## 3 Results and Discussion
For the current anode support PCFC with an anode thickness of 500 \(\upmu\)m and a cathode thickness of 25 \(\upmu\)m, the concentration polarization loss of fuel-diffusing process within anode play the dominant role. From Figure 5, we can observe that the concentration polarization is small, compared with the other ohmic and activation overpotentials. This result is quite different from that of traditional O\({}^{2}\)-SOFC [45], in which the fuel concentration voltage loss is large. This result is attribute to the reason that the vapors are generated in the cathode side of PCFC instead of the anode side. This means that high mole fraction of hydrogen can be maintained over the anode-electrolyte interface of PCFC, even if many hydrogens are consumed. From Figure 5a,b, we can see that the proportion of the activation overpotentials is greatly increased, especially the activation overpotential of oxygen reduction half reaction in the cathode side of PCFC. Figure 4: The distributions of (**a**) the local e\({}^{-}\), O\({}^{2-}\), and H\({}^{+}\) electric charge transfer source in the PCFC cathode. (**b**) The local e\({}^{-}\), O\({}^{2-}\), and H\({}^{+}\) electric current densities in the cathode. In order to more clearly compare the contributions of different overpotentials on the total voltage loss of PCFC at different \(T\), Figure 6 shows the corresponding proportions at the constant output current and voltage cases, respectively. As can be seen from Figure 6a, for \(i_{\text{op}}\) = 0.5 A cm\({}^{-2}\), the activation polarization loss (including \(\eta_{act}^{a}\), \(\eta_{act}^{c1}\), \(\eta_{act}^{c2}\)) goes from 25.0 to 244.2 mV and the ohmic polarization loss goes from 134.4 to 445.5 mV, while the temperature decreases from 1025 K to 825 K. Among them, the activation polarization loss of cathodic oxygen reduction reaction \(\eta_{act}^{c1}\) is significantly increased from 8.5 to 162.1 mV. In Figure 6b, for the same operating voltage of 0.5 V, ohmic polarization accounts for the 63.1%, 74.8%, and 82.5% of the PCFC total voltage losses, while \(T\) is adjusted to 823, 923, and 1023 K, respectively. With the decrease of temperature, the proportion of cathode activation polarization loss increases from 5.4% to 24.3%. The sharp increase of cathode activation polarization loss at a relevant low temperature is considered to be one of the main factors that contributes to the performance degradation of PCFC. Figure 5: Proportion of each polarization loss in the total overpotential: (**a**) 550 \({}^{\circ}\)C and (**b**) 750 \({}^{\circ}\)C.  
From the above result we can find that the oxygen reduction half reaction on the cathode side is a key factor to dominate the voltage loss at the intermediate temperature zone. In Figure 7, the dependence of the PCFC performance on the reference exchange current density \(i_{\text{LSCF,0,ref}}\) is shown. It is found that the PCFC performance at 55 \({}^{\circ}\)C is greatly increased from 0.164 to 0.263 W cm\({}^{-2}\), while the \(i_{\text{LSCF,0,ref}}\) is increased by one order of magnitude. Thus, finding materials with high electrochemical activity of oxygen reduction would be helpful to improve the performance of PCFC around the intermediate temperature zone. Figure 6: The contributions of different overpotentials on the total voltage loss of PCFC at different operation temperatures at (**a**) \(i_{\text{op}}\) = 0.5 A cm\({}^{-2}\) and (**b**) \(V_{\text{op}}\) = 0.5 V.  
Figure 8a shows the H\({}_{2}\) concentration distribution within the PCFC at \(T\) = 550 \({}^{\circ}\)C and \(V_{\text{op}}\) = 0.5 V. Figure 8b further shows the distribution of H\({}_{2}\) consumption rates within the composite anode of PCFC. The calculated result shows that the anode area beyond the cathode area is not electrochemically active. This result is consistent with that obtained by the O\({}^{2-}\)SOFC button cell [4]. Generally, increasing the effective conductivity of the electrode can improve the performance of PCFC.