Theoretical Verification of Wagner`s Equation Considering Polarization Voltage Losses in SOFCs

T. Miyashita*
1-6-3, Mitsuya-kita, Yodogawa-ku, Osaka, 532-0032, Japan.

Article Metrics

CrossRef Citations:
Total Statistics:

Full-Text HTML Views: 222
Abstract HTML Views: 581
PDF Downloads: 219
Total Views/Downloads: 1022
Unique Statistics:

Full-Text HTML Views: 166
Abstract HTML Views: 428
PDF Downloads: 156
Total Views/Downloads: 750

© 2010 T. Miyashita;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the 1-6-3, Mitsuya-kita, Yodogawa-ku, Osaka, 532-0032, Japan; Tel: 090-1204-1259; Fax: +81-797-32-6171; E-mail:


The necessity for experimental verification of leakage currents using Sm-doped ceria electrolytes (SDC) in solid-oxide fuel cells (SOFCs) has been indicated. This paper describes the theoretical limitations of Wagner's equation and details the analytical work that has been performed to support the experimental results. These limitations cannot be solved, even considering polarization voltage losses. Globally, there are several research groups working on SOFCs to solve the current-voltage relation with mixed ionic electronic solid conductors (MIECs). However, this problem must be solved considering the electric field (E) in MIECs. Thus, even though articles have already been published in similar areas, no approach has been taken within this body of work that considers the E in MIECs. In this report, a new calculation method considering E is expressed only from Wagner's equation, with continuity expressed using the Choudhury and Patterson style. The calculated results match the values from conventional models. The constant field approximation is verified using the conventional definition of E. However, the definition of E should be changed when there is a large voltage drop in the thin area of the electrolyte compared with the lattice constant. In this study, the electric field near the cathode is sufficiently large to cause dielectric breakdown, which has never been reported.

Keywords: SOFC, MIEC, ceria, Wagner’s equation, Riess’s model, polarization loss.