## Abstract

Voltammetry, potentiometry, amperometry, and electrochemical impedance spectroscopy (EIS) were used to study practical polymer electrolyte membrane fuel cell (PEMFC) stacks in an attempt to validate the stack-tailored electrochemical methods and to show the range of information about a PEMFC stack obtainable with the methods. In-stack electrode voltammetry allowed to determine the type, i.e., the surface chemistry, of catalysts used to make the stack electrodes and to measure the electrodes’ true active surface areas (EASAs). Stack potentiometry gave the EASAs, too, but only after calibration of the method against voltammetry. The speed of the test is the advantage of the stack potentiometry. An amperometry-based protocol was introduced to measure the hydrogen permeability and electronic shorting of the stack membrane-electrode assemblies. Dependence of the H2 permeability on H2 pressure and the stack temperature was shown. EIS in the hydrogen-pump mode was used to study the anode and electrolyte membrane processes under load. Spectra were dominated by humidification effects, which allowed probing the external humidification distribution to the anodes in the stack. Cathode EIS spectra obtained by subtraction of H2-H2-mode spectra from H2-air-mode spectra were modeled and the ohmic, charge-transfer, and oxygen mass-transport contributions to the stack polarization under load were separated. The variability of these contributions across the stack was discussed.

## 1 Introduction

Over the last decades, polymer electrolyte fuel cells (PEMFC) have become more and more relevant for energy conversion and storage to facilitate the way to emission-free allocation of electrical energy in automotive, stationary, and portable applications. PEMFC stacks [1,2] become available from an increasing number of developers. A few stack designs have reached an energy conversion performance level that enables a wider industrial application in the automotive sector, for example [3,4]. Other developers are working intensively on their stack designs, and new PEMFC stack developers will emerge, too. Several review papers have evaluated the impact of different stack design parameters, such as the flow field design [5], the integrated bipolar plates [6,7], the applied cooling and sealing techniques [8,9], the gas-diffusion layers [10], and the membrane-electrode assemblies (MEAs) [11]. Moreover, it seems a natural tendency that PEMFC stack manufacturers will work with external suppliers of more sophisticated components of the stack, like the MEAs, such that essential information on the components will become external for the stack manufacturers. All these factors create a strong need for PEMFC stack characterization methods that would be able to provide as much information as possible about the stack and the included components. The PEMFC stacks cannot be treated by their manufacturers like black boxes and stack integrators, and system manufacturers need testing methods able to characterize the properties of the stack by “looking” inside the stack without opening it. Such insight can be provided by tailored electrochemical methods. These non-destructive methods enable the in situ and partially in-operando analysis of the stack properties and thus give a direct insight into the behavior of the components during the actual fuel cell operation.

Various electroanalytical methods used to study classical laboratory electrode systems have been adapted for studying PEMFC stacks [12,13]. The portfolio of electrochemical methods currently available for stacks includes current interrupt (internal cell resistance measurement) [14,15], voltammetry (real electrochemically active electrode area measurement, electrocatalyst chemistry assessment, determination of electronic shorting in MEAs, fuel crossover measurement) [16,17], stripping voltammetry (real electrochemically active electrode area measurement, electrocatalyst chemistry assessment) [18], potentiometry (as in voltammetry) [1921], amperometry (fuel crossover measurement) [17,22], and electrochemical impedance spectroscopy (EIS, quantification of different sources of stack polarization under load, structural information about electrodes) [23,24]. These methods have been developed for hydrogen-fueled (H2-PEMFC) as well as methanol-fueled (DMFC) stacks [18,2527].

Some of the above methods are relatively new and not yet established in PEMFC stack testing practice. Especially, the interpretation of results and comparative studies using the different techniques are concerned. Also, the information provided by the different methods sometimes overlaps. Thus, the motivation for the present contribution was to validate as many as possible electrochemical techniques on one practical PEMFC stack design to identify the strengths and limitations of the methods and to demonstrate the range of information about a fuel cell stack obtainable with the methods.

## 2 Experimental

### 2.1 Stack and Test Bench.

Hydrogen-fueled, liquid-cooled PEMFC stacks were subjected to electrochemical tests described in Sec. 2.2. The stacks were provided by the Zentrum für Sonnenenergie- und Wasserstoff-Forschung Baden-Württemberg (ZSW, Ulm, Germany) and represented a typical stationary stack design using composite bipolar plates (Fig. 1(a)). They had 10 cells of 96 cm2 geometrical working area each and a nominal electrical power of 480 W. For the purpose of those electrochemical methods, where a driving voltage was applied to the individual stack cells (voltammetry and hydrogen crossover), low-resistance, and gold-plated electrical contacts to the cells were additionally provided besides the existing cell-voltage-monitoring (CVM) contacts.

Fig. 1
Fig. 1
Close modal

The stacks were tested in three different laboratories on different test benches. By way of example, Fig. 1(b) shows the test bench at the German Aerospace Center and Fig. 1(c) the integrated PEMFC stack in this test bench. The benches were all operated using hydrogen 5.0-grade as fuel, nitrogen 5.2-grade as purge gas, de-ionized water to humidify reactants, and ambient air from oil-less compressors as oxidant. The liquid stack coolant was de-ionized water. The stack temperature was controlled using a temperature sensor placed either in the stack cooling inlet or directly in the stack air outlet port following the guidelines for reliable and comparable stack benchmarking [28]. The pressures of the gases were controlled and are reported at the stack gas outlets. The reactant feed lines were thermally insulated on the whole length up to the stack connectors and heated on a part of the length to prevent reactants’ humidity condensation. The stacks themselves were not thermally insulated. The examined stacks in the three laboratories were characterized after different stack history, and consequently, the obtained result values differ depending on stack lifetime. Nevertheless, the presented coherences between the techniques and the conclusions of the test results were in-line with the findings presented in this paper. For clear presentation, all test results presented in this work are obtained at the laboratories at ICRI (Warsaw, Poland).

### 2.2 Testing Procedures and Setups.

The schematic setup for in-stack electrode voltammetry is given in Fig. 2(a). Voltammetry was performed on a selected cell in the stack, and the studied electrode side (anode or cathode) was connected to the used potentiostat as a working electrode and reference electrode #2 (working electrode sense). The studied side of the stack was provided with pure N2. The other electrode side was connected as a counter electrode and reference electrode #1 (counter electrode sense). This side of the stack was provided with pure H2. Consequently, the studied working electrode was analyzed as a polarizable electrode (under N2) and the counter electrode was used as a quasi-non-polarizable counter electrode (under H2). Both applied gases were pre-humidified to 100% relative humidity calculated at the temperature of the stack, which was kept at 30 °C. The gases were supplied at 1.00 and 2.00 Ndm3/min for the H2 and N2, respectively, and no backpressure was applied to both stack exhausts. These feed gas conditions and the avoidance of backpressure are used to assure good conductivity and low ohmic resistance of the membrane as well as to assure the reliability of the determined EASAs of the individual electrodes. Voltammetry was performed by applying an initial voltage of 0.400 V (working versus counter) for 10 s and then sweeping the voltage to 0.050 V followed by three full voltage cycles between 0.050 and 1.200 V at the scan rate of 10 mV/s (in one lab the respective values were 0.090 V, 0 s, 0.080 V, 0.800 V, and 20 mV/s). The voltage programs were performed with suitable potentiostats (Solartron Analytical SI1287, ZAHNER-elektrik IM6e with PP241, Greenlight Innovations test bench built in). For full-stack analysis, every single cell of the stack had been analyzed separately as described.

Fig. 2
Fig. 2
Close modal

In-stack electrode potentiometry was performed as described in Fig. 2(b). The working electrode and reference electrode #2 (working electrode sense) of the used galvanostat were connected to the current collector of the studied electrode side while counter electrode and reference electrode #1 (counter electrode sense) were connected to the opposite current collector. Stack feeding conditions were identical as in voltammetry except that 7.00 Ndm3/min of N2 were provided to the studied stack side and a back pressure of 30 kPa was used on the N2 exit. Increased N2 flow and increased backpressure at the studied electrode were used to minimize the impact of hydrogen crossover, which also lowers the studied electrode potential and can result in a negative systematic error. In this method, the stack was first kept at the open-circuit voltage under H2 and air for 60 s, and then, the air was switched to N2. The switch caused a slow drop of the cells’ voltages and when the voltages reached around 0.800 V, a small current (0.72 mA/cm2) was applied to the entire stack using a galvanostat (Greenlight Innovations test bench built in) in the direction forcing electrochemical reduction on the studied stack electrodes. The dropping cells’ voltages were simultaneously recorded in time using the test bench CVM unit.

For hydrogen crossover measurements, the same setup was used as for voltammetry and as shown in Fig. 2(a). Again, every single cell of the stack was analyzed separately. The cathode of the examined cell was connected as a working electrode and the anode as a counter electrode. The stack was supplied with 7 Ndm3/min of H2 to the anodes and 2 Ndm3/min of N2 to the cathodes. The gases were humidified to assure 85 and 100% relative humidity for H2 and N2, respectively, at the stack temperature maintained at 65 or 80 °C. The aim of this method is to evaluate hydrogen crossover as close to real operating conditions as possible. Therefore, the anode side of the stack is supplied with H2 in a way corresponding to the nominal operating conditions and nominal operating temperatures are applied. The cathode side is supplied with fully humidified N2 to simulate the wet cathode conditions due to water production under fuel cell operation. The hydrogen crossover current is sensitive to the H2 partial pressure differential. A parameter study was realized by maintaining different levels of backpressures at 0 and 10, 50 and 60, or 100 and 110 kPa for the anode and the cathode sides, respectively. Constant voltages of 0.350, 0.500, and 0.650 V (cathode versus anode) were applied to a selected cell in the stack by a potentiostat and the stabilizing crossover hydrogen oxidation currents were recorded as a function of time for 5 min at each voltage. The last 60 s of the 5-min periods were used to determine the steady-state crossover current for the cell.

## 3 Results and Discussion

### 3.1 Information About Catalysts From Voltammetry and Potentiometry.

The first type of information that could be obtained from in-stack electrode voltammetry was the surface chemistry of the catalysts used in the MEAs. Figure 3(a) shows hydrogen-crossover-corrected anode and cathode voltammograms (CVs) for selected stack electrodes. These CVs were representative of the whole stack. The shape of the characteristic features of the surface processes, namely, the oxide layer formation and reduction, and the under-potential hydrogen adsorption and desorption, indicates that the active parts of both the anode and the cathode catalysts were pure Pt.

Fig. 3
Fig. 3
Close modal
Some additional features of the CVs reveal even more about the catalysts composition. A pair of peaks I and II at around 0.65 V, especially visible on the cathode CV but also notable on the anode CV, can be ascribed to the quinone/hydroquinone surface couple found for carbon electrodes [30]. This strongly suggests that both the anodes and the cathodes utilized carbon-supported Pt catalysts. The feature that confirms this and also allows to qualitatively assess the metal-to-carbon ratio of the catalysts is the magnitude of the pseudo-double-layer charging current density (determined from the minimum of current density after hydrogen desorption and marked by vertical bars in Fig. 3(a)) relative to the area, A in V A/cm2geom., under the hydrogen adsorption portion of the CV (striped area determined by integration in Fig. 4(a)). The ratio of the current density, iDLC, to the area can be used to calculate a specific pseudo-capacitance of the electrode–electrolyte interface cDL in F/cm2
$cDL=0.77⋅2.1⋅10−4Ccm−2⋅iDLC/A$
(1)
Fig. 4
Fig. 4
Close modal

The numerical factors in formula (1) are the factors for the conversion of the hydrogen adsorption charge to the real Pt area [31] and are discussed below in connection with formula (4). This pseudo-capacitance can be compared with the specific capacitance of the pure Pt/ionomer interface determined in studies employing unsupported Pt black catalysts, which usually falls in the range 20–70 µF/cm [32]. From the CVs in Fig. 3(a), the values of 112 and 236 µF/cm2 were obtained for the anode and the cathode, respectively, showing that both interfaces were not pure Pt and that the cathode catalyst had a smaller metal-to-carbon ratio than the anode catalyst.

Even finer details of the catalyst's surface chemistry can be noted. Peaks III and IV visible on the anode CV in Fig. 3(a), which are absent from the cathode CV, suggest that the active particles in the anode had a more significant fraction of the (1,0,0) crystal plane of Pt on the surface compared with the cathode active particles [30]. Such differences may originate from different particle sizes in both catalysts consistent with the fact that a lower metal-to-carbon ratio is typically associated with a smaller Pt particle size [33].

Catalyst poisoning impurities can also be studied with voltammetry. Figure 3(b) shows the first five potential scans during voltammetry of one of the stack cathodes. A notable difference between scans 1–2 and the subsequent scans was that the adsorption/desorption signals for the weakly adsorbed hydrogen were lower and an oxidation peak V was recorded in scan 2. From the potential of the peak V and the fact that it was completely absent from scan 4, one can conclude that the peak was associated with oxidative desorption of a small amount of carbon(II) oxide (COads) from the surface of Pt. COads was detected on all cathodes and anodes in the stack; thus, it most likely originated from carbon(IV) oxide reductive adsorption during the humidified nitrogen flushing of the electrodes [34]
$2Pt+H2(crossover)→2Pt−H$
(2)
$2Pt−H+CO2→Pt2=CO+H2O$
(3)

Under different experimental circumstances, such impurity desorption signals could be used to study catalysts carbon support corrosion or the influence of external impurities supplied to the stack with fuel and/or oxidant.

The most typical information about fuel cell catalysts obtained with electrochemical methods is the EASA (electrochemical active surface area). It is possible to extract EASA information for a limited range of noble metal catalysts and their alloys, Pt being one of them. In this work, voltammetry and potentiometry were used to study the EASAs of the stack electrodes. Figure 4(a) shows the preferred way of determining the under-potential hydrogen adsorption charge, QH in C/cm2geom., from PEMFC stack CVs. The striped area under the cathodic potential scan of the CV is used to extract QH by dividing the area, A in V A/cm2geom., under the hydrogen adsorption portion by the scan rate v in V/s. A simplifying assumption is made about the double-layer capacitance of the electrode not changing in the potential range from the beginning of hydrogen adsorption marked by the point I in the figure to the current minimum before hydrogen evolution marked by point II in the figure. QH is transformed to the EASA in cm2 cm−2geom. using the following formula [30]:
$EASA=QH/(0.77⋅2.1⋅10−4C/cm2)$
(4)

The factor 2.1 104 in C/cm2 corresponds to the equivalent charge of the full monolayer coverage of polycrystalline Pt by hydrogen atoms. 0.77 is the coverage of Pt by hydrogen atoms in acidic aqueous electrolyte attained at point II of the cathodic CV scan determined in a combined voltammetry/Brunauer-Emmett-Teller study [30]. This coverage is transferred to the solid electrolyte studies as a first approximation because of the lack of adequate experimental data to verify it.

Sometimes in the literature, QH is also extracted from the hydrogen desorption portion of a CV, i.e., the fragment of the anodic scan following the cathodic scan, from the point where the current becomes positive (oxidation) to the minimum of current after hydrogen desorption (location of vertical bars in Fig. 3(a)). This method is less reliable for large electrode studies like in the PEMFC stack because of the problems associated with proper baseline correction in an often-skewed anodic scan.

Figure 4(b) shows an example potentiometry curve for a stack cathode with the marked transition time, Δt, between the electrode potential limits of hydrogen adsorption on Pt. Δt multiplied by the applied constant current density should give QH. In reality, it only gives a QH estimate principally because of the considerable hydrogen crossover rate during the potentiometry experiment leading to a drop of electrode potential being faster than if it were only due to the constant current applied. In fact, when the applied current is zero a reproducible potentiometric curve similar to the one presented in Fig. 4(b) is recorded, only the Δt is longer.

The inset to Fig. 4(b) shows an example of experimental dependence of established QH on the current density applied in stack potentiometry. It is seen that as the current density is increased, QH increases tending to a limiting value, which could be explained by the diminishing influence of the hydrogen crossover on the result and point to the limiting value being the right QH estimate. However, a comparison of the limiting QH value from potentiometry with the QH value from voltammetry of the same electrode showed a discrepancy of 25% with the voltammetry value being lower. The explanation of that might be based on different physics of the hydrogen adsorption processes under constant current and sweeping potential but it is beyond the scope of the present study.

From the practical point of view, the data show that the potentiometry method of determining EASAs must be calibrated against voltammetry for the former to be used routinely in stack studies. Two ways of calibration are possible. In one, a current density value for potentiometry would be established that would yield QH values consistent with those from voltammetry. In another approach, a correction factor may be calculated for scaling QH values from potentiometry performed at a selected, practical current density to the proper voltammetry values. Figure 4(c) shows EASA data for stack cathodes, demonstrating that potentiometry gives credible results. The correction factors for the 10 cells were random with an average correction factor of 1.37 ± 0.05.

It should be mentioned that the applied factor of 0.77 for the partial coverage of Pt by hydrogen atoms in Eq. (4) is still under discussion in the literature. Other studies assume a full coverage of the Pt surface by adsorbed hydrogen atoms [20,21]. If we assume a higher coverage of Platinum, the determined EASA values from voltammetry are smaller and the average correction factor for potentiometry would be lower. For full coverage, the correction factor would be 1.06 ± 0.04. Nevertheless, the authors believe that the coverage factor of 0.77, as determined in a combined voltammetry/Brunauer-Emmett-Teller study, is the most reliable value for the calculation of the EASA and that the suggested calibration of potentiometry against voltammetry is required.

### 3.2 Information About Membrane Electrode Assemblies From Hydrogen Crossover Measurements.

The hydrogen crossover measurement is an important PEMFC stack safety diagnostic because thinning of the cells’ polymer electrolyte membranes (PEM) as a result of the polymer degradation can be monitored. Thinning and pinhole formation in the PEM can result in catastrophic failure of the stack. The assessment of hydrogen crossovers through the stack MEAs relies on the determination of the crossover hydrogen oxidation currents, which can be converted to fluxes of molecular hydrogen using Faraday’s relation. The currents can be determined with in-stack cathode voltammetry using very small voltage scan rates but a more straightforward method involves cathode amperometry. It is faster and does not require the consideration of double-layer charging. Figure 5(a) shows the respective way of extracting the electronic-short-corrected crossover current density from steady-state amperometry currents determined using three constant voltage values applied to a selected stack cell. A companion result of this measurement is the geometric-area-normalized resistance of the electronic short in the MEA.

Fig. 5
Fig. 5
Close modal

Although the crossover measurement is done under operating conditions as close as possible to the normal operating conditions of the stack in terms of stack temperature and hydrogen flow, relative humidity, and pressure differential across the MEAs, it must be borne in mind that the actual H2 crossovers in the normal working mode of the stack (H2-air) are substantially higher. This is because the electro-osmotic drag of H2 (crossing H2 is dissolved in the water phase of the membrane) in the working mode is large and is from anode to cathode, while in the crossover experiment it is much smaller, and moreover, it is from cathode to anode. The estimation of the actual H2 crossovers in the working mode is possible from the crossover currents obtained in this experiment and the electro-osmotic drag coefficient for molecular H2 in the given PEM. Nevertheless, the H2 crossovers in the working mode are of not so much interest because they still are still small quantities having no influence on the stack efficiency. For safety assessment, it is enough to monitor and compare the current densities or fluxes of H2 obtained directly from the measurements described herein.

Figure 5(b) collects the electronic-resistance-corrected crossover current densities determined for all stack cells. Values obtained at three different H2 pressures and two stack temperatures are compared. It is seen that the crossover current density is a strong function of both the H2 partial pressure difference across the MEA and the stack temperature. For this reason, crossover current densities should always be compared for the same H2 partial pressure difference (and total pressure difference) and stack temperature. The crossover flux of H2 per unit of H2 pressure at a given temperature is often a quantity useful for comparisons because the flux of H2 is usually linear with the pressure. A regular variability of the H2 crossover rates across the stack is notable at any conditions studied such that the higher the cell index the higher the crossover. A hint on the possible reason for such behavior is obtained from EIS in the hydrogen-pump mode (Sec. 3.3), which revealed a tendency for the high-index cells to operate under drier conditions than the low-index ones in this stack. A drier polymer-electrolyte membrane is more permeable to H2 [35]. For the presented data set, the electronic shorts in all the MEAs were very small and could be quantified only for a few cells in the stack, i.e., in the cases where the random error of the slope of the regression line in Fig. 5(a) was much less than the value of the slope. The respective short resistances determined were on the order of 10 kΩ cm2geom..

### 3.3 Electrochemical Impedance Spectroscopy in Hydrogen-Pump Mode.

The EIS of the PEMFC stack fed with H2 on both the anode and cathode sides under conditions described in Sec. 2.2 was done in an attempt to study uniquely the processes occurring in the hydrogen anodes under load. The assumption was that the EIS spectrum in this mode should be dominated by the impedances of the anode and the electrolyte membrane because the impedance of the cathode possessing the EASA a few times higher than the anode (cf. Figure 3(a)) and evolving H2 under fully humidified conditions should be negligible. Typical H2-H2 spectra recorded for all cells in the stack and under all DC load values are presented in Figs. 6(a) and 6(b). The spectra shown are a result of rejection of cable impedance-influenced points for the highest frequencies and excessively noisy points at the lowest frequencies. Two spectrum types were observed. One spectrum type recorded less frequently had in the Nyquist representation a small, 45-deg-inclined, linear portion in the high-frequency range and a flattened arc in the low-frequency range (Fig. 6(a), circles). In the majority of cases, the high-frequency, linear portion was not pronounced and the circular portion was not flattened (Fig. 6(a), triangles).

Fig. 6
Fig. 6
Close modal

In an attempt to understand the physical origins of the spectrum features, the following observations have been made. When the circular portion of the spectrum was fit with a parallel R-C circuit, the resulting capacitance was always on the order of a few farads per cm2geom.. Obviously, no phase boundary with such high capacitance existed in the stack electrodes. The time constant of the fitted circuit (R-C) was the same for all feeding conditions and DC load values and equal 0.14–0.15 s. At the same time, fitting the whole spectrum with a series connection of a resistance and a Warburg element representing finite-length, transmissive-boundary diffusion gave very poor fitting quality. The size of the circular portion of the spectrum varied with the hydrogen pressure on the cathode side in such a way that increasing the pressure would diminish the circular portion. While the circle diminished with the cathode pressure increase, it also became less flattened, the linear portion of the spectrum at high frequencies became less pronounced, and the high-frequency intercept of the spectrum became lower (compare Fig. 6(a), 60- and 100-kPa data). As the DC load was increased, the character of the spectrum changed to more like for the 60-kPa data in Fig. 6(a). The same spectrum character change occurred when the relative humidity of H2 fed to the anodes was decreased (data not shown).

All these observations led to the conclusion that the H2-H2 spectra were dominated by the humidification-dependent proton transport in the polymer electrolyte of the anode and the membrane. When the proton transport in the anode becomes slow, the resistance of the electrolyte in the anode pores increases and the porous electrode behavior becomes apparent in the impedance spectrum (45-deg line followed by flattened circular portion in Nyquist plot) [36]. The same problem propagating to the membrane will result not only in a pronounced upward shift of the high-frequency intercept of the spectrum but also in a pseudo-capacitive behavior at low frequencies. As shown by Holmström et al. [37] and Wiezell et al. [38], this low-frequency, pseudo-capacitive behavior originates from the fact that the proton transport and the anode charge-transfer kinetics slow down as the current increases because of the electro-osmotic drag of water in the polymer electrolyte of the membrane and the anode causing polymer dry-out. The membrane and the anode charge transfer mimic a capacitor, the impedance of which increases as it is being charged. All the features of the spectra are influenced by the cathode pressure because increased cathode pressure allows to keep more humidity in the membrane and the anode.

Here, we propose two simplified modeling approaches for the PEMFC stack impedance in the hydrogen-pump mode. One is based on the equivalent circuit shown in the inset to Fig. 6(b) and gives good fitting results for the spectra exhibiting the porous electrode behavior (cf. Figs. 6(a) and 6(b), 60-kPa data fit). The porous electrode behavior is modeled using the finite-length, transmissive-boundary Warburg element, WS, and the pseudo-capacitive behavior at low frequencies is modeled with a parallel RA-M-CA-M connection (A-M denotes the anode-membrane origin of the elements). An even simpler equivalent circuit shown in Fig. 6(c) inset, which is lacking the Warburg impedance, can be used for spectra without the porous electrode behavior (cf. Figs. 6(a) and 6(b), 100-kPa data fit).

Using the above interpretation, the H2-H2 spectrum can be used to probe the anode-side humidification conditions in the stack. Figure 6(c) shows the changes of the RA-M model parameter for the different stack cells and different DC load values. It was extracted by fitting the data with the simplest equivalent circuit shown in Fig. 6(c) inset. It is seen that the parameter increased almost linearly with the cell index for any DC load value. This shows that the distribution of water vapor for anode humidification supplied with the hydrogen feed to the different cells was uneven and depended quite strictly on the position of the anode in the stack with the high-index anodes/membranes running drier than the low-index ones. The underlying cause of this behavior requires further study. The notable increase in RA-M at the highest DC load value showed that the electro-osmotic drag over-dried the cells a little bit despite the increased amount of water supplied with the hydrogen stream of constant relative humidity and stoichiometry.

### 3.4 Electrochemical Impedance Spectroscopy in H2-Air Mode.

The EIS spectra in the normal working mode of the PEMFC stack represent the spectra of the H2 anode, the PEM, and the air cathode connected in series, and the determined overall impedance is the sum of the respective impedances. We postulate that once we have a good approximation of the anode-PEM impedance in the H2-air mode, we can subtract this impedance from the overall impedance and obtain the air cathode impedance. As shown in Sec. 3.3, the impedance determined in the H2-H2 mode, which responded to the MEA humidification conditions, could be assigned to the anode-membrane ensemble. To obtain a good matching H2-H2 spectrum adequate for subtraction from the H2-air spectrum, it was necessary to match the anode-PEM humidification conditions in both modes. This was done by adjusting the H2 pressure and the relative humidity on the cathode side in the H2-H2 mode to balance the lack of water production in this mode until the high-frequency resistance in this mode became equal to the one obtained in the H2-air mode. The results of such a procedure for the determination of the air cathode spectrum are presented in Fig. 7 for a selected stack cell. For clarity of comparison of the different spectra, the hydrogen-pump data (blue circles) are shown after the subtraction of its respective modeled RS value, and such modified data were used to correct the H2-air data (green squares) and obtain the cathode data (red triangles).

Fig. 7
Fig. 7
Close modal

The cathode spectra thus obtained at various DC load values had the following features in the Nyquist diagram (Fig. 7(a)): (i) a load-dependent, flattened circular portion at high frequencies and (ii) a largely load-independent, non-flattened circular portion at low frequencies. No linear 45-deg-inclined portion at the highest frequencies could be distinguished. Based on these features and on the PEMFC cathode EIS literature [39], an impedance model for the air cathode is proposed in the form of an equivalent electrical circuit shown in the inset to Fig. 7(b) [40]. The model includes a constant-phase element (CPE, fitted parameters CDL,C, φDL,C) to represent the capacitance of the inhomogeneous electrode–electrolyte boundary. A parallel resistance RA,C represents the (activation) resistance of electron transfer across the electrode–electrolyte boundary. A finite-length, transmissive-boundary Warburg element (fitted parameters RT,C, τT,C, and φT,C) is put in series with the charge-transfer resistance to account for the impedance associated with oxygen transport in the gas-diffusion layer (GDL) of the cathode. The series resistance RS represents the sum of resistances of the bulk electrolyte and the electron conductors. This model gave good fitting quality across the whole data set. An example fit is shown in Fig. 7 with the solid line.

Electrochemical impedance spectroscopy analysis of the stack cathodes’ operation was realized at three DC load values corresponding to activation (9.6 A, 0.1 A/cm2geom.), mixed- (48 A, 0.5 A/cm2geom.), and transport (96 A, 1.0 A/cm2geom.) control regimes. Figure 7(c) demonstrates the polarization curve of the examined stack including operating points for EIS. The results of the EIS analysis are shown in Fig. 8. The series resistance was low and even across the stack under all tested conditions (Fig. 8(a)), showing that the stack displayed no MEA dry-out problems in nominal operation.

Fig. 8
Fig. 8
Close modal

The charge-transfer resistance (Fig. 8(b)) was the highest at the lowest load, then it decreased at the middle load, and increased back at the highest load. Such a behavior can be understood when we consider that, according to theory, RA,C should exponentially decrease with increasing cathode over-potential and that it is also inversely proportional to the oxygen concentration at the cathode catalyst surface. At the highest DC load used, the depletion of oxygen in the catalyst layer might have already begun.

Figure 8(c) shows the values of the capacitive CPE parameter, CDL,C, which is a measure of the cathodes’ double-layer capacitance. The values of the CPE exponent, φDL,C, were 0.8 ± 0.1 for all cases. First, one can notice that CDL,C was the lowest at the lowest DC load and increased with the load increase. This can be explained by considering that the specific capacitance of an oxidized Pt surface is about an order of magnitude lower than that for the bare Pt metal. As the load is increased, the potential of the cathode drops and the coverage of Pt by the oxide decreases. Second, looking at the inset to Fig. 8(c) showing the stack distribution of cathode double-layer charging currents from voltammetry (see Sec. 3.1), one can notice a strong correspondence of the distribution patterns of the currents and CDL,C at 9.6 A. This as well as agreement of capacitances from EIS and voltammetry confirm the right assignment of the high-frequency spectrum feature to the interface charging process.

The fitted values of the Warburg exponent, φT,C, were 0.5 ± 0.1 for all cases suggesting that the assignment of the low-frequency feature of the spectrum to diffusional transport was correct. The mass-transport resistance, RT,C, shown in Fig. 8(d), overall, depended relatively weakly on the stack DC load. More important was the position of the cathode in the stack because the high-index cathodes had a markedly higher RT,C than the low-index cathodes. In the proposed model, the oxygen diffusion time constant, τT,C, is inversely proportional to the effective diffusion coefficient of oxygen in the GDL (τT,C = GDL thickness2/diffusion coefficient). From Fig. 8(e), it can be concluded that the effective oxygen diffusion coefficient clearly increased with the load. Because there was more water going through the cathode GDL as the load increased and that should have lowered the effective diffusion coefficient, such inverse behavior may be explained by the oxygen transport shifting from the diffusional to the convective mode at the high loads and associated high air flows. The extent of this shift was distributed in the stack according to the cell index, and the low-index cathodes were clearly getting more air than the high-index ones. Compensation of the increased water presence by the change to the more effective, convective gas transport in the GDL may explain the general lack of RT,C dependence on the load, while the high-index cathodes experiencing increased RT,C might be consistent with the cell position-dependent air distribution in the stack.

## 4 Conclusions

A set of tailored electrochemical methods applied to practical PEMFC stacks allowed obtaining essential information about the stack MEAs constituents such as the catalysts and the electrolyte membranes, and about the sources of stack cells’ polarization under electrical load. Using the latter, the stack hardware design could be evaluated.

Catalysts' active surface chemistry and the true area were studied with in-stack electrode voltammetry and potentiometry showing that the anodes and the cathodes used slightly different catalyst compositions, although both pure-Pt-based and largely different active surface areas. The distribution of active areas in the stack cathodes and anodes (latter not shown here) was revealed showing important variability. It was also demonstrated that voltammetry and potentiometry are both viable methods for the determination of the catalyst's active surface area but potentiometry needs pre-calibration against voltammetry. Potentiometry is particularly valuable as a fast method to study stacks with many cells subjected to durability tests, for example.

The stack MEAs were tested for H2 permeability and electronic shorting using tailored in-stack amperometry. This new procedure was introduced in the present work. As expected, the H2 crossover rates in the stack cells depended strongly on the H2 pressure and stack temperature, and thus, it is essential to always compare the rates at defined pressure and temperature. The H2 permeability across the stack was even, and negligible electronic shorting was detected in the MEAs.

Electrochemical Impedance Spectroscopy was used to study the anode, the membrane, and the cathode processes under load, separately. The H2 pump mode of stack operation allowed us to determine the anode-membrane impedance. This impedance was influenced by the humidity level of the anode-membrane ensemble and could be used to probe the distribution of humidification water to the different stack anodes. It was shown that the distribution was not even and the amount of water an anode was getting was a clear function of the anode’s position in the stack.

The EIS spectra of air cathodes were obtained by subtracting adequate anode-membrane spectra from the spectra recorded in the normal operating mode of the stack. The cathode impedance could be successfully modeled with an equivalent electrical circuit taking into account the bulk cell resistance, the double-layer charging of the cathode-electrolyte interface, the charge transfer across the same interface, and oxygen transport in the cathode GDL. Thanks to the separation of contributions to the cell polarization, it could be concluded that the work of the cells in the H2-air mode was even across the stack with regard to the ohmic losses, less even with regard to the activation losses, and not even with regard to the oxygen transport losses. In the latter case, a clear dependence of the cathode mass-transport resistance on the position of the cathode in the stack was noted, suggesting graded air stream distribution in the stack.

## Acknowledgment

This research was funded by the European Union Seventh Framework Programme for the Fuel Cells and Hydrogen Joint Undertaking under Grant No. 303445 (Stack-Test: Development of PEM fuel cell stack reference test procedures for industry).

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