On the Identification of Impedance Spectroscopy Processes of an SOFC Under Different Hydrogen Concentrations

Solid oxide fuel cells (SOFCs) are electrochemical devices that can generate electrical power efficiently and discard high quality waste heat for cogeneration applications [1]. SOFC systems are envisioned to play a role in all aspects of energy applications, ranging from portable, residential, all the way up to large power plants. Several SOFC prototypes have been or are currently being designed and/or built for all the aforementioned applications [2,3]. However, reliability and longevity remain a concern for SOFC systems which are expected to operate upwards of 40,000 h. In general, impedance spectroscopy (IS) is capable of separating the cell ohmic contribution from the electrodes polarization. The high frequency intercept in a Nyquist plot describes the ohmic resistance of the cell. The low frequency intercept describes the total polarization of the cell. The difference, subtracting the high frequency intercept from low frequency intercept, gives the total electrode polarization which include both diffusion and activation contributions. The complex nonlinear least squares (CNLS) method is used to fit the experimental data with a circuit model [4]. However, the circuit model must be known before the fitting begins. Impedance spectroscopy has been used very successfully to study symmetric and half cells. However, for full cells, there are still significant differences among researchers. Different circuit models have been employed and most of studies have been done at open circuit voltage (OCV) conditions [5,6]. Warburg and/or Gerisher elements have been used to explain the observed behavior [5,7]; however, in our experience these elements have not been very useful to analyze full cells especially below open circuit voltages [8]. In this work, we have studied the behavior of an SOFC under different fuel conditions. The aim and the novelty is to develop qualitatively IS techniques to distinguish anode processes from the cathode ones. This will benefit the SOFC community when performing reliability studies of full cells in order to determine where the degradation is occurring and which electrode degrades at a faster rate.

In our laboratory, we have the capability of testing several button cells and small stacks for extended times. The cells are obtained from a commercial source of SOFC systems. The anode comprises of the state-of-the-art Ni-yttria stabilized zirconia (Ni-YSZ) cermet, the electrolyte material is a thin YSZ, a buffer layer made of doped ceria is used between the electrolyte to prevent unwanted reactions, and the cathode is made of lanthanum strontium cobalt ferrite (LSCF). Current collectors are applied on both sides and a four probe measurement is made. A typical cross section of the button cell and test setup has been reported elsewhere [8]. The electrolyte layer is approximately 10 μms thick, and the ceria layer is approximately 4 μms while the cell active area is 2.5 cm². The experimental setup consists of an alumina tube where the cell is placed with an appropriate seal. On the air side, a porous ceramic cap prevents cross contamination with the air inside the furnace. A thermocouple is placed close to the cell in order to record an accurate cell temperature. In general, the furnace temperature is a few degrees cooler when the cell is under load due to the cell ohmic heating. The cell setup is first heated in air to seal the cell, then fuel is introduced and the anode is reduced in situ. On the anode side, humidified hydrogen at room temperature (3%) is used at a flow rate of 1.0 standard liter per minute (SLPM). Nitrogen is used to dilute the fuel stream as needed. On the cathode side air is used as the oxidant at a flow rate of 1.0 SLPM. A PARSTAT 2273 from Princeton Applied Research is used to collect the voltage-current density curves and the impedance data reported herein. Voltage-current density curves are taken at 800 °C and the voltage is swept at 3 mVs⁻¹. The impedance measurements are done at OCV and at different applied voltages. The ac amplitude used is 10 mV with 12 datum points per each frequency decade. All obtained spectra were analyzed using the ZSimpWin software obtained from Princeton Applied Research.

The exponent ϕ is related to the angle of rotation of a purely capacitive line on the complex plane plot. Its value is between 0 and 1; where ϕ = 0 represents a resistor and ϕ = 1 represents an ideal capacitor. There seems to be at least four physical and/or chemical processes that dominate the cell impedance. Hence, the proposed equivalent electrical circuit consists of a 2-CPE and a 2-RC model for the whole cell and can be written as LR_o(C₁R₁)(Q₂R₂)(Q₂R₃)(C₄R₄). In this model, L is inductance, R is resistance, Q is the CPE, and C is capacitance. The cell ohmic resistance, R_o, is found by using the intercept value in the high frequency region. The values for R₁, R₂, R_3, and R₄ are found by determining the difference between the intercepts of each arc. The various combined terms R₁ with Q₁, R₂ with Q₂, R₃ with C₃, R₄ with C₄ represents at least one physical or chemical process in the fuel cell. In this cell model, R₁ and R₂ are taken to be the cathode contribution, and R₃ and R₄ are taken to be the anode contribution. The total cell impedance (polarization resistance) is the sum of the anode and cathode impedances. Using a complex nonlinear least squares (CNLS) curve fitting program, the peak frequency and the time constants can be determined for each arc. The impedance data obtained in this work were fitted by the CNLS method using the software purchased from Princeton.

Figure 1 illustrates the voltage-current densities obtained at different fuel conditions and at 800 °C. The legends shown indicate the cell number, testing temperature, and the partial pressure of the anode gas components. Humidified fuel is used at different hydrogen concentrations and nitrogen is used to reduce the partial pressure of hydrogen. The cell performance shown here is quite good as can be seen from the top curve at 97% hydrogen where high current densities are obtained without reaching the diffusion limited region. As the hydrogen partial pressure is reduced to 75%, it can be observed that the diffusion limited region is reached sooner with a limiting current of roughly 3.5 A cm⁻². When the hydrogen partial pressure is reduced further the diffusion region is reached sooner and sooner. The OCV is also affected as lower Nernst voltages are obtained at lower hydrogen concentrations. To further understand the types of losses, the cell area specific resistance (ASR) is reported as a function of voltage in Fig. 2. The ASR is usually calculated using the following equation [1]:

Here, V_OCV is the observed cell voltage at zero current, and V_Cell is the measured cell voltage at a current density i. At OCV, the ASR starts declining as current flows through the cell and decreases charge transfer resistances. The ASR curves show a minimum at lower voltages where diffusion resistances have become significant as reactants are being depleted. The ASR curves shift up as the hydrogen partial pressure is reduced in the fuel stream, indicating higher resistances. The ASR is also larger because of lower Nernst voltages as the hydrogen concentration is reduced.

Figure 3 reports a sample of the IS spectra at OCV at different partial pressures of hydrogen. From this plot, we can observe that the total electrode polarization increase as the hydrogen partial pressure decreases while the high frequency intercept remains reasonably constant within the experimental error. This indicates that the ohmic resistance remains unchanged as conditions change as expected since conductivities should remain constant in the anode side. A total of four semicircles can be visually detected with a small semicircle in the high frequency range. An inset has been added to Fig. 3 to better visualize the four arcs. In addition, the error values obtained from the CNLS fitting is less than 1% which reinforces the assumption that four arcs are present. Choosing fewer arcs, for instance three arcs, does not produce a good fitting and the resulting error is excessive. The lowest frequency semicircle increases drastically with the decrease of the reactant while the highest frequency semicircle changes very little. To further understand the behavior of the four arcs, an applied voltage was imposed to the cell. This approach is equivalent to running the cell at a specified current density. As the cell voltage decrease, as current is drawn, the electrode polarization decreases in all cases. This is shown in Fig. 4 where the cell voltage is now 0.9 V. The ohmic resistance remains reasonably unchanged, however the total polarization has decreased somewhat. This is due to a reduced resistance in charge transfer as current starts flowing through the cell. Decreasing the cell voltages shows the same trend in total polarization but not for all hydrogen concentrations. For instance, for the lowest hydrogen concentration the total polarization starts increasing at about 0.7 V. This is shown in Fig. 5 where clearly the large semicircle at the lowest frequency has become larger. This increase is due to the lack of reactant for the electrochemical reaction to proceed. This trend can be best seen in Fig. 6 where the 5% hydrogen data is plotted as a function of cell voltage. While the ohmic resistance remains reasonably constant, the total polarization first decreases with the cell voltage, then increase as 0.7 V is reached. The electrode polarization order in Fig. 6 is OCV < 0.9 V < 0.8 V but then changes as follows 0.6 V > 0.7 V > 0.8 V. This behavior indicates higher diffusion resistance which become limiting at lower applied voltages. This behavior indicates higher diffusion resistance which becomes limiting at lower applied voltages.

Figure 7 reports the ohmic resistance at different cell voltages or corresponding current density from Fig. 1. Some scatter is observed possible due to experimental uncertainties but one may conclude that the ohmic resistance remains almost constant. Some of the scatter behavior can also be attributed to local ohmic heating which in turn may change the material electrical conductivity. The ohmic resistance values are consistent with the cell's materials used as has been discussed in Ref. [8]. Figure 8 plots the electrode polarization as a function of cell voltage. The electrode polarization decrease as the cell voltage decrease; however, after a certain voltage has been reached and especially for the lowest hydrogen concentration the electrode polarization increase indicating that the diffusion limiting current has been reached. The sum of the ohmic resistance and electrode polarization are consistent with ASR measurements as has been discussed in Ref. [9].

Figure 9 illustrates the result of the modeling study using the LR_o(C₁R₁)(Q₂R₂)(Q₂R₃)(C₄R₄) equivalent circuit. From this graph we can observe that two resistances remain almost unchanged while the other two are changing with a varying hydrogen concentration. Hence, the resistances R₃ and R₄ can be assigned to the anode while R₁ and R₂ can be assigned to the cathode. A previous study has shown a similar behavior when the cathode air was changed to 21% O₂ rest helium and pure oxygen and confirms the resistances assignments [8]. This trend indicates a dependence on both charge transfer and diffusion resistances as hydrogen is reduced. This behavior can be easily seen at OCV, fitting the EIS data at lower cell voltage does not produce a good fit and the four semicircles cannot be resolved accurately. Further testing is need to remove testing uncertainties and obtain better data, and determine if it possible to fit data at different cell voltages. In order to determine if the same trend can be observed again, a new cell was tested. In general, the same trend is observed as can be seen from Fig. 10 where the Nyquist plot is reported. Modeling with the equivalent circuit above also showed similar results as shown in Fig. 11. The trend for the resistance R₃ is to decrease as the hydrogen concentration decreases and the same is observed for the previous cell. The resistance R₄ is related to the diffusion region and seems to remain unchanged. This behavior in not contradictory to the previous trend because most likely the new cell anode has better porosity and is not affecting the resistance values significantly at OCV. A closer look at Fig. 10 indicates that a small circle is present in the low frequency range which is not the case for the cell shown in Fig. 3. The values for R_o and R₁ show the same trend observed in Fig. 9. Last, the values for R₂ seem to exhibit a maximum value, however probably an outlier data point due to experimental error or fitting error.

In this work, we have studied the effect of hydrogen concentration of an SOFC cell. This study indicates that the ohmic resistance remains almost unchanged as the hydrogen concentration and cell voltages are decreased. In general, the total cell polarization decreases with applied voltage but reaches a minimum for the lowest concentration of hydrogen and then increases. Data fitting of the EIS data at different hydrogen concentration indicate that two resistances remain unchanged and can be assigned to the cathode while the other two change and can be assigned to the anode.