## 3 Results and Discussion
### Temperature Dependence of the Polarisation Resistances  
The temperature dependence of the polarisation resistances is depicted in Figure 9 in wet (\(p_{\text{H2O}}\sim 10^{-2}\) atm) and low humidity (\(p_{\text{H2O}}\sim 10^{-5}\) atm) conditions at 450 \({}^{\circ}\)C in O\({}_{2}\) atmosphere. Data were corrected using Equation (20) to account for the electronic leakage through the electrolyte. An obvious observation is that this effect is much more pronounced in low humidity conditions and at higher temperatures, as expected due to the increase in p-type conductivity (Equation (17)). In terms of the magnitude of the corrected total polarisation resistance, we can observe a slight increase in this term in low humidity conditions in the whole measured temperature range (400-550 \({}^{\circ}\)C). Nonetheless, it notable that the opposite trend would be observed, if no short-circuiting correction was used, highlighting the significance of this procedure for the correct interpretation of the impedance data and, thus, the limiting electrode mechanisms. Hence, for a more elaborated interpretation, the individual contributions, with correction, will now be discussed. In this respect, the high-frequency term, \(R_{\text{high,eon}}\), shows a distinctive behaviour upon changes in \(p_{\text{H2O}}\). In wet conditions, this term shows capacitance values in the range of \(10^{-5}\)-\(10^{-6}\) F cm\({}^{-2}\) in all conditions. Such values are typical of charge transfer processes [17; 18], which may involve the oxygen diffusion into the electrode:  
\[\text{O}_{\text{2(ads)}}+2\text{e}^{-}+\text{V}_{\text{O}}^{\bullet\bullet} \rightarrow\text{O}_{\text{O( cathode)}}^{\text{x}} \tag{21}\]  
Figure 9: Temperature dependence of the polarisation resistances with and without the electronic pathway correction for: (a) Wet (\(p_{\text{H2O}}\sim 10^{-2}\) atm) and (b) low humidity (\(p_{\text{H2O}}\sim 10^{-5}\) atm) conditions at 450 \({}^{\circ}\)C in O\({}_{2}\) atmosphere. and/or proton-transfer:  
\[\text{OH}^{\bullet}_{\text{O(electrolyte)}}+\text{O}^{\text{x}}_{\text{O( cathode)}}\to\text{O}^{\text{x}}_{\text{O(electrolyte)}}+\text{OH}^{\bullet}_{\text{O( cathode)}} \tag{22}\]  
Both processes have a negligible \(p_{\text{H2O}}{}^{-m}\) dependence (\(m=0\)), which is in line with that determined for \(R_{\text{high,eon}}\) in this work, in both conditions of humidity. The activation energy found for this term was found to range from 0.7 to 1.1 eV upon increasing the \(p_{\text{H2O}}\) (Table 3). In fact, the activation energy found for this term is slightly higher than that reported for proton mobility (i.e., 0.5 eV [23; 24]). Hence, in wet conditions, a combination of both processes may be occurring. However, the lower activation energy in low humidity conditions may be a result of an increased electronic p-type conductivity in the absence of sufficient humidification of the LNO phase. This is also corroborated by the fact that this term dominates the total polarisation resistance at higher temperatures in low humidity conditions, as expected from the decrease of p-type conductivity with increasing temperature in the LNO phase [14]. The _Gerischer_ response, \(R_{\text{G,eon}}\), occurring at intermediate frequencies, is used here to represent a co-limitation of both surface processes, including oxygen adsorption (\(m=0\)):  
\[\text{O}_{\text{2(g)}}\to\text{O}_{\text{2(ads)}} \tag{23}\]  
and/or oxygen dissociation (\(m=0\)):  
\[\text{O}_{\text{2(ads)}}\to 2\text{O}_{\text{(ads)}} \tag{24}\]  
However, a striking feature is related to the \(Y_{0}\)-parameter, which shows a \(p_{\text{H2O}}{}^{-0.44}\) dependence, thus, suggesting proton transfer (\(m=0.5\)). In wet conditions, the \(Y_{0}\)-parameter shows an activation energy value of 0.49 eV (Table 3), similar to that reported for proton transport (\(E_{\text{a}}=-0.5\) eV [23]). Nonetheless, as pointed out by [PERSON] et al. [18], proton diffusion in LNO electrodes should be limited to a narrow zone close to the electrode/electrolyte.