Comparison of electrochemical impedance spectra for electrolyte-supported solid oxide fuel cells (SOFCs) and protonic ceramic fuel cells (PCFCs)

Protonic ceramic fuel cells (PCFCs) are expected to achieve high power generation efficiency at intermediate temperature around 400–600 °C. In the present work, the distribution of relaxation times (DRT) analysis was investigated in order to deconvolute the anode and cathode polarization resistances for PCFCs supported on yttria-doped barium cerate (BCY) electrolyte in comparison with solid oxide fuel cells (SOFCs) supported on scandia-stabilized zirconia (ScSZ) electrolyte. Four DRT peaks were detected from the impedance spectra measured at 700 °C excluding the gas diffusion process for ScSZ and BCY. The DRT peaks at 5 × 102–1 × 104 Hz and 1 × 100–2 × 102 Hz were related to the hydrogen oxidation reaction at the anode and the oxygen reduction reaction at the cathode, respectively, for both cells. The DRT peak at 2 × 101–1 × 103 Hz depended on the hydrogen concentration at the anode for ScSZ, while it was dependent on the oxygen concentration at the cathode for BCY. Compared to ScSZ, steam was produced at the opposite electrode in the case of BCY, which enhanced the cathode polarization resistance for PCFCs.

www.nature.com/scientificreports/ In this case, the fuel is not diluted by power generation, because steam is produced at the cathode. PCFCs are expected to realize high fuel utilization compared to SOFCs 8 . Furthermore, the ionic conductivities of yttriadoped barium cerate (BCY) and zirconate (BZY) are higher than that of YSZ at intermediate temperatures around 400-600 °C 9 . The maximum power densities were 0.6-1.3 W/cm 2 at 600 °C for anode-supported PCFCs using BCY/BZY-based electrolytes [10][11][12] .
Dissolving transition metal elements such as manganese, iron, cobalt and nickel into BCY 13 and BZY 14 decreases the ionic conductivity. While nickel dissolving into BCY and BZY acted as a sintering aid during the cosintering of the electrolyte thin-film and anode substrate for anode-supported cells during cell manufacturing [15][16][17] , it deteriorated the ionic conductivity and proton transport number [18][19][20] . Transition metal elements also possibly diffuse from cathode materials. Therefore, the deconvolution technique of the anode and cathode polarization resistances is required for evaluating the initial performance and durability of PCFCs.
The polarization resistances were frequently evaluated by the electrochemical impedance spectroscopy (EIS) for various devices such as fuel cells and batteries. An equivalent circuit model is required for complex nonlinear least square (CNLS) fitting to separate each resistance. However, it is sometimes difficult to assume the equivalent circuit model with appropriate initial parameters for the CNLS fitting. The distribution of relaxation times (DRT) analysis is a powerful tool to deconvolute EIS [21][22][23] , which are widely used for fuel cells [24][25][26][27][28] , electrolysis cells 29 , lithium-ion batteries 30 and supercapacitors 31 . For SOFCs [24][25][26] and polymer electrolyte fuel cells (PEFCs) 27 , the anode and cathode polarization resistances were separated with high resolution. The ratios of the anode to cathode polarization resistances were 75:25 and 4:96 for SOFCs 28 and PEFCs 27 , respectively, which was caused by the difference in electrode reactions as shown in Eqs. (1,2) and (3,4). DRT analysis is also a powerful tool for investigating the degradation mechanism during durability tests 32 .
In the present work, the deconvolution technique of the anode and cathode polarization resistances was investigated for PCFCs. While some researchers have applied the DRT analysis to anode-supported PCFCs 33,34 , the physicochemical origins of each DRT peak should be more discussed. We prepared electrolyte-supported SOFCs and PCFCs in order to attach a reference electrode. The ohmic resistances of electrolyte-supported cells are large due to thick electrolyte compared to anode-supported cells. ScSZ and BCY are selected as electrolytes for SOFCs and PCFCs, respectively, because these conductivities are higher than those of YSZ 35 and BZY 36 . The difference in elementary electrode reactions was discussed using the results of DRT analysis for SOFCs and PCFCs.

Results
The theoretical electromotive forces (EMFs; V th ) are as shown in Eqs. (5) and (6) for SOFCs and PCFCs, respectively: where R is the gas constant, T is the absolute temperature, F is the Faraday constant, p a and p c are the partial pressures at the anode and cathode, respectively, and K is the equilibrium constant of 2H 2 (g) + O 2 (g) → 2H 2 O(g). The t is the transport number, which is dependent on p H 2 , p H 2 O and p O 2 for some electrolytes. Hole conduction appears for proton-conductive ceramics such as BCY and BZY at high temperature and oxygen partial pressure 37 , which leads to a decrease in power generation efficiency 38 . Figure 1 shows the temperature dependence of OCVs in H 2 :H 2 O:N 2 = 20:3:77 vol.% (anode) and O 2 :H 2 O:N 2 = 20:3:77 vol.% (cathode) for SOFCs supported on ScSZ electrolyte and PCFCs supported on BCY electrolyte. The dotted line indicates the theoretical EMF, when the transport number is assumed to be unity. The theoretical EMFs of ScSZ and BCY are almost the same in these atmospheres. The OCVs were 15 mV lower than the theoretical EMFs for ScSZ due to gas leakage from the sealant. While the slope of the OCVs was nearly matched that of the theoretical EMFs for ScSZ, it was quite different for BCY. The OCVs were 45 and 70 mV lower than the theoretical EMFs for BCY at 750 and 800 °C, respectively, owing to hole conduction. ScSZ and BCY exhibited nearly the same OCVs at ≤ 700 °C, suggesting the prevention of hole conduction in BCY. The transport number of holes for BCY-based electrolyte is smaller than that for BZY, while the transport number of oxide ions for BCY-based electrolyte is slightly larger than that for BZY 39 . The impedance was measured precisely at 700 °C in the present work. Figures 2 and 3 show the IR-free impedance spectra at 700 °C for SOFCs supported on ScSZ electrolyte and PCFCs supported on BCY electrolyte. The ohmic resistances were subtracted to compare the polarization resistances among anode-cathode (total), anode-reference electrode and cathode-reference electrode impedances in these figures. The polarization resistance of the anode (Fig. 2a) was larger than that of the cathode (Fig. 2c) for ScSZ, while that of the anode (Fig. 3a) was smaller than that of the cathode (Fig. 3c) Fig. 2d), while the impedance decreased across a wide range frequency for BCY (Fig. 3d). The anode-reference electrode and cathode-reference electrode impedances gave rough information about anode and cathode polarization resistances, because the electrochemical potentials of reference electrodes were sensitive against ac amplitude during impedance measurements 40,41 . In the present work, the DRT analysis suggests the deconvolution of the anode and cathode polarization resistances using anode-cathode impedance as shown in Fig. 4, and the DRT peaks were assigned with reference to the dependence of hydrogen and oxygen concentrations in the anode and cathode, respectively. Unfortunately, the impedance spectra were noisy below 10 Hz, because gas leakage might slightly occur through the grain boundary of the BCY electrolyte with insufficient sintering. Ivers-Tiffée and Weber 28 reported the effect of experimental errors on the DRT analysis. The resolution of EIS deconvolution decreases for data with errors. However, the results of Fig. 4 are acceptable, because the gaps of each DRT peak are approximately one order of magnitude against frequency. The DRT analysis was  www.nature.com/scientificreports/ performed using impedance data at frequencies ≥ 10 Hz for BCY. Four DRT peaks were detected for ScSZ and BCY. Although the DRT peak for the gas diffusion process is generally observed below 10 Hz, it is negligible for the electrolyte-supported cells with the thin anode and cathode in the present work. For ScSZ, the P 2 and P 3 peaks decreased with increasing hydrogen concentration at the anode (Fig. 4a), while the P 4 peak decreased with increasing oxygen concentration at the cathode (Fig. 4b). The change in the P 1 peak was small for ScSZ. For BCY, the P 2 peak decreased with increasing hydrogen concentration at the anode (Fig. 4c), while the P 1 , P 3 10 0 10 1 10 2 10 3 10 4 10 5   / Ω Relaxation Time, τ / s  www.nature.com/scientificreports/ and P 4 peaks decreased with increasing oxygen concentration at the cathode (Fig. 4d). The dependence of the P 3 peak was different between ScSZ and BCY. It was previously reported that the DRT peak around 10-100 kHz could be ascribed to the ionic conduction process in mixed ionic-electronic conductors 26,33 . This polarization resistance is dependent on the contact condition and the microstructure of the cathode. The P 1 peak for BCY was relatively larger than that for ScSZ owing to insufficient contact between LSCF and BCY in the present work. The P 2 and P 4 peaks are dependent on the hydrogen concentration at the anode and the oxygen concentration at the cathode, respectively, for both cells. The P 2 peak is related to the hydrogen oxidation reaction, while the P 4 peak is related to the oxygen reduction reaction. On the other hand, the P 3 peak is dependent on the hydrogen concentration at the anode for ScSZ, and the oxygen concentration at the cathode for BCY. Compared to SOFCs, steam was produced at the opposite electrode in the case of PCFCs as shown in Eqs. (1)-(4). Therefore, the P 3 peak is related to the steam production reaction.
The elementary electrode reactions for SOFCs and PCFCs are as follows.

Oxygen reduction reaction.
Steam production.
where the subscripts "ad,surf " and "ad,TPB" represent the adsorbed atom at the surface and triple phase boundary, respectively. Intermediate products such as O − and OH − are temporarily formed during charge transfer (Eqs. (13) and (15)). The polarization resistances are derived using the equivalent circuit model of Fig. 5a with reference to the result of DRT analysis. Figures 5b,c show the temperature dependence of the polarization resistances in H 2 :H 2 O:N 2 = 20:3:77 vol.% (anode) and O 2 :H 2 O:N 2 = 20:3:77 vol.% (cathode) for SOFCs supported on ScSZ electrolyte and PCFCs supported on BCY electrolyte. All polarization resistances for BCY was larger than those for ScSZ. The contact condition between the electrolyte and cathode should be modified to decrease R 1 . The nickel dissolved into BCY in the composite anode and at the interface between the anode and electrolyte, which enhanced R 2 for the hydrogen oxidation reaction 19 . On the other hand, LSCF is well-known as a mixed oxide ionic-electronic conductor. However, proton is not conducted in LSCF. R 3 was enhanced for PCFCs, because the active area for steam production is limited to the two-dimensional interface between the BCY electrolyte and LSCF cathode. R 4 for oxygen reduction reaction for BCY was three times as large as that for ScSZ. The difference in R 4 was smaller than those of the other polarization resistances, as the oxygen reduction reactions of Eqs. (14) and (15) are the same for BCY and ScSZ. The pie charts in Fig. 5b,c depict the ratios of the polarization resistance at 700 °C. The ratios of the anode to cathode polarization resistances were 70:30 and 34:66 for ScSZ and BCY, respectively. For BCY, the DRT peaks were slightly affected by the conductivity of oxide ions. Therefore, we are www.nature.com/scientificreports/ going to perform DRT analysis for the other electrolytes with proton conductivity such as BZY in order to more investigate the assignment of DRT peaks to each elementary reaction process in the near future.

Conclusion
In the present work, the deconvolution technique of the anode and cathode polarization resistances was investigated using DRT analysis for PCFCs supported on a BCY electrolyte in comparison with SOFCs supported on an ScSZ electrolyte. The OCVs for BCY were nearly equal to those for ScSZ and theoretical EMFs at ≤ 700 °C, suggesting the prevention of hole conduction. Four DRT peaks were detected from the impedance spectra measured at 700 °C for ScSZ and BCY. The DRT peak for the gas diffusion process was negligible for electrolyte-supported cells. The DRT peak at 1 × 10 4 -5 × 10 4 Hz, P 1 , was ascribed to the bulk diffusion of oxide ions in the mixed ionicelectronic conductor of LSCF and interface diffusion between the cathode and electrolyte. The DRT peaks at 5 × 10 2 -1 × 10 4 Hz, P 2 , and 1 × 10 0 -2 × 10 2 Hz, P 4 , were related to the hydrogen oxidation reaction at the anode and the oxygen reduction reaction at the cathode, respectively. On the other hand, the DRT peak at 2 × 10 1 -1 × 10 3 Hz, P 3 , was dependent on the hydrogen concentration at the anode for ScSZ, and on the oxygen concentration at the cathode for BCY owing to steam production at the opposite electrodes in SOFCs and PCFCs. The ratios of anode to cathode polarization resistances were 70:30 and 34:66 at 700 °C for ScSZ and BCY, respectively. The polarization resistances of the electrode on the side where steam was produced increased for SOFCs and PCFCs.

Methods
Cell preparation.
(a) Equivalent circuit model   The distribution of relaxation time (DRT) analysis was performed using Z-Assist software (Toyo Corp.) 32 . The real impedance was used for DRT analysis owing to the reduced effects of measurement errors and inductive components compared to the imaginary parts 28 . After DRT analysis, the parameters were refined by CNLS fitting using ZView software (Scribner Associates) assuming an equivalent circuit model with a series connection of resistance (R) and four parallel resistance-capacitance (RC) elements.

Data availability
The data that support the findings of this study are available from the corresponding author upon reasonable request.