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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.
The lifetime and performance of solid-oxide fuel cells (SOFC) and electrolyzer cells (SOEC) can be significantly degraded by oxidation of nickel within the electrode and support structures. This paper documents a detailed computational model describing nickel oxide (NiO) formation as a growing film layer on top of the nickel phase in Ni/YSZ composite electrodes. The model assumes that the oxidation rate is controlled by transport of ions across the film (Wagner's theory). The computational model, which is implemented in a two-dimensional continuum framework, facilitates the investigation of alternative chemical reaction and transport mechanisms. Model predictions agree well with a literature experimental measurement of oxidation-layer growth. In addition to providing insight in interpreting experimental observations, the model provides a quantitative predictive capability for improving electrode design and controlling operating conditions.
The formation of secondary phases in the porous electrodes is a severe mechanism affecting the lifetime of solid oxide fuel cells (SOFC). It can occur via various chemical mechanisms and it has a significant influence on cell performance due to pore clogging and deactivation of active surfaces and triple-phase boundary (TPB). We present a modeling and simulation study of nickel oxide formation (reoxidation) and carbon formation (coking) within the SOFC anode. We use a 2D continuum model based on a multi-phase framework [Neidhardt et al., J. Electrochem. Soc., 159, 9 (2012)] that allows the introduction of arbitrary solid phases (here: Ni, YSZ, NiO, Carbon) plus gas phase. Reactions between the bulk phases are modeled via interface-adsorbed species and are described by an elementary kinetic approach. Published experimental data are used for parameterization and validation. Simulations allow the prediction of cell performance under critical operation conditions, like (i) a non-fuel operation test, where NiO formation is taking place (Figure 1a), or (ii) an open circuit voltage (OCV) stability test under hydrocarbon atmosphere, where solid carbon is formed (Figure 1b). Results are applied for enhanced interpretation of experimental data and for prediction of safe operation conditions.
Lithium–sulfur (Li/S) cells are promising candidates for a next generation of safe and cost-effective high energy density batteries for mobile and stationary applications. At present, most Li/S cells still suffer from relatively poor cyclability, capacity loss under moderate current densities and self-discharge. Furthermore, the underlying chemical mechanisms of the general discharge/charge behavior as well as Li/S-specific phenomena like the polysulfide shuttle are not yet fully understood. Here we present a thermodynamically consistent, fully reversible continuum model of a Li/S cell with simplified four-step electrochemistry, including a simple description of the polysulfide shuttle effect. The model is parameterized using experimental discharge curves obtained from literature and reproduces behavior at various current densities with fairly high accuracy. While being instructively simple, the presented model can still reproduce distinct macroscopic Li/S-cell features caused by the shuttle effect, e.g., seemingly infinite charging at low charge current densities, and suboptimal coulombic efficiency. The irreversible transport of active material from the cathode to the anode results in a voltage drop and capacity loss during cycling, which can also be observed experimentally.
In this paper we present a model of the discharge of a lithium–oxygen battery with aqueous electrolyte. Lithium–oxygen batteries (Li–O2) have recently received great attention due to their large theoretical specific energy. Advantages of the aqueous design include the stability of the electrolyte, the long experience with gas diffusion electrodes (GDEs), and the solubility of the reaction product lithium hydroxide. However, competitive specific energies can only be obtained if the product is allowed to precipitate. Here we present a dynamic one-dimensional model of a Li–O2 battery including a GDE and precipitation of lithium hydroxide. The model is parameterized using experimental data from the literature. We demonstrate that GDEs remove power limitations due to slow oxygen transport in solutions and that lithium hydroxide tends to precipitate on the anode side. We discuss the system architecture to engineer where nucleation and growth predominantly occurs and to optimize for discharge capacity.
Compact solid discharge products enable energy storage devices with high gravimetric and volumetric energy densities, but solid deposits on active surfaces can disturb charge transport and induce mechanical stress. In this Letter, we develop a nanoscale continuum model for the growth of Li2O2 crystals in lithium–oxygen batteries with organic electrolytes, based on a theory of electrochemical nonequilibrium thermodynamics originally applied to Li-ion batteries. As in the case of lithium insertion in phase-separating LiFePO4 nanoparticles, the theory predicts a transition from complex to uniform morphologies of Li2O2 with increasing current. Discrete particle growth at low discharge rates becomes suppressed at high rates, resulting in a film of electronically insulating Li2O2 that limits cell performance. We predict that the transition between these surface growth modes occurs at current densities close to the exchange current density of the cathode reaction, consistent with experimental observations.
In the dual membrane fuel cell (DM-Cell), protons formed at the anode and oxygen ions formed at the cathode migrate through their respective dense electrolytes to react and form water in a porous composite layer called dual membrane (DM). The DM-Cell concept was experimentally proven (as detailed in Part I of this paper). To describe the electrochemical processes occurring in this novel fuel cell, a mathematical model has been developed which focuses on the DM as the characteristic feature of the DM-Cell. In the model, the porous composite DM is treated as a continuum medium characterized by effective macro-homogeneous properties. To simulate the polarization behavior of the DM-Cell, the potential distribution in the DM is related to the flux of protons and oxygen ions in the conducting phases by introducing kinetic and transport equations into charge balances. Since water pressure may affect the overall formation rate, water mass balances across the DM and transport equations are also considered. The satisfactory comparison with available experimental results suggests that the model provides sound indications on the effects of key design parameters and operating conditions on cell behavior and performance.
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.