(Digital Presentation) Clarification Using Jarzynski’s Equality for Three Unexplained Experimental Results in SOFCs Using Sm-Doped Ceria Electrolytes Based on Wagner’s Equation
Authors: Miyashita Tomofumi 
Published: December 2024

A solid oxide fuel cell (SOFC) converts chemical energy from a fuel gas, such as hydrogen or methane, to electrical energy. In yttria-stabilized zirconia (YSZ) films, only oxygen ions are carriers; thus, these films are often used as electrolytes. In these 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) has a higher ionic conductivity than YSZ. Therefore, SDC films are potential electrolyte candidates. However, when SDC electrolytes are used in SOFCs, the OCV at 1073 K is only 0.80 V. This voltage loss can be explained by Wagner’s equation.

Numerous subsequent models have been created based on Wagner’s equation. The current-voltage relationship can be calculated with the cathode and anode polarization voltage losses using the Riess model [1]. Furthermore, Duncan and Wachsman developed a nonlinear model [2]; this model could also be used to clarify the equilibration 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 the thick SDC electrolytes with respect to a change in the anode gas has not yet been clarified using the model of 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 (1.15 V-0.80 V=0.35 V) [6]. Since large leakage currents in the SDC electrolytes do not occur, our explanations appear to deviate from Wagner’s equation. However, we noted that the lack of large leakage currents in the SDC electrolytes is only a side effect. When an SDC electrolyte experiences a large anode voltage loss (0.35 V), the leakage current is very low. This phenomenon is called the “anode shielding effect” [7].

The ionic activation energy of the SDC electrolyte is 0.7 eV (0.35 V×2e=0.7 eV). During the ion hopping processes in the SDC electrolytes, the work done by ions on the surrounding lattice structure is 0.7 eV. Thus, the ions should regain 0.7 eV after hopping. However, when many electrons are present in the hopping path, the hopping process becomes very complex.

Jarzynski’s equality is defined by the Helmholtz energy [8]. Here, the ionic activation energy must be defined as the Gibbs energy. During the ion hopping processes, the PVs change, and the maximum PVs are equal to the ionic activation energies. The above two experimental results occur when the final PVs during the work loss are unchanged and isothermal process under the same temperature of the heat reservoir. Since the ΔPVs are zero, Jarzynski’s equality can be used.

In our third experiment, the cell used contained a 500-mm thick polished YSZ electrolyte on the cathode side, which is in direct contact with a 970-mm thick polished SDC electrolyte on the anode side. The measured OCV was 819 mV at 1073 K; this value was clearly higher than 800 mV [9]. The ionic activation energy of the YSZ electrolyte was 1.1 eV. In this case, the final PVs during the work loss were unchanged, but the final PVs before the work loss were changed from 1.1 eV to 0.8 eV. Since the ΔPVs were not zero, the voltage for compensation (Vcomp) due to the change in activation energy is as follows:

Vconp = kBT/2e×ln(1.1 eV/0.7 eV) (1)

The value of 19 mV (819 mV-800 mV=19 mV) was small. However, this value can be increased using any other electrolyte instead of YSZ.

Consequently, the three unexplained experimental results can be explained by Jarzynski’s equality.

References:

[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] C. Jarzynski, Phys. Rev. Lett., 78(23), 2690 (1997). doi: 10.1103/PhysRevLett.78.2690.

[9] T. Miyashita, ECSarXiv (2020) “Open-Circuit Voltage Anomalies in Yttria-Stabilized Zirconia and Samaria-Doped Ceria Bilayered Electrolytes.”