiphase pore-scale model. The proposed computational framework is applied to several test cases. Cases with simple and idealized pore structures are used to demonstrate and validate the coupling of water generation, emergence and transport. The computational efficiency of the multiscale method is investigated. The results show that an estimation of the effective diffusivity considering water blockage effects is of importance to the reduction of the computational cost in the multiscale method. At low saturation levels, the effective diffusivity evaluated using global saturation is found to be sufficient. It is found that, as the saturation level increases, a more accurate estimation using a local saturation level leads to better performance. The application to an experimental case is presented to demonstrate the potential of the proposed framework.

Copper electrodeposition processes for filling metallized through-hole (TH) and through-silicon vias (TSV) depend on spatially selective breakdown of a co-adsorbed polyether-chloride adlayer within the recessed surface features. In this work, a co-adsorption-dependent suppression model that has previously captured experimental observations of localized Cu deposition in TSV is used to explore filling of TH features. Simulations of potentiodynamic and galvanostatic TH filling are presented. An appropriate applied potential or current localizes deposition to the middle of the TH. Subsequent deposition proceeds most rapidly in the radial direction leading to sidewall impingement at the via center creating two blind vias. The growth front then evolves primarily toward the two via openings to completely fill the TH in a manner analogous to TSV filling. Applied potentials, or currents, that are overly reducing result in metal ion depletion within the via and void formation. Simulations in larger TH features (i.e., diameter = 85 μm instead of 10 μm) indicate that lateral diffusional gradients within the via can lead to fluctuations between active and passive deposition along the metal/electrolyte interface.

A multidimensional multiphysics model is presented to describe the external short circuit behavior of lithium-ion cells of various formats and sizes at different convective cooling conditions. For this purpose, a previously published homogenized physical-chemical model of the external short circuit behavior of a small-sized lithium-ion cell was combined with an electrical and a thermal model to describe in-plane inhomogeneities in current density and heat generation rate throughout the electrodes, together with the resulting temperature distribution within the cell's jelly roll or electrode stack. With the investigated cylindrical, prismatic, and pouch-type cell formats combined with cell capacities ranging from consumer-sized to automotive applications, a comprehensive cell design study is presented during external short circuits. The investigated surface and tab cooling strategies reveal a limited cooling capability of each cell format and size, which seems to be defined by the ratio of cooled surface area to electrode area as well as the thermal resistivity of the respective cell geometry. The simulation results show that only thin cells with a large ratio of cooling surface to electrode area can be physically maintained within an uncritical operating window of cell temperature and state of charge in case a low-resistance external short circuit is applied.

Whilst extensive research has been conducted on the effects of temperature in lithium-ion batteries, mechanical effects have not received as much attention despite their importance. In this work, the stress response in electrode particles is investigated through a pseudo-2D model with mechanically coupled diffusion physics. This model can predict the voltage, temperature and thickness change for a lithium cobalt oxide-graphite pouch cell agreeing well with experimental results. Simulations show that the stress level is overestimated by up to 50% using the standard pseudo-2D model (without stress enhanced diffusion), and stresses can accelerate the diffusion in solid phases and increase the discharge cell capacity by 5.4%. The evolution of stresses inside electrode particles and the stress inhomogeneity through the battery electrode have been illustrated. The stress level is determined by the gradients of lithium concentration, and large stresses are generated at the electrode-separator interface when high C-rates are applied, e.g. fast charging. The results can explain the experimental results of particle fragmentation close to the separator and provide novel insights to understand the local aging behaviors of battery cells and to inform improved battery control algorithms for longer lifetimes.

A mathematical model to calculate tertiary current distributions in electrochemical reactors is presented taking into account the potential and concentration fields together with the hydrodynamics under laminar or turbulent conditions. Multiple reactions with different kinetic controls are considered at both electrodes. The computational algorithm solving the model was implemented in OpenFOAM. It allows the calculations for a given local potential at the working electrode, potentiostatic control, or for a fixed cell potential difference and also for a current flowing through the cell, galvanostatic operation. The model was validated by using the reduction of ferricyanide and the oxidation of ferrocyanide from dilute solutions as main test reactions and hydrogen and oxygen evolution as secondary ones, in a modified hydrocyclone. A close agreement between experimental and predicted current distributions was obtained. The hydrocyclone presents a promising electrochemical performance being the mass-transfer conditions in its cylindrical part better than in the conical region. The computational tool developed in this paper can be employed to optimize both cells stack design and system operation conditions. Likewise, the algorithm can also be used to check, when limiting current studies are needed, whether the desired reaction is under mass-transfer or charge-transfer control for a given geometric configuration.

High-concentration aqueous electrolytes have shown promise as candidates for a safer battery system. Ionic conductivity is a key property required in high performing electrolytes; the Advanced Electrolyte Model (AEM) has previously shown great accuracy in predicting ionic conductivity in highly-concentrated non-aqueous electrolytes. This work provides extensive experimental data for mixed and highly concentrated aqueous electrolyte systems, rapidly generated via a robotic electrolyte testing apparatus. These data demonstrate exceptional accuracy from AEM in predicting conductivity in aqueous systems, with the accuracy being maintained even in highly-concentrated and mixed-salt regimes. Sensitivity of the model to choice of a key solvation parameter, reference ligand-ion length, is explored. Walden analysis using transport properties predicted by the model for aqueous salts and mixed salt systems is also included, as well as predictions of cation transference number for salts and mixed salts. These predictions are explained in terms of AEM's underlying chemical physics modeling.

The formic acid oxidation reaction (FAOR) is a model electrocatalytic reaction involving multiple proton-coupled electron transfer steps. Despite of repeated research extending over more than fifty years, the FAOR is still an active research field in which several important questions including reaction mechanisms, the activity dependence on the electrode structure, the hysteresis between positive- and negative-going scan in cyclic voltammetry (CV), and, especially, the pH effect, remain elusive yet. To shed some light on these puzzles, we herein develop a microkinetic model for the FAOR at Pt(111) which uses a reaction mechanism supported by microscopic and mechanistic information from density functional theory calculations and spectroscopic characterizations, formulates the mechanism using fully microkinetic modeling without designating a rate-determining step, and incorporates double-layer effects by means of a mean-field description for the electrode-electrolyte interphase. Moreover, chemisorbed intermediates play multifaceted roles in this formulism: they are reactants with lateral interactions, site-blockers, as well as modifiers of the double-layer structure and properties. The model is parameterized using CV data of Pt(111) in perchlorate electrolyte with different pHs, revealing that HCOO_m is the main active intermediate with HCOO⁻ as the main precursor. CO_ad on defect sites induces the voltage hysteresis through modifying surface charging relation (the main effect) and blocking adsorption sites (the minor effect). It is also found that the higher current density as the pH increases from 0.11 to 1.42 is the result of two opposing factors: higher concentration of HCOO⁻ in bulk solution and stronger double layer effects that suppress HCOO_m formation. The presented work demonstrates that consideration of double-layer effects and an integrated view of multifaceted roles of reaction intermediates are a sheer necessity for FAOR.

The direct modeling-based Lattice Boltzmann Agglomeration Method (LBAM) is used to explore the electrochemical kinetics and multi-scalar/multi-physics transport inside the detailed structure of the porous and catalyst layers inside polymer electrolyte membrane fuel cells (PEMFCs). The complete structure of the samples is obtained by both micro- and nano- X-ray computed tomography (CT). LBAM is able to predict the electrochemical kinetics in the nanoscale catalyst layer and investigate the electrochemical variables during cell operation. This work shows success in integrating the lattice elements into an agglomerate structure in the catalyst layer. The predictions of LBAM were compared with a macro-kinetics model and experimental data. The overall predictions reveal that the local saturation of liquid water, distributions of electrochemical variables, and mass fraction across the samples can be controlled by the regulation of operating conditions. LBAM is a highly effective method of predicting the partial flooding issue, understanding the transport resistance, and investigating transport inside the porous transport layer that affects the overall cell performance in the PEMFC. The outcome of this work will be used for the optimization of porous structure design, durability, and water management improvement, for novel porous materials, particularly in the catalyst layer.

Scientific discoveries and inventions are driving novel technological concepts that demand unprecedented control at the microscopic scale during processing. Challenges arise because critically important events occur at the atomistic scale, while the corresponding technological processes are designed to operate and be controlled at the macroscale. New approaches are therefore needed that couple traditional engineering design methods with non-continuum stochastic phenomena. This work provides perspectives on what is needed to implement deep integration of engineering design procedures with molecular-scale knowledge.

In this work we discuss the modeling procedure and validation of a non-porous intercalation half-cell during galvanostatic discharge. The modeling is based on continuum thermodynamics with non-equilibrium processes in the active intercalation particle, the electrolyte, and the common interface where the intercalation reaction occurs. The model is in detail investigated and discussed in terms of scalings of the non-equilibrium parameters, i.e. the diffusion coefficients and of the active phase and the electrolyte, conductivity and of both phases, and the exchange current density , with numerical solutions of the underlying PDE system. The current density i as well as all non-equilibrium parameters are scaled with respect to the 1-C current density of the intercalation electrode. We compute then numerically the cell voltage E as function of the capacity Q and the C-rate C_h. Within a hierarchy of approximations we provide computations of E(Q) for various scalings of the diffusion coefficients, the conductivities and the exchange current density. For the later we provide finally a discussion for possible concentration dependencies.

Understanding the dynamics of an electrochemical double layer (EDL) is of fundamental importance to a wide array of electrochemical energy devices. We develop in this study a modified concentrated solution theory to simulate EDL dynamics in the concentrated regime, in which the driving force of ion transport in EDL is derived from a free energy functional that considers ion size effect, short-range correlations, and solvent polarization. The model features a mobility matrix with non-zero off-diagonal elements due to short-range correlations. Model results are compared with molecular dynamic simulations and surface force measurement for an EDL in ionic liquids. The model gives out insights into how the ion size, various short-range correlations, and the solvent polarization affect the charging dynamics. The model is instrumental to design, optimization and control of high-power electrochemical devices.

The Gas Diffusion Layer (GDL) is an important fibrous porous material within all fuel cells that manage the transport of electrons, heat and fluids in order to generate power. The microstructural morphology of electrically conductive solid porous media can be manipulated to produce structures with a larger effective electrical conductivity and reactant permeability when compared to current Gas Diffusion Layers (GDL) used in fuel cells. Using a numerical modelling approach, we simulated single phase flow and the electrical conductance in void and solid spaces, respectively. The simulations were completed in OpenFOAM which employs the finite volume approach. Simulations revealed that effective electrical conductivity is dependent on the electron path tortuosity τ_E and the porosity . Therefore control of these micro-structural properties will allow for lower ohmic and mass transport losses. To aid the analysis, analytical and semi-empirical equations were developed based upon physical parameters to predict the effective electrical conductivity of connected porous media independent of isotropy. We propose that regular ordered structures via additive manufacturing techniques will allow for greater fuel cell performance.

We introduce theory to study the convection of active species with redox reactions at solid/solution interfaces within porous media, motivated by applications in energy storage devices where cyclic charge and discharge with recirculating flow requires the consideration of transient mass transfer. We show that under pseudo-steady conditions the coupled mass transfer problem involving redox of active species can be simplified to a linear, time-independent auxiliary problem. The proposed model is then solved numerically for porous media containing periodically spaced cylinders in crossflow. The results show three transport mechanisms depending on Péclet number Pe. Interactions between solid surfaces induced either by diffusion or advection produce spatial variation of surface flux. With Pe increasing from unity, advection initially causes diffusive flux to redistribute, causing a rise in Sherwood number Sh (non-dimensional mass transfer coefficient). The locations of flux maxima coincide with those of vorticity and strain rate for Pe above a certain "saturation" value. The variations of Sh with porosity and Pe are interpreted using a regime map that is defined based on the spatial variance of solute concentration. The auxiliary problem introduced provides a framework to predict mass transfer coefficients for arbitrary microstructures to guide the design of high-performance electrodes.

Establishing a link between atomistic processes and battery cell behavior is a major challenge for lithium ion batteries. Focusing on liquid electrolytes, we describe parameter-free molecular dynamics predictions of their mass and charge transport properties. The simulations agree quantitatively with experiments across the full range of relevant ion concentrations and for different electrolyte compositions. We introduce a simple analytic form to describe the transport properties. Our results are used in an extended Newman electrochemical model, including a cell temperature prediction. This cross-scale approach provides quantitative agreement between calculated and measured discharge voltage of a battery and enables the computational optimization of the electrolyte formulation.

The loss of electrochemical active surface area (ECSA) at the cathode is one of the main causes of performance degradation in Polymer Electrolyte Membrane Fuel Cells (PEMFCs). In order to investigate the catalyst degradation and the influence of the operating conditions we develop a multiscale degradation model which includes the formation and reduction of platinum oxides, platinum dissolution, particle growth due to Ostwald ripening, platinum ion transport through the ionomer and platinum band formation in the membrane. This degradation model is coupled with a 2D PEMFC performance model and predictions regarding ion concentration, ECSA evolution and particle growth are validated with dedicated experiments and literature data. Degradation under several AST protocols and under steady state operation are compared and discussed. The importance of a spatially resolved catalyst degradation model is conveyed by the occurrence of a depletion zone in the catalyst layer close to the membrane due to the platinum migration into the membrane. By comparing the correlation between platinum mass loss in the catalyst layer and the ECSA loss we conclude that catalyst degradation under AST conditions with nitrogen is not representative for the degradation under normal operation.

Two novel scale-bridging algorithms to model reaction-diffusion transport in porous media are presented. The algorithms are based on direct numerical simulations and couple the information of a micro-scale model, which accounts for the large field of view provided by micro X-ray computed tomography (X-ray CT), and a nano-scale model, which locally resolves transport in the fine structure extracted from nano X-ray CT. The micro-scale model is discretized in the through-plane direction into a 1D grid, where effective properties and internal boundaries are determined based on the results from the nano-scale model. The validated algorithms are used to examine transport of oxygen in precious group metal-free electrodes considering both zero- and first-order kinetics. Unlike conventional methods, the results show that the effective diffusivity is not a passive property but increases in regions where the reaction-rate coefficient is large. The proposed algorithms account for the multiscale coupling of reaction-diffusion transport and material microstructure, thus improving the predictions compared to conventional methods.

The energy hierarchy, of the main chemical species involved in the reaction mechanism relevant to the electrodeposition of aluminum in 1-Butyl-3-methylimidazolium chloride/aluminum trichloride solution (BMImCl/AlCl₃), is studied by using ab-initio based theoretical calculations. Eventually, a reasonable theoretical estimate of energies, involved in the principal reactions ruling the aluminum electrodeposition from BMImCl ionic liquid solutions, is obtained. For screening purposes (geometry optimization and Hessian calculations) the CAMB3LYP density functional, DFT, has been used. Then single point (exploiting CAMB3LYP optimized geometries) energy data are obtained at the Møller-Plesset (MP2) level of the theory. They are used to cross-check DFT results. A reaction mechanism emerges in which, although the species AlCl⁻₄ is formed with very high efficiency from the neutral species AlCl₃, the competing reaction points to an almost complete conversion of aluminum to the dimeric form into bulk solution. This is observed in the absence and, most importantly, in the presence of a coordinating BMIm⁺ cation. In this respect, the presence of BMIm⁺ does not seem to affect significantly the equilibrium between the monomeric and dimeric forms of aluminum. This outcome is very interesting because the dimeric species is directly reduced to yield the metal aluminum. Indeed, a larger concentration of Al₂Cl⁻₇ gives due reason for a more effective electrodeposition process, as it is experimentally observed in the ionic liquid medium.

A one-dimensional (1D) homogeneous unit cell model was developed to study the performance of the molten carbonate direct carbon fuel cell (DCFC), which uses solid carbon as fuel and molten carbonate as electrolyte. It is the first unit cell model for the molten carbonate DCFC in which both 4-electron carbon oxidation and 2-electron CO oxidation reactions, as well as the reverse Boudouard reaction, are considered. The simulation results verify that, besides the relatively sluggish kinetics of the anodic reactions, cell performance is mainly limited by ohmic losses in the anode. Further modeling exploration reveals that a minimum effective electronic conductivity of around 0.56 S/cm is required to facilitate proper electrical conduction in the cathode to attain high DCFC performance. It was found that there are optimal volume fractions for the carbon fuel and liquid electrolyte in the anode. If the effective electronic conductivity of the cathode falls to 0.56 S/cm, optimal volume fractions also exist for the solid material and liquid electrolyte in the cathode. The detailed modeling analysis showed that performance improvement at high operating temperature was mainly attributed to improvement of anodic kinetics and reduction of ohmic loss in the electrolyte of electrodes and electrolyte matrix.

Lithium ion capacitors (LICs) store energy using double layer capacitance at the positive electrode and intercalation at the negative electrode. LICs offer the optimum power and energy density with longer cycle life for applications requiring short pulses of high power. However, the effect of electrode balancing and pre-lithiation on usable energy is rarely studied. In this work, a set of guidelines for optimum design of LICs with activated carbon (AC) as positive electrode and lithium titanium oxide (LTO) as negative electrode was proposed. A physics-based model has been developed and used to study the relationship between usable energy at different effective C rates and the mass ratio of the electrodes. The model was validated against experimental data from literature. The model was then extended to analyze the need for pre-lithiation of LTO. The limits for pre-lithiation in LTO and use of negative polarization of the AC electrode to improve the cell capacity have been analyzed using the model. Furthermore, the model was used to relate the electrolyte depletion effects to poorer power performance in a cell with higher mass ratio. The open-source model can be re-parameterised for other LIC electrode combinations, and should be of interest to cell designers.

During fuel cell operation, the polymer electrolyte membranes are subjected to chemical and mechanical degradation that have an adverse impact on the membrane lifetime and thus overall durability of the fuel cell. To understand the synergistic effect of these two fundamentally different modes of degradation, it is therefore essential to consider both these effects when modeling membrane failure. A kinetic approach using a fracture percolation model is presented in this work that takes into consideration the hazard rates of chemical and mechanical degradation of the membrane incorporated into a two-dimensional membrane lattice network. While the chemical hazard rate is based on the rate of mass loss occurring during fuel cell operation, the mechanical hazard rate is evaluated based on a stress-induced, thermally activated process. The model captures the characteristic mechanisms of failure under the action of these fundamentally different modes, and converts the hazard functions into realistic time scale. The individual effects of the two modes are then incorporated in the model to predict in agreement with measured data, the time to fracture initiation in the membrane for a given combination of chemical and mechanical load.

Inverse opals (IO) are three-dimensional ordered porous microstructures with a large specific surface area and high mechanical stability. They exhibit nanoscale geometric features, where surface stresses gain an appreciable impact on the elastic behavior and electrochemical surface reactions. With this study, we aim to gain an understanding of the influence of an IO cathode's geometry on its chemo-mechanical behavior. We are particularly interested in the impact of the IO's pore radius on the mechanical stresses, charge kinetics, and the magnitude of capacity losses. To that end, we performed a Finite Element study considering stress-coupled diffusion, mechanically modulated surface reactions, and surface-stress-induced bulk stresses. An inhomogeneous pressure develops in the polyconcave electrode structure, effecting a local reduction of electrode overpotential. This leads to size-dependent losses in the accessible capacity of the electrode material. Its high surface-to-volume ratio, on the other hand, results in significantly enhanced insertion/extraction rates. With decreasing pore size, we observe both faster insertion and a reduction in the achievable lithiation. An optimal electrode pore radius can thus be determined from balancing the requirements of high charge rate against the surface-stress-induced losses in the accessible capacity.

This review presents the main principles underlying the theoretical description of the behavior of regular and random arrays of nanometric active sites. It is further shown how they can be applied for establishing a useful semi-analytical approximation of the arrays responses under diffusion limited conditions when they involve the common situation of active sites with identical sizes. This approximation is general and, as exemplified for different type of arrays, can be employed for describing the behavior of any array involving arbitrary distributions of their active sites onto the substrate surface. Furthermore, this efficient approach allows statistical characterization of active sites distributions of any array based on chronoamperometric data.

pH distribution and non-equilibrium state of water in hydrogen evolution reaction are studied using continuum models. In the first model, we analyze the pH distribution in a rotating ring disk electrode system, where the hydrogen evolution occurs on the disk electrode. The model predicts a pH distribution comparable to the experimental data and the nonequilibrium state of water (cH^*cOH>1.0 × 10⁻¹⁴) in a small portion of the diffusion layer (ca. 5 μm in thickness) adjacent to the bulk electrolyte under forced convection. The second model explores the pH distribution on an electrode with nanovoids in hydrogen evolution reaction in an acidic media. The value of cH^*cOH shifts significantly when close to the electrode surface, e.g., ≤ 2 μm, indicating pH is not viable to assess its impact on an electrochemical reaction involving hydroxide ions. Modeling results also prove that, for an electrode with nanovoids, the concentration gradient of hydroxide between the plain field and the bottom of the nanovoid is minimal. Therefore it should not be the root cause for the differential kinetics of metal electrodeposition inside/outside the nanovoids.

Many electrochemical processes involve gas evolution and bubble generation on the electrodes. Understanding the behavior of bubbles on the electrode surface and in the electrolyte is crucial to the design and optimization of the electrochemical process. Gas bubbles tend to coalesce and detach from the electrode surface once they are formed and as they grow, but these processes have not been investigated and understood well. The phase-field modeling method is excellent at tracking the interface between different phases, and the simulation results can give a precise prediction of the interaction between phases. In this research, taking advantage of the phase-field method, a gas-liquid two-phase model has been constructed to investigate the bubble coalescence and detachment in the electrochemical system. Sophisticated, tiny gas bubble coalescence on and off electrode and the detachment of bubbles from the electrode surface were predicted by the model. The results are helpful for the understanding of these transient processes in the electrochemically generated bubble-liquid system.

The effect of temperature on the kinetics of electrochemical insertion/removal of lithium in graphite is analyzed by kinetic Monte Carlo methods. Different electrochemical techniques are simulated at different temperatures and responses are compared with experimental results. Simulated voltammograms show, similarly to experiment, how the behavior of the system becomes closer to equilibrium as temperature increases. Calculated chronoamperometric profiles show a different qualitative behavior in the current at different temperatures, especially in the Cottrell representation peaks, explained in terms of the relative importance of diffusive versus charge transfer processes at different temperatures. Results at room temperature are in good agreement with experiment, and we further evaluate trends at elevated temperature that have not yet been described in experimental or theoretical works. Exchange current densities for different degrees of lithium intercalation at different temperatures are predicted using potentiostatic simulations, showing an Arrhenius-type relationship. The dependence of the exchange current on electrolyte composition is simulated by investigating the effect of different activation energy barriers at different temperatures. The influence of temperature on diffusion coefficients as a function of lithiation fraction in graphite is simulated and related to Arrhenius plots, explaining the experimentally observed changes in diffusion phenomena with lithium composition and temperature.

This article introduces a lumped electrochemical model for lithium-ion batteries. The governing equations of the standard 'pseudo 2-dimensional' (p2D) model are volume-averaged over each region in a cathode-separator-anode representation. This gives a set of equations in which the evolution of each averaged variable is expressed as an overall balance containing internal source terms and interfacial fluxes. These quantities are approximated to ensure mass and charge conservation. The averaged porous domains may thus be regarded as three 'tanks-in-series'. Predictions from the resulting equation system are compared against the p2D model and simpler Single Particle Model (SPM). The Tanks-in-Series model achieves substantial agreement with the p2D model for cell voltage, with error metrics of <15 mV even at rates beyond the predictive capability of SPM. Predictions of electrochemical variables are examined to study the effect of approximations on cell-level predictions. The Tanks-in-Series model is a substantially smaller equation system, enabling solution times of a few milliseconds and indicating potential for deployment in real-time applications. The methodology discussed herein is generalizable to any model based on conservation laws, enabling the generation of reduced-order models for different battery types. This can potentially facilitate Battery Management Systems for various current and next-generation batteries.

In this paper, the possibility of using generalized Peukert's equations C =C_m/(1 + (i/i₀)ⁿ), C = 0.522C_mtanh((i/i₀)ⁿ/0.522)/(i/i₀)ⁿ, and C = C_merfc((i/i_k − 1)/(1/n))/erfc(−n) for the calculation of lithium-ion cells' released capacity at different discharge currents is analyzed. It is proven that these equations correspond well to the experimental data over the entire change range of the discharge currents. Furthermore, it is demonstrated that the parameter n depends on neither cell capacity nor its format or manufacturer; however, it grows with an increase of the ratio i₀/С_m (or i_k/С_m), which depends on an electrode's effective thickness and the electrochemical system of the lithium-ion cells. Additionally, it is possible to consider the dependence of a lithium-ion cell's released capacity on a discharge current value as the statistical phase transition subjected to the normal distribution law. The proposed statistical mechanism explains the changes of the parameters n and i₀ (i_k) based on the type of battery studied.

A first principle model was used to fit the impedance data of intrinsic pseudocapacitors based on polypyrrole and manganese dioxide electrodes and was validated by successfully predicting charge/discharge characteristics. The model performs non-linear regression to an electrochemical impedance spectroscopy (EIS) data using a rigorous prototypical model of pseudocapacitance, which emphasizes an integrated description of the various components of the capacitor at the microscopic and macroscopic level. Parametric studies showcase further how important microscopic variables in pseudocapacitors influence both impedance spectra and galvanostatic discharge.

The electrochemical oxidation of HCl to Cl₂ plays an important role in the production of polycarbonates and polyurethanes. Recently, the gas-phase oxidation of HCl proved to be significantly more efficient than the current state-of-the-art process based on the oxidation of hydrochloric acid. In experimental investigations of this gas-phase reactor, a limiting current can be observed that is so far not understood but impedes the overall reactor performance. In the present work, a nonisothermal multiphase agglomerate model is developed to investigate the underlying reasons for this limiting behavior in more detail. It is shown that the thermal management of the cell plays a significant role and that minor changes to its thermal resistance lead to the limiting behavior being caused by either flooding of the cathode or dehydration of the membrane and anode. An optimization of operational and structural parameters of the cell based on these insights leads to an increase in the limiting current by more than 90%. Interestingly, under these conditions a third phenomenon, the rate determining Tafel step in the microkinetic reaction mechanism of the HCl oxidation, limits the overall reactor performance. These insights harbor the potential for enormous energetic savings in this industrially highly relevant process.

A major cause of failure of a lead acid battery (LAB) is sulfation, i.e. accumulation of lead sulfate in the electrodes over repeated recharging cycles. Charging converts lead sulfate formed during discharge into active materials by reduction of Pb²⁺ ions. If this is controlled by mass transfer of the ions to the electrochemically active area, charging voltage can far exceed the OCV of a charged battery. Then, charge is partly consumed to electrolyse water, and for evolution of hydrogen and oxygen. It causes sulfation since regeneration of active materials will be incomplete. A mathematical model is developed incorporating resistance to mass transfer of Pb²⁺ ions into the rate of charge transfer reactions, changes in areas of active materials and sulfate particles, and dependence of electrodes' resistance on content of lead sulfate. It was used to show that this mechanism of sulfation does lead to failure of flooded LABs because of increased resistance of electrodes, and to predict cycle life. Capacity fade, and increased cycle life when recharging protocol uses lower DoD are other features of degradation which the model predicts. The model also predicts the observed increase in cycle life when conducting additives are added to the negative electrode.

Building a complete cell impedance model and quickly calculating its frequency response are essential for battery design, optimization, and online management. Based on the widely accepted pseudo-two-dimensional (P2D) model, we build a complete full-order partial-dierential-equation (PDE) model for porous-electrode lithium-ion cells that includes a configurable electrical double-layer model at the solid-electrolyte interface (SEI). With the help of a numeric method, cell impedance and frequency responses of the cell's electrochemical variables at different locations inside the cell are obtained and analyzed. Moreover, in order to achieve the fast calculation of impedance and frequency responses, we derive transfer functions of the internal electrochemical variables, which give a set of exact closed-form equations for cell impedance and internal-variable frequency responses. The Nyquist plot results calculated by the closed-form equations are exactly consistent with the results of numeric simulations using the full-order model, which verifies the accuracy of the transfer functions and the effectiveness of the simplified method.

A theory is developed for calculating the delayed repassivation ("stifling") rate constant for stable pits on a metal surface with attention being paid to pitting of the carbon steel overpack in the Belgian supercontainer concept of the disposal of high-level nuclear waste. It is shown that, under the conditions that are expected to exist at the overpack surface, substantial concentration and potential drops cannot exist between the pit internal surface and the external surface far away from the pit mouth. This conclusion is valid for both open and semi-closed pits, if there is no porous, high resistance, corrosion product layer (salt film and/or remnants of the ruptured passive film) between the active metal surface inside the pit and the external surface, as supported by recent artificial pit experiments. It is shown that the existence of a low conductivity, corrosion product layer between the active pit base and the external surface can protect pits from the repassivation. The condition of repassivation is based upon the concept of the existence a critical pit propagation rate, V_cr, corresponding to a critical coupling current. If the rate of pit propagation becomes less than V_cr the pit passivates, because the coupling current is too low to maintain the necessary aggressive conditions within the pit cavity. A model and computer code have been developed for estimating the probability of failure in the Belgian high-level nuclear waste (HLNW) disposal repository.

In this work, we designed sintered titanium powder-based porous transport layers (PTLs) for polymer electrolyte membrane (PEM) electrolyzers by tailoring the powder diameter and porosity via a new approach. We examined how the PTL powder diameter and porosity influence reactant transport and PTL-catalyst layer (CL) interfacial contact by using a stochastic generation model combined with a pore network model. We enhanced reactant transport by increasing powder diameter and porosity, as shown through increases in single- and two-phase permeabilities of liquid water. Compared to the impact of increasing the powder diameter, increasing the PTL porosity dominated the impact on permeability of liquid water. However, we observed a trade-off to the benefits of increasing the powder diameter such that larger powders led to a higher surface roughness at the PTL-CL interface. From this work, we recommend that the PTL powder diameter and porosity must be strategically selected for the desired target operating conditions of the PEM electrolyzer. We recommend a PTL with d_P = 25 μm and ε = 26.5% for an electrolyzer cell operating at non-starvation conditions, and a PTL with d_P = 25 μm and ε = 40.5% for an electrolyzer cell operating at starvation conditions.

High energy-density batteries are crucial to energy storage solutions. In lithium-on batteries (LIBs), Si nanopillars are promising anodes due to their highest theoretical specific capacity. However, volume expansion and fracture during cycling inhibit its widespread adaptation. Ge, which is isomorphic with Si, shows better fracture resistance and higher cycle life but has higher molecular weight and cost. Alloying Si with Ge offers a trade-off in optimizing stresses, weight and cost. Here, we computationally evaluate the effect of alloying Si with Ge in reducing stresses generated during lithiation. Hollowing, which creates additional free surface for expansion is also considered. First, we model the stress evolution in nanopillars of Si, Ge, Si–Ge core-shell and Si_0.5Ge_0.5 alloy. Alloying Si with Ge uniformly, reduces the maximum circumferential stress by around 17%, however, the Si core-Ge shell structure shows stress reduction only when lithiation is confined only to the Ge. Stresses in Si/Ge alloyed nanotubes considering lithiation from the outer boundary as well as from both boundaries are considered. We find a non-monotonous change in lithiation stress with varying radius ratio (R_in/R_out) and R_in/R_out = 0.4 leads to the least maximum Hoop stress. The stress reduction in Si-nanotubes in such configuration is found to be 16%.

Battery electrodes are composed of polydisperse particles and a porous, composite binder domain. These materials are arranged into a complex mesostructure whose morphology impacts both electrochemical performance and mechanical response. We present image-based, particle-resolved, mesoscale finite element model simulations of coupled electrochemical-mechanical performance on a representative NMC electrode domain. Beyond predicting macroscale quantities such as half-cell voltage and evolving electrical conductivity, studying behaviors on a per-particle and per-surface basis enables performance and material design insights previously unachievable. Voltage losses are primarily attributable to a complex interplay between interfacial charge transfer kinetics, lithium diffusion, and, locally, electrical conductivity. Mesoscale heterogeneities arise from particle polydispersity and lead to material underutilization at high current densities. Particle-particle contacts, however, reduce heterogeneities by enabling lithium diffusion between connected particle groups. While the porous composite binder domain (CBD) may have slower ionic transport and less available area for electrochemical reactions, its high electrical conductivity makes it the preferred reaction site late in electrode discharge. Mesoscale results are favorably compared to both experimental data and macrohomogeneous models. This work enables improvements in materials design by providing a tool for optimization of particle sizes, CBD morphology, and manufacturing conditions.

A particle model for ionomer attachment on carbon black in a Polymer Electrolyte Fuel Cell (PEFC) catalyst layer was developed based the random walk method. Two different methods of particle attachment were used that resemble different catalyst ink preparation conditions: the solution method and the colloidal method. In the solution method, the simulation of attachment is conducted on the aggregate structures and in the colloid method, the attachment is simulated on the agglomerate structures. The distribution of carbon black, ionomer and void space was used in a multiscale electrochemical simulator that calculated the mass/charge transfer and reaction in the catalyst layer. The results of effective oxygen diffusion coefficients are consistent with experimental result and show why the Bruggeman correlation often is a poor approximation for upscaling the effective diffusive and conductive components in PEFC porous media. The solution method allowed for a better proton conduction through the ionomer but resulted in a thicker ionomer film that increased the oxygen diffusive resistance. However, solution and colloidal method resulted in similar cell performances. Our model can aid in the design to develop fuel cell catalyst layers with improved performance.

With the growing use of X-ray computed tomography (X-ray CT) datasets for modelling of transport properties, comes the need to define the representative elementary volume (REV) if considering three dimensions or the representative elementary area (REA) if considering two dimensions. The resolution used for imaging must be suited to the features of interest in the sample and the region-of-interest must be sufficiently large to capture key information. Polymer electrolyte fuel cells have a hierarchical structure, with materials spanning multiple length scales. The work presented here examines the nature of the REA throughout a 25 cm² membrane electrode assembly (MEA), focusing specifically on the micron length scale. Studies were carried out to investigate key structural (volume fraction, layer and penetration thickness, pore diameters) and transport (effective diffusivity) properties. Furthermore, the limiting current density of the nine regions was modelled. Stochastic heterogeneity throughout the sample results in local variations throughout. Finally, effects of resolution were probed by imaging using a range of optical magnifications (4× and 20×). The correlated and competing effects of voxel resolution and sampling size were found to cause difficulties where loss of clarity in the boundaries between phases occurs with larger imaging volumes.

Most cathode materials for lithium-ion batteries exhibit a low electronic conductivity. Hence, a significant amount of conductive graphitic additives are introduced during electrode production. The mechanical stability and electronic connection of the electrode is enhanced by a mixed phase formed by the carbon and binder materials. However, this mixed phase, the carbon binder domain (CBD), hinders the transport of lithium ions through the electrolyte pore network. Thus, reducing the performance at higher currents. In this work we combine microstructure resolved simulations with impedance measurements on symmetrical cells to identify the influence of the CBD distribution. Microstructures of NMC622 electrodes are obtained through synchrotron X-ray tomography. Resolving the CBD using tomography techniques is challenging. Therefore, three different CBD distributions are incorporated via a structure generator. We present results of microstructure resolved impedance spectroscopy and lithiation simulations, which reproduce the experimental results of impedance spectroscopy and galvanostatic lithiation measurements, thus, providing a link between the spatial CBD distribution, electrode impedance, and half-cell performance. The results demonstrate the significance of the CBD distribution and enable predictive simulations for battery design. The accumulation of CBD at contact points between particles is identified as the most likely configuration in the electrodes under consideration.

We present and validate a mathematical model for multicomponent thermodynamic activity in phase-separated cation-exchange membranes (e.g., perfluorinated sulfonic-acid ionomers). The model consists of an expression for the free energy of the membrane and of the surrounding electrolyte solution. A modified Stokes-Robinson ionic solvation framework treats the solution-like non-idealities resulting from hydration, electrostatics, ion association, and physical interactions in bulk solution and in ionomer hydrophilic domains. Inside the membrane, a mechanics-based composite approach accounts for the swelling of the hydrophobic matrix. Treating the membrane microstructure as a disordered system of domains calculates steric exclusion of ions. Electroneutrality guarantees that the charge of mobile ions in the membrane is equal to the charge on polymer groups. Osmotic coefficients for electrolytes from literature parameterize solution-like interactions while mechanical and X-ray scattering characterization gives most membrane-specific parameters. Model predictions compare favorably to measured membrane thermodynamics (i.e., water and ion uptake) in dilute and concentrated binary and ternary salt electrolytes and in water vapor. Interactions between ions in the membrane are similar to those present in bulk electrolytes. Our results reveal that water and ion uptake is dictated by a balance between solution-like energetics and membrane swelling.

Multicomponent mass-transport in cation-exchange membranes involves the movement of multiple species whose motion is coupled one to another. This phenomenon mediates the performance of numerous electrochemical and water purification technologies. This work presents and validates against experiment a mathematical model for multicomponent mass transport in phase-separated cation-exchange membranes (e.g., perfluorinated sulfonic-acid ionomers). Stefan-Maxwell-Onsager theory describes concentrated-solution transport. Hydrodynamic theory provides constitutive relations for the solute/solvent, solute/membrane, and solvent/membrane friction coefficients. Classical porous-medium theories scale membrane tortuosity. Electrostatic relaxation creates friction between ions. The model uses calculated ion and solvent partitioning between the external solution and the membrane from Part I of this series and incorporates the corresponding ion speciation into the transport coefficients. The proposed transport model compares favorably to properties (e.g., membrane conductivity, transference numbers, electroosmosis, and permeability) measured in dilute and concentrated aqueous binary and ternary electrolytes. The results reveal that the concentration and type of ions in the external solution alter the solvent volume fraction and viscosity in the hydrophilic pathways of the membrane, changing macroscale ionomer conductivity, permeability, and transference numbers. This work provides a physicochemical framework to predict ion-exchange-membrane performance in multicomponent systems exhibiting coupled transport.

Transport through vanadium redox-flow-battery membranes strongly influences cell performance. In this work, we use a multicomponent concentrated-solution model of transport and thermodynamics in phase-separated cation-exchange membranes, the most common separator type, to develop structure-performance relationships. The model incorporates species partitioning into the membrane, thermodynamic nonidealities, and Stefan-Maxwell-Onsager frictions between species. Molecular-thermodynamics and -transport theories parameterize the model. We validate the calculations against measured Coulombic and voltage efficiencies of a vanadium flow battery as a function of current density. Our model shows that species transport is the result of collective interactions between all species present in the system. The magnitude of coupling suggests that predictions made using dilute-solution theory for transport in these systems will be misleading in many situations. As a demonstration of the capabilities of the model, we predict cell performance, incorporating these interactions, as a function of electrolyte concentration and composition and membrane equivalent weight and backbone modulus. We find that electrolytes with high sulfuric acid concentrations provide the greatest cell performance (quantified by maximizing power density at a target energy efficiency). In the case of membrane properties, low equivalent-weight polymers perform better; at high equivalent weights, a low membrane modulus is preferred.

The mechanical state within a parallel-plate electrolytic capacitor is examined by appending a local momentum balance to a quasielectrostatic theory that describes charge screening in both the electrolyte and the electrodes. A classical diffuse-double-layer model, which treats the capacitor's separator as a dilute electrolytic solution, is augmented to include metal electrodes, modelled as electron gases. When accounted for in this way, the electrodes are found to impact the interfacial capacitance significantly, as well as exerting compressive stress on the electrolyte. Nonlinear and quadratically perturbed theories are explored, the former around a single plate and the latter around the entire capacitor. Perturbation reveals several mechanical scaling laws generally applicable to capacitive metal/electrolyte interfaces. The two-plate model rationalizes the exponential decay of disjoining pressure between voltage-biased plates as their separation distance grows, as well as retrieving the well-known properties of a dielectric capacitor when the plate separation is small. This was Paper 1964 presented at the Dallas, Texas, Meeting of the Society, May 26-May 30, 2019.