Impedance Spectroscopy Characterization of Oxygen Transport in Low– and High–Pt Loaded PEM Fuel Cells

We report fitting of the physics–based model for the cathode side impedance to the experimental spectra of low–Pt loaded (0.1/0.1 mgPt cm−2) and high–Pt loaded (0.4/0.4 mgPt cm−2) PEM fuel cells measured in the range of current densities from 50 to 400 mA cm−2. Fitting allowed us to separate the oxygen diffusion coefficients in the catalyst layer Dox and in the gas–diffusion layer Db , and the respective mass transfer coefficients of the electrodes of both types. In the low–Pt electrode, Dox is an order of magnitude lower, than in the high–Pt electrode; however, due to 4–fold difference in the electrode thickness, the respective mass transfer coefficients are close to each other. In both the electrodes, the oxygen diffusion and the mass transfer coefficients in the GDL are nearly the same and they are much higher, than the respective coefficients in the CCLs. The ORR Tafel slope and Dox exhibit linear growth with the cell current density; both effects could be attributed to “cleaning” of Pt surface from oxides at lower cell potential. © The Author(s) 2017. Published by ECS. This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 License (CC BY, http://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse of the work in any medium, provided the original work is properly cited. [DOI: 10.1149/2.1131714jes] All rights reserved.

A future of polymer electrolyte membrane fuel cells (PEMFCs) on the automotive market depends on their reliability and cost. At present, the cathode side of a typical PEMFC used in a 50-kW stack employs Pt loading of 0.4 mg Pt cm −2 . With the power density on the order of a 0.5 W cm −2 , this requires 40 g of expensive Pt per stack. Clearly, lowering of Pt content while keeping the cell performance is a problem of highest priority for the fuel cell industry. US Department of Energy has set a target of 0.125 g Pt /kW by the year 2020; at present, typical Pt loading is about 1 g Pt /kW.
The hydrogen oxidation on the anode side is fast and it typically requires much less Pt, than the oxygen reduction on the cathode side. The largest Pt consumer in a PEMFC is, thus, a cathode catalyst layer (CCL), which converts fluxes of protons and electrons into water with the aid of oxygen. CCL is a composite structure of interpenetrating clusters of proton-conducting ionomer (typically Nafion), voids for oxygen transport and Pt/C particles, which transport electrons through the layer and provide the sites for the oxygen reduction reaction (ORR).
So far, the effect of Pt/C content on the transport and kinetic properties of the CCL remains poorly understood. Experiments show that lowering of Pt content to 0.1 mg Pt cm −2 strongly reduces the cell performance at higher current densities. Gretszler et al. showed that this lowering mathematically is equivalent to ∼35 nm bulk-like ionomer film covering the surface of Pt/C agglomerates in the CCL. 1 However, this Nafion film thickness largely exceeds the value predicted by molecular dynamics simulations 2,3 and the recently measured value of 7 nm. 4 Weber and Kusogly 5 and Kusoglu et al. 6 reported evidences that the structure of Nafion film covering Pt/C particles strongly differs from the structure of bulk Nafion due to confinement effects. Recently, Freiberg et al. 7 attributed increase in the cell resistance in low-Pt loaded electrodes to the diffusive oxygen transport resistance in a Nafion film covering Pt/C agglomerates. Kulikovsky provided model-based arguments in favor of a limiting rate of oxygen adsorption on the Pt surface in low-Pt electrodes. 8 This mechanism has also been considered by Kongkanand and Mathias. 9 The situation with the Nafion content in the electrode is further complicated by the nonuniformities of Nafion distribution in the CCL. Orfanidi et al. 10 suggested that in the standard Pt/C electrodes, the thickness of Nafion film covering Pt/C agglomerates is strongly nonuniform. They managed to homogenize this thickness by * Electrochemical Society Member. z E-mail: tatyanar@hawaii.edu; A.Kulikovsky@fz-juelich.de functionalization of carbon surface by NH x groups. Moreover, they showed that this technique homogenizes also the Nafion distribution through the catalyst layer depth. A strong nonuniformity of proton conductivity through the CCL depth has been reported by Lefebvre, 11 Li and Pickup 12 and by Reshetenko and Kulikovsky. 13,14 A detailed discussion of the effects of Nafion loading is given in a recent review of Huang et al. 15 Measurements of an oxygen mass transport resistance in a low-Pt electrode have been performed using the method of limiting current density in a cell fed with diluted oxygen, 1,16,17 and in a hydrogenpumped cell. 7,9 Both methods enable determination of the GDL masstransfer resistance; however, measuring of the CCL oxygen transport properties by the limiting current methods is less reliable. The reason is that the limiting current is identified as a "vertical" part of the cell polarization curve. 1,16,17 This part is achieved due to oxygen transport in the GDL; at this current, the oxygen concentration at the CCL/GDL interface approaches zero, and only a small CCL sub-layer located at this interface contributes to the current production. This means, that the method "feels" the oxygen transport at the CCL/GDL interface, which may differ from the transport in the bulk CCL. Moreover, this method does not allow to separate contributions of the Knudsen oxygen transport in the CCL and the microporous layer (MPL), which further reduces the accuracy of returned transport coefficients.
Below, we report characterization of low-and high-Pt loaded cathodes at various current densities based on impedance measurements, which allow us to separate the oxygen transport coefficients in the CCL and GDL. We have measured impedance spectra of PEMFCs equipped with the low-and high-Pt loaded membrane electrode assemblies (MEAs). Further, we have fitted the physics-based model for the PEMFC impedance to the measured spectra and we report the dependencies of fitting parameters on the cell current density. The model takes into account the variation of CCL proton conductivity through the electrode depth, which is quite a strong function according to our previous studies. 13,14 The model also accounts for the impedance due to oxygen transport in the channel Z h ; this allowed us to fit the experimental spectra from the lowest to the highest measured frequency. A more detailed CFD-based impedance model of Bao and Bessler 18 includes the impedance Z h ; however, the model below partly employs analytical solutions, and in contrast to, 18 it is fast enough to perform fitting of the experimental spectra. It should be noted, that unlike the limiting current method, our impedance model works from relatively high down to low cell currents, when the whole electrode thickness contributes to current production and oxygen is transported through the entire CCL depth.

Experimental
All electrochemical measurements were carried out using a segmented cell system and a test station developed at Hawaii Natural Energy Institute. The whole system allows us to perform simultaneous recording of spatially resolved current, voltage and impedance responses from a segmented cell which is operated as a single cell using the test station and standardized testing protocols. Such operation minimizes impacts from the segmented cell setup and represents operating conditions that are identical to real since only overall cell current or voltage is controlled by the test station. Details of the segmented cell system are presented in our previous publications. 19,20 The cell was operated with commercially available 100 cm 2 catalyst coated membranes (CCMs) provided by Gore. Samples with low and high platinum content were evaluated in this work. The catalyst loadings were 0.1/0.1 and 0.4/0.4 mg Pt cm −2 for anode/cathode and for low-and high-Pt CCM, respectively. Sigracet 25 BC (thickness 235 μm, 80% porosity) was used as the anode and cathode gas diffusion layers (GDLs). 25 BC consists of carbon paper substrate and microporous layer with the thickness of 40-45 μm. Segmentation was applied for the cathode whereas the anode was unsegmented. The total active area of membrane electrode assembly (MEA) was 76 cm 2 . The gasket material was made of Teflon, with the thicknesses of 125 μm for both electrodes and low-and high-Pt samples.
The polarization curve (VI curve) and EIS measurements were performed with H 2 /air at a cell operating temperature of 80 • C. The anode/cathode conditions were 2/9.5 stoichiometry, 100/50% relative humidity and 48.3/48.3 kPa gauge backpressure. The VI curve recording was combined with spatial EIS. The selected frequency range for the EIS experiments was 0.05 Hz to 10 kHz and the amplitude of the sinusoidal current signal perturbation was 2 A, which resulted in a cell voltage response of 10 mV or lower. Impedance spectra were measured simultaneously from 10 segments and from the whole cell.
The MEAs structure was studied by scanning electron microscopy (SEM), using Hitachi S-4800 field emission microscope with an accelerating voltage of 5 kV.

Impedance Model
The impedance model used in this work is based on the transient charge and mass conservation equations in the CCL, GDL and in the air channel. The CCL performance model has been discussed in detail in Ref. 21, while the GDL and channel model have been developed in Ref. 22. However, the latter model has been constructed assuming fast oxygen transport in the CCL. Here, we build a complete model for the CCL, GDL and channel performance which is free from this limitation. Further, the CCL model we use here takes into account the variation of proton conductivity through the electrode depth. The main model assumptions are as following.
1. The flow in the cathode channel is a plug flow (a well mixed flow with a constant velocity). 2. The oxygen transport in the catalyst and gas-diffusion layers obeys to the Fick's law with the effective diffusion coefficients D ox and D b , respectively. Note that D b takes into account oxygen transport in the gas-diffusion media and in the microporous layer (MPL). Oxygen transport in Pt/C agglomerates is neglected (for discussion of this issue see Ref. 23). 3. The cell is operated far from equilibrium and the ORR kinetics is described by the Tafel law with the first-order dependence on the oxygen concentration. 4. The CCL proton conductivity decays exponentially with the distance from the membrane. 13,14 Performance model for the CCL.-The core of the impedance model is a system of transient equations for the CCL performance: [24][25][26] Here C dl is the double layer volumetric capacitance (per unit electrode volume, F cm −3 ), η is the positive by convention ORR overpotential, t is time, j is the local proton current density, x is the distance from the membrane through the CCL depth, i * is the volumetric exchange current density (A cm −3 ), c is the local oxygen concentration, c in h is its reference concentration, b is the Tafel slope, σ 0 is the CCL proton conductivity at the membrane interface, s(x) is the conductivity shaping function, and D ox is the effective oxygen diffusion coefficient in the CCL. Eq. 1 is the proton charge conservation, Eq. 2 is the Ohm's law relating the proton current density to the gradient of overpotential, and Eq. 3 is the oxygen mass conservation equation in the CCL with the Fick's law of diffusion. Note that the CCL proton conductivity is assumed to be a function of the coordinate through the CCL depth. Detailed discussion of Eqs. 1-3 is given in Ref. 21.
Substitution of Eq. 2 into Eq. 1 leads to a diffusion-type equation for the overpotential. Linearization and Fourier-transform of the resulting system yields the pair of linear equations for the smallamplitude perturbations of overpotential η 1 and oxygen concentration c 1 in the frequency domain (see Ref. 21 for details): where the superscripts 0 and 1 mark the steady-state solution and the amplitude of a small harmonic perturbation, respectively, and the following dimensionless variables have been used Here ω = 2πf is the angular frequency of the applied signal, Z is the impedance (see below), are the scaling parameters for time, current density, and diffusion coefficient, respectively. Below, we will assume that s(x) is exponential function where β is the inverse characteristic scale of the exponent. Experimental and modeling study 13,14 have shown that Eq. 9 provides a good fit of the spectra in the high-frequency range.
The system of Equations 4,5 subject to the boundary conditions The first of Eqs. 10 fixes the perturbation amplitudeη 1 1 of applied signal atx = 1; the second one means zero proton current at the CCL/GDL interface. Eqs. 11 express zero oxygen flux through the membrane and continuity of the oxygen concentration at the CCL/GDL interface, respectively. Here,c 1 b is the perturbation amplitude of the oxygen concentration in the GDL.

Oxygen transport in the GDL.-The equation forc 1
b is obtained from the oxygen mass balance in the GDL, which in the dimensionless variables 7 has the form are the dimensionless oxygen concentration and the effective oxygen diffusion coefficient in the GDL, respectively.
Eq. 12 is linear and hence the equation for the oxygen concentration perturbation The boundary conditions for this equation arẽ where l b is the GDL thickness, andc 1 h is the amplitude of the oxygen concentration perturbation in the channel. The first condition means continuity of the oxygen flux at the CCL/GDL interface, and the second one expresses continuity of the oxygen concentration perturbation at the GDL/channel interface. The equation forc 1 h is discussed in the next section.

Oxygen transport in the channel.-The equation forc 1
h has been derived in Ref. 22; here, for completeness, we briefly reproduce the main points of this derivation. The mass balance equation for the oxygen concentration c h in the channel is [15] where z is the coordinate along the channel, is the oxygen flux through the GDL/channel interface and c in h is the inlet oxygen concentration. In dimensionless form, Eq. 15 reads L is the channel length, and J is the mean current density in the cell. Note that the product λJ =Ñ in h , whereÑ in h is the dimensionless inlet oxygen flux in the channel. This flux is assumed to be fixed, i.e., in the equations below, the product λJ is not affected by perturbations. Under fixed λJ , Eq. 16 is linear and hence an equation for the perturbation amplitudẽ where A and B are the coefficient functions given in Appendix.
As discussed in Ref. 27, the total cell impedance is well approximated by the local impedance calculated at the pointz * where the local current density equals the mean cell current density. Hence, we solve Eq. 19, and for further calculations we takec 1 h (z * ), wherez * is a solution to equation j 0 = J : Here, the left side is the local current density. Solving Eq. 20, we get where f λ = −λ ln 1 − 1 λ .

Reduction of the performance equations and impedance.-Eq. 19 contains a single unknown function,c 1
h . At large cell current, this equation can only be solved numerically. The rest of the problem reduces to numerical solution of the system 4, 5. Indeed, Eq. 13 and the system 4, 5 are linked through the boundary conditions at the CCL/GDL interface, Eqs. 11,14. Solving Eq. 13 and settingx = 1 in the solution, we get wherec 1 h =c 1 h (z * ), as discussed in the previous section. With this, the second of Eqs. 11 transforms into the Robin-type boundary condition: Thus, withc 1 h at hand, solution to the system 4, 5 with the boundary conditions discussed above yields the local shapesc 1 (x) andη 1 (x).
The static shapesη 0 andc 0 appearing in Eqs. 4, 5 are solutions to the dimensionless steady-state version of the system 1-3: [25] where j lim = 4F D b c in h /l b . Solution to the system 24, 25 requires setting of the static overpotentialη 0 0 . However, the impedance measurements are usually performed at the fixed static current densityj 0 . The system 24, 25 can be reformulated in terms of the proton current density, 28 which yields  [28] which follows from the static version of Eq. 1. Numerical solution of the system 4, 5 with the boundary conditions 10,23, and the first of Eqs. 11 yields the amplitude of ovepotential perturbationη 1 (x). Note that the oxygen transport in the GDL and channel is included into the system 4, 5 through the boundary condition 23. Finally, the impedance of the cathode side ("CCL+GDL+channel") is calculated according toZ = −η 1 ∂η 1 /∂x x=0,z=z * [29] Numerical details.-Fitting has been performed in Maple environment using the matrix form of a built-in Maple procedure Nonlin-earFit. This routine takes as an input a procedure which returns the local sum of squares of the form where Z re , Z im stand for the real and imaginary parts of the impedance, the superscripts model and ex p denote the model and experimental values, respectively, and N is the total number of points in the experimental spectrum. Note that the model impedance in Eq. 30 is calculated for the same frequency, as the experimental impedance. Model components of impedance have been calculated from Eq. 29, whereη 1 has been determined from numerical solution of the system 4,5. The static shapesη 0 andc 0 have been calculated from numerical solution of the system 26,27 and Equation 28. The systems of complex ODE's have been converted to equivalent real systems for the real and imaginary components of the unknown functions; the resulting systems have been solved using a built-in Maple procedure dsolve. The static shapesη 0 andc 0 have been updated after every 10-th iteration with NonlinearFit. Total number of iterations has typically been around 100; for a single spectrum it takes less than an hour on a 1.7-GHz notebook.

Results and Discussion
SEM pictures of the high-and low-Pt MEAs are shown in Figure 1. As can be seen, the two MEAs differ by the thickness of the catalyst layer: in agreement with the ratio of catalyst loadings in the two cells, in the low-Pt cell, the CCL thickness is roughly four times less, than in the high-Pt cell ( Figure 1). The geometrical and operating parameters for the two cells are collected in Table I. As λ in our experiments has been sufficiently large, only spectra of the whole cell have been processed. In general, processing of the local spectra improves statistics of the results; however, local oxygen concentration at the individual segments is unknown, which lowers the accuracy of the local spectra fitting.
Six parameters have been declared as the fitting ones: the Tafel slope b, the proton conductivity at the CCL/membrane interface σ 0 , the double layer capacitance C dl , the oxygen diffusion coefficients in the CCL D ox , and in the GDL D b , and the oxygen stoichiometry λ. Though λ is known from the experiment, we claimed it as a fitting parameter as variable λ effectively takes into account under-rib oxygen transport in the meander flow field. For both the cells, parameter β in Eq. 9 have been fixed at 6.5; this value has been determined by fitting the spectra for the current density of 50 mA cm −2 with β as a fitting parameter. Control fitting of the spectrum for j 0 = 400 mA cm −2 with β declared as a fitting parameter gave β = 6.41 and only marginal variation of the other parameters. Figures 2, 3 show the experimental and fitted model Nyquist spectra of a low-and high-Pt loaded cells, respectively. Figures 4, 5 show the Bode plots corresponding to the current densities of 50 and 400 mA cm −2 for the low-Pt and high-Pt cells, respectively. As can be seen, the quality of fitting is good. Note that the fitted model points The dependence of fitting parameters on the cell current density j 0 is shown in Figures 6-8. In the low-and high-Pt cells, the Tafel slope exhibits a weak linear growth with j 0 ; in the low-Pt cell, the Tafel slope is up to 30% higher, than in the high-Pt cell (Figure 6a). In both the cells, mean proton conductivity rapidly increases with the cell current, and in the low-Pt cell this parameter is lower, than in the high-Pt cell (Figure 6b). The double layer capacitance is nearly the same in both the cells, and it decreases with j 0 reaching a plateau at 10 F cm −3 (Figure 6c). In both the cells, the CCL oxygen diffusivity  D ox exhibits linear growth with j 0 . In the low-Pt cell, D ox is nearly an order of magnitude lower, than in the high-Pt cell (Figure 7a, see below). The GDL oxygen diffusivity exhibits a weak growth with j 0 in a high-Pt cell, and it is nearly independent on j 0 in a low-Pt cell (Figure 8a). Note that the model above takes into account doubling of the effective Tafel slope at higher currents due to finite rates of proton and/or oxygen transport in the cell. In other words, Figure 6a shows a true "kinetic" value of this parameter. The growth of the Tafel slope with the cell current density could be explained by change of the ORR preferential location on a Pt surface. Pt nanoparticle is a multifaceted object with the facets having different crystallographic structure. 29 With the growth of the cell current density, the ORR preferential location may shift from one facet type to another, which translates into variation of the Tafel slope. Another reason for a growth of b with j 0 could be "cleaning" of Pt surface from oxides with the lowering of the cell potential. 30 Note that the higher Tafel slope in the low-Pt cell is in line with the observation that this parameter increases with j 0 (Figure 6a). Indeed, at a fixed current density per geometrical cell area j 0 , the current density per unit Pt active surface (ECSA) in the low-Pt cell would be higher, than in the high-Pt cell.
The growth of the mean proton conductivity of the CCL with j 0 has been reported in Ref. 31; possible explanation is the growth of a number of current-conducting channels in the Nafion film covering the Pt/C agglomerates. 31 Lower proton conductivity of a low-Pt CCL as compared to the conductivity of a high-Pt CCL can be explained as following. The conductivity is determined mainly by the HF shape of impedance spectra; it shows the rate of the proton transport to the catalyst sites. The proton pathway includes the Nafion and/or water film covering the Pt/C agglomerates and, possibly, the proton transport inside the agglomerates. Molecular dynamics simulations of Malek et al. 2,3 show that larger amount of Pt increases the amount of water on the surface of Pt/C particles, which may facilitate the proton transport to the Pt surface. Further, according to, 3 Pt content strongly affects the structure and connectivity of Nafion cluster in the CCL.
In contrast to the proton conductivity, the volumetric double layer capacitance of both CCLs is nearly the same (Figure 6c). Indeed, the volumetric density of Pt particles in both the electrodes is the same, which translates into close values of C dl . Lowering of C dl with the growth of the cell current is most probably due to increasing  with j 0 amount of liquid water in the catalyst layer. Part of the Pt electroactive surface appears to be flooded, which reduces the double layer capacitance of the electrode.
The CCL oxygen diffusivity increases with the cell current, and in the low-Pt cell this parameter is nearly an order of magnitude lower, than in the high-Pt cell (Figure 7a). However, due to the 4fold difference in the electrode thickness (Table I), the mass transfer where i = {CCL,GDL}, and l i and D i are the thickness and the oxygen diffusivity of the i-th layer. Note that in our model, D ox is an effective parameter; Eq. 3 only implies the Fick's law for the oxygen flux in the CCL, not specifying the physical nature of O 2 transport. In particular, the model does not separate the oxygen transport in the void pores and in the Nafion film covering Pt/C agglomerates. Attempt to apply the model 23 to separate the oxygen diffusion through the Nafion film has failed. With the expected Nafion film thickness on the order of 10 nm and the oxygen diffusion coefficient in Nafion on the order of 10 −6 cm 2 s −1 (Ref. 32), the characteristic angular frequency for oxygen transport in the Nafion film is about 10 5 Hz. This frequency is far above the frequency range used in experiments (50 mHz-10 kHz), and the impedance model 23 cannot capture this processes. As discussed by Malek et al., 3 Pt affects the structure of Nafion and void clusters in the CCL shifting the pore size distribution to larger pores, which facilitates the transport of gaseous oxygen through the electrode. Another reason for lower D ox in a low-Pt cell could be limiting rate of the oxygen adsorption on the Pt surface. In a low-Pt electrode, this process may increase the slope of a high-current part of the cell polarization curve, like a diffusive transport limitation. 8 Much lower D ox in the low-Pt electrode (Figure 7a) can, therefore, be attributed either to the influence of Pt loading on the structure of Nafion cluster, 3 or to the limiting rate of oxygen adsorption on the Pt surface. The physical origin of the linear growth of D ox with j 0 is not clear and it requires further studies. Note that this growth correlates with the linear increase of the Tafel slope in the CCL (Figure 6a). If the growth of the Tafel slope is caused by cleaning of Pt surface from oxides, than the growth of D ox could be caused by increasing amount of sites available for oxygen adsorption, which translates into higher effective oxygen diffusivity of the CCL.
Different values of the GDL oxygen diffusivity D b in the lowand high-Pt cells (Figure 8a) seemingly is due to variations in the preparation conditions of the two MEAs. As the thicknesses of the GDLs used in low-and high-Pt cells are nearly the same, the respective mass transfer coefficients are close to each other (Figure 8a). Comparing Figures 7 and 8 we see that in both the cells, the mass transfer coefficient of the CCL is an order of magnitude lower, than this coefficient of the GDL. The GDL mass transfer coefficient of a high-Pt cell (Figure 8b) agrees with the limiting current method measurements reported by  Conclusions Impedance spectra of the low-Pt (0.1/0.1 mg Pt cm −2 ) and high-Pt (0.4/0.4 mg Pt cm −2 ) cells have been measured for the cell current density j 0 in the range of 50 to 400 mA cm −2 . The impedance model, which takes into account nonuniformity of the proton conductivity through the CCL depth and the oxygen transport in the channel has been fitted to the spectra from the lowest to the highest frequencies.
The j 0 -dependencies of the ORR Tafel slope, mean proton conductivity, the double layer capacitance, and of the CCL and the GDL oxygen diffusivities are presented.
r The ORR Tafel slope in both the CCLs linearly increases with the cell current density; in the low-Pt cell, this parameter is about 20% higher, than in the high-Pt cell.
r The mean through the CCL depth proton conductivity increases with j 0 by an order of magnitude, from the value of less than 0.005 −1 cm −1 at j 0 = 50 mA cm −2 up to 0.04 −1 cm −1 at j 0 = 400 mA cm −2 . In a low-Pt electrode this parameter is lower, than in the high-Pt electrode.
r In both the cells, the double layer capacitance per unit electrode volume is nearly the same, decreasing from about 30 F cm −3 at small currents to the plateau on the level of 10 F cm −3 at large currents.
r The effective oxygen diffusion coefficient in the CCL of the low-Pt electrode is nearly an order of magnitude lower, than this coefficient in a high-Pt electrode. However, due to four times lower low-Pt CCL thickness, the oxygen mass transfer coefficients in both the catalyst layers are of the same order of magnitude.
r The GDL oxygen diffusion coefficient in the low-Pt electrode is three to two times higher, than in the high-Pt electrode.
r The concerted linear growth of the Tafel slope and the CCL effective oxygen diffusivity D ox with the cell current density could be attributed to "cleaning" of Pt surface from oxides with the decreasing of the cell potential. Pt cleaning means more sites available for oxygen adsorption, which translates into higher D ox .

Acknowledgments
T. Reshetenko is grateful to funding from US Office of Naval Research (N00014-12-1-0496), US Army Research Office (W911NF-15-1-0188) and the Hawaiian Electric Company for ongoing support of the Hawaii Sustainable Energy Research Facility. The authors also thank Gunter Randolf for valuable support with the system operation.

Appendix: Coefficient Functions in Eq. 19
The coefficient functions A and B in Eq. 19 are given by 22

List of Symbols
Marks dimensionless variables b Tafel slope, V