ADVANTAGES OF THE IS METHOD
- (1) The linearity of the method involves the interpretation of the results in terms of the theory of linear systems - the output signal is a linear function of the input signal: {/(output) = / (input)Z.
- (2) The impedance measured in a fairly wide frequency domain contains all the information that can be obtained using various constant current methods.
- (3) Experimental efficiency (the amount of information obtained compared with the cost of the experiment) is very high.
- (4) The reliability of the data is easily verified using the methods of integral transformation (the Kramers-Kronig relation is the integral relationship between the real and imaginary parts of any complex function, analytic in the upper half-plane), which are independent of the physical processes under investigation.
However, important restrictions are imposed on the object of study. First of all. the response of the system must be described by linear formulas, and thus the principle of superposition must be respected. Besides, the system must be stable, that is, when the disturbance is removed, it must return to its original state. The system should be causal, that is, it should not give a click-through until the disturbance signal is applied. And finally, the impedance must be finite and physical system cannot contain features in the development of their properties.
STUDYING THE ELECTROCHEMICAL CHARACTERISTICS OF SOLID OXIDE FUEL CELLS
Consider the design and features of solid oxide fuel cells (SOFCs)1 that convert the chemical energy of a fuel into electrical and thermal energy (Figure 3.4, SOFC operation concept). SOFCs are a class of fuel cells characterized by the use of a solid oxide material as the electrolyte. SOFCs use a solid oxide electrolyte to conduct negative oxygen ions from the cathode to the anode. Electro moving force arises as a result of redox reactions involving free electrons on the electrodes of the fuel cell, and the electrodes are separated by an electrolyte, a material that conducts ions well in the reaction and is an insulator for electrons. SOFCs have a feature that distinguishes them against the background of similar systems. Oxygen
FIGURE 3.4 SOFC operation concepts.
Reproduced from Xia, Zou, Yan, and Li (2018) under the terms of ССЛ License.
ions are not rare or toxic. All functional parts of SOFC, including electrolyte, are solid oxides that are highly stable and chemically inert compounds. The flip side of the chemical stability of oxygen compounds is the low mobility of its ions in oxides. Ionic conductivity has an activation character that grows with temperature. SOFC operating temperatures are in the range of 700-900°C. In laboratory samples, satisfactory current densities can be achieved even at 500°C; however, as a rule, such samples have a critically small resource.
A fundamental component of SOFC is an electrode. From the generalization of the literature on various types of yttria-stabilized zirconia (YSZ) electrodes, it is clear that the resistance is highly dependent on the nature of the electrode. Different processes can limit depending on the composition of the electrode, processing parameters, and measurement conditions. Some trends may be revealed for high-, medium-, and low-frequency modes. At high frequency mode, the contribution presumably associated with the structure of the electrode may appear for porous and composite electrodes.
Wilson and Barnett (2008) propose 8YSZ systems (8 mol% of Y202-stabilized Zr02) with alloy content of yttrium oxide of 8 mol% with a characteristic composite structure size of 0.1 - 5 pm. Fuel (for example, hydrogen) is oxidized by oxygen ions coming from the electrolyte membrane at the anode according to the following reaction: H2(g) + 02-= H20(g) + 2e (Figure 3.5). The electrons obtained in the reaction pass through an external circuit to the cathode, where they reduce oxygen: >/202 (g) + 2e~= 02. The reaction includes reagents from the gas phase and occurs on the surface of the electrodes, and therefore, to reduce their resistance, they are made porous. Typical power density obtained from a unit area of an electrolyte membrane is 200-2000 mW/cnr (Gewies, & Bessler, 2008).
The EIS method (Fedotov, & Bredikhin. 2013; Lasia, 1999) was adapted to studying SOFC. IS provides information on the characteristic times and resistances of various transfer processes that occur during operation of the fuel element. Each process is modeled, to a first approximation, by a chain of parallel connected resistances R and capacitance C, where the resistance corresponds to the active resistance introduced by this process into the total resistance of the element. The characteristic time (/ = RC) corresponds to the relaxation time of the process. Consider how the resistance of gas flows appears. The reaction requires access of hydrogen and water vapor to the anode. The difficulty in transporting hydrogen and water vapor leads to a change in their chemical potentials in the reaction zone, which leads to a decrease in the cell voltage linear
FIGURE 3.5 Scheme of the reaction at the three-phase boundary in the porous anode. Adapted with permission from VVaag ct al., 2013, Copyright 2013, American Chemical Society.
in current at relatively low currents. Thus, this effect looks like the appearance of additional active resistance in the circuit of the element. When measuring impedance, in addition to resistance, a capacitance is also associated with this process, which reflects the ability of gas channels to accumulate matter.
In the Nyquist, coordinates of such a model corresponds a semicircle. Real processes are displayed by curves close in shape to a semicircle. In Figure 3.6, authors have presented the impedance spectrum calculated in the framework of this model. The impedance of the system Ni-8YSZ composite consists of two main parts: the low-frequency and the high-frequency semicircles, as well as the third, mid-frequency part. The anode was impregnated with nickel nanograins to test this model (see Figure 3.5). Nickel nanograins significantly increase the length of the three-phase
FIGURE 3.6 Nyquist plots of EIS data measured and equivalent circuit fit of the EIS data SOFC sample (vNiO = 50).
boundary, slightly affecting the volume ratios of the conducting phases, which leads to the required decrease in the reaction resistivity with virtually no change in other system parameters.
The equivalent electric circuit is shown in Figure 3.6. From left to right: the first RC circuit with a characteristic frequency of the order of megahertz corresponds to the resistance and capacity of the electrolyte. At high frequencies, the cell begins to behave like a capacitor due to the inertness of oxygen ions compared to electrons. The electrolyte is sandwiched between two electron-conducting anodes, like an insulator between the plates of a capacitor. The last RC circuit describes the gas resistance, or low-frequency part of the impedance.
In Nakajima, Kitahara, and Konomi (2010) an impedance separation analysis of the anode and cathode of a practical SOFC is conducted. EIS with a two-electrode setup is applied to an anode-supported intermediate temperature microtubular SOFC composed of a Ni/ZrO20.9Y2O3 0.1 cermet anode, a Lao.gSro^Gao.sMgo^Cb.s electrolyte, and a Lao.bSr o^Coo^Feo.gOi cathode (Figure 3.7). Measurements are carried out for the cell operated at 700°C with varying flow rates and compositions of the H2/N2 mixture gas fed into the anode and the 02/N2 mixture gas fed into the cathode. The anode and cathode impedances are thereby separately assigned to low- and high-frequency impedance spectra, respectively. An equivalent circuit model is applied to the spectra to acquire the polarization resistances and associated capacitances for the charge and mass transfer processes at the anode and cathode and the cell ohmic resistance. The variations in these circuit parameters are then obtained in accordance with current densities and anode gas-feed conditions. In addition, the hydrogen diffusion length correlated with the Nernst loss in the axial direction of the anode substrate tube is estimated. These parameters obtained separately and simultaneously for each part of the cell are informative for a detailed analysis and diagnosis of practical SOFCs under operation.
FIGURE 3.7 Experimental setup of the microtubular SOFC.
SOFC has advantages including high-efficiency power generation by operation at 500-1000°C, which results in a low environmental load. Moreover, SOFCs provide high- quality waste heat, and the use of hydrocarbon fuels such as city gas, liquefied petroleum gas, and alcohol is relatively easy. However, for practical use, optimization of the electrode and electrolyte materials and the structure of the cell are required to improve the performance. In addition, optimization of the operation conditions and improvement of cell durability need to be addressed. Thus, fundamental data for the diagnosis of cell status under operation are of great importance. Monitoring the status is also necessary to prevent a serious accident due to the breakdown of the cell. EIS has been widely employed for such analysis. In particular, methods are needed for diagnosis of the operating status of the polymer electrolyte fuel cell by analyzing the variation of resistances and capacitances of equivalent circuit models of the polymer electrolyte fuel cell (Nakajima, Konomi, Kitahara. & Tachibana, 2008). Many EIS analyses for SOFCs have been reported in Ishihara, Shibayama, Nishiguchi. and Takita (2000).
An EIS analysis of a microtubular intermediate temperature SOFC with a two-electrode setup that can be operated in the intermediate temperature range of 500-800°C was carried out under operation with varying anode and cathode gas flow rates and compositions (Figure 3.8a, b). All
FIGURE 3.8 (a) Complex plane and (b) Bode plots for the SOFC at 0.71 A/cnr and 700°C under different anode gas flow rates.
FIGURE 3.9 Equivalent circuit of SOFC.
measurements were performed using an anode-supported microtubular SOFC (Kawakami et al.. 2006) with outer and inner diameters of 5 and 3 mm, respectively. The thickness of the electrolyte was 30 mm ( Saito et al., 2005). The anode substrate tube was made of NiO/ZrCbO.OYiOjO.l. An anode interlayer of NiO/Ce0.9Gdo.iOi.95 for low-temperature operation was coated onto the anode substrate. Lao.gSro.^Gao.sMgo.iCF.g was employed as the electrolyte. A layer of Ce0.6 La,)4Oi 8 was inserted between the anode interlayer and electrolyte to prevent undesirable nickel diffusion during cell fabrication at high temperature.
The behaviors of the impedances and the equivalent circuit parameters of the cell were clarified. In a cell with distinctively different anode and cathode time constants, the impedances associated with the anode and cathode reactions and ohmic resistance appeared in different frequency regions in the impedance spectra, depending on the anode and cathode gas-feed conditions. Hence, those impedances can be analyzed simultaneously and separately without the reference electrode. This is informative for a detailed analysis and diagnosis of practical SOFCs. Thereby, the variations in the equivalent circuit parameters (Figure 3.9) for the charge and mass transfers at the anode and cathode and ohmic resistance under operation condition can be obtained separately. In addition, average diffusion length associated with the Nernst loss in the anode can be estimated from the parameters. Monitoring these parameters allows diagnosing the status of the electrodes, gas feed, and electrolyte/current collector individually. This enables the detection of the degradation of each part of a cell and abnormal operating state before serious accident.
