Adaptation of a PEMFC Reference Electrode to PEMWE: Possibilities and Limitations

First, polarization measurements at ambient pressure conditions are recorded. Polarization behavior is assessed by a galvanostatic step profile with current density steps between 0.005 and 1 A cm⁻² with impedance measurements at every current density step for determining high-frequency resistance R_HF. A frequency range of 100 kHz to 0.1 kHz with 11 points per decade is used. The amplitude for EIS is set to 5 mV. The polarization measurements are carried out thrice. Throughout the manuscript, the following materials will be referred to as standard materials. The standard PTL materials are titanium fiber PTL with a thickness of 0.2 mm for the anode side and carbon paper for the cathodic PTL (Freudenberg, E20H). The standard CCM is a 127 μm thick Nafion™ membrane with catalyst loadings of 2 mg_Ir cm⁻² and 1 mg_Pt cm⁻² (Hiat). The exemplary cell characterization in the results section is shown for a low loading CCM (0.5 mg_Ir/cm² and 0.5 mg_Pt/cm² (Hiat)) and an iridium-coated PTL. Material indications can also be seen in Table S1 in the SI. The characterization is carried out at a water and cell temperature of 80 °C.

As the next step, 119 experiments are carried out to analyze the functionality of the reference electrode. The stability tests consist of a constant current hold at 100 mA cm⁻² for 5 min. The majority of the experiments are carried out with materials as those described in the cell characterization procedure. In addition, the following materials are used to investigate the influence of different materials on the results. Tests 14–24 are carried out with a two-layered PTL on the anode side. During tests 43–50, lower catalyst loadings (0.5 mg_Ir cm⁻² and 0.5 mg_Pt cm⁻², HIAT) and iridium-coated PTLs are used. Materials specifications can also be found in Table S1 in the SI.

In the framework of the HFR measurements and potential distribution analyses, water recirculation temperature and cell compression are changed. The temperature variation is performed with cathode PTL and CCM, as described in the cell characterization section. However, the anode PTLs are two-layered titanium fiber material (Numbers 14–16 in Table S1 in the SI). A run-in at 60 °C, with the cell being compressed to 2.5 kN, is carried out as a first step. Therefore, the cell characterization protocol presented above is used. In the second step, water is cooled to 40 °C, the third is heated to 60 °C, and the fourth to 80 °C. Each time, the cell characterization measurement protocol from above is carried out.

Last, the cell compression is varied. The cell is run in at 60 °C and compressed to 2.5 kN. Then the compression in the system is reduced to 1.25 kN, then stepped up to 3.25 kN in 1 kN steps. The measurement protocol from the cell characterization procedure presented above is carried out at each step. Material is outlined in the temperature variation and corresponds to 17–19 in Table S1 in the SI.

Measured voltages are corrected by the potential of the Pt wire and thus presented against SHE potential. See Eq. 4 for the cathode measurement. The same procedure is valid for the anode.

$$\begin{eqnarray}&&{U}_{{\rm{C}}-{\rm{RE}}}={U}_{{\rm{C}}-{\rm{RE}}}^{{\rm{measured}}}+{E}^{{\rm{DHE}}}\end{eqnarray} \tag{ 4 }$$

The potential of the platinum wire, E^DHE, depends on the surrounding humidified hydrogen flow and can be calculated via the Nernst equation, Eq. 5.

$$\begin{eqnarray}&&{E}^{{\rm{DHE}}}=0\,{\rm{V}}-\displaystyle \frac{RT}{2F}\,\mathrm{ln}\left(\displaystyle \frac{{p}_{{{\rm{H}}}_{2}}^{{\rm{DHE}}}{c}_{{{\rm{H}}}^{+}}^{{{\rm{Mem}},{\rm{ref}}}^{2}}}{{p}_{{{\rm{H}}}_{2}}^{{\rm{DHE}},{\rm{ref}}}{c}_{{{\rm{H}}}^{+}}^{{{\rm{Mem}}}^{2}}}\right)\end{eqnarray} \tag{ 5 }$$

In Eq. 5, R is the gas constant, T is the local temperature (35 °C), F is Faraday's constant, c_H+ ^Mem is the proton concentration in the membrane, and p_H2 is the partial pressure of the hydrogen gas. Proton reference concentration equals 1 mol l⁻¹. A proton concentration of 0.54 M for fully saturated Nafion™ was found in the literature. ²⁸ This concentration corresponds to a pH value of 0.27. No information was found regarding the dependence of membrane proton concentration on the operating current. Therefore, the value is assumed to be constant in the course of this work. The partial pressure of hydrogen can be calculated via the measured pressure in the FC test station's inlet tube, the relative humidity (RH), and the partial pressure of water vapor. The latter can be calculated from Antoine's equation (Eq. 6). The constants were obtained from the National Institute of Standards and Technology based on Bridgman and Aldrich data. ²⁹

$$\begin{eqnarray}&&{p}_{{{\rm{w}}}_{{\rm{sat}}}}={10}^{{A}_{{\rm{sat}}}-\displaystyle \frac{{B}_{{\rm{sat}}}}{T-{C}_{{\rm{sat}}}}}1.01325\,{10}^{5}\end{eqnarray} \tag{ 6 }$$

The partial pressure of hydrogen is calculated according to Eq. 7. The pressure in the humidified hydrogen line p^recirc is set and controlled during the experiment.

$$\begin{eqnarray}&&{p}_{{{\rm{H}}}_{2}}^{{\rm{DHE}}}={p}^{{\rm{recirc}}.}-RH\,{p}_{{{\rm{w}}}_{{\rm{sat}}}}\end{eqnarray} \tag{ 7 }$$

The HFR is measured via EIS. It is assumed that the ohmic cell resistance equals the measured high-frequency impedance, where the imaginary part of the impedance equals zero. In this work, it is calculated by linear interpolation of data at the intercept with the x-axis (-Im = 0) in the Nyquist plot. This procedure is well known in full cell measurements. In this contribution, additional half-cell HFR values are measured. A typically obtained Nyquist plot is presented in Fig. 4a. Materials used for this example correspond to number 50 in Table S1 in the SI. In some cases, several intercepts with the zero-axis can be found. In these cases, the intercept at lower frequencies is used to calculate the HFR value (R_HF). Figure 4b is a higher magnification of Fig. 4a focusing on the cathode-to-RE (C-RE) signal. At frequencies above 28 kHz, the Nyquist diagram displays artifacts in the form of large outliers. In the course of this work, the share of the respective half-cell HFR from the full cell HFR is shown. The value is calculated by dividing the half-cell HFR by the full cell HFR.

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Data from polarization and HFR measurements are used together to calculate the HFR corrected voltage. This is shown for the full cell measurements in Eq. 8 but also applies to half-cell measurements.

$$\begin{eqnarray}&&{U}_{{{\rm{iR}}}_{{\rm{HF}}}{\rm{free}}\,}={U}_{{\rm{cell}}}-i\,{R}_{{\rm{HF}}}\end{eqnarray} \tag{ 8 }$$

Calculating HFR corrected voltages (${{\boldsymbol{U}}}_{{\bf{i}}{{\bf{R}}}_{{\bf{H}}{\bf{F}}}{\bf{f}}{\bf{r}}{\bf{e}}{\bf{e}}}$) is a necessary step to be able to complete the Tafel analysis. In this work, the Tafel analysis is carried out via linear interpolation in a logarithmic current density region, 0.01–0.1 A cm⁻², of the HFR corrected voltage for the full cell. It is assumed, that all other losses are negligible at these low current densities. This is demonstrated in Eq. 9, where η_act, the kinetic overpotential, is the difference between ${{\boldsymbol{U}}}_{{\bf{i}}{{\bf{R}}}_{{\bf{H}}{\bf{F}}}{\bf{f}}{\bf{r}}{\bf{e}}{\bf{e}}}$ and the reversible full cell voltage U_rev, b is the Tafel slope, and i₀ [A cm⁻²] is the apparent exchange current density. Again, equations are shown for the full cell but also apply to both half-cells.

$$\begin{eqnarray}&&{\eta }_{\mathrm{act}}=b\,log\left(\frac{i}{{i}_{0}}\right)\end{eqnarray} \tag{ 9 }$$

For large overpotentials, the Tafel analysis is justified. For small kinetic overpotentials, it is common to simplify the Butler-Volmer equation with a linear approximation. The linearity between the kinetic overpotential and current density is shown in Eq. 10, where α_f is the charge transfer coefficient for the forward reaction and α_b for the backward reaction.

$$\begin{eqnarray}&&{\eta }_{\mathrm{act}}=\frac{i}{{i}_{0}}\frac{R\,T}{F\left({\alpha }_{{\rm{f}}}+{\alpha }_{{\rm{b}}}\right)}\end{eqnarray} \tag{ 10 }$$

For comparison, the Tafel approximation is used first for all kinetic analyses. It should be noted that the HER is usually a fast reaction and crosses into the linear approximation range. Linear regression is carried out when the Tafel approximation results in low b and large i₀ values. The sum of the charge transfer coefficients α_f and α_b can be assumed to equal one. ³⁰

Tafel fitting for the half-cells is described in Eq. 9. The Nernst potential for each electrode can be calculated as follows in Eqs. 11 and 12, where c_H+ ^CL is the proton concentration in the CL. The product gases are assumed to be fully humidified at the reaction site. Reference concentrations are equal to 1 mol l⁻¹.

$$\begin{eqnarray}&&{E}^{{\rm{C}},{\rm{rev}}}=0\,{\rm{V}}+\displaystyle \frac{RT}{2F}\,\mathrm{ln}\left({\left(\displaystyle \frac{{c}_{{{\rm{H}}}^{+}}^{{\rm{Cl}}}}{{c}_{{{\rm{H}}}^{+}}^{{\rm{Cl}},{\rm{ref}}}}\right)}^{2}\displaystyle \frac{{c}_{{{\rm{H}}}_{2}}^{{\rm{ref}}}}{{c}_{{{\rm{H}}}_{2}}}\right)\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{E}^{{\rm{A}},{\rm{rev}}}=\displaystyle \frac{{\rm{\Delta }}{G}^{0}}{2F}+\displaystyle \frac{RT}{2F}\,\mathrm{ln}\left({\left(\displaystyle \frac{{c}_{{{\rm{H}}}^{+}}^{{\rm{Cl}}}}{{c}_{{{\rm{H}}}^{+}}^{{\rm{Cl}},\,{\rm{ref}}}}\right)}^{2}\sqrt{\displaystyle \frac{{c}_{{{\rm{O}}}_{2}}}{{c}_{{{\rm{O}}}_{2}}^{{\rm{ref}}}}}\right)\end{eqnarray} \tag{ 12 }$$

While the proton concentration in the membrane used in Eq. 5 is a literature value of 0.54 M, the value for the ionomer of the CL is unknown. Proton concentration in Nafion™ depends on the water content. ²⁸ For PEMFC, the water content in the CL is lower compared to the membrane. ³¹ For PEMWE, no study was found regarding water contents in Nafion™ CLs. Moreover, the proton activity at the reaction site (catalyst particle) might be locally different from the bulk CL. The proton activity is uncertain, yet it plays a critical role in determining the reversible potential of the cathode and consequently impacts the kinetic analysis of the HER. Below, we will provide a brief analysis of the influence.

The sensitivity of E^C,rev to c^cl _H+ is shown as follows for two cases. First, the potential is calculated with the membrane proton concentration of 0.54 M. Second, the Nafion™ volume fraction in the CL is assumed to be 25%. All other influences on the proton concentration discussed above are neglected. Thus, a proton concentration of 0.54/4 M is used. It should be noted that this is only valid on a macroscopic scale. At 60 °C and ambient gas pressure at the electrode (not to be confused with hydrogen pressure in the recirculation line for the DHE), E^C,rev(0.54 M) is −15.1 mV while E^C,rev(0.14 M) is −54.9 mV. This leads to a change in i₀ in Eq. 9 in multiple orders of magnitude. In this work, the latter value is used for kinetic analysis. Moreover, it is not clear if the proton concentration changes with different operating currents. Future investigation via in operando pH measurements at the CL is required to validate the assumption of a fixed pH value.

Misalignment of anodic and cathodic CL and different kinetics are known to influence the potential distribution outside the active area. While misalignments result in shifts in both directions depending on which electrode is shorter, kinetic effects cause shifts towards the electrode with faster reaction kinetics. In the context of PEMWE, this translates to a shift towards the cathode, thereby resulting in a greater HFR at the anode. Therefore, this work aims to analyze these effects, with an emphasis on misalignment, on the current measurements. Therefore, the share of anode vs cathode HFR is calculated for all tests with EIS measurement. The results can be seen in Fig. 8. Material coincides with the one in Fig. 7b and is indicated in Table 1, SI.

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In some cases, the HFR of anode-to-RE accounts for half of the ohmic resistance. In other cases, it lies above or below 50%. A certain variation of the anode-to-RE HFR is expected due to different contributions from, e.g., contact resistances between CL and PTL on the anode and cathode side. However, large variations between 6 and 85% are expected to be caused by asymmetrical potential distribution outside the active area of the membrane. In other words, the symmetry factor changes drastically throughout cell setups and even different tests with identical setups. It cannot be assumed that the symmetry factor is around 0.5. This inhibits any further improvement of the loss breakdown, e.g., dissection of the ohmic resistance into its contributions.

In addition, an SEM image of a CCM cross-section can be found in Fig. S3 in the SI. The image points towards a misalignment of the anode and cathode CLs.

As discussed in the previous section, misalignment is a possible cause that limits further loss breakdown. Testing has shown that it appears to be present in the majority of the cases. As a first step to analyzing this limitation, an extreme case is designed. Namely, the active areas are intentionally misaligned by consecutively covering a part of the PTL on the anode and cathode sides. The setup for a covered anode can be seen in Fig. 9. The remaining active area was measured with a caliper to 3.4 ± 0.02 cm². Materials used correspond to numbers 6–8 in Table S1 in the SI.

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Even though the area underneath the PTL covered with Kapton® is isolated electrically, and from fluid transport, the CL in that region might still participate to a lower amount in the reaction due to in-plane electric and mass transport in the CL. Therefore, the exact active area is expected to be larger than the uncovered area. However, HFR values will be presented as area-specific values for the uncovered area.

For a covered anode PTL, the potential at the RE is expected to shift closer to the cathode side (compare Fig. 3, middle). Therefore, a smaller HFR from the RE towards the cathode is expected. For a covered cathode PTL, the HFR_A-RE is expected to be lower. Measurements follow these expectations, as can be seen in Fig. 10. For non-covered PTLs, the HFR_A-RE is smaller than the HFR_C-RE. This can in parts be explained by faster cathode kinetics, as explained in the materials and methods section, and in parts points towards a larger anode. Values are measured at a current density of 1 A cm⁻². The absolute values can be found in Table S2 in the SI. The sum of HFR towards the anode and cathode slightly deviates from the measured full cell HFR. Therefore, the percentages in Fig. 10 do not add up to 100% in all cases.

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In previous works, intentional misalignment is used to isolate the CL, PTL, and contact resistances from the membrane resistance. ²⁰ From the present measurements, the sum of CL, PTL, and contact resistances for the anode is expected to be smaller than 12.5 ± 0.07 mΩ cm² and, on the cathode side, 3.5 ± 0.02 mΩ cm². However, these values can still include a fraction of the membrane resistance. Moreover, the actual active area is unknown, increasing the uncertainty of these values.

The previous section dealt with extreme misalignment and how the ohmic resistance from PTL, CL, and contacts can be narrowed down. Another way to dissect protonic resistance in the membrane from other ohmic resistances is via temperature variation. This is carried out in the following. Materials corresponding to numbers 14–16 in Table 1, SI. It should be noted that different materials are used in the intentional misalignment section, and results cannot be transferred directly. Subsequently, the equations for fitting are presented.

Fitting for HFR contributions and the symmetry factor

Temperature changes strongly affect the membrane resistance, which is a large part of the HFR. Other contributions to the HFR are only slightly affected by temperature changes. Previous work by Schuler et al. took advantage of this to separate ohmic resistance into contributions from the setup, interfaces, and the membrane via full cell measurements. Equation 13 was introduced in their work, with δ being the swollen membrane thickness and σ the ionic membrane conductivity. The value E_K in the temperature correction term equals 7.83 kJ Mol⁻¹. The parameter R_Int accounts for the temperature-invariant resistance at the anode and cathode. ³²

In the present work, Eq. 13 is supplemented by Eqs. 14 and 15 for anode and cathode HFR, respectively. Subsequently, the impact of temperature on the reaction kinetics and its corresponding influence on the symmetry factor is omitted from consideration.

$$\begin{eqnarray}&&HF{R}_{{\rm{tot}}}=\displaystyle \frac{{\delta }^{{\rm{tot}}}}{\sigma \,\exp \left(\displaystyle \frac{{E}_{{\rm{K}}}}{R\,T}\right)}+{R}_{{\rm{Int}}}^{{\rm{C}}}+{R}_{{\rm{Int}}}^{{\rm{A}}}\end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray}&&HF{R}_{{\rm{A}}-{\rm{RE}}}=\displaystyle \frac{\chi \,{\delta }^{{\rm{tot}}}}{\sigma \,\exp \left(\displaystyle \frac{{E}_{{\rm{K}}}}{R\,T}\right)}+{R}_{{\rm{Int}}}^{{\rm{A}}}\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&HF{R}_{{\rm{C}}-{\rm{RE}}}=\displaystyle \frac{\left(1-\chi \right){\delta }^{{\rm{tot}}}}{\sigma \,\exp \left(\displaystyle \frac{{E}_{{\rm{K}}}}{R\,T}\right)}+{R}_{{\rm{Int}}}^{{\rm{C}}}\end{eqnarray} \tag{ 15 }$$

A current density of 1 A cm⁻¹² is used for the HFR calculation. First, Fig. 11 shows the share of anode and cathode HFR over temperature. It can be seen that the anode value is larger, and its share increases with higher temperatures. That points towards a larger PTL, CL, and contact resistance on the anode side. The absolute values can be found in Table S3 in the SI.

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Figure 12 shows the results from fitting HFR values (cell, A-RE, and C-RE) at three different temperatures to Eqs. 13–15. Fitting is carried out with a Matlab^® solver for nonlinear least-squares problems (lsqnonlin) with a trust-region-reflective algorithm. A global search is used with a multistart object set to 100.

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Theoretical data meets the measured values. The calculated parameters result in an ionic membrane conductivity of 1.5 S cm⁻¹ and a symmetry factor of 0.34. literature values for the ionic membrane conductivity are reported to be 2.29 S cm⁻¹. ³² The value calculated here results in a slightly lower conductivity, but it also accounts for variations in membrane thickness. The membrane thickness used in the present calculation is valid for dry Nafion™. In operando thickness is expected to be larger due to swelling. The calculated symmetry factor is smaller than 0.5. This indicates that the potential is shifted more toward the anode side. In terms of misalignment, the cathode CL would be smaller.

The fitted anodic constant resistance contribution is 0.07 Ω cm². For the cathodic constant resistance contribution, a value of 0 Ω cm² is fitted. The anodic temperature invariant resistance is significant, accounting for almost half the total anodic resistance at 80 °C. The value for the cathode side is calculated to be zero. However, the PTL, CL, and contact resistance cannot be zero. That indicates that the fitted parameters are not consistent with reality. As a possible reason, the membrane thickness may change with temperature due to different swelling behavior. That would affect the symmetry factor. The model would need to be extended outside the scope of this work.

Another way to change the HFR share is by changing the compression of the cell. Figure 13 shows the share of anode and cathode HFR over cell compression. Absolute values can be found in Table S4 in the SI. HFR is measured at 1 A cm⁻². The anode-to-RE HFR is always larger. Both values converge with more extensive compression. Larger cell compression can lead to better contact between different layers and better catalyst utilization for a certain range. Moreover, the membrane thickness will shrink with higher cell compression. However, there is no physical description of the compression dependence for the different resistance contributions. Therefore, no fitting is carried out. Anode and cathode HFR values convergeing with compression can have two reasons. 1) the symmetry factor itself is affected and is shifted closer to 0.5 and 2) anode and cathode contact resistances behave differently with compression. For 2), the observed behavior would show an anodic contact resistance that can be significantly improved with higher compression.

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Hitherto, HFR has been analyzed at the current density of 1 A cm⁻². However, the temperature field is expected to change at varying current densities. Since the temperature was shown to impact the anodic and cathodic HFR values, a closer look at their behavior over current density is carried out.

Figure 14 shows the share of anode and cathode HFR over current density at 60 °C. Absolute values for anode, cathode, and full cell HFR and different temperatures over current density can be seen in Fig. S4 in the SI. Material corresponds to numbers 15 in Table S1 in the SI. It can be observed that the anode share slightly decreases with higher current density. The cathode share behaves oppositely, showing a steady increase. The increase can be observed at the absolute full cell level, too.

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The reaction front within the CL is known to change over current density. ³³ Depending on numerous factors (proton and electron conductivity, kinetic parameters, structural parameters, amongst others), the reaction occurs at different locations over the trough-plane axes of the CL. Especially when unequal kinetic regions are considered for the half-cell reactions in a cell (e.g. logarithmic Tafel kinetics vs linear, fast kinetics) the reaction front will shift differently in the anode compared to the cathode CL over current density. This behavior could be the present case where the sluggish reaction at the anode side might shift towards the membrane. This goes hand in hand with more significant effective ohmic resistance for the cathode and smaller for the anode with a larger current density.