# Perspectives on Cathodes for Protonic Ceramic Fuel Cells
## 1 Introduction
[16] as follows:  
\[2H^{+}+\frac{1}{2}\mathrm{O}_{2}+2e^{-}\to H_{2}\mathrm{O}_{(g)} \tag{1}\]  
\[\mathrm{O}_{2(g)}\to\mathrm{O}_{2(ad)} \tag{2}\]  
\[\mathrm{O}_{2(ad)}\to 2\mathrm{O}_{(ad)} \tag{3}\]  
\[\mathrm{O}_{(ad)}\to\mathrm{O}_{(TPB)} \tag{4}\]  
\[\mathrm{O}_{(TPB)}+2\ e^{-}\to\mathrm{O}_{(TPB)}^{2-} \tag{5}\]  
\[\mathrm{O}_{(TPB)}^{2-}+2H^{+}\to H_{2}\mathrm{O}_{(TPB)} \tag{6}\]  
\[\mathrm{H}_{2}\mathrm{O}_{(TPB)}\to H_{2}\mathrm{O}_{(g)}. \tag{7}\]  
Analogous to the oxide-ionic conducting SOFCs, the cathodic, multistep reaction encompassed in Equations (2)-(7) may be considered as the \"electrode surface path\" [17]. It includes the diffusion of oxygen from the gas phase to adsorption (ad) on the electrode \begin{table}
\begin{tabular}{c c c c} \hline
**Basic Concept** & **Abbreviation** & **Basic Concept** & **Abbreviation** \\ \hline Area Specific Resistance & ASR & Protonic Ceramic Fuel Cells & PCFCs \\ \hline Distribution of Relaxation Times & DRT & Ruddlesden–Popper & RP \\ \hline Electrode Polarization Resistance & R\({}_{\mathrm{p}}\) & Secondary Ion Mass Spectroscopy & SIMS \\ \hline Electrochemical Impedance Spectroscopy & EIS & Solid Oxide Fuel Cells & SOFCs \\ \hline Maximum Power Density & MPD & Thermogravimetric Analysis & TGA \\ \hline Mixed Oxide-Ion Electron Conductors & MIECs & Triple Phase Boundary & TPB \\ \hline Oxygen Reduction Reaction & ORR & Triple Protonic Oxide-Ionic Electron Hole & \\  & & Conducting Oxides & \\ \hline Protonic Ceramic Electrolysis Cells & PCECs & & \\ \hline \end{tabular}
\end{table} 
Table 1: General abbreviations. surface (2), oxygen dissociation at the surface (3), and diffusion to the triple phase boundary (TPB) (4), where protonic species from the electrolyte combine with the dissociated and reduced oxygen (5) to produce water (6), which is finally evaporated to the gas phase (7). The issue of cathode design, replacing platinum with oxides, has been addressed with different approaches. Then, the oxidation reaction is necessarily more complex than the scheme above. These strategies include:  
1. Improving the electronic conductivity in proton-conducting oxides via substitution of mixed-valence cations (Figure 1a). 2. Incorporation of a mixed oxide-ion-electronic conductor (MIEC) analogous to the classical oxide-ion conducting SOFC cathode (Figure 1b). 3. Employing so-called triple-conducting oxides (TCOs) with proton, oxide-ion, and electron conductivity (Figure 1c). 4. Designing composite electrodes with a proton-conducting oxide (including improving electron conductivity via strategy (i) and an oxide-ion and electron-conducting component (Figure 1d). Figure 1: Electrochemical reaction steps corresponding to the cathodic reduction reaction occurring through: (**a**) the “electrode-surface path” (1) and “bulk-electrode path for protons” (2) for a mixed protonic–electronic conductor; (**b**) the “electrode-surface path” (1) and “bulk-electrode path for oxide ions” (2) for a mixed oxide-ionic–electronic conducting electrode; (**c**) the “electrode-surface path” (1), “bulk-electrode path for protons”, (2) and “bulk-electrode path for oxide ions” (3) for a triple protonic–oxide-ionic–electronic conducting oxide; (**d**) “bulk-electrode path for oxide ions” (1), “bulk-electrode path for protons” (2) and (3), for a composite based on an oxide ionic–electronic conductor and a mixed protonic–electronic conductor. There is inevitably a certain degree of overlap among these categories. Depending on conditions of temperature and atmosphere, many proton-conducting oxides also exhibit electron-hole or oxide-ion conductivity. Hence, materials categorized as mixed protonic-electronic conductors may, under certain conditions, be triple oxide-ion proton electron-hole conductors, which is a subject of much current interest in the design of cathodes for PCFCs. Similarly, materials designated as triple conductors are not expected to exhibit transport by all three species over a wide range of conditions.