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Impedance modelling of porous electrode structures in polymer electrolyte membrane fuel cells
Journal of Power Sources 444 (2019) 227279
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Impedance modelling of porous electrode structures in polymer electrolyte membrane fuel cells Marcel Heinzmann *, Andr�e Weber, Ellen Ivers-Tiff�ee Institute for Applied Materials (IAM-WET), Karlsruhe Institute of Technology (KIT), Adenauerring 20b, 76131, Karlsruhe, Germany
H I G H L I G H T S
� Identification of loss processes by the distribution of relaxation times. � Application of physically meaningful transmission line model. � Quantification of polarization contributions at various operating conditions. � Derivation of electrode material properties. A R T I C L E I N F O
A B S T R A C T
Keywords: Polymer electrolyte membrane fuel cell Electrochemical impedance spectroscopy Distribution of relaxation times Equivalent circuit model Transmission line model Ionic conductivity
Electrochemical Impedance Spectroscopy (EIS) is a suitable tool for identifying the performance-related polar ization processes in a polymer electrolyte membrane fuel cell. A physically meaningful impedance model is needed when drawing conclusions about further cell improvement. This study focuses on the characterization of the porous electrode structure by applying a transmission line model (TLM) to the measured spectra. The fitting procedure is supported by the distribution of relaxation times (DRT) method enabling a separation of loss processes by their individual time constants. We are able to separate and quantify (i) the gas diffusion in the porous media (2–10 Hz), (ii) the charge transfer resistance at the Pt catalyst (2–200 Hz), and (iii) the ionic transport resistance in the catalyst layer (300–30,000 Hz), across a broad range of operating conditions (current density, relative humidity, gas compositions). The TLM approach directly reveals the electrodes’ transport and reaction properties, e.g. ionic conductivity and the Tafel slope. Under high electrical load the ionic transport losses in the catalyst layer contribute more to polarization than expected. Interestingly, the oxygen reduction reaction is found to be describable with a single, current-independent Tafel slope.
1. Introduction For the development of physicochemically meaningful models of fuel cells and batteries the individual loss mechanisms that occur during operation and that limit cell performance and efficiency have to be identified and quantified. Electrochemical impedance spectroscopy (EIS) in combination with the distribution of relaxation times (DRT) is a powerful approach to unfold complex electrochemical systems [1,2]. Commonly impedance spectra are evaluated by a complex nonlinear least squares fit (CNLS) to a model function given by an equivalent circuit model (ECM) [3–7]. As number, size and time constants of the polarization processes are often not known in advance, the assessment of a meaningful ECM remains challenging. To overcome this issue, we use a different approach based on a pre-identification of the electrochemical
processes by the distribution of relaxation times (DRT) and the subse quent application of the DRT in the CNLS-fit [8]. This approach was successfully applied to solid oxide fuel cells [9] and lithium-ion batteries [10,11], enabling the deconvolution and quantification of the different loss mechanisms in the cells. The first application of the DRT approach to PEM fuel cells is discussed in a previous study [12]. We carefully evaluated the impedance spectra of a PEM single cell at clearly defined operating points. This enables us to separate five different polarization contributions (with individual relaxation frequencies from 2 Hz to 30 kHz). Furthermore, we assigned the individual processes to their respective physical origins by a systematic variation of operating parameters. An even more detailed description of the electrodes considering material and microstructural parameters is possible by models
* Corresponding author. E-mail address: [email protected] (M. Heinzmann). https://doi.org/10.1016/j.jpowsour.2019.227279 Received 18 July 2019; Received in revised form 5 September 2019; Accepted 7 October 2019 Available online 22 October 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.
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considering ionic, electronic and species transport and its coupling by the electrochemical reactions in porous multiphase electrodes. To cover the details in such electrodes in an ECM, the application of appropriate transmission line models (TLM) is envisaged [13,14]. The combination of EIS and DRT is a powerful tool to resolve and parameterize TLMs even for full cells and their electrodes as shown for SOFC in Refs. [15–17] and for lithium-ion batteries in Ref. [18]. In this contribution we will present and compare several models in terms of fit quality and physical inter pretation for PEM fuel cells. We will show that the often preferred, simple Randles circuit [19–23] is not able to describe the complex impedance of a porous electrode structure. Beyond that, the TLM en ables us to extract physical parameters of the transport (ionic conduc tivity) and the reaction processes (Tafel slope) across a wide range of operating conditions.
air). A detailed view is given by the DRT analysis (Fig. 1b,d): DRT calculation enables the deconvolution of five clearly separable peaks (P1 – P5) with different characteristic frequencies from 2 Hz to 30 kHz. The area specific resistance (ASR) of each process is shown by the area under the peak. In our previous work we assigned the individual processes to their respective physical origins by a systematic and targeted variation of operating parameters [12] (Table 1). In the full cell spectrum we can clearly distinguish between (i) gas diffusion in the porous structure of gas diffusion layer and catalyst layer at the cathode (P1: 2–10 Hz), (ii) the oxygen reduction reaction at the Pt catalyst (P2: 2–200 Hz) and (iii) the proton transport in the cathode catalyst layer (P3 – P5: 300 Hz–30 kHz). It should be noted that P2 might be superimposed by a side peak of P1 and therefore be affected for low oxygen partial pres sures (see Table 1). Fig. 5 shows that the charge transfer resistance associated with P2 does not depend on the oxygen partial pressure. In addition, we have shown that the anode processes, superimposed by the dominating cathode processes in the same frequency range, are negligibly low (less than 4% of the total polarization) when operated with hydrogen. For that reason, the present work solely focuses on the cathode processes.
2. Experimental 2.1. Single cell tests and impedance analysis The analyzed PEM fuel cells are commercial MEAs of type Green erity® H500EL2 with platinum loadings of 0.4 mgPtcm 2 (cathode) and 0.2 mgPtcm 2 (anode). Single cells with an active surface area of 1 cm2 were sandwiched between gas diffusion layers (GDL 29 BC from SGL®) and placed into an in-house developed fuel cell housing. The active electrode area contacting is realized by gold flow fields with parallel flow channels (cross-section: 1 mm � 1 mm). The housing is compressed by stainless steel heat exchanger plates containing a thermal fluid. The cell temperature is controlled by a Julabo F32-ME thermostat. The GDL contact pressure is independent from the sealing pressure, and contin uously adjustable from 0 to 200 N. The gas is supplied by mass flow controllers, supplying a well-defined mixture of oxygen, nitrogen and hydrogen to cathode and anode. The humidities in the oxidant and fuel are generated in catalytic burner chambers ahead of the cell by reacting hydrogen and oxygen [24]. Our setup ensures clearly defined operating conditions with low lateral gradients; it thus enables us to derive un ambiguous parameter dependencies. More details about the cell setup and testing conditions are given in our previous work [12]. Impedance spectra were recorded across a wide range of operating conditions (variation of current density, relative humidity and gas compositions) using a Zahner® Zennium E potentiostat [12]. Steady-state conditions during impedance measurements were assured by a waiting time of 60 min before each measurement. Linearity was assured by choosing a perturbation amplitude of 12 mV within a fre quency range from 1 MHz down to 50 mHz (pseudo-galvanostatic mode). A Kramers-Kronig Test was applied to the data to ensure the validity of the measured spectra [25–27]. It revealed errors below 0.2% within the evaluated frequency range. For data analysis, we computed the distribution of relaxation times (DRT) to identify the loss processes and their relaxation frequencies [1,12]. Subsequently, the impedance spectra were fitted to the equivalent circuit models (ECM; described below). Both the DRT calculation and the CNLS-fit were performed in MathWorks Matlab™. The CNLS approximation is evaluated by the relative fitting error for the real (Z0 ) and imaginary (Z00 ) parts for all analyzed frequencies: ΔZ’ðωÞ ¼
Z ’fit ðωÞ Z ’meas ðωÞ Z ’meas ðωÞ
(1)
ΔZ } ðωÞ ¼
Z "fit ðωÞ Z "meas ðωÞ Z "meas ðωÞ
(2)
3. Modelling 3.1. Equivalent circuit modelling The intention is to set up a physically motivated equivalent circuit model (ECM), which is able to describe the impedance response of the cell or of an individual electrode, thus enabling quantification of the individual loss processes. The most common equivalent circuit is the Randles circuit [23], which has been widely applied in literature [19–22]. This circuit con sists of an electrolyte resistance, R0 , in series with the parallel combi nation of the double-layer capacitance, Cdl , and an impedance of faradaic reaction. The double-layer capacitance is often replaced by a constant phase element (CPE), originating from a non-uniform current distribution along the electrode surface. For PEM fuel cells the imped ance of the faradaic reaction consists of a charge transfer resistance, RCT , and a Warburg element, describing diffusion-related processes. The impedance expression for the generalized, finite length Warburg element (GFLW) is given by Ref. [28]: tanh½ðjωTW Þp � ZW ðωÞ ¼ RW ⋅ ðjωTW Þp
(3)
For a perfect one-dimensional diffusion limitation the p is equal to 0.5. Here RW denotes the diffusion resistance and TW the time constant. For simplification, the Warburg element is often connected in series to the parallel combination of the charge transfer resistance and the double-layer capacitance. This is valid if the time constant of the diffusion processes is significantly larger than those of the charge transfer reaction [29]. In the following, this circuit will be referred to as ECM (1RQ). However, for the porous electrode structures typically found in real cells, the impedance spectra are usually more complicated. As such, the Randles circuit may not provide appropriate fitting results [6]. An ac curate analysis of the impedance spectra (with the help of the DRT method) leads to the same conclusion: Fig. 1b shows the identification of various polarization contributions with individual time constants (P1 – P5), just barely describable with the Randles circuit. For that reason, one possibility is to add one [30] or more [31,32] RQ elements to the circuit. We propose using an extended impedance model with three RQ elements instead of one, from here on referred to as ECM (3RQ). This is a convenient way of modelling the impedance with its numerous polari zation contributions, although physical correlation is reduced. The in dividual elements may not represent individual and independent physical mechanisms.
2.2. Impedance analysis and process assignment Fig. 1a,c give an example of typical PEMFC impedance spectra as a function of current density (cell operated at T ¼ 80 � C, 70% R.H.: H2/ 2
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Fig. 1. Impedance spectra (a,c) and calculated DRTs (b,d) as a function of current density and with separation of individual polarization contributions (T ¼ 80 � C, 70% R.H., and H2/air).
under low humidity are challenging and often cannot be adequately described [6,7]. This then often leads to unclear or ambivalent fitting results and makes it difficult to evaluate the obtained parameter. One possibility for reducing degrees of freedom is the analysis of the elec trode microstructure and to keep the corresponding parameters fixed during the fitting process. Because it is extremely difficult to find the microstructural parameters for the obtained commercial cell in litera ture, we followed a different approach by using the DRT analysis to evaluate the fit result. This allowed us to control the fitting process without further model assumptions or simplifications. The impedance of a porous electrode (thickness L, c.f. Fig. 2) can be described by the following equation [13]: � � � � χχ 2κ χ 2 þ χ 22 L þκ⋅ 1 (4) ⋅coth ZTLM ðωÞ ¼ 1 2 ⋅ L þ sinhðL=κÞ κ χ1 þ χ2 χ1 þ χ2
Table 1 Process assignment of identified polarization contributions to the underlying physical mechanisms. Process
Dependencies
Relaxation frequency
Physical origin
P1
j, pO2,cat, R.H.
2–10 Hz
P2
j, pO2,cat (strong), R.H. (low) R.H.
2–200 Hz
gas diffusion of oxygen in GDL and CCL charge transfer kinetics at the cathode (ORR) proton conduction in the ionomer of the cathode catalyst layer (subordinate anode processes)
P3 – P5
300 Hz–30 kHz
3.2. TLM approach for PEMFC cathodes
The value κ is the ratio between the resistances of the charge transfer reaction at the Pt catalyst and the sum of the resistances for the ionic and electronic paths: sffiffiffiffiffiffiffiffiffiffiffiffiffiffi ζ κ¼ (5) χ1 þ χ2
There have been some analytical literature studies on the influence of the electrode structure on the impedance behavior using a TLM. For example, Eikerling et al. [33] investigated the effects of the layer thickness and Reshetenko et al. [34] investigated the influence of a non-uniform Nafion loading. However, application of a TLM to the measured impedance spectra remains challenging. Therefore, TLMs are often applied in H2/N2 mode in order to determine the ionic transport resistance in equilibrium state [3–5]. However, during a transfer to operation under load the consideration of water management and the humidity change remain difficult. Investigations in H2/O2 operation and
The circuit elements χ1 and χ2 describe the ionic and electronic re sistances (Ω⋅m 1) and ζ describes the charge transfer resistance between both paths (Ω⋅m). Due to the high conductivity of carbon, the losses of the electronic path can be neglected (χ2 � 0) [3], which in turn allows a simplified expression for the overall impedance of the cathode catalyst 3
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layer (CCL): � � L ZTLM ðωÞ ¼ κ ⋅ χ 1 ⋅coth κ
(6)
The layer thickness of the CCL was determined to 13 μm and was fixed during the fitting process. Fig. 2d and e shows simulated spectra and the related DRTs of the TLM impedance function (Eq. (6)) at various ionic resistances (χ 1 ¼ rion ) from 5000 Ωm 1 to 15,000 Ωm 1. These values are quite plausible, as the mean value (10,000 Ωm 1) refers to a fit from real measurement (T ¼ 80 � C, 70% R.H.). It can be seen, that the DRT calculation of the TLM impedance shows several peaks: One main peak at lower fre quencies (50 Hz) representing the charge transfer reaction at the Ptcatalyst and additional side peaks at higher frequencies (500–30,000 Hz) related to the proton transport in the ionomer. This behavior can be explained by the impedance shape of the TLM: Starting from high frequencies, a 45� branch emerges which turns into a semi circle (Fig. 2d). The DRT calculation now attempts to simulate the impedance shape with help of a certain number of RC elements (which in turn show up as an ideal semicircle) (Fig. 2e). It is easy to understand that a 45� branch cannot be represented by a single semicircle, but rather by a combination of several semicircles of different sizes. In addition to that, it can be seen that the side peaks are affected by the ionic resistance. A quite similar behavior is visible in Fig. 4 showing a humidity variation that has a strong impact on the conductivity of the ionomer. Thus the side peaks at 200–30,000 Hz are strongly affected. 4. Results and discussion 4.1. Comparison of different ECMs Fig. 3 shows a comparison of all three applied models (ECM (1RQ), ECM (3RQ), and ECM (TLM)). The upper row displays the measured impedance spectra (black circles) at 80 � C, 70% R.H., 382 mA cm 2 and H2/air operation. The orange line represents the CNLS-fit to the respective model and shows good agreement with the measured impedance for all three models. A detailed view of the fit quality is given by the calculated model residuals (Fig. 3, middle row). The best agree ment between applied model and measured impedance is given by ECM (3RQ), which is due to the higher number of independent elements. ECM (1RQ) and ECM (TLM) show almost equal residuals. Now, considering the DRT analysis of the spectra as well as the partial DRTs of the fitted elements (Fig. 3, bottom row), clear differences are observable. ECM (1RQ) cannot reproduce the polarization contri butions as seen in the DRT, even though the impedance shape is reproduced very well. Processes P1 and P2 (with their characteristic frequencies of ~10 Hz and ~50 Hz, respectively) cannot be replicated by the model. Instead, the model only creates one process with a fre quency of about 25 Hz. In addition, there is a clear overestimation of the gas diffusion resistance, represented by the GFLW element. However, ECM (3RQ) and ECM (TLM) show better accordance of identified processes with simulated partial DRTs considering the relax ation frequencies. They are therefore better suited for an accurate description of the underlying processes. Both models are able to rebuild all identified processes and to properly hit their characteristic frequencies. In order to identify the advantages, differences and disadvantages of ECM (3RQ) and ECM (TLM), we applied a set of impedance spectra with varied relative humidity. Fig. 4a,c shows the impedance spectra and calculated DRTs for relative humidities from 40% to 90% R.H. (T ¼ 80 � C, j ¼ 146 mA cm 2, H2/O2). It becomes obvious that the change in humidity affects the secondary peaks, PCCL ion , at medium and high frequencies (50 Hz–50 kHz), which had previously been assigned to the proton transport in the CCL [12], whereas the main peak PCT (charge
Fig. 2. Electrode structure of a catalyst layer (cathode) with reaction mecha nisms and transport paths (a), transmission line model (b) and equivalent cir cuit elements (c). Simulated impedance spectra (d) and DRTs (e) of the TLM impedance at various ionic resistances.
4
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Fig. 3. Measured and simulated impedance spectra, relative error for real and imaginary parts and DRT of measured and simulated spectra for: (a) The established ECM with one RQ element fitted to the measured spectra. (b) An extended model approach with three RQ elements. (c) A TLM model approach with consideration of transport paths within a porous electrode structure. The shown spectra are recorded at T ¼ 80 � C, 70% R.H. and j ¼ 382 mA cm 2 (H2/air).
transfer) at ~25 Hz is hardly affected. The low frequency feature (gas diffusion) at ~10 Hz is not observable in this investigation due to operation with oxygen instead of air and therefore improved oxidant supply to the electrode. Fig. 4b shows the obtained model parameters by a fit of ECM (3RQ) to the impedance data. In this case, RRQ;1 describes the main peak (charge transfer) at ~25 Hz while RRQ;2 and RRQ;3 describe the secondary peaks (proton transport in the CCL) at higher frequencies. It becomes evident that it is challenging to create stable and reproducible fitting results. A clear assignment of the individual ele ments to the associated processes is difficult, and therefore the resistance values and time constants fluctuate. This prevents a further meaningful physical interpretation of the results. The TLM approach delivers (i) the specific charge transfer resistance, rCT ; and (ii) the specific ionic transport resistance, rCCL ion ¼ χ 1 , in the CCL. In addition, the effective ionic conductivity of the ionomer within the catalyst layer, σ CCL ion , can be calculated as follows:
σ CCL ion ¼
L 1 ¼ R⋅A rCCL ion ⋅A
allows the establishment of a clear physical relationship between the obtained model parameters and the investigated processes. Conse quently, the further quantification of the loss processes is therefore based on the application of ECM (TLM). Furthermore, the CNLS-fit procedure benefits from the DRT approach, as the DRT extracts the relaxation frequencies for each process, and thus delivers useful starting parameters. 4.2. Quantification of loss processes To quantify the individual loss processes and their resistance con tributions, the chosen ECM (TLM) was applied to an extensive set of measured spectra across a wide range of operating conditions. We were thereby able to determine the area specific values of: - (i) the charge transfer resistance, RCT , of the oxygen reduction reaction:
(7)
RCT ¼
Now, regarding the results of the TLM fit (Fig. 4d), the obtained parameters are much more stable and reasonable. The specific charge transfer resistance, rCT , shows almost no dependency on humidity, which also reflects the observations of the DRT results. In addition, the ionic conductivity, σ CCL ion , shows a strong increase with increasing hu midity (0.13 S m 1 at 40% R.H. to 1.1 S m 1 at 90% R.H.), which in turn is consistent with literature data [5,7]. A comparison of the ionic con ductivity in the CCL to the membrane conductivity and a classification to other materials is given in section 4.3. These results impressively show that the use of a TLM approach
rCT ⋅A L
(8)
- (ii) the Warburg resistance, RW , representing the gas diffusion losses in the porous media of gas diffusion layer and catalyst layer. - (iii) the ohmic resistance, R0 , which summarizes the membrane resistance and the electrical transport contributions in all cell components. - (iv) the ionic transport resistance, RCCL ion , in the cathode catalyst layer [3,35,36]:
5
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Fig. 4. Impedance spectra (a) and calculated DRTs (c) for a variation of relative humidity (from 40% R.H. to 90% R.H. at j ¼ 146 mA cm 2). (b) Obtained model parameters for application of ECM (3RQ). (d) Area specific charge transfer resistance and ionic conductivity determined by application of ECM (TLM).
1 CCL RCCL ion � ⋅r ion ⋅L⋅A 3
decrease with current density from 5.42 Ω cm2 (at 8 mA cm 2/0.14 atm) to 71 mΩ cm2 (at 1 A cm 2/0.14 atm), but almost no dependence to oxygen partial pressure. R0 and RCCL ion are almost independent from current density and oxygen partial pressure, as expected. RW is strongly influenced by current den sity and oxygen partial pressure and accounts for the largest share, at 1 A cm 2/0.14 atm (0.4 Ω cm2). Low oxygen partial pressure and/or high current densities are known to cause major diffusional losses [21]. In the following, some example operating conditions are chosen to further clarify the dependencies of the calculated ASR to the operating parameters and to display the individual contributions to the overall resistance. Fig. 6 gives an example of dependence on (a) current density, (c) oxygen partial pressure and (e) relative humidity. In addition to that, the individual contributions to the overall resistance are given in Fig. 6b, d,f. Fig. 6b shows that under typical operating conditions (T ¼ 80 � C, 70% R.H., H2/air and 1.0 A cm 2) the gas diffusion losses, RW , are the dominating loss process and that they contribute 63% to the overall resistance, followed by ohmic losses, R0 (17%), charge transfer losses, RCT , (11%) and ionic transport losses in the CCL, RCCL ion (9%). Now, when using oxygen instead of air (Fig. 6d), the diffusion losses, RW , become negligibly low (4%). Ohmic losses, R0 , become dominant (43%), fol lowed by charge transfer losses, RCT , (27%) and ionic transport losses in the CCL, RCCL ion (26%). In order to show the influence of reduced hu midification, Fig. 6f gives an example of the loss composition at 40% R. H. (T ¼ 80 � C, pO2 ¼ 0.55 atm and 1.0 A cm 2). Ionic transport losses in the CCL, RCCL ion , account for slightly more than half (52%), followed by the ohmic losses, R0 (37%). In total, approximately 90% of the total losses consist of ionic transport losses (in the membrane and CCL). This illus trates the importance of adequate humidification. Charge transfer los ses, RCT , (9%) and gas diffusion losses, RW , (8%) remain at low values in this case.
(9)
Fig. 5a shows the obtained ASR values as derived from the CNLS-fit for the current density range from 8 mA cm 2 to 1 A cm 2 and relative humidity from 40% to 90% R.H. We can observe a strong decrease of RCT with current density from 5.45 Ω cm2 (at 8 mA cm 2/70% R.H.) to 37 mΩ cm2 (at 1 A cm 2/70% R.H.). This is in good agreement with literature, as the ORR is known to be the dominating loss process at low current densities [37–39]. Moreover, we can observe only some small changes of RCT with relative humidity. In contrast to that, R0 and RCCL ion are strongly influenced by relative humidity. R0 changes from 160 mΩ cm2 (at 1 A cm 2/40% R.H.) to 71 mΩ cm2 (at 1 A cm 2/90% R.H.), whereas RCCL ion shows an even more pronounced decrease from 222 mΩ cm2 (at 1 A cm 2/40% R.H.) to 40 mΩ cm2 (at 1 A cm 2/90% R.H.). This is also quite plausible, since increased humidity leads to an improved conductivity of both the membrane and the ionomer in the catalyst layer. The differently pro nounced dependency on relative humidity (of R0 and RCCL ion ) indicates the use of different ionomer materials in membrane and catalyst layer (discussed in section 4.3 in more detail). In addition, RCCL ion shows a small decrease with current density (at low relative humidity), whereas R0 is almost independent from current density. This is related to an increased ionic conductivity in the catalyst layer at higher current densities, which can be explained by the water that forms at the cathode side. RW , reflecting the gas diffusion losses, remains at low values (<20 mΩ cm2 at 1 A cm 2) due to operation with oxygen instead of air, in this case. Furthermore, the feature is only identifiable for higher currents (j > 0.6 A cm 2): accordingly, the RW has been set to zero for lower currents during the fitting process. Fig. 5b shows the obtained ASR values as a function of current density (from 8 mA cm 2 to 1 A cm 2) and oxygen partial pressure (from 0.14 atm (air) to 0.67 atm (oxygen)). RCT here again shows a strong 6
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d is the thickness of membrane, which was determined to be ~24 μm. The term A reflects the geometric area, and in our case is 1 cm2 RPEM ion represents the membrane resistance and can be calculated as follows: RPEM ion ¼ R0
Rel
(11)
The ohmic resistance, R0 , is given by the CNLS-fit and the summa rized electrical transport losses, Rel , which were determined to 17.6 mΩ cm2 in our former study [12]. The ionic conductivities of membrane and catalyst layer (of the investigated H500EL2) are depicted in Fig. 7a as a function of relative humidity (yellow and orange triangles). The data points are fitted to a semi-empirical power law ansatz. The conductivities of the membrane and catalyst layer show (as already discussed in 4.2) a differently pronounced relative humidity dependence (c.f. slopes 1.56 and 2.90 in Fig. 7a). We assume that the ionomer materials used in membrane and catalyst layer have different properties. Ionomers with lower equivalent weights are usually used in the electrodes to increase the conductivity of the catalyst layers. As the used materials are unknown, we compared them to a well-known Nafion® ionomer material. For example, Nafion® 117 has been widely investigated in literature [40]. In addition, we conducted some independent measurements on a Nafion® 112 membrane and revealed the membrane resistance via EIS measurements. Fig. 7a illustrates that both the literature results (Nafion® 117) and our own measurements (Nafion® 112) show the same specific conductivity. Furthermore, we can observe that the membrane conductivity of the investigated H500EL2 is below the conductivity of Nafion® 112/117, especially for high relative humidities. The lower conductivity might be related to a reinforcement in the membrane. This behavior is discussed in Ref. [41] for Gore-Select® membranes. Beyond that, the slopes in the double-logarithmic plot of the Nafion® 112/117 conductivity and the calculated ionic conductivity of the catalyst layer are comparable (c.f. slopes 2.58/2.59 to 2.90 in Fig. 7a). This suggests that the utilized ionomer in the catalyst layer shows, at least, the same behavior and dependence to humidity as the Nafion® 112/117. We can thereby calculate the structural parameter ψ Ionomer of the electrode’s ionomer content as follows:
ψ Ionomer ¼
4.3. Determination of material parameters 4.3.1. Ionic conductivity The general performance of the cell highly depends on its structural and material properties. This is particularly true of the electrode. As discussed in 4.1, the TLM approach enables us to reveal physical pa rameters which directly represent the structure and materials of the catalyst layer. The ionic conductivity within the catalyst layer, σCCL ion , can be calculated by using Eq. (7). For a comparison, the membrane con ductivity is given by: d RPEM ion ⋅A
(12)
Moreover, we studied the effect of conductivity change during operation with high current densities (Fig. 7b). In the case of high hu midification (90% R.H.) neither membrane nor catalyst layer conduc tivity do change with current increase. This can be explained by an almost completely saturated membrane and/or ionomer. However, in the case of low relative humidity (40% R.H.), the conductivity remains constant for low current densities (j < 100 mA cm 2), but then increases if higher current densities are applied to the cell. Due to the increased water production, the humidity in the membrane and catalyst layer in creases. The effect is even more pronounced for the catalyst layer, so we can assume an accumulation of water in this region. If we compare the values at 1 A cm 2 with a low current condition, the humidity within the catalyst layer corresponds to a value of about 50% R.H. (with 40% R.H. of applied gases).
Fig. 5. Area specific values of (i) charge transfer resistance, RCT , (ii) gas diffusion resistance, RW , (iii) ohmic resistance, R0 , and (iv) ionic transport resistance in the catalyst layer, RCCL ion ; all obtained from the CNLS-fit procedure using ECM (TLM): (a) ASR values as a function of current density (8 mA cm 2 to 1 A cm 2) and relative humidity (40%–90% R.H., pO2 ¼ 0.55 atm). (b) ASR values as a function of current density (8 mA cm 2 to 1 A cm 2) and oxygen partial pressure (0.14 atm (air) to 0.67 atm (oxygen), 70% R.H.). All measure ments were performed at 80 � C.
σ PEM ion ¼
σ CCL εIonomer ion ¼ ¼ 0:064 σ PEM τIonomer ion
4.3.2. Tafel slope The interactions between the transport process and reaction process in the electrode structure play a major role in the performance and the design of the electrode. In addition to the ionic conductivity of the electrode, the actual charge transfer (related to the oxygen reduction reaction) plays an important role. In general, the Butler-Volmer equa tion can be used to describe the ORR at the Pt catalyst: � � � � �� nF nF j ¼ j0 exp α ηact exp ð1 αÞ ηact (13) RT RT
(10)
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Fig. 6. Area specific values of (i) charge transfer resistance, RCT , (ii) gas diffusion resistance, RW , (iii) ohmic resistance, R0 , and (iv) ionic transport resistance in the 2 � catalyst layer, RCCL ion : (a) As a function of current density (56/146/382/1000 mA cm ) (T ¼ 80 C, 70% R.H., H2/air). (c) As a function of oxygen partial pressure (0.14/0.23/0.40/0.67 atm) (T ¼ 80 � C, 70% R.H., j ¼ 1.0 A cm 2). (e) As a function of relative humidity (40%–90% R.H.) (T ¼ 80 � C, pO2 ¼ 0.55 atm, j ¼ 1.0 A cm 2). Percentage losses for the use of air (b), oxygen (d) and low relative humidity (f).
Here j0 is the exchange current density of the cathode, n the number of exchanged electrons (in our case n ¼ 2), α the charge transfer coeffi cient and ηact the activation overpotential. The differential resistance is given by the derivation of the overvoltage to the current density: Ract ¼
∂ηact ∂j
The exchange current density, j0 , for the oxygen reduction reaction in PEM fuel cells is usually very small (in the range of 1 mA cm 2) [22, 43]. We can therefore use the simplified Tafel equation under our con ditions (j ¼ 8 mA cm 2 … 1.0 A cm 2). The resistance of the activation polarization can then be easily derived, as follows:
(14)
Ract ¼
However, a problem arises; Eq. (13) cannot be solved for ηact. There are two simplifications given in literature for the Butler-Volmer equation [42]:
(15)
(ii) and the well-known Tafel equation for j/j0 > 4: � � nF j ¼ j0 ⋅exp α ηact RT
(16)
(17)
where the pre-factor is often summarized in the Tafel slope b: 1 RT b¼ ⋅ α nF
(i) A linear approximation, valid for j/j0 < 2: nF j ¼ j0 ⋅ ηact RT
∂ηact 1 RT 1 ¼ ⋅ ⋅ ∂j α nF j
(18)
The Tafel slope is a value widely given in literature to describe the reaction processes at the Pt catalyst. Wang et al. report values varying from α ¼ 1 at low current densities to α ¼ 0.5 at high current densities, which the authors correlate to the potential-dependent adsorption of oxygen-containing species [44]. However, Neyerlin et al. pointed out that a single Tafel slope is able to accurately describe the ORR kinetics in PEM fuel cells [43], if mass transport losses at high current densities are considered. This has been shown by means of polarization curve fits. 8
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Fig. 7. Ionic conductivity of membrane (H500EL2, Nafion 112, Nafion 117) and catalyst layer (H500EL2) at T ¼ 80 � C: (a) As a function of relative humidity (j ¼ 56 mA cm 2). (b) As a function of current density (40% R.H. and 90% R.H).
From our point of view, Neyerlin’s findings are also reflected in the impedance representation. If we consider the total electrode resistance RTLM (including charge transfer kinetics and ionic transport losses in the ionomer) to be described with one Tafel slope, we then see that this does not work (Fig. 8a, squares). Now, from an accurate TLM approach we are able to clearly distinguish between the sole charge transfer resistance, RCT, and the transport losses, and we are able to describe the charge transfer resistance, RCT, within the whole current regime with only one Tafel slope (Fig. 8a, circles). In addition, we found a small dependency of Tafel slopes to relative humidity (Fig. 8b and c). Our approach shows Tafel slopes from ~110 mV⋅dec 1 (40% R.H.) to 130 mV⋅dec 1 (90% R.H.).
Fig. 8. Evaluation of Tafel slopes (T ¼ 80 � C): (a) Model fit for two cases ((i) Ract ¼ RTLM; (ii) Ract ¼ RCT; both at 70% R.H.)). (b) Model fit in the low current region. (c) Tafel slope as a function of relative humidity.
were shown to be capable of reproducing the impedance of the PEM cathode. Beyond that, the TLM clearly distinguishes between the loss contribution of the charge transfer reaction at the Pt catalyst and the ionic transport losses within the ionomer of the cathode catalyst layer. We investigated a wide range of operating conditions and calculated the area specific resistance (ASR) values of (i) ohmic losses, (ii) the gas diffusion in the porous media, (iii) the charge transfer kinetics at the Pt catalyst, and (iv) the ionic transport losses in the catalyst layer. As ex pected, charge transfer is the dominant loss mechanism in the low cur rent region (87% at j ¼ 56 mA cm 2, 70% R.H. and H2/air). However, under high electrical load (and with sufficient oxygen supply), the ionic transport losses in the catalyst layer contribute more to the total losses than expected (52% at 1.0 A cm 2, 40% R.H. and H2/O2). Gas diffusion
5. Conclusions In this study, impedance data from a commercial PEMFC single cell were analyzed. A novel approach was presented, where equivalent cir cuit model (ECM) and starting parameters for the complex nonlinear least squares (CNLS) fitting process were obtained by a preidentification of the impedance response by the distribution of relaxa tion times (DRT). An ECM consisting of RQ elements connected in series, as well as the more physically motivated transmission line model (TLM), 9
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losses need only be considered if the oxygen supply is low (pO2 < 0.4 atm and j > 0.6 A cm 2), but can also play a major role (63% at 1.0 A cm 2, 70% R.H. and H2/air). In addition, the ionic conductivity of the catalyst layer and the Tafel slope were derived from the impedance data. Effective ionic conduc tivities from 0.13 S m 1 at 40% R.H. to 1.1 S m 1 at 90% R.H. were found. The dependency on relative humidity is in good agreement with the widely investigated Nafion® 112/117 membranes and thus a structural parameter of the ionomer phase in the electrode could be determined to 0.064. Moreover, the TLM approach reveals the pure charge transfer resistance without any superimposed transport losses. This enables one to derive a single, current-independent Tafel slope, which represents the reaction kinetics of the ORR. We found values ranging from ~110 mV⋅dec 1 (40% R.H.) to 130 mV⋅dec 1 (90% R.H.).
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Ivers-Tiff� ee, A method for improving the robustness of linear Kramers-Kronig validity tests, Electrochim. Acta 131 (2014) 20–27, https:// doi.org/10.1016/j.electacta.2014.01.034. [27] M. Sch€ onleber, Kramers-Kronig Validity Test Lin-KK for Impedance Spectra (n.d.), https://www.iam.kit.edu/wet/english/Lin-KK.php. [28] V. Brichzin, J. Fleig, H. Habermeier, G. Cristiani, J. Maier, The geometry dependence of the polarization resistance of Sr-doped LaMnO3 microelectrodes on yttria-stabilized zirconia, Solid State Ion. 152–153 (2002) 499–507. [29] M. Sch€ onleber, Verfahren zur Charakterisierung des Niederfrequenzverhaltens von Lithium-Ionen-Batterien, Band 32, KIT Scientific Publishing, Karlsruhe, 2017. [30] D. Malevich, E. Halliop, B.A. Peppley, J.G. Pharoah, K. Karan, Investigation of charge-transfer and mass-transport resistances in PEMFCs with microporous layer using electrochemical impedance spectroscopy, J. Electrochem. Soc. 156 (2009) B216–B224, https://doi.org/10.1149/1.3033408. 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Acknowledgements We gratefully acknowledge the Schaeffler Technologies AG & Co. KG for funding. We also thank the Zentrum für Sonnenenergie-und Was serstoff-Forschung Baden Württemberg (ZSW) for the preparation and manufacturing of the MEAs. The authors thank L. J€ orissen from ZSW for many fruitful discussions. Sincere thanks are given to J. Packham for proof-reading the manuscript. References [1] H. Schichlein, A.C. Müller, M. Voigts, A. Krügel, E. Ivers-Tiff�ee, Deconvolution of electrochemical impedance spectra for the identification of electrode reaction mechanisms in solid oxide fuel cells, J. Appl. Electrochem. 32 (2002) 875–882, https://doi.org/10.1023/A:1020599525160. [2] E. Ivers-Tiff�ee, A. Weber, Evaluation of electrochemical impedance spectra by the distribution of relaxation times, J. Ceram. Soc. Jpn. 125 (2017) 193–201, https:// doi.org/10.2109/jcersj2.16267. [3] D. Malevich, J.G. Pharoah, B.A. Peppley, K. Karan, On the determination of PEM fuel cell catalyst layer resistance from impedance measurement in H2/N2 cells, in: ECS Trans, 2011, pp. 721–732. [4] J.H. Jang, S. Jeon, J.H. Cho, S. Kim, S. Lee, E. Cho, H. Kim, J. Han, T. Lim, Complex capacitance analysis of ionic resistance and interfacial capacitance in PEMFC and DMFC catalyst layers, J. Electrochem. Soc. 156 (2009) 1293–1300, https://doi. org/10.1149/1.3187928. [5] Y. Liu, M.W. Murphy, D.R. Baker, W. Gu, C. Ji, J. Jorne, H.A. Gasteiger, Proton conduction and oxygen reduction kinetics in PEM fuel cell Cathodes : effects of ionomer-to-carbon ratio and relative humidity, J. Electrochem. Soc. 156 (2009) B970–B980, https://doi.org/10.1149/1.3143965. [6] S.M. Rezaei Niya, M. Hoorfar, Study of proton exchange membrane fuel cells using electrochemical impedance spectroscopy technique - a review, J. Power Sources 240 (2013) 281–293, https://doi.org/10.1016/j.jpowsour.2013.04.011. [7] M. Cimenti, D. Bessarabov, M. Tam, J. Stumper, Investigation of proton transport in the catalyst layer of PEM fuel cells by electrochemical impedance spectroscopy, in: ECS Trans, 2010, pp. 147–157. [8] D. Klotz, J.P. Schmidt, A. Kromp, A. Weber, E. Ivers-Tiff�ee, The distribution of relaxation times as beneficial tool for equivalent circuit modeling of fuel cells and batteries, in: ECS Trans, 2012, pp. 25–33. [9] A. Leonide, V. Sonn, A. Weber, E. Ivers-Tiff� ee, Evaluation and modeling of the cell resistance in anode-supported solid oxide fuel cells, J. Electrochem. Soc. 155 (2008) B36–B41, https://doi.org/10.1149/1.2801372. [10] J. Illig, M. Ender, T. Chrobak, J.P. Schmidt, D. Klotz, E. Ivers-Tiffee, Separation of charge transfer and contact resistance in LiFePO4-cathodes by impedance modeling, J. Electrochem. Soc. 159 (2012) A952–A960, https://doi.org/10.1149/ 2.030207jes. [11] J.P. Schmidt, T. Chrobak, M. Ender, J. Illig, D. Klotz, E. Ivers-Tiff�ee, Studies on LiFePO4 as cathode material using impedance spectroscopy, J. Power Sources 196 (2011) 5342–5348, https://doi.org/10.1016/j.jpowsour.2010.09.121. [12] M. Heinzmann, A. Weber, E. Ivers-Tiff�ee, Advanced impedance study of polymer electrolyte membrane single cells by means of distribution of relaxation times, J. Power Sources 402 (2018), https://doi.org/10.1016/j.jpowsour.2018.09.004. [13] J. Bisquert, Influence of the boundaries in the impedance of porous film electrodes, Phys. Chem. Chem. Phys. 2 (2000) 4185–4192. [14] J. Euler, W. Nonnenmacher, Stromverteilung in por€ osen elektroden, Electrochim. Acta 2 (1960) 268–286. [15] S. Dierickx, J. Joos, A. Weber, E. Ivers-Tiff� ee, Advanced impedance modelling of Ni/8YSZ cermet anodes, Electrochim. Acta 265 (2018) 736–750, https://doi.org/ 10.1016/j.electacta.2017.12.029. [16] S. Dierickx, T. Mundloch, A. Weber, E. Ivers-Tiff� ee, Advanced impedance model for double-layered solid oxide fuel cell cermet anodes, J. Power Sources 415 (2019) 69–82, https://doi.org/10.1016/j.jpowsour.2019.01.043.
10
Contents lists available at ScienceDirect
Journal of Power Sources journal homepage: www.elsevier.com/locate/jpowsour
Impedance modelling of porous electrode structures in polymer electrolyte membrane fuel cells Marcel Heinzmann *, Andr�e Weber, Ellen Ivers-Tiff�ee Institute for Applied Materials (IAM-WET), Karlsruhe Institute of Technology (KIT), Adenauerring 20b, 76131, Karlsruhe, Germany
H I G H L I G H T S
� Identification of loss processes by the distribution of relaxation times. � Application of physically meaningful transmission line model. � Quantification of polarization contributions at various operating conditions. � Derivation of electrode material properties. A R T I C L E I N F O
A B S T R A C T
Keywords: Polymer electrolyte membrane fuel cell Electrochemical impedance spectroscopy Distribution of relaxation times Equivalent circuit model Transmission line model Ionic conductivity
Electrochemical Impedance Spectroscopy (EIS) is a suitable tool for identifying the performance-related polar ization processes in a polymer electrolyte membrane fuel cell. A physically meaningful impedance model is needed when drawing conclusions about further cell improvement. This study focuses on the characterization of the porous electrode structure by applying a transmission line model (TLM) to the measured spectra. The fitting procedure is supported by the distribution of relaxation times (DRT) method enabling a separation of loss processes by their individual time constants. We are able to separate and quantify (i) the gas diffusion in the porous media (2–10 Hz), (ii) the charge transfer resistance at the Pt catalyst (2–200 Hz), and (iii) the ionic transport resistance in the catalyst layer (300–30,000 Hz), across a broad range of operating conditions (current density, relative humidity, gas compositions). The TLM approach directly reveals the electrodes’ transport and reaction properties, e.g. ionic conductivity and the Tafel slope. Under high electrical load the ionic transport losses in the catalyst layer contribute more to polarization than expected. Interestingly, the oxygen reduction reaction is found to be describable with a single, current-independent Tafel slope.
1. Introduction For the development of physicochemically meaningful models of fuel cells and batteries the individual loss mechanisms that occur during operation and that limit cell performance and efficiency have to be identified and quantified. Electrochemical impedance spectroscopy (EIS) in combination with the distribution of relaxation times (DRT) is a powerful approach to unfold complex electrochemical systems [1,2]. Commonly impedance spectra are evaluated by a complex nonlinear least squares fit (CNLS) to a model function given by an equivalent circuit model (ECM) [3–7]. As number, size and time constants of the polarization processes are often not known in advance, the assessment of a meaningful ECM remains challenging. To overcome this issue, we use a different approach based on a pre-identification of the electrochemical
processes by the distribution of relaxation times (DRT) and the subse quent application of the DRT in the CNLS-fit [8]. This approach was successfully applied to solid oxide fuel cells [9] and lithium-ion batteries [10,11], enabling the deconvolution and quantification of the different loss mechanisms in the cells. The first application of the DRT approach to PEM fuel cells is discussed in a previous study [12]. We carefully evaluated the impedance spectra of a PEM single cell at clearly defined operating points. This enables us to separate five different polarization contributions (with individual relaxation frequencies from 2 Hz to 30 kHz). Furthermore, we assigned the individual processes to their respective physical origins by a systematic variation of operating parameters. An even more detailed description of the electrodes considering material and microstructural parameters is possible by models
* Corresponding author. E-mail address: [email protected] (M. Heinzmann). https://doi.org/10.1016/j.jpowsour.2019.227279 Received 18 July 2019; Received in revised form 5 September 2019; Accepted 7 October 2019 Available online 22 October 2019 0378-7753/© 2019 Elsevier B.V. All rights reserved.
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considering ionic, electronic and species transport and its coupling by the electrochemical reactions in porous multiphase electrodes. To cover the details in such electrodes in an ECM, the application of appropriate transmission line models (TLM) is envisaged [13,14]. The combination of EIS and DRT is a powerful tool to resolve and parameterize TLMs even for full cells and their electrodes as shown for SOFC in Refs. [15–17] and for lithium-ion batteries in Ref. [18]. In this contribution we will present and compare several models in terms of fit quality and physical inter pretation for PEM fuel cells. We will show that the often preferred, simple Randles circuit [19–23] is not able to describe the complex impedance of a porous electrode structure. Beyond that, the TLM en ables us to extract physical parameters of the transport (ionic conduc tivity) and the reaction processes (Tafel slope) across a wide range of operating conditions.
air). A detailed view is given by the DRT analysis (Fig. 1b,d): DRT calculation enables the deconvolution of five clearly separable peaks (P1 – P5) with different characteristic frequencies from 2 Hz to 30 kHz. The area specific resistance (ASR) of each process is shown by the area under the peak. In our previous work we assigned the individual processes to their respective physical origins by a systematic and targeted variation of operating parameters [12] (Table 1). In the full cell spectrum we can clearly distinguish between (i) gas diffusion in the porous structure of gas diffusion layer and catalyst layer at the cathode (P1: 2–10 Hz), (ii) the oxygen reduction reaction at the Pt catalyst (P2: 2–200 Hz) and (iii) the proton transport in the cathode catalyst layer (P3 – P5: 300 Hz–30 kHz). It should be noted that P2 might be superimposed by a side peak of P1 and therefore be affected for low oxygen partial pres sures (see Table 1). Fig. 5 shows that the charge transfer resistance associated with P2 does not depend on the oxygen partial pressure. In addition, we have shown that the anode processes, superimposed by the dominating cathode processes in the same frequency range, are negligibly low (less than 4% of the total polarization) when operated with hydrogen. For that reason, the present work solely focuses on the cathode processes.
2. Experimental 2.1. Single cell tests and impedance analysis The analyzed PEM fuel cells are commercial MEAs of type Green erity® H500EL2 with platinum loadings of 0.4 mgPtcm 2 (cathode) and 0.2 mgPtcm 2 (anode). Single cells with an active surface area of 1 cm2 were sandwiched between gas diffusion layers (GDL 29 BC from SGL®) and placed into an in-house developed fuel cell housing. The active electrode area contacting is realized by gold flow fields with parallel flow channels (cross-section: 1 mm � 1 mm). The housing is compressed by stainless steel heat exchanger plates containing a thermal fluid. The cell temperature is controlled by a Julabo F32-ME thermostat. The GDL contact pressure is independent from the sealing pressure, and contin uously adjustable from 0 to 200 N. The gas is supplied by mass flow controllers, supplying a well-defined mixture of oxygen, nitrogen and hydrogen to cathode and anode. The humidities in the oxidant and fuel are generated in catalytic burner chambers ahead of the cell by reacting hydrogen and oxygen [24]. Our setup ensures clearly defined operating conditions with low lateral gradients; it thus enables us to derive un ambiguous parameter dependencies. More details about the cell setup and testing conditions are given in our previous work [12]. Impedance spectra were recorded across a wide range of operating conditions (variation of current density, relative humidity and gas compositions) using a Zahner® Zennium E potentiostat [12]. Steady-state conditions during impedance measurements were assured by a waiting time of 60 min before each measurement. Linearity was assured by choosing a perturbation amplitude of 12 mV within a fre quency range from 1 MHz down to 50 mHz (pseudo-galvanostatic mode). A Kramers-Kronig Test was applied to the data to ensure the validity of the measured spectra [25–27]. It revealed errors below 0.2% within the evaluated frequency range. For data analysis, we computed the distribution of relaxation times (DRT) to identify the loss processes and their relaxation frequencies [1,12]. Subsequently, the impedance spectra were fitted to the equivalent circuit models (ECM; described below). Both the DRT calculation and the CNLS-fit were performed in MathWorks Matlab™. The CNLS approximation is evaluated by the relative fitting error for the real (Z0 ) and imaginary (Z00 ) parts for all analyzed frequencies: ΔZ’ðωÞ ¼
Z ’fit ðωÞ Z ’meas ðωÞ Z ’meas ðωÞ
(1)
ΔZ } ðωÞ ¼
Z "fit ðωÞ Z "meas ðωÞ Z "meas ðωÞ
(2)
3. Modelling 3.1. Equivalent circuit modelling The intention is to set up a physically motivated equivalent circuit model (ECM), which is able to describe the impedance response of the cell or of an individual electrode, thus enabling quantification of the individual loss processes. The most common equivalent circuit is the Randles circuit [23], which has been widely applied in literature [19–22]. This circuit con sists of an electrolyte resistance, R0 , in series with the parallel combi nation of the double-layer capacitance, Cdl , and an impedance of faradaic reaction. The double-layer capacitance is often replaced by a constant phase element (CPE), originating from a non-uniform current distribution along the electrode surface. For PEM fuel cells the imped ance of the faradaic reaction consists of a charge transfer resistance, RCT , and a Warburg element, describing diffusion-related processes. The impedance expression for the generalized, finite length Warburg element (GFLW) is given by Ref. [28]: tanh½ðjωTW Þp � ZW ðωÞ ¼ RW ⋅ ðjωTW Þp
(3)
For a perfect one-dimensional diffusion limitation the p is equal to 0.5. Here RW denotes the diffusion resistance and TW the time constant. For simplification, the Warburg element is often connected in series to the parallel combination of the charge transfer resistance and the double-layer capacitance. This is valid if the time constant of the diffusion processes is significantly larger than those of the charge transfer reaction [29]. In the following, this circuit will be referred to as ECM (1RQ). However, for the porous electrode structures typically found in real cells, the impedance spectra are usually more complicated. As such, the Randles circuit may not provide appropriate fitting results [6]. An ac curate analysis of the impedance spectra (with the help of the DRT method) leads to the same conclusion: Fig. 1b shows the identification of various polarization contributions with individual time constants (P1 – P5), just barely describable with the Randles circuit. For that reason, one possibility is to add one [30] or more [31,32] RQ elements to the circuit. We propose using an extended impedance model with three RQ elements instead of one, from here on referred to as ECM (3RQ). This is a convenient way of modelling the impedance with its numerous polari zation contributions, although physical correlation is reduced. The in dividual elements may not represent individual and independent physical mechanisms.
2.2. Impedance analysis and process assignment Fig. 1a,c give an example of typical PEMFC impedance spectra as a function of current density (cell operated at T ¼ 80 � C, 70% R.H.: H2/ 2
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Fig. 1. Impedance spectra (a,c) and calculated DRTs (b,d) as a function of current density and with separation of individual polarization contributions (T ¼ 80 � C, 70% R.H., and H2/air).
under low humidity are challenging and often cannot be adequately described [6,7]. This then often leads to unclear or ambivalent fitting results and makes it difficult to evaluate the obtained parameter. One possibility for reducing degrees of freedom is the analysis of the elec trode microstructure and to keep the corresponding parameters fixed during the fitting process. Because it is extremely difficult to find the microstructural parameters for the obtained commercial cell in litera ture, we followed a different approach by using the DRT analysis to evaluate the fit result. This allowed us to control the fitting process without further model assumptions or simplifications. The impedance of a porous electrode (thickness L, c.f. Fig. 2) can be described by the following equation [13]: � � � � χχ 2κ χ 2 þ χ 22 L þκ⋅ 1 (4) ⋅coth ZTLM ðωÞ ¼ 1 2 ⋅ L þ sinhðL=κÞ κ χ1 þ χ2 χ1 þ χ2
Table 1 Process assignment of identified polarization contributions to the underlying physical mechanisms. Process
Dependencies
Relaxation frequency
Physical origin
P1
j, pO2,cat, R.H.
2–10 Hz
P2
j, pO2,cat (strong), R.H. (low) R.H.
2–200 Hz
gas diffusion of oxygen in GDL and CCL charge transfer kinetics at the cathode (ORR) proton conduction in the ionomer of the cathode catalyst layer (subordinate anode processes)
P3 – P5
300 Hz–30 kHz
3.2. TLM approach for PEMFC cathodes
The value κ is the ratio between the resistances of the charge transfer reaction at the Pt catalyst and the sum of the resistances for the ionic and electronic paths: sffiffiffiffiffiffiffiffiffiffiffiffiffiffi ζ κ¼ (5) χ1 þ χ2
There have been some analytical literature studies on the influence of the electrode structure on the impedance behavior using a TLM. For example, Eikerling et al. [33] investigated the effects of the layer thickness and Reshetenko et al. [34] investigated the influence of a non-uniform Nafion loading. However, application of a TLM to the measured impedance spectra remains challenging. Therefore, TLMs are often applied in H2/N2 mode in order to determine the ionic transport resistance in equilibrium state [3–5]. However, during a transfer to operation under load the consideration of water management and the humidity change remain difficult. Investigations in H2/O2 operation and
The circuit elements χ1 and χ2 describe the ionic and electronic re sistances (Ω⋅m 1) and ζ describes the charge transfer resistance between both paths (Ω⋅m). Due to the high conductivity of carbon, the losses of the electronic path can be neglected (χ2 � 0) [3], which in turn allows a simplified expression for the overall impedance of the cathode catalyst 3
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layer (CCL): � � L ZTLM ðωÞ ¼ κ ⋅ χ 1 ⋅coth κ
(6)
The layer thickness of the CCL was determined to 13 μm and was fixed during the fitting process. Fig. 2d and e shows simulated spectra and the related DRTs of the TLM impedance function (Eq. (6)) at various ionic resistances (χ 1 ¼ rion ) from 5000 Ωm 1 to 15,000 Ωm 1. These values are quite plausible, as the mean value (10,000 Ωm 1) refers to a fit from real measurement (T ¼ 80 � C, 70% R.H.). It can be seen, that the DRT calculation of the TLM impedance shows several peaks: One main peak at lower fre quencies (50 Hz) representing the charge transfer reaction at the Ptcatalyst and additional side peaks at higher frequencies (500–30,000 Hz) related to the proton transport in the ionomer. This behavior can be explained by the impedance shape of the TLM: Starting from high frequencies, a 45� branch emerges which turns into a semi circle (Fig. 2d). The DRT calculation now attempts to simulate the impedance shape with help of a certain number of RC elements (which in turn show up as an ideal semicircle) (Fig. 2e). It is easy to understand that a 45� branch cannot be represented by a single semicircle, but rather by a combination of several semicircles of different sizes. In addition to that, it can be seen that the side peaks are affected by the ionic resistance. A quite similar behavior is visible in Fig. 4 showing a humidity variation that has a strong impact on the conductivity of the ionomer. Thus the side peaks at 200–30,000 Hz are strongly affected. 4. Results and discussion 4.1. Comparison of different ECMs Fig. 3 shows a comparison of all three applied models (ECM (1RQ), ECM (3RQ), and ECM (TLM)). The upper row displays the measured impedance spectra (black circles) at 80 � C, 70% R.H., 382 mA cm 2 and H2/air operation. The orange line represents the CNLS-fit to the respective model and shows good agreement with the measured impedance for all three models. A detailed view of the fit quality is given by the calculated model residuals (Fig. 3, middle row). The best agree ment between applied model and measured impedance is given by ECM (3RQ), which is due to the higher number of independent elements. ECM (1RQ) and ECM (TLM) show almost equal residuals. Now, considering the DRT analysis of the spectra as well as the partial DRTs of the fitted elements (Fig. 3, bottom row), clear differences are observable. ECM (1RQ) cannot reproduce the polarization contri butions as seen in the DRT, even though the impedance shape is reproduced very well. Processes P1 and P2 (with their characteristic frequencies of ~10 Hz and ~50 Hz, respectively) cannot be replicated by the model. Instead, the model only creates one process with a fre quency of about 25 Hz. In addition, there is a clear overestimation of the gas diffusion resistance, represented by the GFLW element. However, ECM (3RQ) and ECM (TLM) show better accordance of identified processes with simulated partial DRTs considering the relax ation frequencies. They are therefore better suited for an accurate description of the underlying processes. Both models are able to rebuild all identified processes and to properly hit their characteristic frequencies. In order to identify the advantages, differences and disadvantages of ECM (3RQ) and ECM (TLM), we applied a set of impedance spectra with varied relative humidity. Fig. 4a,c shows the impedance spectra and calculated DRTs for relative humidities from 40% to 90% R.H. (T ¼ 80 � C, j ¼ 146 mA cm 2, H2/O2). It becomes obvious that the change in humidity affects the secondary peaks, PCCL ion , at medium and high frequencies (50 Hz–50 kHz), which had previously been assigned to the proton transport in the CCL [12], whereas the main peak PCT (charge
Fig. 2. Electrode structure of a catalyst layer (cathode) with reaction mecha nisms and transport paths (a), transmission line model (b) and equivalent cir cuit elements (c). Simulated impedance spectra (d) and DRTs (e) of the TLM impedance at various ionic resistances.
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Fig. 3. Measured and simulated impedance spectra, relative error for real and imaginary parts and DRT of measured and simulated spectra for: (a) The established ECM with one RQ element fitted to the measured spectra. (b) An extended model approach with three RQ elements. (c) A TLM model approach with consideration of transport paths within a porous electrode structure. The shown spectra are recorded at T ¼ 80 � C, 70% R.H. and j ¼ 382 mA cm 2 (H2/air).
transfer) at ~25 Hz is hardly affected. The low frequency feature (gas diffusion) at ~10 Hz is not observable in this investigation due to operation with oxygen instead of air and therefore improved oxidant supply to the electrode. Fig. 4b shows the obtained model parameters by a fit of ECM (3RQ) to the impedance data. In this case, RRQ;1 describes the main peak (charge transfer) at ~25 Hz while RRQ;2 and RRQ;3 describe the secondary peaks (proton transport in the CCL) at higher frequencies. It becomes evident that it is challenging to create stable and reproducible fitting results. A clear assignment of the individual ele ments to the associated processes is difficult, and therefore the resistance values and time constants fluctuate. This prevents a further meaningful physical interpretation of the results. The TLM approach delivers (i) the specific charge transfer resistance, rCT ; and (ii) the specific ionic transport resistance, rCCL ion ¼ χ 1 , in the CCL. In addition, the effective ionic conductivity of the ionomer within the catalyst layer, σ CCL ion , can be calculated as follows:
σ CCL ion ¼
L 1 ¼ R⋅A rCCL ion ⋅A
allows the establishment of a clear physical relationship between the obtained model parameters and the investigated processes. Conse quently, the further quantification of the loss processes is therefore based on the application of ECM (TLM). Furthermore, the CNLS-fit procedure benefits from the DRT approach, as the DRT extracts the relaxation frequencies for each process, and thus delivers useful starting parameters. 4.2. Quantification of loss processes To quantify the individual loss processes and their resistance con tributions, the chosen ECM (TLM) was applied to an extensive set of measured spectra across a wide range of operating conditions. We were thereby able to determine the area specific values of: - (i) the charge transfer resistance, RCT , of the oxygen reduction reaction:
(7)
RCT ¼
Now, regarding the results of the TLM fit (Fig. 4d), the obtained parameters are much more stable and reasonable. The specific charge transfer resistance, rCT , shows almost no dependency on humidity, which also reflects the observations of the DRT results. In addition, the ionic conductivity, σ CCL ion , shows a strong increase with increasing hu midity (0.13 S m 1 at 40% R.H. to 1.1 S m 1 at 90% R.H.), which in turn is consistent with literature data [5,7]. A comparison of the ionic con ductivity in the CCL to the membrane conductivity and a classification to other materials is given in section 4.3. These results impressively show that the use of a TLM approach
rCT ⋅A L
(8)
- (ii) the Warburg resistance, RW , representing the gas diffusion losses in the porous media of gas diffusion layer and catalyst layer. - (iii) the ohmic resistance, R0 , which summarizes the membrane resistance and the electrical transport contributions in all cell components. - (iv) the ionic transport resistance, RCCL ion , in the cathode catalyst layer [3,35,36]:
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Fig. 4. Impedance spectra (a) and calculated DRTs (c) for a variation of relative humidity (from 40% R.H. to 90% R.H. at j ¼ 146 mA cm 2). (b) Obtained model parameters for application of ECM (3RQ). (d) Area specific charge transfer resistance and ionic conductivity determined by application of ECM (TLM).
1 CCL RCCL ion � ⋅r ion ⋅L⋅A 3
decrease with current density from 5.42 Ω cm2 (at 8 mA cm 2/0.14 atm) to 71 mΩ cm2 (at 1 A cm 2/0.14 atm), but almost no dependence to oxygen partial pressure. R0 and RCCL ion are almost independent from current density and oxygen partial pressure, as expected. RW is strongly influenced by current den sity and oxygen partial pressure and accounts for the largest share, at 1 A cm 2/0.14 atm (0.4 Ω cm2). Low oxygen partial pressure and/or high current densities are known to cause major diffusional losses [21]. In the following, some example operating conditions are chosen to further clarify the dependencies of the calculated ASR to the operating parameters and to display the individual contributions to the overall resistance. Fig. 6 gives an example of dependence on (a) current density, (c) oxygen partial pressure and (e) relative humidity. In addition to that, the individual contributions to the overall resistance are given in Fig. 6b, d,f. Fig. 6b shows that under typical operating conditions (T ¼ 80 � C, 70% R.H., H2/air and 1.0 A cm 2) the gas diffusion losses, RW , are the dominating loss process and that they contribute 63% to the overall resistance, followed by ohmic losses, R0 (17%), charge transfer losses, RCT , (11%) and ionic transport losses in the CCL, RCCL ion (9%). Now, when using oxygen instead of air (Fig. 6d), the diffusion losses, RW , become negligibly low (4%). Ohmic losses, R0 , become dominant (43%), fol lowed by charge transfer losses, RCT , (27%) and ionic transport losses in the CCL, RCCL ion (26%). In order to show the influence of reduced hu midification, Fig. 6f gives an example of the loss composition at 40% R. H. (T ¼ 80 � C, pO2 ¼ 0.55 atm and 1.0 A cm 2). Ionic transport losses in the CCL, RCCL ion , account for slightly more than half (52%), followed by the ohmic losses, R0 (37%). In total, approximately 90% of the total losses consist of ionic transport losses (in the membrane and CCL). This illus trates the importance of adequate humidification. Charge transfer los ses, RCT , (9%) and gas diffusion losses, RW , (8%) remain at low values in this case.
(9)
Fig. 5a shows the obtained ASR values as derived from the CNLS-fit for the current density range from 8 mA cm 2 to 1 A cm 2 and relative humidity from 40% to 90% R.H. We can observe a strong decrease of RCT with current density from 5.45 Ω cm2 (at 8 mA cm 2/70% R.H.) to 37 mΩ cm2 (at 1 A cm 2/70% R.H.). This is in good agreement with literature, as the ORR is known to be the dominating loss process at low current densities [37–39]. Moreover, we can observe only some small changes of RCT with relative humidity. In contrast to that, R0 and RCCL ion are strongly influenced by relative humidity. R0 changes from 160 mΩ cm2 (at 1 A cm 2/40% R.H.) to 71 mΩ cm2 (at 1 A cm 2/90% R.H.), whereas RCCL ion shows an even more pronounced decrease from 222 mΩ cm2 (at 1 A cm 2/40% R.H.) to 40 mΩ cm2 (at 1 A cm 2/90% R.H.). This is also quite plausible, since increased humidity leads to an improved conductivity of both the membrane and the ionomer in the catalyst layer. The differently pro nounced dependency on relative humidity (of R0 and RCCL ion ) indicates the use of different ionomer materials in membrane and catalyst layer (discussed in section 4.3 in more detail). In addition, RCCL ion shows a small decrease with current density (at low relative humidity), whereas R0 is almost independent from current density. This is related to an increased ionic conductivity in the catalyst layer at higher current densities, which can be explained by the water that forms at the cathode side. RW , reflecting the gas diffusion losses, remains at low values (<20 mΩ cm2 at 1 A cm 2) due to operation with oxygen instead of air, in this case. Furthermore, the feature is only identifiable for higher currents (j > 0.6 A cm 2): accordingly, the RW has been set to zero for lower currents during the fitting process. Fig. 5b shows the obtained ASR values as a function of current density (from 8 mA cm 2 to 1 A cm 2) and oxygen partial pressure (from 0.14 atm (air) to 0.67 atm (oxygen)). RCT here again shows a strong 6
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d is the thickness of membrane, which was determined to be ~24 μm. The term A reflects the geometric area, and in our case is 1 cm2 RPEM ion represents the membrane resistance and can be calculated as follows: RPEM ion ¼ R0
Rel
(11)
The ohmic resistance, R0 , is given by the CNLS-fit and the summa rized electrical transport losses, Rel , which were determined to 17.6 mΩ cm2 in our former study [12]. The ionic conductivities of membrane and catalyst layer (of the investigated H500EL2) are depicted in Fig. 7a as a function of relative humidity (yellow and orange triangles). The data points are fitted to a semi-empirical power law ansatz. The conductivities of the membrane and catalyst layer show (as already discussed in 4.2) a differently pronounced relative humidity dependence (c.f. slopes 1.56 and 2.90 in Fig. 7a). We assume that the ionomer materials used in membrane and catalyst layer have different properties. Ionomers with lower equivalent weights are usually used in the electrodes to increase the conductivity of the catalyst layers. As the used materials are unknown, we compared them to a well-known Nafion® ionomer material. For example, Nafion® 117 has been widely investigated in literature [40]. In addition, we conducted some independent measurements on a Nafion® 112 membrane and revealed the membrane resistance via EIS measurements. Fig. 7a illustrates that both the literature results (Nafion® 117) and our own measurements (Nafion® 112) show the same specific conductivity. Furthermore, we can observe that the membrane conductivity of the investigated H500EL2 is below the conductivity of Nafion® 112/117, especially for high relative humidities. The lower conductivity might be related to a reinforcement in the membrane. This behavior is discussed in Ref. [41] for Gore-Select® membranes. Beyond that, the slopes in the double-logarithmic plot of the Nafion® 112/117 conductivity and the calculated ionic conductivity of the catalyst layer are comparable (c.f. slopes 2.58/2.59 to 2.90 in Fig. 7a). This suggests that the utilized ionomer in the catalyst layer shows, at least, the same behavior and dependence to humidity as the Nafion® 112/117. We can thereby calculate the structural parameter ψ Ionomer of the electrode’s ionomer content as follows:
ψ Ionomer ¼
4.3. Determination of material parameters 4.3.1. Ionic conductivity The general performance of the cell highly depends on its structural and material properties. This is particularly true of the electrode. As discussed in 4.1, the TLM approach enables us to reveal physical pa rameters which directly represent the structure and materials of the catalyst layer. The ionic conductivity within the catalyst layer, σCCL ion , can be calculated by using Eq. (7). For a comparison, the membrane con ductivity is given by: d RPEM ion ⋅A
(12)
Moreover, we studied the effect of conductivity change during operation with high current densities (Fig. 7b). In the case of high hu midification (90% R.H.) neither membrane nor catalyst layer conduc tivity do change with current increase. This can be explained by an almost completely saturated membrane and/or ionomer. However, in the case of low relative humidity (40% R.H.), the conductivity remains constant for low current densities (j < 100 mA cm 2), but then increases if higher current densities are applied to the cell. Due to the increased water production, the humidity in the membrane and catalyst layer in creases. The effect is even more pronounced for the catalyst layer, so we can assume an accumulation of water in this region. If we compare the values at 1 A cm 2 with a low current condition, the humidity within the catalyst layer corresponds to a value of about 50% R.H. (with 40% R.H. of applied gases).
Fig. 5. Area specific values of (i) charge transfer resistance, RCT , (ii) gas diffusion resistance, RW , (iii) ohmic resistance, R0 , and (iv) ionic transport resistance in the catalyst layer, RCCL ion ; all obtained from the CNLS-fit procedure using ECM (TLM): (a) ASR values as a function of current density (8 mA cm 2 to 1 A cm 2) and relative humidity (40%–90% R.H., pO2 ¼ 0.55 atm). (b) ASR values as a function of current density (8 mA cm 2 to 1 A cm 2) and oxygen partial pressure (0.14 atm (air) to 0.67 atm (oxygen), 70% R.H.). All measure ments were performed at 80 � C.
σ PEM ion ¼
σ CCL εIonomer ion ¼ ¼ 0:064 σ PEM τIonomer ion
4.3.2. Tafel slope The interactions between the transport process and reaction process in the electrode structure play a major role in the performance and the design of the electrode. In addition to the ionic conductivity of the electrode, the actual charge transfer (related to the oxygen reduction reaction) plays an important role. In general, the Butler-Volmer equa tion can be used to describe the ORR at the Pt catalyst: � � � � �� nF nF j ¼ j0 exp α ηact exp ð1 αÞ ηact (13) RT RT
(10)
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Fig. 6. Area specific values of (i) charge transfer resistance, RCT , (ii) gas diffusion resistance, RW , (iii) ohmic resistance, R0 , and (iv) ionic transport resistance in the 2 � catalyst layer, RCCL ion : (a) As a function of current density (56/146/382/1000 mA cm ) (T ¼ 80 C, 70% R.H., H2/air). (c) As a function of oxygen partial pressure (0.14/0.23/0.40/0.67 atm) (T ¼ 80 � C, 70% R.H., j ¼ 1.0 A cm 2). (e) As a function of relative humidity (40%–90% R.H.) (T ¼ 80 � C, pO2 ¼ 0.55 atm, j ¼ 1.0 A cm 2). Percentage losses for the use of air (b), oxygen (d) and low relative humidity (f).
Here j0 is the exchange current density of the cathode, n the number of exchanged electrons (in our case n ¼ 2), α the charge transfer coeffi cient and ηact the activation overpotential. The differential resistance is given by the derivation of the overvoltage to the current density: Ract ¼
∂ηact ∂j
The exchange current density, j0 , for the oxygen reduction reaction in PEM fuel cells is usually very small (in the range of 1 mA cm 2) [22, 43]. We can therefore use the simplified Tafel equation under our con ditions (j ¼ 8 mA cm 2 … 1.0 A cm 2). The resistance of the activation polarization can then be easily derived, as follows:
(14)
Ract ¼
However, a problem arises; Eq. (13) cannot be solved for ηact. There are two simplifications given in literature for the Butler-Volmer equation [42]:
(15)
(ii) and the well-known Tafel equation for j/j0 > 4: � � nF j ¼ j0 ⋅exp α ηact RT
(16)
(17)
where the pre-factor is often summarized in the Tafel slope b: 1 RT b¼ ⋅ α nF
(i) A linear approximation, valid for j/j0 < 2: nF j ¼ j0 ⋅ ηact RT
∂ηact 1 RT 1 ¼ ⋅ ⋅ ∂j α nF j
(18)
The Tafel slope is a value widely given in literature to describe the reaction processes at the Pt catalyst. Wang et al. report values varying from α ¼ 1 at low current densities to α ¼ 0.5 at high current densities, which the authors correlate to the potential-dependent adsorption of oxygen-containing species [44]. However, Neyerlin et al. pointed out that a single Tafel slope is able to accurately describe the ORR kinetics in PEM fuel cells [43], if mass transport losses at high current densities are considered. This has been shown by means of polarization curve fits. 8
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Fig. 7. Ionic conductivity of membrane (H500EL2, Nafion 112, Nafion 117) and catalyst layer (H500EL2) at T ¼ 80 � C: (a) As a function of relative humidity (j ¼ 56 mA cm 2). (b) As a function of current density (40% R.H. and 90% R.H).
From our point of view, Neyerlin’s findings are also reflected in the impedance representation. If we consider the total electrode resistance RTLM (including charge transfer kinetics and ionic transport losses in the ionomer) to be described with one Tafel slope, we then see that this does not work (Fig. 8a, squares). Now, from an accurate TLM approach we are able to clearly distinguish between the sole charge transfer resistance, RCT, and the transport losses, and we are able to describe the charge transfer resistance, RCT, within the whole current regime with only one Tafel slope (Fig. 8a, circles). In addition, we found a small dependency of Tafel slopes to relative humidity (Fig. 8b and c). Our approach shows Tafel slopes from ~110 mV⋅dec 1 (40% R.H.) to 130 mV⋅dec 1 (90% R.H.).
Fig. 8. Evaluation of Tafel slopes (T ¼ 80 � C): (a) Model fit for two cases ((i) Ract ¼ RTLM; (ii) Ract ¼ RCT; both at 70% R.H.)). (b) Model fit in the low current region. (c) Tafel slope as a function of relative humidity.
were shown to be capable of reproducing the impedance of the PEM cathode. Beyond that, the TLM clearly distinguishes between the loss contribution of the charge transfer reaction at the Pt catalyst and the ionic transport losses within the ionomer of the cathode catalyst layer. We investigated a wide range of operating conditions and calculated the area specific resistance (ASR) values of (i) ohmic losses, (ii) the gas diffusion in the porous media, (iii) the charge transfer kinetics at the Pt catalyst, and (iv) the ionic transport losses in the catalyst layer. As ex pected, charge transfer is the dominant loss mechanism in the low cur rent region (87% at j ¼ 56 mA cm 2, 70% R.H. and H2/air). However, under high electrical load (and with sufficient oxygen supply), the ionic transport losses in the catalyst layer contribute more to the total losses than expected (52% at 1.0 A cm 2, 40% R.H. and H2/O2). Gas diffusion
5. Conclusions In this study, impedance data from a commercial PEMFC single cell were analyzed. A novel approach was presented, where equivalent cir cuit model (ECM) and starting parameters for the complex nonlinear least squares (CNLS) fitting process were obtained by a preidentification of the impedance response by the distribution of relaxa tion times (DRT). An ECM consisting of RQ elements connected in series, as well as the more physically motivated transmission line model (TLM), 9
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losses need only be considered if the oxygen supply is low (pO2 < 0.4 atm and j > 0.6 A cm 2), but can also play a major role (63% at 1.0 A cm 2, 70% R.H. and H2/air). In addition, the ionic conductivity of the catalyst layer and the Tafel slope were derived from the impedance data. Effective ionic conduc tivities from 0.13 S m 1 at 40% R.H. to 1.1 S m 1 at 90% R.H. were found. The dependency on relative humidity is in good agreement with the widely investigated Nafion® 112/117 membranes and thus a structural parameter of the ionomer phase in the electrode could be determined to 0.064. Moreover, the TLM approach reveals the pure charge transfer resistance without any superimposed transport losses. This enables one to derive a single, current-independent Tafel slope, which represents the reaction kinetics of the ORR. We found values ranging from ~110 mV⋅dec 1 (40% R.H.) to 130 mV⋅dec 1 (90% R.H.).
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