(Digital Presentation) Additional Voltage Loss in Terms of Electromagnetic Potential Related to Jarzynski’s Equality Using Sm-Doped Ceria Electrolytes in Wagner’s Equation for SOFCs
Authors: Miyashita Tomofumi 
Published: July 2022

A solid oxide fuel cell (SOFC) converts chemical energy from a fuel gas, such as hydrogen or methane, to electrical energy. Yttria-stabilized zirconia (YSZ) films are often used as electrolytes in which only oxygen ions are carriers. In such cases, the open circuit voltage (OCV = 1.15 V at 1073 K) is equal to the Nernst voltage (Vth = 1.15 V at 1073 K).
Samaria-doped ceria (SDC) have higher ionic conductivity. Therefore, SDC films are possible electrolyte candidates. However, when SDC electrolytes are used in SOFCs, the OCV is only 0.80 V at 1073 K. The voltage loss has been explained by Wagner’s equation.
Numerous subsequent models have been created based on Wagner’s equation. Using the Riess model, the current-voltage relationship can be calculated with the cathode and anode polarization voltage losses [1]. Furthermore, a nonlinear model was created by Duncan and Wachsman [2]. This model can also be used to explain the equilibrium process.
According to the Riess model, the OCV should decrease during electrode degradation. However, experimentally, the OCV does not change during electrode degradation [3]. The change in the equilibration of thick SDC electrolytes in response to a change in the anode gas has never been explained using the model defined by Duncan and Wachsman. Experimentally, when a very thick (6.6 mm) SDC electrolyte is used, the OCV can reach 0.80 V in only 5 minutes [4]. According to Weppner, the corresponding delay in the electron diffusion current should be more than 2080 minutes [5].
We proposed a current-independent anode voltage loss (0.35 V = 1.15 V- 0.80 V) [6]. Since we disproved the existence of large leakage currents in SDC electrolytes, our explanations seem to disregard and disprove Wagner’s equation. However, we noticed that the dismissal of this idea regarding large leakage currents in SDC electrolytes is nothing more than a side effect. When SDC electrolytes experience a large anode voltage loss (0.35 V), the leakage currents are very small. This is called the “anode shielding effect” [7].
The ionic activation energy (Ea) of SDC electrolytes is 0.7 eV (= 0.35 V ×2e). During ion hopping processes in SDC electrolytes, the work done by ions on the surrounding lattice structure is 0.7 eV. The ions should regain the 0.7 eV after hopping. However, when there are many electrons in the hopping path, hopping processes are very complex, and calculating the loss of work is challenging. Jarzynski’s equality is a very useful method of calculating the loss of work only from the first equilibrium state to the second equilibrium state. Because the distribution of hopping ions always should be a canonical ensemble, the loss of work can be calculated. When there are enough electrons, the ions cannot regain the 0.7 eV, and voltage loss (0.35 V) occurs [8].
To assist the above explanation, we use the electromagnetic potential to explain the voltage loss that occurs during ion hopping. We noticed that the potential of ions during hopping can be calculated from the Lorenz gauge condition.
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] 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.
[8] T. Miyashita, Miyashita, ECSarXiv (2020) “Open-Circuit Voltage Anomalies in Yttria-Stabilized Zirconia and Samaria-Doped Ceria Bilayered Electrolytes”, https://ecsarxiv.org/xhn73/