# Perspectives on Cathodes for Protonic Ceramic Fuel Cells
## 2 Mixed Proton-Electron-Conducting Cathodes  
The introduction of a mixed proton-electron conductor (PEC) as air electrode extends the electrochemical reaction from the triple-phase boundaries at the cathode-electrolyte interface to the whole electrode surface. Thus, the model for Pt may be extended to include H\({}^{+}\) migration from the H\({}^{+}\)-conducting electrolyte through the cathode and over the cathode surface to the reaction sites (Figure 1a) [19], assuming that oxide-ion transport is negligible in the cathode material. This approach involves a new electrochemical path for the cathodic reaction, which may coexist in parallel with the \"electrode surface path\", and is addressed as \"bulk electrode path for protons\". This multistep reaction path may be schematized as follows:  
\[O_{2(g)}\to O_{2(ad)} \tag{8}\]  
\[O_{2(ad)}\to 2O_{(ad)} \tag{9}\]  
\[O_{(ad)}+2e^{-}\to O_{(ad)}^{2-} \tag{10}\]  
\[2H_{(electrolyte)}^{+}\to 2H_{(bulk-electrode)}^{+} \tag{11}\]  
\[2H_{(bulk-electrode)}^{+}\to 2H_{(as)}^{+} \tag{12}\]  
\[2H_{(as)}^{+}+O_{(ad)}^{2-}\to H_{2}O_{(ad)} \tag{13}\]  
\[H_{2}O_{(ad)}\to H_{2}O_{(g)}. \tag{14}\]  
According to the electrochemical steps described by Equations (8)-(14), oxygen gas is diffused, adsorbed, dissociated, and reduced, as it occurs in the \"surface electrode path\" (Equations (8)-(10)). In contrast, the protonic species are transferred from the electrolyte to the cathode component (Equation (11)) and diffuse through the electrode bulk (Equation (12)) to the active sites (\(H_{(as)}^{+}\) in Equation (12)), corresponding to the whole surface of the electrode, where the reaction with the adsorbed oxide ions produces water (13), which is then desorbed from the surface to the gas phase (14). The diffusion of protonic species toward the reaction sites on the electrode component may occur through the electrode bulk (Equation (12)) and/or through the electrode surface, according to:  
\[2H^{+}_{surfac}\to 2H^{+}_{(as)}. \tag{15}\]  
High electronic conductivity is required in the cathode compartment not only for the reduction reaction (Equation (10)) but also so that current flow around the cell is as uninhibited as possible. Several studies have been performed with the aim of increasing the electronic conductivity of proton-conducting oxides. One of the earliest attempts by [PERSON] et al. [20], dating back to 1996, involved doping the BaCe\({}_{0.8}\)V\({}_{0.2}\)O\({}_{3-\delta}\) (BCY20; abbreviations of commonly used compositions are listed in Table 2) proton conductor with praseodymium on the perovskite B-site. Greater Pr content in the BaCe\({}_{0.9,y}\)Pr\({}_{y}\)Gd\({}_{0.1}\)O\({}_{3-\delta}\) solid solution increases electron-hole conductivity, and a cathodic overpotential resistance of 0.47 \(\Omega\cdot\)cm\({}^{2}\) is reported at 800 \({}^{\circ}\)C for BaPr\({}_{0.8}\)Gd\({}_{0.2}\)O\({}_{9}\)[21]. Praseodymium has proved to be a popular dopant for enhancing mixed conductivity in proton-conducting perovskites, since mixed Pr\({}^{3+}\) and Pr\({}^{4+}\) valence states generate considerable electron-hole transport. Consequently, the high Pr contents in Ba(Pr,R)O\({}_{3-\delta}\) (R = Zr, Ce) phases are associated with predominant electron conductivity; however, proton conductivity diminishes with Pr content, and stability in wet and dry reducing conditions, wet oxidizing conditions, and CO\({}_{2}\)-containing atmospheres is dramatically poorer [22; 23; 24]. Nevertheless, a stable power output is reported for a BaPr\({}_{0.8}\)In\({}_{0.2}\)O\({}_{3-\delta}\) cathode with a peak power density of 0.688 W\(\cdot\)cm\({}^{-2}\) at 750 \({}^{\circ}\)C on a BaCe\({}_{0.7}\)Zr\({}_{0.1}\)Y\({}_{0.1}\)Y\({}_{0.1}\)O\({}_{3-\delta}\) (BCZYYb711) electrolyte [25].