Calculation of the oxygen potential profile across solid-state electrochemical cells

Although several methods of solving the charge and mass transport equations in solid electrolytes wired for device applications have been reported in the literature, there are several inconsistencies. Yuan and Pal have expressed some misgivings regarding the earlier treatment of Choudhury and Patterson. The recent analysis by Nafe is at variance with the analysis of Yuan and Pal. This paper presents a critical examination of various methods for solving transport equations in solid-state electrochemical devices based on mixed ionic-electronic conductors. A complete equivalence between the approaches of Yuan and Pal and Choudhury and Patterson is demonstrated. The oxygen chemical potential profiles generated by both models are identical for a variety of boundary conditions and circuit parameters for a typical cell configuration. The concept of 'fictitious conductivity' introduced by Nafe is found to be inappropriate. It implies linear variation of the electrochemical potential of electrons inside the electrolyte, which is not generally valid for a mixed conductor. The oxygen chemical potential profiles inside the electrolyte calculated using Nafe's equation for different conditions differ substantially from those predicted by the other models. The. awed theoretical formulation is responsible for this mismatch. The methods of Choudhury and Patterson, Riess, and Yuan and Pal are essentially equivalent.