Exchange current model for (La0.8Sr0.2)0.95MnO3 (LSM) porous cathode for solid oxide fuel cells
Graphical abstract
Introduction
The porous microstructure of SOFC electrodes is considered to have a significant effect on their power generation performance because the electrochemical reaction within the electrodes requires the sufficient transport of gas species, electrons and oxide ions through the complex multiphase porous structure. The recent development and improvement of 3D imaging techniques, such as focused ion beam scanning electron microscopy (FIB-SEM) and X-ray computed tomography, have enabled us to obtain detailed electrode microstructures in three dimensions [1], [2], [3], which are useful for obtaining insights into microstructure–performance relationships.
Three-dimensional datasets of porous electrodes can also be applied to the numerical analysis of electrode electrochemical performance [4], [5], [6], [7], [8], [9], where the rate equations for the electrochemical reactions are among the most essential factors that determine the accuracy of the simulation. Rate equations are often expressed by Butler–Volmer-like forms that include the density of the reaction sites, i.e., triple-phase boundaries (TPBs) or double-phase boundaries (DPBs), and the exchange current density per unit reaction site area/length. The TPB density is considered important for conventional cermet materials, such as Ni-YSZ (yttria-stabilized zirconia) and LSM-YSZ (lanthanum strontium manganite/yttria-stabilized zirconia), while the DPB density is considered important for mixed ionic-electronic conductors, such as doped ceria and LSCF (lanthanum strontium cobalt ferrite). For conventional cermet electrodes, the exchange current density per unit TPB length (i0,TPB) has been measured from experiments using thin and dense patterned electrodes because of the advantage that the TPB length is well defined from their geometry.
In the case of LSM-YSZ cathodes, Radhakrishnan et al. [10] conducted electrochemical measurements at various temperatures (650–800 °C) and oxygen partial pressures (0.01–1 atm) using patterned LSM cathodes with a thickness of 500 nm. Konno et al. [11] derived a power-law-type formula for i0,TPB based on the experimental results of Radhakrishnan et al. This empirical formula can be applied to numerical simulations. However, in our preliminary study, a large discrepancy was observed between numerical simulation results for a LSM cathode using this empirical formula and experimental results. One of the possible reasons for this is that the small ionic conductivity of LSM can expand the reaction region from TPBs to DPBs (LSM-pore boundaries) in a thin and dense patterned electrode. For instance, Brichzin et al. [12] conducted experiments on patterned electrodes with thicknesses of 100 and 250 nm and found that the thickness of the patterned LSM electrodes affected the activation overpotential. Furthermore, Horita et al. [13] observed oxygen ion diffusion inside a patterned LSM cathode with a thickness of 490 nm by secondary ion mass spectrometry and reported that the oxide ions were transferred through the thin and dense LSM. Yasuda et al. [14] also reported that under an oxygen partial pressure of 100 torr (ca. 0.13 atm), oxygen ions could penetrate through a thin and dense LSM. These studies [12], [13], [14] show that charge transfer can occur at DPBs in thin patterned electrodes. This is also supported by a report of Gong et al. [15], according to which the DPB reaction in LSM cathodes can only be negligible at a distance exceeding about 1 μm from the LSM/electrolyte interface at 800 °C. Most of the DPBs in the thin patterned LSM cathodes used in Refs. [12], [13], [14] existed within 500 nm from the LSM/electrolyte interface, and therefore they are expected to be electrochemically active. This makes it difficult to evaluate i0,TPB from experiments using the thin and dense patterned LSM cathodes. Therefore, an empirical formula for i0,TPB in LSM cathodes should be derived from actual porous LSM cathodes to minimize the contribution of the DPBs to the electrochemical activity of the electrode. Although the TPB length cannot be easily measured in actual porous electrodes, FIB-SEM enables us to evaluate the TPB density even in complex microstructures with a resolution of 10 nm order.
In this study, we conduct electrochemical measurements of porous LSM electrodes (particle diameter: ca. 3 μm) to derive an empirical formula for i0,TPB over a range of temperatures (800–950 °C) and oxygen partial pressures (0.05–0.25 atm). After the experiments, the porous LSM cathode is imaged by FIB-SEM and the TPB density is evaluated. From these experimental datasets, we estimate i0,TPB values, from which an empirical formula for i0,TPB derived from porous LSM cathodes is proposed and compared with a formula derived from patterned LSM cathodes [11]. The formula is then adopted in a 3D numerical simulation of an LSM-YSZ composite cathode and the results are compared with experimental results to confirm the validity of the formula derived in this study.
Section snippets
Derivation of the exchange current density model
The relationship between the charge transfer current density (ict [A m−2]) and the activation overpotential (ηact [V]) is often described by Butler–Volmer-like forms [16] using the TPB density (lTPB [m−1]) and the exchange current density per unit TPB length (i0,TPB [A m−1]):where T is the temperature, F is the Faraday constantant and R is the gas constant. To experimentally estimate i0,TPB, the following are required: (i) the relationship between
Validation of the formula for i0,TPB
To confirm the validity of the empirical formula for i0,TPB, we conducted (1) electrochemical measurements of an LSM-YSZ composite cathode to obtain i − ηact characteristics and (2) FIB-SEM imaging of the cathode after the experiment to obtain its microstructure. Note that LSM-YSZ composite cathode was made in the same method as described in Section 2.1.1 using LSM-YSZ paste (50 wt% LSM–50 wt% YSZ, LSMYSZ-I, NexTech materials). Using the obtained 3D microstructure and the i0,TPB model derived
Conclusions
In this study, an empirical formula for the exchange current density per unit TPB length in a lanthanum strontium manganite cathode for SOFCs was derived through electrochemical measurement of a porous LSM cathode and microstructural analysis by FIB-SEM. From the electrochemical measurement, the dependence of the activation overpotential on the electrode temperature and oxygen partial pressure was obtained, which was used to calculate the exchange current density within the cathode. Combined
Acknowledgments
This work was supported by the New Energy and Industrial Technology Development Organization (NEDO) under the Development of System and Elemental Technology for Solid Oxide Fuel Cell (SOFC) Project and by a Grant-in-Aid for JSPS Fellows.
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