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Multi-phase management is crucial for performance and durability of electrochemical cells such as batteries and fuel cells. In this paper we present a generic framework for describing the two-dimensional spatiotemporal evolution of gaseous, liquid and solid phases, as well as their interdependence with interfacial (electro-)chemistry and microstructure in a continuum description. The modeling domain consists of up to seven layers (current collectors, channels, electrodes, separator/membrane), each of which can consist of an arbitrary number of bulk phases (gas, liquid, solid) and connecting interfaces (two-phase or multi-phase boundaries). Bulk and interfacial chemistry is described using global or elementary kinetic reactions. Multi-phase management is coupled to chemistry and to mass and charge transport within bulk phases. The functionality and flexibility of this framework is demonstrated using four application areas in the context of post-lithium-ion batteries and fuel cells, that is, lithium-sulfur (Li-S) cells, lithium-oxygen (Li-O) cells, solid oxide fuel cells (SOFC) and polymer electrolyte membrane fuel cells (PEFC). The results are compared to models available in literature and properties of the generic framework are discussed.
n this work a mathematical model for describing the performance of lithium-ion battery electrodes consisting of porous active material particles is presented. The model represents an extension of the Newman-type model, accounting for the agglomerate structure of the active material particles, here Li(Ni1/3Co1/3Mn1/3)O2 (NCM) and Li(Ni1/3Co1/3Al1/3)O2 (NCA). To this goal, an additional pore space is introduced on the active material level. The space is filled with electrolyte and a charge-transfer reaction takes place at the liquid-solid interface within the porous active material particles. Volume-averaging techniques are used to derive the model equations. A local Thiele modulus is defined and provides an insight into the potentially limiting factors on the active material level. The introduction of a liquid-phase ion transport within the active material reduces the overall transport losses, while the additional active surface area within the agglomerate lowers the charge-transfer resistance. As a consequence, calculated discharge capacities are higher for particles modeled as agglomerates. This finding is more pronounced in the case of high C-rates
Nickel cobalt aluminum oxide (NCA) based lithium-ion battery electrodes exhibit a distinct asymmetry in discharge/charge behavior towards high bulk stoichiometry (low state of charge). We show that basic electrochemical relationships, that is, the Nernst equation and the Butler-Volmer equation, are able to reproduce this behavior when a two-step reaction mechanism is assumed. The two-step mechanism consists of (1) lithium-ion adsorption from the electrolyte onto the active material particle surface under electron transfer, and (2) intercalation of surface-adsorbed lithium atoms into the bulk material. The asymmetry of experimental half-cell data of an NCA electrode cycled at 0.1 C-rate can be quantitatively reproduced with this simple model. The model parameters show two alternative solutions, predicting either a saturated (highly-covered) or a depleted surface for high bulk lithiation.
Cell lifetime diagnostics and system be-havior of stationary LFP/graphite lithium-ion batteries
(2018)
In this article the high-temperature behavior of a cylindrical lithium iron phosphate/graphite lithium-ion cell is investigated numerically and experimentally by means of differential scanning calorimetry (DSC), accelerating rate calorimetry (ARC), and external short circuit test (ESC). For the simulations a multi-physics multi-scale (1D+1D+1D) model is used. Assuming a two-step electro-/thermochemical SEI formation mechanism, the model is able to qualitatively reproduce experimental data at temperatures up to approx. 200 °C. Model assumptions and parameters could be evaluated via comparison to experimental results, where the three types of experiments (DSC, ARC, ESC) show complementary sensitivities towards model parameters. The results underline that elevated-temperature experiments can be used to identify parameters of the multi-physics model, which then can be used to understand and interpret high-temperature behavior. The resulting model is able to describe nominal charge/discharge operation behavior, long-term calendaric aging behavior, and short-term high-temperature behavior during extreme events, demonstrating the descriptive and predictive capabilities of physicochemical models.
This article presents a comparative experimental study of the electrical, structural and chemical properties of large‐format, 180 Ah prismatic lithium iron phosphate (LFP)/graphite lithium‐ion battery cells from two different manufacturers. These cells are particularly used in the field of stationary energy storage such as home‐storage systems. The investigations include (1) cell‐to‐cell performance assessment, for which a total of 28 cells was tested from each manufacturer, (2) electrical charge/discharge characteristics at different currents and ambient temperatures, (3) internal cell geometries, components, and weight analysis after cell opening, (4) microstructural analysis of the electrodes via light microscopy and scanning electron microscopy, (5) chemical analysis of the electrode materials using energy‐dispersive X‐ray spectroscopy, and (6) mathematical analysis of the electrode balances. The combined results give a detailed and comparative insight into the cell characteristics, providing essential information needed for system integration. The study also provides complete and self‐consistent parameter sets for the use in cells models needed for performance prediction or state diagnosis.
Electrochemical impedance spectroscopy (EIS) is a widely-used diagnostic technique to characterize electrochemical processes. It is based on the dynamic analysis of two electrical observables, that is, current and voltage. Electrochemical cells with gaseous reactants or products (e.g., fuel cells, metal/air cells, electrolyzers) offer an additional observable, that is, the gas pressure. The dynamic coupling of current and/or voltage with gas pressure gives rise to a number of additional impedance definitions, for which we use the term electrochemical pressure impedance. It also gives rise to different experimental probing approaches. In this article we present a model-based study of electrochemical pressure impedance spectroscopy (EPIS). Possible quantifications and realizations of EPIS are discussed. The study of generic cell geometries consisting of gas reservoir, diffusion layer(s) and electrochemically active layer(s) reveals distinct spiral-shaped features in the Nyquist plot. Using the example of a sodium/oxygen (Na/O2) cell, the dynamic spatiotemporal behavior of the state variables is quantified and interpreted. Results are compared to first experimental EPIS measurements by Hartmann et al. [J. Phys. Chem. C118, 1461, 2014]. A sensitivity analysis highlights the properties of EPIS with respect to geometric, transport, and kinetic parameters. We demonstrate that EPIS is sensitive to transport parameters that are not well-accessible with standard EIS.
Electrochemical impedance spectroscopy (EIS) is a widely-used diagnostic technique to characterize electrochemical processes. It is based on the dynamic analysis of two electrical observables, that is, current and voltage. Electrochemical cells with gaseous reactants or products (e.g., fuel cells, metal/air cells, electrolyzers) offer an additional observable, that is, the gas pressure. The dynamic coupling of current and/or voltage with gas pressure gives rise to a number of additional impedance definitions, for which we have introduced the term electrochemical pressure impedance spectroscopy (EPIS) [1,2]. EPIS shows a particular sensitivity towards transport processes of gas-phase or dissolved species, in particular, diffusion coefficients and transport pathway lengths. It is as such complementary to standard EIS, which is mainly sensitive towards electrochemical processes. This sensitivity can be exploited for model parameterization and validation. A general analysis of EPIS is presented, which shows the necessity of model-based interpretation of the complex EPIS shapes in the Nyquist plot (cf. Figure). We then present EPIS simulations for two different electrochemical cells: (1) a sodium/oxygen battery cell and (2) a hydrogen/air fuel cell. We use 1D or 2D electrochemical and transport models to simulate current excitation/pressure detection or pressure excitation/voltage detection. The results are compared to first EPIS experimental data available in literature [2,3].
Mass transfer phenomena in membrane fuel cells are complex and diversified because of the presence of complex transport pathways including porous media of very different pore sizes and possible formation of liquid water. Electrochemical impedance spectroscopy, although allowing valuable information on ohmic phenomena, charge transfer and mass transfer phenomena, may nevertheless appear insufficient below 1 Hz. Use of another variable, that is, back pressure, as an excitation variable for electrochemical pressure impedance spectroscopy is shown here a promising tool for investigations and diagnosis of fuel cells.
We present an electrochemical model of a lithium iron phosphate/graphite (LFP/C6) cell that includes combined aging mechanisms: (i) Electrochemical formation of the solid electrolyte interphase (SEI) at the anode, leading to loss of lithium inventory, (ii) breaking of the SEI due to volume changes of the graphite particles, causing accelerated SEI growth, and (iii) loss of active material due to of loss percolation of the liquid electrolyte resulting from electrode dry-out. The latter requires the introduction of an activity-saturation relationship. A time-upscaling methodology is developed that allows to simulate large time spans (thousands of operating hours). The combined modeling and simulation framework is able to predict calendaric and cyclic aging up to the end of life of the battery cells. The aging parameters are adjusted to match literature calendaric and cyclic aging experiments, resulting in quantitative agreement of simulated nonlinear capacity loss with experimental data. The model predicts and provides an interpretation for the dependence of capacity loss on temperature, cycling depth, and average SOC. The introduction of a percolation threshold in the activity-saturation relationship allows to capture the strong nonlinearity of aging toward end of life (“sudden death”).
Lithium-ion pouch cells with lithium titanate (Li4Ti5O12, LTO) anode and lithium nickel cobalt aluminum oxide (LiNi0.8Co0.15Al0.05O2, NCA) cathode were investigated experimentally with respect to their electrical (0.1C…4C), thermal (5 °C…50 °C) and long-time cycling behavior. The 16 Ah cell exhibits an asymmetric charge/discharge behavior which leads to a strong capacity-rate effect, as well as a significantly temperature-dependent capacity (0.37 Ah ∙ K−1) which expresses as additional high-temperature feature in the differential voltage plot. The cell was cycled for 10,000 cycles inbetween the nominal voltage limits (1.7–2.7 V) with a symmetric 4C constant-current charge/discharge protocol, corresponding to approx. 3400 equivalent full cycles. A small (0.192 mΩ/1000 cycles) but continuous increase of internal resistance was observed. Using electrochemical impedance spectroscopy (EIS), this could be identified to be caused by the NCA cathode, while the LTO anode showed only minor changes during cycling. The temperature-corrected capacity during 4C cycling exhibited a decrease of 1.28%/1000 cycles. The 1C discharge capacity faded by only 4.0% for CC discharge and 2.3% for CCCV discharge after 10,000 cycles. The cell thus exhibits very good internal-resistance stability and excellent capacity retention even under harsh (4C continuous) cycling, demonstrating the excellent stability of LTO as anode material.
The measurement of the active material volume fraction in composite electrodes of lithium-ion battery cells is difficult due to the small (sub-micrometer) and irregular structure and multi-component composition of the electrodes, particularly in the case of blend electrodes. State-of-the-art experimental methods such as focused ion beam/scanning electron microscopy (FIB/SEM) and subsequent image analysis require expensive equipment and significant expertise. We present here a simple method for identifying active material volume fractions in single-material and blend electrodes, based on the comparison of experimental equilibrium cell voltage curve (open-circuit voltage as function of charge throughput) with active material half-cell potential curves (half-cell potential as function of lithium stoichiometry). The method requires only (i) low-current cycling data of full cells, (ii) cell opening for measurement of electrode thickness and active electrode area, and (iii) literature half-cell potentials of the active materials. Mathematical optimization is used to identify volume fractions and lithium stoichiometry ranges in which the active materials are cycled. The method is particularly useful for model parameterization of either physicochemical (e.g., pseudo-two-dimensional) models or equivalent circuit models, as it yields a self-consistent set of stoichiometric and structural parameters. The method is demonstrated using a commercial LCO–NCA/graphite pouch cell with blend cathode, but can also be applied to other blends (e.g., graphite–silicon anode).
Impedance of the Surface Double Layer of LSCF/CGO Composite Cathodes: An Elementary Kinetic Model
(2014)
One of the bottlenecks hindering the usage of polymer electrolyte membrane fuel cell technology in automotive applications is the highly load-sensitive degradation of the cell components. The cell failure cases reported in the literature show localized cell component degradation, mainly caused by flow-field dependent non-uniform distribution of reactants. The existing methodologies for diagnostics of localized cell failure are either invasive or require sophisticated and expensive apparatus. In this study, with the help of a multiscale simulation framework, a single polymer electrolyte membrane fuel cell (PEMFC) model is exposed to a standardized drive cycle provided by a system model of a fuel cell car. A 2D multiphysics model of the PEMFC is used to investigate catalyst degradation due to spatio-temporal variations in the fuel cell state variables under the highly transient load cycles. A three-step (extraction, oxidation, and dissolution) model of platinum loss in the cathode catalyst layer is used to investigate the cell performance degradation due to the consequent reduction in the electro-chemical active surface area (ECSA). By using a time-upscaling methodology, we present a comparative prediction of cell end-of-life (EOL) under different driving behavior of New European Driving Cycle (NEDC) and Worldwide Harmonized Light Vehicles Test Cycle (WLTC).
Oxidation of the nickel electrode is a severe aging mechanism of solid oxide fuel cells (SOFC) and solid oxide electrolyzer cells (SOEC). This work presents a modeling study of safe operating conditions with respect to nickel oxide formation. Microkinetic reaction mechanisms for thermochemical and electrochemical nickel oxidation are integrated into a 2D multiphase model of an anode‐supported solid oxide cell. Local oxidation propensity can be separated into four regimes. Simulations show that the thermochemical pathway generally dominates the electrochemical pathway. As a consequence, as long as fuel utilization is low, cell operation considerably below electrochemical oxidation limit of 0.704 V is possible without the risk of reoxidation.
Model-based analysis of Electrochemical Pressure Impedance Spectroscopy (EPIS) for PEM Fuel Cells
(2019)
Electrochemical impedance spectroscopy (EIS) is a widely-used diagnostic technique to characterize electrochemical processes. It is based on the dynamic analysis of two electrical observables, that is, current and voltage. Electrochemical cells with gaseous reactants or products, in particular fuel cells, offer an additional observable, that is, the gas pressure. The dynamic coupling of current or voltage with gas pressure gives rise to a number of additional impedance definitions, for which we have previously introduced the term electrochemical pressure impedance spectroscopy (EPIS) [1,2]. EPIS shows a particular sensitivity towards transport processes of gas-phase or dissolved species, in particular, diffusion coefficients and transport pathway lengths. It is as such complementary to standard EIS, which is mainly sensitive towards electrochemical processes. First EPIS experiments on PEM fuel cells have recently been shown [3].
We present a detailed modeling and simulation analysis of EPIS of a PEM fuel cell. We use a 1D+1D continuum model of a fuel/air channel pair with GDL and MEA. Backpressure is dynamically varied, and the resulting simulated oscillation in cell voltage is evaluated to yield the ▁Z_( V⁄p_ca ) EPIS signal. Results are obtained for different transport situations of the fuel cell, giving rise to very complex EPIS shapes in the Nyquist plot. This complexity shows the necessity of model-based interpretation of the complex EPIS shapes. Based on the simulation results, specific features in the EPIS spectra can be assigned to different transport domains (gas channel, GDL, membrane water transport).
Battery degradation is a complex physicochemical process that strongly depends on operating conditions. We present a model-based analysis of lithium-ion battery degradation in a stationary photovoltaic battery system. We use a multi-scale multi-physics model of a graphite/lithium iron phosphate (LiFePO4, LFP) cell including solid electrolyte interphase (SEI) formation. The cell-level model is dynamically coupled to a system-level model consisting of photovoltaics (PV), inverter, load, grid interaction, and energy management system, fed with historic weather data. Simulations are carried out for two load scenarios, a single-family house and an office tract, over annual operation cycles with one-minute time resolution. As key result, we show that the charging process causes a peak in degradation rate due to electrochemical charge overpotentials. The main drivers for cell ageing are therefore not only a high state of charge (SOC), but the charging process leading towards high SOC. We also show that the load situation not only influences system parameters like self-sufficiency and self-consumption, but also has a significant impact on battery ageing. We assess reduced charge cut-off voltage as ageing mitigation strategy.
This article presents the development, parameterization, and experimental validation of a pseudo-three-dimensional (P3D) multiphysics model of a 350 mAh high-power lithium-ion pouch cell with graphite anode and lithium cobalt oxide/lithium nickel cobalt aluminum oxide (LCO/NCA) blend cathode. The model describes transport processes on three different scales: Heat transport on the macroscopic scale (cell), mass and charge transport on the mesoscopic scale (electrode pair), and mass transport on the microscopic scale (active material particles). A generalized description of electrochemistry in blend electrodes is developed, using the open-source software Cantera for calculating species source terms. Very good agreement of model predictions with galvanostatic charge/discharge measurements, electrochemical impedance spectroscopy, and surface temperature measurements is observed over a wide range of operating conditions (0.05C to 10C charge and discharge, 5°C to 35°C). The behavior of internal states (concentrations, potentials, temperatures) is discussed. The blend materials show a complex behavior with both intra-particle and inter-particle non-equilibria during cycling.
Modeling and simulation play a key role in analyzing the complex electrochemical behavior of lithium-ion batteries. We present the development of a thermodynamic and kinetic modeling framework for intercalation electrochemistry within the open-source software Cantera. Instead of using equilibrium potentials and single-step Butler-Volmer kinetics, Cantera is based on molar thermodynamic data and mass-action kinetics, providing a physically-based and flexible means for complex reaction pathways. Herein, we introduce a new thermodynamic class for intercalation materials into the open-source software. We discuss the derivation of molar thermodynamic data from experimental half-cell potentials, and provide practical guidelines. We then demonstrate the new class using a single-particle model of a lithium cobalt oxide/graphite lithium-ion cell, implemented in MATLAB. With the present extensions, Cantera provides a platform for the lithium-ion battery modeling community both for consistent thermodynamic and kinetic models and for exchanging the required thermodynamic and kinetic parameters. We provide the full MATLAB code and parameter files as supplementary material to this article.
Modeling and Simulation the Influence of Solid Carbon Formation on SOFC Performance and Degradation
(2013)
Combined heat and power production (CHP) based on solid oxide fuel cells (SOFC) is a very promising technology to achieve high electrical efficiency to cover power demand by decentralized production. This paper presents a dynamic quasi 2D model of an SOFC system which consists of stack and balance of plant and includes thermal coupling between the single components. The model is implemented in Modelica® and validated with experimental data for the stack UI-characteristic and the thermal behavior. The good agreement between experimental and simulation results demonstrates the validity of the model. Different operating conditions and system configurations are tested, increasing the net electrical efficiency to 57% by implementing an anode offgas recycle rate of 65%. A sensitivity analysis of characteristic values of the system like fuel utilization, oxygen-to-carbon ratio and electrical efficiency for different natural gas compositions is carried out. The result shows that a control strategy adapted to variable natural gas composition and its energy content should be developed in order to optimize the operation of the system.
Modelling detailed chemistry in lithium-ion batteries: Insight into performance, ageing and safety
(2018)
Lithium‐ion battery cells are multiscale and multiphysics systems. Design and material parameters influence the macroscopically observable cell performance in a complex and nonlinear way. Herein, the development and application of three methodologies for model‐based interpretation and visualization of these influences are presented: 1) deconvolution of overpotential contributions, including ohmic, concentration, and activation overpotentials of the various cell components; 2) partial electrochemical impedance spectroscopy, allowing a direct visualization of the origin of different impedance features; and 3) sensitivity analyses, allowing a systematic assessment of the influence of cell parameters on capacity, internal resistance, and impedance. The methods are applied to a previously developed and validated pseudo‐3D model of a high‐power lithium‐ion pouch cell. The cell features a blend cathode. The two blend components show strong coupling, which can be observed and interpreted using the results of overpotential deconvolution, partial impedance spectroscopy, and sensitivity analysis. The presented methods are useful tools for model‐supported lithium‐ion cell research and development.
Muli-scale thermos-electrochemical modelling of aging mechanisms in an LFP/graphite lithium-ion cell
(2017)
Lithium–oxygen cells with nonaqueous electrolyte show high overpotentials during charge, indicating asymmetric charge/discharge reaction mechanisms. We present a kinetic modeling and simulation study of the lithium–oxygen cell cycling behavior. The model includes a multistep reaction mechanism of the cell reaction (2Li + O2 ⇄ Li2O2) forming lithium peroxide by precipitation, coupled to a 1D porous-electrode transport model. We apply the model to study the asymmetric discharge/charge characteristics and analyze the influence of a redox mediator dissolved homogeneously in the liquid electrolyte. Model predictions are compared to experimental galvanostatic cycling data of cells without and with 2,2,6,6-tetramethylpiperidinyloxyl (TEMPO) as redox mediator. The predicted discharge behavior shows good agreement with the experimental results. A spatiotemporal analysis of species concentrations reveals inhomogeneous distributions of dissolved oxygen and reaction products within the cathode during discharge. The experimentally observed charge overpotentials as well as their reduction by using a redox mediator can be qualitatively reproduced with a partially irreversible reaction mechanism. However, the proposed models fail to reproduce the particular shape of the experimental charge curve with continuously increasing charge overpotential, which implies that part of the reaction mechanism is still open for investigation in future work.
On the Fundamental and Practical Aspects of Modeling Complex Electrochemical Kinetics and Transport
(2018)
Numerous technologies, such as batteries and fuel cells, depend on electrochemical kinetics. In some cases, the responsible electrochemistry and charged-species transport is complex. However, to date, there are essentially no general-purpose modeling capabilities that facilitate the incorporation of thermodynamic, kinetic, and transport complexities into the simulation of electrochemical processes. A vast majority of the modeling literature uses only a few (often only one) global charge-transfer reactions, with the rates expressed using Butler–Volmer approximations. The objective of the present paper is to identify common aspects of electrochemistry, seeking a foundational basis for designing and implementing software with general applicability across a wide range of materials sets and applications. The development of new technologies should be accelerated and improved by enabling the incorporation of electrochemical complexity (e.g., multi-step, elementary charge-transfer reactions and as well as supporting ionic and electronic transport) into the analysis and interpretation of scientific results. The spirit of the approach is analogous to the role that Chemkin has played in homogeneous chemistry modeling, especially combustion. The Cantera software, which already has some electrochemistry capabilities, forms the foundation for future capabilities expansion.