Investigation of the active thickness of solid oxide fuel cell electrodes using a 3D microstructure model

Composite electrodes comprising a rare-earth nickelate phase and a doped rare-earth ceria phase with a high level of rare-earth doping have been studied as oxygen electrodes. While rare-earth nickelates have shown great promise as oxygen electrodes in both solid oxide fuel cells (SOFC) and solid oxide electrolysis cells (SOECs), they become unstable in contact with rare-earth doped ceria. In this work we describe a strategy to eliminate this instability and enable the use of these electrodes as stable high performance oxygen electrodes in both SOFC and SOEC applications. The performance of such composite electrodes is explored using a symmetrical cell approach, and through the electrical conductivity relaxation (ECR) method and compare it to state-of-the-art oxygen electrodes comprising strontium doped lanthanum manganite (LSM) – yttria stabilized zirconia (YSZ) composite electrodes. The symmetrical cell tests which reveal the stabilized nickelate-ceria electrodes to be superior, are also well-correlated with the results of testing complete cells in both SOFC and SOEC modes. Based on these results we make the case for deploying these stabilized nickelate-ceria composite electrodes as oxygen electrodes in reversible SOFC-SOEC systems.

Introduction With the recent enhancement of renewable energy utilization, large scale energy conversion and storage become more important to control the surplus electric power due to the unsteady power generation. Reversible hydrogen energy storage system via solid oxide electrolysis cell (SOEC) and solid oxide fuel cell (SOFC) are expected as a high efficient device because of its high operating temperature (600℃~1000℃). It is possible to unify them to one device as reversible system (RSOFC/EC), but it is necessary to understand the mechanism of FC/EC reactions and design the device with a good balance between FC and EC in order to apply them for an actual energy system. While SOFC reaction models and many electrochemical data of electrodes have been developed and reported by many researchers, there are few reports to investigate the reaction model of SOEC. Thus, it is possible to predict the performance of SOEC based on a comprehensive SOFC/EC models and experimental data of SOFC, because the reactions of SOFC and SOEC are a reversible relationship and the equal value of IR loss can be applied. However, the comprehensive SOFC/EC electrochemical model has not been established. A series of experimental data of anodic and cathodic current density vs. the potential should be investigated at various conditions to develop the SOFC/EC model. In this work, a series of anodic and cathodic electrode performance was taken using a SOFC in various conditions. Furthermore, attempting to predict SOEC performance from SOFC performances, we proposed and discussed a new model of electrolysis based on our developed SOFC model. Experimental The Disks of 8 mol% Y2O3-ZrO2 (YSZ; 0.25 mm thickness, 20 mm diameter) were used as the electrolyte and the anode was a Ni/YSZ or Ni/GDC composite, and the cathode was a La0.8Sr0.2MnO3/ScSZ composite. We measured the dependence of the current density of anodes on oxygen activity with wide range to get both power generation and electrolysis data for various gas composition (PH2=0.3~0.99 atm, PH2O=0.01, 0.03, 0.05 atm). Results and Discussion 1. Method to fit parameters on the SOFC/EC model We have developed the electrochemical reaction model on the fuel electrode (=anode) based on the equilibrium of competitive adsorption and oxygen activity, ao , specified by anode potential (Eq.1, Table.1) [1]. The SOFC model was constructed by assuming competitive adsorption equilibrium of H2, H2O and O on Ni surfaces at three-phase boundary and the rate-determining step to be Langmuir-type reactions of H with O (Table.1). We obtained an equation of the electrical current density, i, as a function of the oxygen activity (ao ) calculated from the anode potential which is simply measured from experiments. To confirm effectiveness of the model, we fitted the model to actual experimental data described by i vs. ao . From the equations of model on Table.1, each current density of SOFC (ia ) and SOEC(ic ) are described as Eq.2. To draw the plot of i vs. ao on the model, the rate constants (ka, kc ) and the equilibrium constants (KO, KH, KH2O ) need to be defined as reliable value. Thus, from the equilibrium potential vs. 1 atm O2 (Eq.3), we defined the rate constant of kc as Eq.4. When the kc became a dependent variable of ka , then we fitted ia to power generation experimental data described by i vs. ao so that the values of KHKO/KH2O were fitted approximately. Finally, i c model could be drawn on the plot of i vs. ao and the maximum value of i c was obtained by Eq.5 which is independent of ao and Eq.6 was obtained using Eq.4. 2. Experimental results and parameter fitting on the SOFC/EC model As the expreimental results, the maximum power density of SOFC with Ni/YSZ was 588.5 mW/cm2 for FC mode at PH2=0.99 atm, PH2O=0.01 atm, and ic(max) was 0.285 A/cm2 for EC mode at PH2O=0.03 atm. However, ic(max) calculated by the model (Eq.6) was 0.050 A/cm2. Also, in case of SOFC with Ni/GDC, ic(max) was 0.400 A/cm2 for EC mode at PH2O=0.03 atm, while ic(max) calculated by the model (Eq.6) was 0.055 A/cm2. The electrolysis current density measured by our RSOFC/EC showed 6 times higher than model values approximately. This result suggested the possibility that additional parallel reaction path was existed. In this presentation, we will discuss the possible electrochemical paths to explain the disagreement between the model and the experimental data. Finally, the comprehensive SOFC/EC model will be proposed to predict EC performance using SOFC data.

Topology-informed machine learning for efficient prediction of solid oxide fuel cell electrode polarization

Solid Oxide Fuel Cells (SOFCs) are widely considered to be an ideal power source across a range of industries in the near future due to their high efficiency, high power density, and fuel flexibility. However, for widespread usage of SOFCs to be feasible, certain disadvantages, such as their high operating temperature, electrochemical losses, and high cost of manufacturing, must be solved. In particular, the field of materials research occupies a unique position of being able to quickly and simultaneously solve many of these issues through the development of material compositions and structures that do not currently exist in the industry. Especially relevant to solid oxide fuel cells in particular, is the impact that the electrodes’ geometries and compositions have on the operating performance. The electrodes’ ability to quickly move reactants to the interface of the electrolyte and remove products to the bulk flow comes into play as the fuel cell operates at higher current densities and concentration losses become prominent. Therefore, the microstructures present throughout the electrodes’ depth plays a vital role in improving overall cell performance. However, current fuel cell research has not yet effectively captured and defined the connections of the microstructure parameters and measured their impact on cell behavior. Additionally, homogeneous electrode design and implementation have dominated the research and commercial space thus far. The technique of functional material grading, which has begun to see wide research and commercial usage for such problems as acoustic impedance matching, thermal control, and mechanical design will be leveraged for the enhancement of SOFC electrodes. Functionally graded electrodes have been used in solid oxide fuel cell research in recent years in an effort to improve the cell performance by altering the microstructure including porosity, particle size, and composition of electronic and ionic conductors near the triple phase boundary region. Normally the functional grading process adds additional fabrication steps making it less desirable as an optimization process and easy manufacturing method. However, by using an additive manufacturing process it eliminates the need for multiple discrete graded layers to be deposited to obtain a graded electrode functional layer. This study seeks to explore the correlations of geometry and structure parameters from the meso-scale through to the micro-scale level, together with mass transfer, ionic and electronic transport, and gas-surface electrochemical reactions inside the electrodes to guide future additive manufacturing of SOFCs. Outlined is the development of an effective medium model for simulating the performance of fuel cell microstructures as a function of specific operating ranges in temperature, pressure, and in fuels used. Smooth and continuous linear and nonlinear functional gradation profiles of porosity and material composition are studied within the framework of an effective medium boundary value problem where the electrochemical relations, such as the Butler-Volmer equation, percolating conduction paths, and gas diffusion are solved using the finite difference method. The form of these relations for homogeneous electrodes was analyzed by Costamagna, et. al [1], who also defined outstanding problems with regards to optimizing SOFC electrodes [2]. Globally optimal linear and nonlinear gradation profiles and cell parameters are derived as a function of particle sizes, ratio of conductivities, and desired operating conditions and scored based on their reduction of cell overpotentials.[1] Costamagna, P., P. Costa, and V. Antonucci, Micro-modelling of solid oxide fuel cell electrodes. Electrochimica Acta, 1998. 43(3-4), pp.375-394.[2] Costamagna, P., P. Costa, and E. Arato, Some more considerations on the optimization of cermet solid oxide fuel cell electrodes. Electrochimica Acta, 1998. 43(8), pp.967-972. Figure 1

Understanding and optimizing electrochemically active zone for oxygen reduction reaction in solidoxide fuel cells (SOFCs) cathodes are indispensable to maximize device’s performance. For mixed ionicand electronic conductors, the range of this zone depends on the oxygen surface exchange and solid-stateoxygen/electron transport properties of materials [1]. This aspect is also critical to realize validcharacterization of the electrode’s electrochemical activities. For instance, when a material’s electronicconductivity is low or the electrical contact points are spaced beyond a critical distance, the electrodepolarization resistance measured by electrochemical impedance spectroscopy will be controlled by the sheetresistance not the oxygen exchange resistance [2]. The situation becomes more complicated as the electricalconductivity of porous layer, which is an advantageous structure with large surface area and facile gas phasetransport, considerably deviates from the material’s intrinsic property. It is expected that porosity,connectivity, and impurity contents can have significant impact on porous electrode’s electronic conduction[3].In this context, we have studied effective in-plane electronic conductivity of lanthanum strontiumcobalt ferrite (LSCF) porous layers. The in-plane conductivity was measured by four-line probeconfiguration [4], modified from the widely used four-point probe technique to be applied for a porouslayer. We have confirmed that the in-plane electrical conductivity of screen-printed LSCF porous layers isone or two orders of magnitude lower than the material’s bulk property in ambient air, depending ontemperatures. This electronic conductivity deviation was taken into account to rationally designcombination of electrode thickness and current collector spacing and, in turn, to guarantee a validassessment of electrode performance. In addition, we found that electrical conductivity of LSCF porouslayers decreases by 20~30 %, within relatively short period of time (250~400 hours) upon repeated thermalcycles (500 ℃ to 700 ℃). Furthermore, we found that in-plane conductivity of thin (<10 µm) electrodes isstrongly dependent on the measurement time and the local atmospheric environment relative to thickerelectrodes. Special attention is required to use a thin electrode to evaluate electrode performance.This work was supported by the US Department of Energy (DOE), Office of Fossil Energy, (Officeof Clean Coal & Carbon Management), “Solid Oxide Fuel Cell Manufacturing in Support of Office ofFossil Energy” program through Argonne National Laboratory under FWP No. 27327.1.[1] S.B. Adler et al. J. Electrochem. Soc. 143 (1996) 3554-3564; S.B. Alder Solid State Ionics 111 (1998)125-134.[2] B.A. Boukamp et al. Solid State Ionics 192 (2011) 404-408; B.A. Boukamp et al. Solid State Ionics 283(2015) 81-90.[3] L. Holzer et al. J. Mater. Sci. 48 (2013) 2934-2952.[4] S.W. Peterson et al. J. Electrochem. Soc. 161 (2014) A2175-A2181.

Reconstruction of solid oxide fuel cell electrode microstructure and analysis of its effective conductivity

Solid oxide fuel cell / electrolysis cell (SOFC / EC) can be expected as energy converters with high efficiency. In SOFC / EC material developments, the coverages of the chemical species at the three-phase boundary (TPB) are directly linked to the electrode performance. Accordingly, it is important to estimate the surface coverages at TPB to develop a new electrode. However, it is difficult to directly analyze and evaluate the coverages at the reaction field of the oxide / metal composites at high temperature (> 600 °C). Therefore, it is required to construct electrochemical kinetics with the various parameters, such as reaction constants and adsorption equilibrium constants.In order to determine the coverages at the TPB, it has demands not only to construct an appropriate electrochemical model but also both to develop a method for fitting a large number of parameters included in the model and to acquire a series of various experimental data sufficient for fitting. These requirements are not fully satisfied in previous researches [1-2]. Therefore, the chemical properties of the electrode surface have not been clarified while the reaction mechanism on the H2 electrode has been understood in FC operation.In this study, the determination method of surface coverage using an electrochemical reaction model for H2 / H2O porous electrodes composed of Ni / YSZ was established. We considered that the local equilibrium between oxygen and oxide ions is achieved in the solid electrolyte, and proposed a H2 electrode reaction model consisting of a competitive adsorption reaction as Langmuir-Hinshelwood type at TPB. Using the model, a relational expression between the electric current density and the coverage could be obtained.The equation includes the parameters of current density (i), oxygen activity (a O), the partial pressures of hydrogen (P H2) and water (P H2O), the kinetics constant of the water generation reaction at FC operation (k a), and the adsorption equilibrium constant of H, O, OH and H2O (K H, K O, K OH and K H2O). a O(eq) is the oxygen activity at equilibrium potential. The i, P H2, P H2O, a O and a O(eq) could be obtained by experimental conditions and data while ka , K H, K O, K OH and K H2O are unknown constants without appropriate fitting. The simple optimization method cannot approximate optimal solutions and determine the coverages because this model is multivariate function, which has 5 parameters.As a method for quantifying the coverage of chemical species by fitting the experimental data to the reaction model, the method using a genetic algorithm was applied. The genetic algorithm is one of the multivariable optimization methods, which efficiently approximates the optimized value of the parameters by alternation of generations created by operations composed of selection, crossover, and mutation [3]. By taking advantage of the characteristics of the genetic algorithm that randomly generates and converges initial value candidates during optimization, multiple optimal solutions can be efficiently obtained with preventing the drop to local optimum by increasing the number of trials. The most effective optimal solution could be determined from them.As the various electrochemical data for estimating the surface coverage at a temperature of 900 °C, the electrochemical data of both FC / EC under 12 conditions, in which P H2 and P H2O were changed were got using the same cell. The current interruption method was used to separate the overvoltage and ohmic voltage loss of the H2/H2O electrode during power generation and electrolysis under constant current, and then, the oxygen activity was calculated from the ohmic free-anode potential (vs. 1 atom O2). Using genetic algorithm, optimization schemes were attempted more than 50,000 times and searched for the parameter set with the smallest error between the experimental value and the estimated value from the obtained optimal solutions. The outline of the optimization process was shown in Fig. 1.As a result of fitting various reaction constants to the model with optimal solutions, the relationship between i and a O could be roughly expressed by multiple reaction rate constants and equilibrium constants, and the coverages could be quantified. Furthermore, it was possible to draw the chemical state at TPB of Ni / YSZ electrodes during FC operation.[1] W. G. Bessler et al., Phys. Chem. Chem. Phys., 12, 13888 (2010).[2] M. Ihara et al., J. Electrochem. Soc., 148(3), A209 (2001).[3] M. Srinivas et al., IEEE, 27(6), 17 (1994). Figure 1

Recent progress in micro-scale three-dimensional (3D) characterization techniques such as focused ion beam – scanning electron microscopy (FIB-SEM) and X-ray nanotomography has brought unprecedented opportunities in linking material microstructure to performance and properties. The link between solid oxide fuel cell (SOFC) electrode microstructure and performance is sometimes established by effective medium theory, where effective performance parameters are calculated from a representative volume element (RVE), an adequate volume that statistically represents global microstructure. However, different from performance, degradation and failure have not been addressed by mean parameters from effective medium theory. With the advent of modern 3D characterization techniques, there are new approaches in linking microstructure and degradation. This work aims to emphasize distributions (and outliers), rather than the mean, in better establishing the link between microstructure and degradation, failure, and performance. Using an open source finite element framework (MOOSE, Idaho National Laboratory) on a high performance computing platform (Joule, National Energy Technology Laboratory), a numerical transport and reaction model is applied to microstructural meshes to compute local distributions of electrochemical parameters. The microstructural meshes are obtained from the plasma sourced FIB-SEM characterization of a commercial SOFC electrode. The RVE size with respect to the computed distributions is determined based on examining the distributions from a series of microstructural meshes with various sizes. To validate the distributions, the averaged numbers from the distributions are compared with the effective medium theories in the literature. Finally, features such as the tails of the distributions and the local gradients of the electrochemical parameters are highlighted and discussed.

Synthetical designing of solid oxide fuel cell electrodes: Effect of particle size and volume fraction

Quantitative estimation of triple phase boundaries in solid oxide fuel cell electrodes via artificial neural network

Gadolinium doped ceria (GDC) gains increasing attention as a promising material for both solid oxide fuel cells (SOFCs) and solid oxide electrolysis cells (SOECs). The GDC-based electrodes demonstrate positive features, e.g. enhanced electrochemical performance in low operation temperatures, resistivity to sulfur poisoning and carbon deposition, etc. As GDC is a mixed electronic-ionic conductor in reducing atmosphere, electrochemical reactions can be supported by the double phase boundary (DPB) at the GDC surface. Several studies demonstrated that the DPB reaction may dominate the electrochemical performance over triple phase boundary (TPB) reaction in Ni-GDC electrodes, where it can account for as much as 95 % of the total reaction depending on the cermet microstructure [1]. Recent studies even show that pure ceria electrodes can achieve substantial power density [2,3]. In this context, the microstructure design principle for GDC-based electrodes should focus on maximizing GDC surface area. Particularly, GDC electrodes with infiltrated GDC nanoparticles or electro-catalytic nanoparticles may achieve competitive performance compared with the conventional Ni-YSZ electrodes. Although many strategies have been proposed to improve performance of GDC-based electrodes, it is difficult to quantitatively compare all the reported results. Furthermore, the correlation between microstructure and performance of pure GDC electrode are still scarce.Several different types of GDC-based electrodes are fabricated and tested in the unified characterization procedure in this study. Four basic designs are considered, i.e. Ni-GDC, GDC-perovskite composites, GDC electrodes with deposited Ni nanoparticles and pure GDC electrodes. Several strategies to modify the GDC surface area are discussed. In addition, the substantial enhancements in the DPB density and electrochemical performance were achieved by precipitating Ni-nanoparticles directly on sub-micron GDC powders at 2wt.% loading. The performance of electrodes was evaluated by electrochemical impedance spectra measurements with various humidity and temperature conditions. The results showed clear dependance between GDC surface area and electrode performance. At the same time, it should be noted that the electrode active thickness depends on the electrode microstructure. In particular, it is in the range of 5 µm for the pure nano-GDC electrode. When the GDC electrode is thicker than the active thickness, it results in large Ohmic resistance due to the electronic conduction in the porous electrode.[1] A. Nenning, M. Holzmann, J. Fleig, A.K. Opitz, Mater. Adv. 2 (2021) 5422–5431.[2] M. Ouyang, A. Bertei, S.J. Cooper, Y. Wu, P. Boldrin, X. Liu, M. Kishimoto, H. Wang, M. Naylor Marlow, J. Chen, X. Chen, Y. Xia, B. Wu, N.P. Brandon, J. Energy Chemistry. 56 (2021) 98–112.[3] W. Jung, K.L. Gu, Y. Choi, S.M. Haile, Energy Env. Sci. 7 (2014) 1685–1692.

A strong correlation exists between the performance of Solid Oxide Fuel Cells (SOFCs) and their electrode microstructures, requiring an improved understanding of this relationship if more effective application-specific SOFC electrodes are to be designed. A model has been developed capable of generating a random 3D electrode microstructure and predicting its performance by analyzing structure properties such as porosity, percolation of the various phases and the length and distribution of triple phase boundaries. A Monte Carlo process is used initially to randomly position spherical particles of the three different phases, in a packed bed. Next, the pore former particles are removed. The remaining particles are then expanded uniformly to represent the sintering process, resulting in a network of particles of ionic and electronic phases overlapping each other, creating a distinctive, examinable electrode. This paper presents the impact of a range of technologically important parameters such as particle size and sintering expansion coefficient on electrode performance.

Stochastic 3D microstructure reconstruction and mechanical modeling of anisotropic battery separators

Percolation theory to predict effective properties of solid oxide fuel-cell composite electrodes

Design of optimal microstructures for infiltrated solid oxide fuel cell (SOFC) electrodes is a complicated process because of the multitude of the electrochemical and physical phenomena taking place in the electrodes in different temperatures, current densities and reactant flow rates. In this study, a stochastic geometric modeling method is used to create a range of digitally realized infiltrated SOFC electrode microstructures to extract their geometry-related electrochemical and physical properties. Triple Phase Boundary (TPB), active surface density of particles along with the gas transport factor is evaluated in those realized models to adapt for various infiltration strategies. Recently, additive manufacturing or freeze type casting methods enable researchers to investigate the performance of directional electrodes to get the maximum electrochemical reaction sites, gas diffusivity and ionic conductivity simultaneously. A series of directional backbones with different amount of virtually deposited electrocatalyst particles are characterized in the first step. The database of microstructural parameters (inputs) and effective geometric properties (outputs) is used to train a range neural network. A microstructure property hull is created using the best neural network model to discover the range of effective properties, their relative behaviour and optimum microstructure. The characteristics of models is shown that there is not any contradiction between the high level of TPB and contact surface density of particles, but the highest amount of gas diffusivity can be found in the microstructures with lower level of reaction sites. Also increasing the contact surface density has a negative effect on gas transport but the high level of TPB density is feasible in the full range of microstructures. In the other hand, TPB density and gas diffusion into the models are inversely related, although there are a limited number of microstructures with high level of reaction sites and acceptable gas diffusivity. Finally, using a simple optimization process, the microstructures with the highest level of reaction sites and gas transport factor are identified which have the backbone porosity of about 50%, and extremely higher gain growth rate normal to the electrolyte. Additive manufacturing and 3D printing methods will enhance researchers in the future to create the real directional electrodes on the base of these proposed models.