Fundamental Thermodynamic Limitations in Wagner’s Equation in Solid State Electrochemistry

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

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© 2009 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; E-mail:


The use of samarium-doped ceria (SDC) electrolytes in SOFCs (solid oxide fuel cells) lowers the open circuit voltage (OCV) below the Nernst voltage (Vth), which is obtained using yttria-stabilized zirconia (YSZ) electrolytes. The OCV is classically calculated with Wagner’s equation. However, using SDC electrolytes requires both qualitative and quantitative experimental verification of leakage currents. There are additional limitations to using Wagner’s equation with SDC electrolytes due to linear transport theory. A constant voltage loss without leakage currents due to a mixed ionic and electronic conducting (MIEC) dense anode has been proposed, and a local equilibrium can be used to address the transition state during ion hopping. Only carrier species having sufficient energy to overcome the activation energy can contribute to current conduction, which is determined by incorporating a different constant in the definitions of chemical potential and electrical potential. This difference explains the results using dense MIEC anodes. In this study, the fundamental thermodynamic basis of this topic is discussed by considering the Boltzmann distribution.

Keywords: SOFC, Ceria, MIEC, Wagner’s equation, The Boltzmann distribution.