Theoretical Insights into Equilibrium Potentials in Electrochemical Cells with Multiple Mobile Charge Carriers

Equilibrium potentials are fundamental in electrochemistry, as they quantify the relation between chemical and electrostatic driving forces. For cells with multiple mobile charge carriers in the electrolyte—including those associated with electronic leakage—the calculation of equilibrium potentials is more complex than for cells with only one charge carrier, leading to inconsistent formulations in literature. The objective of this paper is to provide a theoretical framework for understanding and calculating equilibrium potentials in such cells, exemplified by the case of protonic ceramic cells. The analysis shows that reversible cell potentials cannot be predicted by Nernst equations based solely on the gas phase and instead require consideration of thermodynamic properties of the electrolyte. The impact of thermodynamically non-equilibrated inlet gases (like mixed fuels) on potentials in cells with multiple mobile charge carriers is investigated by use of mixed-potential theory. Finally, a distinction is made between reversible and measurable cell potential at open circuit, exemplified with BCZYYb-based cell simulations. Further analysis shows the potential difference is caused by overpotentials in electrodes and membrane. A theoretical scenario in which electronic leakage is prohibited reveals that the mere presence of multiple mobile charged defects causes differences between measurable and reversible cell potentials.