Additional Voltage Loss Considering Jarzynski’s Equality Using Sm-Doped Ceria Electrolytes in Wagner’s Equation for SOFCs
Authors: Miyashita Tomofumi 
Published: July 2021

A solid oxide fuel cell (SOFC) directly converts chemical energy from a fuel gas, such as hydrogen or methane, to electrical energy. A solid oxide film is used as the electrolyte, in which the main carriers are oxygen ions. The use of high ion-conducting electrolyte materials, such as samaria-doped ceria (SDC), has been studied to lower the operating temperature. Using SDC electrolytes in solid oxide fuel cells, the open circuit voltage (OCV = 0.80 V at 1073 K) decreases to a smaller value than the Nernst voltage (Vth = 1.15 V at 1073 K), which is obtained using yttria stabilized zirconia (YSZ) electrolytes. This low value has been explained by Wagner’s equation.
Based on Wagner’s equation, numerous excellent models have been created. The Riess model is a very famous method for calculating the current-voltage relationship [1]. Using the Riess model, the current-voltage relationship can be calculated with the electrode polarization voltage loss. Furthermore, a nonlinear model was created by Duncan and Wachsman [2]. Using the model described by Duncan and Wachsman, both the electrode polarization voltage loss and the equilibration process can be explained.
Previously, we proposed that it is necessary to experimentally verify the existence of leakage currents using Sm-doped Ceria electrolytes in SOFCs. According to the Riess model, the OCV should change during electrode degradation. However, experimentally, the OCV does not change during electrode degradation [3]. Using the model defined by Duncan and Wachsman, the equilibration process that occurs in response to a change in the anode gas for thick Sm-doped ceria electrolytes has never been explained. Experimentally, using a very thick (6.6 mm) SDC electrolyte, the OCV can reach 0.80 V in only 5 minutes [4]. The corresponding electron diffusion current delay should be more than 2080 minutes [5].
Next, we proposed an additional voltage loss (0.35 V = 1.15 V- 0.80 V) near the anode [6]. Furthermore, using Jarzynski’s equality, we attempted to explain this voltage loss [7]. The ionic activation energy (Ea) in SDC electrolytes is 0.7 eV. Considering the separation of the Boltzmann distribution during ion hopping by Ea (= 0.7 eV), according to Jarzynski’s equality, the distribution of hopping ions should be a canonical ensemble. When the electrical potential changed due to neutralization by free electrons during ion hopping, 0.7 eV was dissipated by the electrons. Oxygen ions have an electric charge (2e-), so the OCV is 0.8 V= 1.15 V - 0.7 eV/2e [7].
Our explanations seem to disregard and disprove Wagner’s equation and other excellent subsequent theories. The reason for this contradiction is that we disproved the existence of large leakage currents in SDC electrolytes. However, we noticed that the dismissal of this idea regarding leakage currents in SDC electrolytes is nothing more than a side effect of introducing a large anode voltage loss (0.35 V). When there is a large voltage loss near the anode in an SDC electrolyte, the leakage currents should be very small. This is called the “anode shielding effect” [8].
Our conclusion is that Wagner’s equation becomes more useful after considering the additional voltage loss based on Jarzynski’s equality. Furthermore, subsequent theories such as the Riess model and the Duncan and Wachsman model become more useful. Consequently, it is necessary to introduce new thermodynamics based on Jarzynski’s equality, an addition that will improve Wagner’s equation and subsequent theories.
Reference:
[1] I. Riess, J. Phys. Chem. Solids., 47(2), 129 (1986). doi: 10.1016/0022-3697(86)90121-6.
[2] K. L. Duncan and E. D. Wachsman, J. Electrochem. Soc., 156, B1030 (2009). doi:
10.1149/1.315851.
[3] T. Miyashita, J. Mater. Sci., 41(10), 3183 (2006). doi: 10.1007/s10853-006-6371-8.
[4] T. Miyashita, J. Electrochem. Soc., 164(11) 3190 (2017). doi: 10.1149/2.0251711jes
[5] J. Liu and W. Weppner, Ionics, 5(1–2), 115 (1999). doi: 10.1007/BF02375914.
[6] T. Miyashita, J. Mater. Sci., 40(22), 6027 (2005). doi: 10.1007/s10855-005-4560-2.
[7] T. Miyashita, Miyashita, ECSarXiv (2020) “Open-Circuit Voltage Anomalies in Yttria-Stabilized Zirconia and Samaria-Doped Ceria Bilayered Electrolytes”,

https://ecsarxiv.org/xhn73/

[8] B. Dalslet, P. Blennow, P. V. Hendriksen, N. Bonanos, D. Lybye, and M. Mogensen, J. Solid State Electrochem., 10(8), 547 (2006). doi: 10.1007/s10008-006-0135-x.