## 3 Results and Discussion  
In Figure 2, the calculated \(i_{qp}\)-\(V_{qp}\) curves at operating temperatures of 550, 650, and 750 \({}^{\circ}\)C are compared with the that obtained by experimental in Ref. [34]. \(i_{qp}\) and \(V_{\mathrm{op}}\) are the operating electric current density and the corresponding output voltage, respectively. Good agreements between the simulated and experimental results in various temperatures verifies the validation of the established electrochemical and multi-physical coupling model. As can be seen from Figure 3, the cathode activation overpotential-c1 of O\({}_{2}\) = 2O\({}^{2-}\) + 2e\({}^{-}\) increases with the decreasing temperature, and the electrochemical active region of the PCFC cathode increases gradually. At 550 \({}^{\circ}\)C, the oxygen reduction reaction occurring at the LSCF-pore DPB areas mainly occurs within 8 \(\upmu\)m from the electrolyte surface. At the same time, similar results can be obtained for other output voltages. Therefore, for PCFCs using LSCF-BZCY 7/3 mixed cathode, the cathode thickness of 8 \(\upmu\)m is sufficient to support most cathodic electrochemical reactions at intermediate operating temperatures. This result is reasonable. For most of the SOFCs working around 800 \({}^{\circ}\)C, the main cathode  
Figure 2: Comparison of the \(i_{qp}\)-\(V_{qp}\) curves between the calculated and experimental results at various temperatures. electrochemical active zones were found to be concentrated within 10 \(\upmu\)m for both LSM-YSZ and LSCF-SDC composite cathodes [45; 46]. For PCFC, when the working temperature decreases from 800 \({}^{\circ}\)C to 550 \({}^{\circ}\)C, the ionic conductivity greatly decreases and the electronic conductivity only slightly changes. Thus, the electrochemical active zone will be further compressed forward to the dense electrolyte direction for the minimal total energy loss. Under the working condition \(T=550\)\({}^{\circ}\)C and \(V_{\text{op}}=0.5\) V, Figure 4a further shows the distributions of the local e\({}^{-}\), O\({}^{2-}\), and H\({}^{+}\) electric charge transfer source. The corresponding electric current densities in the PCFC cathode are also displayed in Figure 4b. Different from the cathode reaction of O\({}^{2-}\)-SOFC, oxygen ions in the composite cathode of PCFC are not generated at LSCF-pore DPBs and consumed at the LSCF-BZCY-pore TPBs. O\({}^{2-}\) is an intermediate transform substance between electrons and protons. Thus, there is a peak distribution within the composite cathode of PCFC. Since the electron conductivity in the LSCF-BZCY composite cathode is much higher than that of oxygen ions and protons, in order to achieve the minimal total energy loss of all physical transporting processes, the electrochemical active zones for the e\({}^{-}\)-O\({}^{2-}\) and O\({}^{2-}\)-H\({}^{+}\) charge transfers are concentrated to a small distance away from the dense electrolyte. With the shortening of the distance from the electrolyte surface, the reaction between the protons and oxygen ions to produce steam becomes more intense, resulting in the rapid consumption of oxygen ion current, which makes the oxygen ion current in the cathode show a trend to first increase and then decrease. In Figure 5, the proportion of each polarization loss in the total voltage loss at 550 and 750 \({}^{\circ}\)C are shown. \(\eta_{act}^{a}\) refers to the active overpotential of the anodic half reaction. \(\eta_{act}^{c1}\) and \(\eta_{act}^{c2}\) refer to the active overpotentials of the oxygen reduction half reaction \(0.5\text{O}_{2}+2\text{e}^{-}\rightarrow\text{O}^{2-}\) and vapor generation reaction \(\text{O}^{2-}+2\text{H}^{+}\rightarrow\text{H}_{2}\text{O}\), respectively. \(\eta_{olm}\) includes the ohmic loss referring to the e\({}^{-}\), H\({}^{+}\), and O\({}^{2-}\) transports. \(\eta_{con}\) is the concentration polarization of both cathode and anode.