Analysis of Gas Permeation Phenomena in a PEM Water Electrolyzer Operated at High Pressure and High Current Density

The 5 cm² active area MEAs used in this study were prepared by a decal transfer method that has been described previously.⁷ Iridium black (Heraeus Metal Processing, Ltd., Ireland) was used as catalyst for the oxygen evolution reaction (OER) on the anode with loadings of 0.9 ± 0.3 mg_Ir cm⁻², while platinum supported on Vulcan XC72 carbon (45.8 wt% Pt/C; TEC10V50E from Tanaka, Japan) with loadings of 0.3 ± 0.1 mg_Pt cm⁻² was used as a cathode catalyst for the hydrogen evolution reaction (HER). The catalyst inks were prepared with catalyst powder, solvent (2-propanol purity ≥99.9% from Sigma Aldrich, Germany), and Nafion^® ionomer solution (20 wt% ionomer; D2021 from IonPower, USA). ZrO₂ grinding balls (5 mm diameter) were added for the 24 h mixing procedure on a roller mill. The ink was coated onto a 50 μm thick PTFE foil (from Angst+Pfister, Germany) using a Mayer-rod coating machine. To fabricate the 5 cm² active area MEAs, the electrodes were cut to size and then hot-pressed onto Nafion^® 117/212 membranes (178 μm/51 μm thick; from Quintech, Germany) for 3 min at 155 °C at a pressure of 2.5 MPa. The electrode loadings were calculated from the weight difference of the PTFE decal before and after the transfer step, measured with a microbalance (±15 μg; XPE105DR from Mettler Toledo, Germany). The ionomer content was fixed at 8.9 wt% for the anode while an ionomer to carbon (I/C) mass ratio between 0.6/1–1.2/1 was used for the cathode electrodes.

As porous transport layers (PTLs), sintered titanium (Ti) (from Mott Corporation, USA) with a porosity of ≈50% and a thickness of 280 ± 10 μm on the anode and carbon fiber paper (TGP-H-120 from Toray, no MPL) with a thickness of 370 ± 10 μm on the cathode were used. A 10 μm PTFE sub-gasket was used to prevent the MEA from being cut by the sharp edges of the Ti PTL. The cell was sealed with two 310 ± 10 μm thick PTFE gaskets to achieve a ≈25% compression of the carbon PTL (corresponding to a compression of ≈1.7 MPa), whereby the Ti PTL is assumed to be incompressible.

All tests were performed on a Greenlight E40 Electrolyzer Test Station equipped with a potentiostat and a booster (Reference 3000 and 30 °A booster, Gamry). The absolute pressure on the cathode was varied between 1.47 and 30.47 bar_a, while the anode was kept at ambient pressure. Taking into account the vapor pressure of water at 80 °C (0.47 bar) this translates into H₂ partial pressures between 1 – 30 bar on the cathode. Note that in the following, all pressure values refer to the H₂ partial pressure and not to the total pressure in the cathode compartment. Cell and reactant inlet temperatures were set to 80 °C and DI water was supplied at a flow rate of 10 ml min⁻¹ to the anode. Hydrogen was supplied to the cathode and oxygen to the anode at flow rates between 50 and 200 ml min⁻¹ (note that all gas flow rates are referenced to standard conditions of 0 °C and 1.013 bar). A ≈2 h lasting cell-warmup and a conditioning procedure were performed before the measurements. During the conditioning, the current density was ramped to 1 A cm⁻² over 200 s and held for 30 min. Three polarization curves with current densities starting from 0.01 and increasing to 6 A cm^-2 were recorded afterwards. Each current density step was held for 5 min followed by an AC impedance measurement in a range of 20 kHz–10 Hz to determine the high frequency resistance (HFR). During the H₂ permeation rate measurements the current density was varied between 0–6 A cm⁻² with hold times from 90–180 min for each current step. Additional polarization curves were recorded following the permeation measurement at each H₂ pressure step as well as at the end of test.

The test setup used in this work to determine the H₂ permeation rates is based on the analysis of the H₂ volume fraction (on a dry basis) in the O₂ exhaust of the anode, using a mass spectrometer (cf Fig. 1). A defined flow of dry H₂ gas can be supplied to the cathode inlet of the electrolyzer cell, while defined flows of H₂O and O₂ gas can be supplied to the anode inlet. The product gas at the anode outlet of the cell is typically a mixture of H₂O, O₂, and H₂ that permeates from the cathode compartment through the membrane into the anode compartment. Water is then separated from the product gas by a heat exchanger and a water separator unit implemented in the test station (E40 from Greenlight, Canada), as shown in Fig. 1). The dry product gas, consisting of a mixture of O₂ and H₂ is then analyzed by a quadrupole mass spectrometer (Cirrus™3 from MKS). Thorium filaments are used to ensure a sufficient filament lifetime in the highly corrosive O₂ environment. The capillary which supplies the gas to be analyzed to the mass spectrometer requires a minimum flow of 20 ml min⁻¹. Consequently, if the O₂ production rate during electrolyzer operation is too low (i.e., at low current densities) or for the permeation cell measurements (cf Fig. 2) where no O₂ is produced at all, additional O₂ gas needs to be supplied in order to ensure sufficient gas flow to the capillary. The amount of O₂ supplied to the anode inlet (cf Fig. 1) is regulated by a mass flow controller to achieve a total gas flow at the anode outlet of at least 50 ml min⁻¹. Furthermore, this additional O₂ flow prevents the formation of explosive gas mixtures in the anode gas stream (lower explosion limit for H₂ in O₂: ≈4%¹²). Of course, the additional O₂ flow needs to be considered when calculating the actual H₂ in O₂ content that would be obtained in a PEM-WE (i.e., in the absence of adding O₂ to the anode inlet) that is shown in Fig. 8.

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During the measurements, the anode compartment is kept at ambient pressure, while the H₂ partial pressure on the cathode is varied between 1–30 bar. The pressure in the cathode compartment is controlled by a back pressure regulator which requires a continuous gas flow to maintain a constant pressure. Hence, an additional H₂ gas flow of 50 ml min⁻¹ is supplied to the cathode inlet during all measurements in order to ensure a sufficient gas flow even at low current densities (i.e., at low H₂ production rates) and during the permeation cell measurements (cf Fig. 2). A more detailed description of the MEAs and the transport processes taking place in the cell can be found in the following sections for the respective test setups.

In general, diffusion of H₂ from the cathode to the anode can occur through the polymer phase as well as the liquid phase in ionomeric membranes.²⁰ For Nafion^® membranes the contribution of diffusion through the polymer phase is very small and it is generally assumed that diffusion through the liquid phase is the dominating mechanism²¹; a quantitative separation of the permeation of various gases through a Nafion^® membrane was also given by Mittelsteadt and Liu.²⁰ The diffusive H₂ flux according to Fick's law can be expressed as

$$\begin{eqnarray}&&{N}_{{{\rm{H}}}_{2}}^{{\rm{diff}}}\,=\,{D}_{{{\rm{H}}}_{2}}^{{\rm{eff}}}\cdot \displaystyle \frac{{\rm{\Delta }}{c}_{{{\rm{H}}}_{2}}}{{t}_{{\rm{memb}}}}\end{eqnarray} \tag{ 1 }$$

Here, ${\rm{\Delta }}{{\boldsymbol{c}}}_{{{\bf{H}}}_{2}}$ represents the H₂ concentration gradient between anode and cathode. Assuming a negligible H₂ concentration in the anode compartment compared to that in the cathode compartment, ${\rm{\Delta }}{{\bf{c}}}_{{{\bf{H}}}_{2}}$ is directly proportional to the partial pressure of H₂ in the cathode compartment. ${{\boldsymbol{D}}}_{{{\bf{H}}}_{2}}^{{\bf{e}}{\bf{f}}{\bf{f}}}$ is the effective diffusion coefficient of the membrane which is a function of porosity and tortuosity,²⁷ i.e., of the water content of the membrane, while ${{\boldsymbol{t}}}_{{\bf{m}}{\bf{e}}{\bf{m}}{\bf{b}}}$ represents the membrane thickness. Assuming a constant water content of the membrane, the diffusive H₂ flux is expected to scale linearly with the H₂ partial pressure on the cathode of the electrolyzer.

Convective transport of H₂ dissolved in liquid water due to a net water transport through the membrane is another possible mechanism of H₂ crossover and can be described as²⁷

$$\begin{eqnarray}&&{N}_{{{\rm{H}}}_{2}}^{{\rm{conv}}}={v}_{{{\rm{H}}}_{2}{\rm{O}}}\cdot {c}_{{{\rm{H}}}_{2}}\end{eqnarray} \tag{ 2 }$$

where ${{\boldsymbol{\upsilon }}}_{{{\bf{H}}}_{2}{\bf{O}}}$ is the velocity of water moving through the membrane and ${{\boldsymbol{c}}}_{{{\bf{H}}}_{2}}$ is the concentration of dissolved H₂ in the water phase. Differential pressure operation is a possible reason for a net water transport and, consequently, a convective H₂ flux from cathode to anode. Here, the total pressure difference between cathode and anode, ${\rm{\Delta }}{\boldsymbol{P}},$ would be directly proportional to the H₂ permeation rate according to Darcy's law²⁷

$$\begin{eqnarray}&&{N}_{{{\rm{H}}}_{2}}^{{\rm{diff}}-{\rm{press}}}={D}_{{{\rm{H}}}_{2}}^{{\rm{diff}}-{\rm{press}}}\cdot \displaystyle \frac{{p}_{{{\rm{H}}}_{2},{\rm{cath}}}\cdot {\rm{\Delta }}P}{{t}_{{\rm{memb}}}}\end{eqnarray} \tag{ 3 }$$

where ${{\boldsymbol{p}}}_{{{\bf{H}}}_{2},{\bf{c}}{\bf{a}}{\bf{t}}{\bf{h}}}$ is the H₂ partial pressure on the cathode, ${{\boldsymbol{t}}}_{{\bf{m}}{\bf{e}}{\bf{m}}{\bf{b}}}$ the membrane thickness, and ${{\boldsymbol{D}}}_{{{\bf{H}}}_{2}}^{{\bf{d}}{\bf{i}}{\bf{f}}{\bf{f}}-{\bf{p}}{\bf{r}}{\bf{e}}{\bf{s}}{\bf{s}}}$ a transport coefficient which depends on the permeability of the membrane, the solubility of H₂ in water, and the dynamic viscosity. If the pressure in the anode compartment is much smaller than in the cathode compartment, the partial pressure of H₂, ${{\boldsymbol{p}}}_{{{\bf{H}}}_{2},{\bf{c}}{\bf{a}}{\bf{t}}{\bf{h}}},$ equals approximately the total pressure difference, ${\rm{\Delta }}{\boldsymbol{P}},$ and the convective H₂ permeation should scale quadratically with ${{\boldsymbol{p}}}_{{{\bf{H}}}_{2},{\bf{c}}{\bf{a}}{\bf{t}}{\bf{h}}}.$

Electro-osmotic drag of water is another possible source of convective H₂ transport. Here, water is transported from anode to cathode, at a rate which is directly proportional to the amount of protons transported, i.e., to the current density.²⁷

$$\begin{eqnarray}&&{N}_{{{\rm{H}}}_{2}}^{{\rm{drag}}}={D}_{{{\rm{H}}}_{2}}^{{\rm{drag}}}\cdot {p}_{{{\rm{H}}}_{2},{\rm{an}}}\cdot i\end{eqnarray} \tag{ 4 }$$

Here, ${\boldsymbol{i}}$ is the current density and ${{\boldsymbol{p}}}_{{{\bf{H}}}_{2},{\bf{a}}{\bf{n}}}$ the H₂ partial pressure on the anode while ${{\boldsymbol{D}}}_{{{\bf{H}}}_{2}}^{{\bf{d}}{\bf{r}}{\bf{a}}{\bf{g}}}$ is a transport coefficient which depends on the solubility of H₂ in water and the electro-osmotic drag coefficient that describes the ratio of the number of water molecules dragged along per proton. Since convective transport of H₂ due to the electro-osmotic drag would occur from anode to cathode, it would actually lead to a lower overall H₂ crossover flux from cathode to anode and would only affect it during electrolyzer operation, i.e., when a current is drawn.

Note that in the following, the term "permeation" is used to describe the measured H₂ crossover from cathode to anode, even though, strictly speaking, the term permeation would only apply to a partial gradient driven transport (Eq. 1) and not to the convective transport processes. Furthermore, H₂ permeation rates are referenced to the dry thickness of the membranes.

First, to validate the H₂ permeation measurement method based on the quantification of the H₂ concentration in the O₂ exit stream of the anode compartment of a PEM-WE by mass spectrometric analysis, the H₂ permeation rates through Nafion^® membranes are measured as a function of the H₂ partial pressure. The thus determined H₂ permeation rates are then compared with those determined by the well-established electrochemical method to quantify H₂ permeabilities, which is based on the electrooxidation of H₂ that is permeating through an MEA with the same membrane from a H₂-filled compartment into a N₂-filled compartment of a fuel cell or electrolyzer cell.^18,21

For the here used H₂ permeation measurement method that is based on quantifying the H₂ concentration in the O₂-containing anode compartment, a Nafion^® membrane is assembled between the PTLs (Ti sinter on anode and carbon paper on cathode) in the cell hardware (cf Fig. 2a). A mixture of O₂ (50 ml min⁻¹ for p_H2 ≤ 10 bar and 100 ml min⁻¹ for p_H2 > 10 bar) and H₂O (10 ml min⁻¹) is supplied to the anode inlet in order to ensure sufficient humidification of the membrane as well as a sufficient gas flow to the mass spectrometer (see Experimental section). On the cathode, H₂ gas is supplied at a flow rate of 50 ml min⁻¹ and the H₂ partial pressure is varied from 1–30 bar while the anode is kept at ambient pressure. A hold time of 15 min is applied for each pressure step to give the system enough time to stabilize and to obtain a constant signal in the mass spectrometer. Each pressure step is measured twice (once while increasing the pressure and once while decreasing the pressure), and the deviation between the obtained values was always <0.4 mA cm⁻² (≈0.02 mmol m^-2 s⁻¹). The averaged H₂ permeation rates calculated from the mass spectrometer (MS) data are shown in Fig. 2c as a function of H₂ partial pressure for a Nafion^® 117 (referenced to a dry thickness of ≈178 μm) and a Nafion^® 212 (referenced to a dry thickness of ≈51 μm) membrane. For both Nafion^® 117 (red symbols/line in Fig. 2c) and Nafion^® 212 (blue symbols/line in Fig. 2c), the permeation rate increases linearly with H₂ partial pressure. Furthermore, the H₂ partial pressure normalized permeation rate (i.e., the slope of the lines in Fig. 2c) of the thin Nafion^® 212 membrane (1.10 mA cm⁻² bar⁻¹) is a factor ≈3.5 higher compared to the Nafion^® 117 membrane (0.31 mA cm⁻² bar⁻¹), exactly matching the inverse of the thickness ratio between the two membranes (178 μm/51 μm ≈ 3.5). Both findings indicate that diffusion-driven H₂ permeation according to Eq. 1 is the dominating process, since the H₂ diffusion rate is directly proportional to the H₂ partial pressure and to the inverse of the membrane thickness (cf Eq. 1). If convective transport due to the pressure difference between anode and cathode were to have a significant influence, a quadratic dependency on H₂ pressure would be expected (cf Eq. 3), which clearly is not observed in these measurement.

To validate the H₂ permeation rates obtained by quantifying the concentration of crossover H₂ in O₂ with the mass spectrometer setup (cf Fig. 2a), we will now compare them with the results from an electrochemical measurement technique frequently used to determine H₂ permeation rates.^18,21 The setup for this measurement is described in Fig. 2b. An MEA is fabricated with a Nafion^® 212 membrane and carbon supported platinum (Pt/C) electrodes (≈0.3 mg_Pt cm⁻²) with a standard ionomer/carbon mass ratio of 0.6/1 on both sides of the MEA. This MEA is then assembled between the Ti sinter and the carbon paper PTLs in the same electrolyzer cell hardware, and N₂ gas (50 ml min⁻¹) along with water (5 ml min⁻¹) are supplied to the anode compartment while H₂ (50 ml min⁻¹) is supplied to the cathode compartment. A positive potential of 0.4 V is applied to the anode and, consequently, H₂ permeating through the membrane to the anode is oxidized to protons at the Pt catalyst (note that the counter reaction in the H₂ compartment is the H₂ evolution reaction), whereby the measured limiting current density represents the rate of H₂ permeation through the membrane. This measurement was performed for H₂ partial pressures from 1–30 bar and the results are shown by the green symbols/line in Fig. 2c. The results fit perfectly with the H₂ permeation rate obtained for a Nafion^® 212 membrane with the mass spectrometer setup (cf Fig. 2a). On account of this excellent agreement between these two methods, we consider our test setup based on a mass spectrometer to analyze the H₂ content in the O₂-rich anode gas suitable for H₂ permeation measurements during operation of a PEM-WE which will be discussed in the next section.

To determine the H₂ permeation rate during electrolyzer operation, i.e., as a function of the applied current density, the setup shown in Fig. 3a is used. MEAs are fabricated based on either a Nafion^® 212 or a Nafion^® 117 membrane. The anode electrode consists of Ir-black (0.9 ± 0.3 mg_Ir cm⁻²), while a Pt/C cathode (0.3 ± 0.1 mg_Pt cm⁻²) with a standard ionomer/carbon mass ratio of 0.6/1 is used. The MEAs are assembled between Ti sinter (anode) and carbon paper (cathode) PTLs in the cell hardware. After a conditioning procedure described in the Experimental section, H₂ permeation rates are measured for different current densities up to 5 A cm⁻² for the Nafion^® 117 membrane and up to 6 A cm⁻² for the Nafion^® 212 membrane. The maximum current density is determined by an upper potential limit of 2.4 V. Permeation rates at a current density of zero are recorded while a potential of 1.3 V is applied to the iridium anode. At this potential, the surface of the iridium catalyst is oxidized and, consequently, exhibits a very low HOR activity.¹³ This is crucial, since H₂ oxidation on the anode would reduce the amount of H₂ detected at the anode outlet by the MS and, therefore, would lead to an underestimation of the H₂ permeation rate. The current measured during the potential hold at 1.3 V is <1 mA cm⁻² (<0.05 mmol m⁻² s⁻¹), proving that the HOR activity of the iridium catalyst is negligible, which is a prerequisite for the here used H₂ permeation rate measurements. Furthermore, the potential hold at 1.3 V ensures that the anode catalyst is never exposed to a reducing atmosphere. This is important since it was shown that frequent cycling between a reducing and an oxidizing atmosphere on the anode can lead to a significant alteration of the catalyst properties, which could also influence H₂ permeation measurements.²⁸

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The obtained H₂ permeation rates for H₂ partial pressures between 1 – 30 bar as a function of current density are shown in Fig. 3b for a Nafion^® 117 membrane and in Fig. 3c for a Nafion^® 212 membrane. Full symbols along with full lines represent the data measured while increasing the current density, whereas open symbols along with dotted lines show the data obtained while decreasing the current density. The error bars represent an overall error of the H₂ permeation measurement based on the accuracy of the mass spectrometer, fluctuations of the operating conditions, as well as uncertainties related to the active area in the cell (a detailed explanation can be found in the Appendix). Brown crosses give the H₂ permeation rates measured with the permeation cell setup shown in Fig. 2a. It can be observed that these values very closely match the H₂ permeation rates for the Nafion^® 212 membrane measured for the setup shown in Fig. 3a during the potential hold at 1.3 V (cf Fig. 3c, comparing the brown crosses and the symbols at 0 A cm⁻²), while they are up to ≈15% lower for the Nafion^® 117 membrane (cf Fig. 3b). A possible explanation for this deviation is an insufficient humidification of the membrane in the permeation cell test setup shown in Fig. 2a, where the membrane was equilibrated with liquid water by supplying 5 ml_H2O min⁻¹ to the anode for ≈2 h. However, studies on the water uptake of Nafion^® membranes show that an equilibration time of up to 150 h. can be required for a Nafion^® 117 membrane at 80 °C.²⁹ For the measurements performed with the test setup shown in Fig. 3a, on the other hand, conditioning of the MEA included a current hold at 1 A cm⁻² as well as several polarization curves. This not only results in a longer overall conditioning time, but also the transport of water from anode to cathode due to the electro-osmotic drag during electrolyzer operation is expected to lead to a faster equilibration of the membrane. Since in general a longer equilibration time is expected for a thicker membrane, this could explain why a difference in H₂ permeation rates at 0 A cm⁻² is observed for the Nafion^® 117 membrane (≈15%, cf Fig. 3b), but not for the Nafion^® 212 membrane (cf Fig. 3c).

From Figs. 3b and 3c it can be observed that the H₂ permeation rate increases with the current density for both membranes. With both membranes, there is a hysteresis in the H₂ permeation rates, with the values being lower while increasing the current density (solid symbols/lines) compared to when subsequently decreasing the current density. A possible explanation for this phenomenon is that even though a hold time of 90–180 min was applied at each measurement point, the H₂ permeation rate was still not completely constant (i.e., it was still slowly increasing with time), especially for the measurements taken while increasing the current density.

The relative increase of the H₂ permeation rate with current density is most pronounced for small H₂ partial pressures. For an MEA with the Nafion^® 117 membrane, the H₂ permeation rate at a pressure of 1 bar reaches a value of 3.3 mA cm⁻² at a current density of 5 A cm⁻², which is ≈15 times higher than the expected value at this H₂ partial pressure that is measured at 0 A cm⁻². A similar increase is observed for the Nafion^® 212 membrane, where a value of 15.2 mA cm⁻² is reached at a current density of 6 A cm^-2, ≈20 times higher than the value obtained at 0 A cm⁻². For higher operating pressures, the relative increase is smaller, with only ≈16% at 5 A cm⁻² and 30 bar for the Nafion^® 117 membrane, while the permeation rate can be considered essentially independent of current density (within the range of the measurement error) for the Nafion^® 212 membrane at 30 bar. The observed increase of permeation rate with current density has been shown frequently in the literature,^23,24,30 albeit to different extents, which indicates a strong influence of the measurement method and/or the cell setup (cell hardware, PTL, MEA, etc.,) on this phenomenon.²⁶ Possible reasons for this current dependency will be discussed briefly in terms of the simple models for H₂ transport through the membrane presented in the Theory section. Diffusive flux of H₂ according to Eq. 1 only depends on the H₂ concentration gradient between cathode and anode, ${\rm{\Delta }}{c}_{{{\rm{H}}}_{2}},$ the membrane thickness, ${t}_{{\rm{memb}}},$ and the effective diffusion coefficient, ${D}_{{{\rm{H}}}_{2}}^{{\rm{eff}}},$ i.e., it should not directly depend on the current density. However, if one of the above mentioned parameters were to be affected by the current density, this would indeed lead to a current density dependence of the H₂ permeation rate. For example, there are in principle two possibilities to increase the effective H₂ concentration at/near the membrane/cathode interface with increasing current densities, which have been discussed in the literature^14,23–25: either an increase in the local H₂ partial pressure at the membrane/cathode interface due to limited removal rates of the evolved H₂ or H₂ super-saturation in the ionomer phase at high H₂ production rates (i.e., at high current densities). An increased H₂ concentration in the ionomer phase at/near the membrane/cathode interface either by an increased p_H2 or by H₂ super-saturation would directly translate into an increase of the diffusive H₂ flow. With regards to the H₂ diffusion coefficient, ${D}_{{{\rm{H}}}_{2}}^{{\rm{eff}}},$ there are two possible effects which must be considered: (i) ${D}_{{{\rm{H}}}_{2}}^{{\rm{eff}}}$ is expected to increase with temperature, so that a local temperature increase at the MEA due to the high amount of heat produced at high current densities could lead to an increase of the H₂ permeation rate; (ii) a change in the water content of the membrane with current density could also affect ${D}_{{{\rm{H}}}_{2}}^{{\rm{eff}}}.$ Due to the electro-osmotic drag water is transported from anode to cathode, which could lead to a more homogeneous water distribution across the membrane at high current densities. However, this may be negatively affected by differential pressure operation and the corresponding hydraulic water transport from cathode to anode. For the conceivable variations in MEA temperature and membrane water content, one would expect, however, that the variation of ${D}_{{{\rm{H}}}_{2}}^{{\rm{eff}}}$ could not account for the above described more than 10-fold increase in the H₂ permeation rate.

Convective transport due to a total pressure difference between cathode and anode was shown to be insignificant by the permeation cell measurements presented in the previous section. There, the permeation rate was found to be perfectly first order with respect to p_H2 (cf Fig. 2c), as predicted in the absence of a total pressure difference driven flux (as discussed in the Theory section). Another possible effect on H₂ permeation could be the convective flux of water due to the electro-osmotic drag that is a function of current density. However, since the electro-osmotic drag of protons goes from the anode to the cathode, dragging along H₂O and thus H₂ dissolved in H₂O, it would lead to a lowering of the overall H₂ permeation rate from cathode to anode with increasing current density, i.e., the opposite of what we observe. Hence, the effect of the electro-osmotic drag is either negligible or is compensated by other effects which lead to an increase of H₂ permeation rate with current density.

In recent studies, Trinke et al. suggested that H₂ super-saturation in the ionomer phase of the cathode catalyst layer is the main reason for the increase of the H₂ permeation rate with current density, and that the extent of this increase depends on the mass transport properties of the cathode catalyst layer.³¹ The authors changed the ionomer content in the cathode and, consequently, the void volume fraction of the catalyst layer; they found that with increasing ionomer content the mass transport overpotential increased similar to what was shown previously by Rheinländer et al.³² Additionally, they observed a stronger increase of the H₂ permeation rate with current density for a higher ionomer content.³¹ While they ascribed this to an increasing degree of H₂ super-saturation in the ionomer phase with current density, a partial pressure build-up at/near the membrane/cathode interface could also explain this phenomenon. A similar behavior was observed in the present study when the ionomer/carbon (I/C) mass ratio in the cathode electrode was increased from its standard value of 0.6/1 to higher values of 1.2/1 (cf Fig. 4). By increasing the cathode I/C ratio, the volume fraction of ionomer in the cathode catalyst layer increases while its void volume fraction decreases, as is shown in Fig. 4a. Here, the catalyst volume fraction (V_cat; gray bars) is determined from the measured catalyst loading (L_cat), the average density of the 45.8 wt% Pt/C catalyst (ρ_cat ≈ 3.1 g cm⁻³), and the measured cathode layer thickness (t_cath), as outlined in detail in Ref. 7 For the calculation of the ionomer volume fraction (V_ion, brown bars), swelling of the ionomer due to water uptake is accounted for by considering a water content of λ = 21 (λ being the moles of water per mole of sulfonic acid group) for the applied operating conditions (liquid water at 80 °C),^29,33 which leads to a ≈80% volume increase of the ionomer compared to the dry ionomer (for details, see Ref. 7). The void volume fraction (V_void) then equates to V_void = 100% - V_cat - V_ion, which becomes rather small at an I/C mass ratio of 1.2/1 (white bars in Fig. 4a).

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This low void volume fraction and the high ionomer volume fraction in cathode electrodes with high I/C ratios has two possible consequences: (i) a low V_void will likely impede the removal of the evolved H₂ gas, which would lead to a partial pressure build-up at the membrane/cathode interface and thus to an increase of the H₂ concentration in the ionomer phase (as predicted by Henry's law), which in turn would increase the H₂ permeation rate acc. to Eq. 1; and/or (ii) a high V_ion might lead to a restricted transfer of the evolved H₂ from the catalyst surface through the ionomer film covering the catalyst surface into the open pore volume, which could lead to H₂ super-saturation in the ionomer phase, which in turn again would increase the H₂ permeation rate. While Trinke et al. suggest that H₂ super-saturation is responsible for the increase of the H₂ permeation rate with current density,³¹ a local H₂ pressure build-up was also suggested to cause this effect. Both phenomena would lead to an increase in the H₂ permeation rate with increasing current density, which would be expected to be increasingly more pronounced with increasing I/C ratio of the cathode electrode. This is indeed observed for the H₂ permeation rate vs current density recorded at 10 bar H₂ shown in Fig. 4b: between 0 A cm⁻² and 4 A cm⁻², the H₂ permeation rate increases by a factor of ≈1.4, ≈2.5, and ≈3.3 for cathode electrode I/C ratios of 0.6/1 (green symbols/lines), 0.9/1 (purple symbols/lines), and 1.2/1 (dark red symbols/lines), respectively. If this were simply due to a local H₂ partial pressure build-up at the membrane/cathode interface (p_H2,local(i)), p_H2,local(i) at 4 A cm⁻² over that at 0 A cm⁻² would have to increase by the same factor. As p_H2,local at 0 A cm⁻² must correspond to the H₂ partial pressure in the cathode compartment (p_H2,cathode), the H₂ partial pressure difference between the cathode compartment and the membrane/cathode interface at a given current density (Δp_cathode(i)) would then correspond to p_H2,local(i) - p_H2,cathode. Based on this, the increase of the H₂ permeation rate between 0 A cm⁻² and a given current density would be proportional to Δp_cathode(i)/p_H2,cathode, which for the observed increase of the H₂ permeation rate between 0 and 4 A cm⁻² at 10 bar (see above) would amount to Δp_cathode(i) ≈ 4 bar, ≈ 15 bar, and ≈ 23 bar, for the cathode electrode I/C ratios of 0.6/1, 0.9/1, and 1.2/1, respectively.

Assuming that Δp_cathode(i) produced by a hindered H₂ transport through the void volume of the cathode electrode for a given cathode electrode I/C ratio (i.e., for a given V_void) were independent of the total H₂ pressure in the cathode compartment (p_H2,cathode), the relative increase of the H₂ permeation rate between 0 A cm⁻² and a given current density would again be expected to be proportional to Δp_cathode(i)/p_H2,cathode, so that it should diminish as p_H2,cathode increases. This would be consistent with the observations shown in Fig. 3b and 3c, where the relative current density dependence of the H₂ permeation rate diminishes with increasing p_H2,cathode. While this local H₂ pressure build-up seems to be a reasonable explanation for the increase of the H₂ permeation rate with current density, the effect of H₂ super-saturation is another possible explanation.

In terms of the practical application of PEM-WEs, a substantial increase of the H₂ permeation rate with current density could be problematic, since it would result in a lower faradaic efficiency and could lead to the formation of a sufficiently high H₂ concentration in the anode gas even at high current densities, possibly exceeding the explosive limit. To illustrate the extent of an increasing H₂ permeation rate with current density, the H₂ permeation rates determined for Nafion^® 117 MEAs with either the standard cathode electrode I/C ratio of 0.6/1 (solid symbols/lines) or with the highest here examined I/C ratio of 1.2/1 (open symbols, dotted lines) are plotted in Fig. 5a for two different H₂ pressures in the cathode compartment (p_H2,cathode): (i) for a H₂ partial pressure of 1 bar (purple symbols/lines), where the strongest increase of the H₂ permeation rate with current density is observed, and (ii) at an application-relevant PEM-WE operating pressure of 30 bar (turquoise symbols/lines). As expected, the increase of the H₂ permeation rate with current density is more pronounced for cathode electrodes with the high I/C ratio of 1.2/1 compared to the standard I/C ratio of 0.6/1, both for 1 bar as well as for 30 bar. This clearly demonstrates the importance of designing cathode electrodes with an as low as possible I/C ratio, whereby for the standard cathode electrode I/C ratio of 0.6/1e proton conduction related voltage losses at 80 °C are <10 mV at 3 A cm^−2..⁷ The relative H₂ permeation rate at p_H2,cathode = 1 bar shown in Fig. 5b increases rather dramatically from 0 to 4 A cm⁻², namely by a factor of ≈9 (cathode I/C of 0.6/1) and ≈25 (cathode I/C of 1.2/1), consistent with the strong current density dependence of the H₂ permeation rate at 1 bar reported in the literature.^24,30 While a similarly high factor at p_H2,cathode = 30 bar would lead to very poor if not unacceptable faradaic efficiencies, the relative increase of the H₂ permeation rate at 30 bar is fortunately quite small, corresponding to a factor of only ≈1.1 (cathode I/C of 0.6/1) and ≈1.6 (cathode I/C of 1.2/1). This shows that at realistic PEM-WE operating conditions (i.e., at a H₂ pressure of 30 bar) and for a cathode electrode which is optimized with regards to its mass transport properties (i.e., with regards to its I/C ratio), the increase of the H₂ permeation rate with current density is almost negligible. In the following section, we will discuss the impact of the measured H₂ permeation rates on the efficiency and the operating range of a PEM-WE.

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In this section, the measured H₂ permeation rates will be used to discuss the overall efficiency and the feasible operating range of a PEM-WE for the membranes with different dry thicknesses investigated in this study (Nafion^® 117 and Nafion^® 212 with ≈178 μm and ≈51 μm, respectively). In today's PEM-WEs, relatively thick membranes (e.g., Nafion^® 117) are used, because they are mechanically robust and provide a good compromise between ohmic resistance and low gas permeability.³⁴ However, thinner membranes offer a high potential for reduction of H₂ generation costs,¹ as will be illustrated in the following.

Figure 6a shows a PEM-WE polarization curve of an MEA with a Nafion^® 117 membrane at a temperature of 80 °C and a H₂ partial pressure of 30 bar in the cathode compartment (the anode compartment is kept at ambient pressure), which today would be operated at a maximum current density of 1 – 2 A cm⁻² in a commercial electrolyzer.⁹ In general, increasing the current density can be a way to lower H₂ generation costs by reducing the total cell area required to achieve a given target H₂ production rate, i.e., lowering the capital expenditures. However, at higher current densities the cell voltage increases significantly due to the high ohmic resistance of the thick proton-conducting membrane, leading to a lower efficiency. This is illustrated by the following voltage loss analysis, that was performed analogous to how it was done in our previous work.⁷ Briefly, the overpotential for the OER (ΔE_OER) was determined by a Tafel analysis, based on a Tafel slope of ≈45 mV dec⁻¹ (determined in the 10–100 mA cm⁻² region) and a mass activity of ≈63 A g_Ir⁻¹ (determined at an iR-free cell voltage of 1.5 V) and is represented by the purple shaded areas in Fig. 6. Due to the fast kinetics of the HER, the resulting HER overpotential (ΔE_HER) is negligible as shown in our previous studies.^7,35 The overpotential due to ohmic losses (ΔE_ohmic) was determined by multiplying the ohmic resistance with the current density (ΔE_ohmic = i·R_Ω) and is illustrated by the orange shaded areas in Fig. 6. The ohmic resistance (R_Ω) represents the sum of the ionic resistance of the membrane (R_memb) and the electrical resistance (R_el) and is obtained by extracting the high frequency resistance (HFR) from the measured impedance spectra. The remaining overpotential (ΔE_transport), i.e., the difference between the measured cell voltage (E_cell) and the sum of the reversible cell voltage (E_rev), the OER overpotentials (ΔE_OER), and ohmic losses (ΔE_ohmic), is attributed to transport phenomena (ΔE_transport = E_cell - (E_rev + ΔE_OER + ΔE_ohmic)). This includes voltage losses due to proton transport in the catalyst layers (${R}_{{{\rm{H}}}^{+},{\rm{an}}}^{{\rm{eff}}},$ ${R}_{{{\rm{H}}}^{+},{\rm{cath}}}^{{\rm{eff}}}$) as well as mass transport losses (ΔE_mt)⁷ and is represented by the green shaded areas in Fig. 6.

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This analysis of the various voltage loss contributions shows that at the highest current density of 5 A cm⁻² ≈ 64% of the total voltage loss are due to ohmic losses (ΔE_ohmic) that are mostly due to the proton conduction resistance of the thick Nafion^® 117 membrane (see orange shaded area in Fig. 6a). Since the electrical resistance represents only a small fraction of the ohmic resistance (≈12 mΩcm² for the setup used in this study⁷), reducing the ionic membrane resistance offers the largest leverage to improve high current density performance. Figure 6b shows the result of reducing the membrane thickness by a factor of ≈3.5 by using a Nafion^® 212 (51 μm dry thickness) instead of the Nafion^® 117 (178 μm dry thickness). With the thinner membrane, the ΔE_ohmic contribution at the highest current density of 5 A cm⁻² is lowered by a factor of ≈2, now accounting for only ≈44% of the total voltage loss. Simultaneously, at the frequently used voltage efficiency target of 70% based on the lower heating value (LHV) of H₂ (corresponding to ≈1.79 V), the current density increases from 1.6 A cm⁻² to 3.5 A cm⁻² (see red and blue dashed lines in Fig. 6), i.e., by a factor of ≈2.3 for the MEA with the thinner Nafion^® 212 membrane. This increase of the stack's H₂ output translates directly into a stack cost reduction by a factor of ≈2.3 while the same voltage efficiency is retained. From this example, it becomes clear that minimizing the membrane thickness offers great potential for cost reduction.

While the voltage efficiency of a thin Nafion^® 212 membrane is quite superior, it obviously exhibits a higher H₂ permeation rate which results in a lower faradaic efficiency, especially if the electrolyzer is operated at elevated pressure. In general, however, pressurized electrolysis is beneficial compared to ambient pressure operation, because it reduces the energy demand for subsequent mechanical compression as well as the effort for gas drying due to the lower water content at higher pressure.^1,36 Typical operating pressures of commercial PEM-WEs are in a range of 20–50 bar,^9,37 and a H₂ partial pressure of 30 bar is chosen here for the following analysis. The overall efficiency taking into account the voltage efficiency as well as the faradaic efficiency is presented in Fig. 7a for MEAs based on a Nafion^® 117 membrane (red lines in Fig. 7a) and a Nafion^® 212 membrane (blue lines). The voltage efficiency based on the LHV of H₂, ${\eta }_{{\rm{voltage}}},$ can be calculated by dividing the reaction enthalpy for water in its gaseous state, ${\rm{\Delta }}{H}^{0}$ (−242 kJ mol⁻¹, corresponding to an LHV-equivalent voltage of 1.25 V) by the actual electrical energy input determined from the operating cell potential, ${E}_{{\rm{cell}}}:$

$$\begin{eqnarray}&&{\eta }_{{\rm{voltage}}}=\left|\displaystyle \frac{-{\rm{\Delta }}{H}^{0}}{2\cdot {\rm{F}}\cdot {E}_{{\rm{cell}}}}\right|\end{eqnarray} \tag{ 5 }$$

The dashed lines in Fig. 7a show the voltage efficiency, ${\eta }_{{\rm{voltage}}},$ at a H₂ partial pressure of 30 bar, at ambient anode compartment pressure, and at a temperature of 80 °C, as determined from the measured polarization curves in Fig. 6 in combination with Eq. 5. Obviously, the MEA with the thin Nafion^® 212 membrane (blue line) exhibits a higher voltage efficiency than that with the thick Nafion^® 117 membrane, especially at high current densities, due to the lower ohmic resistance as already discussed in Fig. 6.

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On the other hand, the faradaic efficiency can be calculated as

$$\begin{eqnarray}&&{\eta }_{{\rm{faradaic}}}=\displaystyle \frac{{i}_{{\rm{cell}}}-{i}_{{{\rm{H}}}_{2}}-{i}_{{{\rm{O}}}_{2}}}{{i}_{{\rm{cell}}}}\end{eqnarray} \tag{ 6 }$$

where ${i}_{{\rm{cell}}}$ is the current density at which the cell is operated—corresponding to a certain theoretical H₂ production rate—and ${i}_{{{\rm{H}}}_{2}}$ and ${i}_{{{\rm{O}}}_{2}}$ are the H₂ and the O₂ permeation current densities in units of mA cm⁻². Let us first estimate the relative contribution of ${i}_{{{\rm{O}}}_{2}}$ compared to ${i}_{{{\rm{H}}}_{2}}$ for the here considered PEM-WE operation with ${p}_{{{\rm{H}}}_{2}}$ ≈ 30 bar in the cathode compartment and with ambient pressure in the anode compartment (corresponding to ${p}_{{{\rm{O}}}_{2}}$ ≈ 0.5 bar at 80 °C), first looking into the case where no electrolysis current is applied: even though ${i}_{{{\rm{O}}}_{2}}$ in PFSA membranes is very similar to ${i}_{{{\rm{H}}}_{2}}$ at equal partial pressures of O₂ and H₂ (note: while the O₂ permeability is ≈2 times lower than that of H₂,¹⁴ each mol of O₂ consumes two moles of H₂ upon its reaction to H₂O on the cathode catalyst), the ≈60-fold higher partial pressure of H₂ compared to O₂ equates to a ≈60-fold lower ${i}_{{{\rm{O}}}_{2}}$ compared to ${i}_{{{\rm{H}}}_{2}}.$ Therefore, under these pressure conditions and at 0 A cm⁻², ${i}_{{{\rm{O}}}_{2}}$ is negligible compared to ${i}_{{{\rm{H}}}_{2}}.$ On the other hand, under PEM-WE operation at ambient anode compartment pressure, the O₂ permeation rate was found to increase by a factor of ≈17 between 0 and 2 A cm⁻²¹⁵ (analogous to what is observed for the H₂ permeation rate; cf Fig. 5b), so that on the basis of this report the ratio of ${i}_{{{\rm{H}}}_{2}}$ over ${i}_{{{\rm{O}}}_{2}}$ is projected to change to ≈3/1 at 2 A cm⁻². While this would not be entirely negligible anymore, the contribution of ${i}_{{{\rm{O}}}_{2}}$ to the overall faradaic efficiency at >1 A cm⁻² can nevertheless be neglected, since the faradaic efficiency is well above 95% at current densities of >1 A cm⁻². Therefore, we have neglected ${i}_{{{\rm{O}}}_{2}}$ in the following calculation of the faradaic efficiency that is based only on the current dependent H₂ permeation rates taken from Fig. 3 (using the average value of the measurements taken at increasing and decreasing current density), and which is represented by the dotted lines in Fig. 7a. As expected, the faradaic efficiency is higher for the MEA with the thick membrane, especially at <0.5 A cm⁻², where the H₂ production rate is relatively low compared to the losses due to H₂ permeation; again, as argued above, the contribution of ${i}_{{{\rm{O}}}_{2}}$ to the faradaic efficiency is negligible at such low current densities for the here considered PEM-WE operation at a H₂ partial pressure of 30 bar and ambient pressure in the anode compartment.

The overall efficiency, taking into account voltage losses as well as losses due to H₂ permeation can now be calculated as

$$\begin{eqnarray}&&{\eta }_{{\rm{total}}}={\eta }_{{\rm{voltage}}}\cdot {\eta }_{{\rm{faradaic}}}\end{eqnarray} \tag{ 7 }$$

and is represented by the full lines in Fig. 7a. An optimum in total efficiency of 77% is achieved for the MEA based on a Nafion^® 117 membrane at a current density of ≈0.3 A cm⁻². For the Nafion^® 212 membrane, a maximum in efficiency of 75% is obtained at a significantly higher current density of ≈0.8 A cm⁻². In general, the MEA with the thick Nafion^® 117 membrane shows a higher efficiency compared to the thin Nafion^® 212 membrane at low current densities, where losses due to H₂ permeation are the dominating effect (as discussed above, the contribution by ${i}_{{{\rm{O}}}_{2}}$ is projected to be negligible at <1 A cm⁻²). At high current densities, on the other hand, ohmic losses are dominating the overall efficiency while faradaic losses are almost negligible. Consequently, the MEA with the thin Nafion^® 212 membrane exhibits a higher efficiency at current densities above ≈0.7 A cm⁻². Considering that operation at high current densities is preferred to reduce the electrolyzer stack costs, a thin membrane would always be favorable in terms of efficiency.

However, besides of the maximum efficiency at a certain operating point, the dynamic operating range, i.e., the range of current densities over which an electrolyzer can be operated, is another important factor for the application of PEM-WEs, especially in the context of an increasing share of renewable energy sources and the resulting intermittent energy output. Defining a minimum total efficiency of 70% (LHV basis) as a target for PEM-WE operation, the MEA with the thick Nafion^® 117 membrane could be operated in a range from 0.07 – 1.4 A cm⁻² (cf red dashed bar in Fig. 7b) and the MEA with the thin Nafion^® 212 membrane in a range from 0.23–3.1 A cm⁻² (cf blue dashed bar in Fig. 7b). Translated into a dynamic stack power range (P_stack = E_cell × i_cell), this corresponds to ≈0.11 – 2.5 W cm⁻² and ≈0.36 – 5.5 W cm⁻² for Nafion^® 117 and Nafion^® 212, respectively. This shows that when a minimum efficiency of 70% is the only criteria that is taken into account, a reasonably large dynamic stack power range with a factor of ≈23 (Nafion^® 117) and ≈15 (Nafion^® 212) can be achieved for both membranes.

For a practical application, however, the lower limit in current density at which an electrolyzer can be operated will not be defined solely by an efficiency requirement, but the H₂ concentration in the anode compartment as a result of the H₂ permeation through the membrane has also to be considered. Since the HOR activity of iridium-based catalysts is negligible in the relevant anode potentials,¹³ permeating H₂ will only be removed by the exiting anode gas, so that the H₂ volume fraction (${x}_{{{\rm{H}}}_{2}}$) in the O₂-containing anode compartment can simply be calculated from the H₂ permeation rates (in terms of ${i}_{{{\rm{H}}}_{2}}$) from Fig. 3 and the PEM-WE current (i_cell) under the assumption that a loss of O₂ on the anode due to permeation to the cathode is negligible:

$$\begin{eqnarray}&&{x}_{{{\rm{H}}}_{2}}={i}_{{{\rm{H}}}_{2}}/\left({i}_{{{\rm{H}}}_{2}}+0.5\cdot {i}_{{\rm{cell}}}\right)\end{eqnarray} \tag{ 8 }$$

Figure 8 shows the resulting values of ${x}_{{{\rm{H}}}_{2}}$ vs current density for different H₂ partial pressures for Nafion^® 117 (Fig. 8a) and for Nafion^® 212 (Fig. 8b). The lower explosive limit for H₂ in O₂ is ≈4%.¹² but in a real system we assume that a safety factor of at least two would be applied, which means that the H₂ in O₂ volume fraction should not exceed 2%, a value which is marked by the dashed red line in Fig. 8. At a H₂ partial pressure of 30 bar and a temperature of 80 °C, this requirement would result in a lower limit for operation of 1.1 A cm^-2 for the Nafion^® 117 membrane (cf Fig. 8a), while safe operation would not be possible below 3.4 A cm⁻² for the Nafion^® 212 membrane (cf Fig. 8b). Taking into account the current density range imposed by the efficiency target of 70% LHV (cf Fig. 7) as well as the upper limit for ${x}_{{{\rm{H}}}_{2}}$ of 2%, the MEA with a Nafion^® 117 membrane could only be operated in a very small window of current densities from 1.1–1.4 A cm⁻², while both criteria cannot be fulfilled simultaneously for the Nafion^® 212 based MEA. Therefore, without additional mitigation strategies to lower the H₂ concentration in the anode compartment, the desired PEM-WE operating conditions of 30 bar and 80 °C with a reasonable dynamic range would not be possible with MEAs based on either of the two membranes.

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On the materials level, this issue could be addressed by using membranes that have a higher proton conductivity to H₂ permeability ratio (σ_H+/P_H2 ratio) than PFSA membranes,³⁸ but so far alternative membrane materials such as hydrocarbon (HC) based membranes do not show a more than ≈1.5 – 2 times higher σ_H+/P_H2 ratio than conventional PFSA membranes.^38,39 While this would be a benefit, it would still not provide a sufficiently large dynamic power range; furthermore, the durability of HC based membranes still needs to be improved.³⁹ Therefore, other mitigation strategies have currently to be employed in order to prevent the formation of an explosive gas mixture at low current densities in a PEM-WE. A detailed analysis of different mitigation strategies for PEM-WE as well as for alkaline electrolysis can be found in a recent study by Trinke et al.²⁷ The simplest options are to reduce the operating temperature and/or the H₂ pressure in order to reduce H₂ permeation and to extend the operating range to lower current densities. However, lower temperatures result in higher kinetic overpotentials and lower proton conductivity, i.e., in a lower efficiency, while a lower H₂ output pressure translates into a higher energy demand for subsequent mechanical compression. Therefore, for electrolysis at higher pressures, the formation of an explosive gas mixture even at low current densities is generally prevented by the incorporation of a H₂/O₂ recombination catalyst to react the permeated H₂ to water. Typically, a platinum catalyst is used, which can be placed at several locations within the cell. In some instances, it is used in a gas recombiner positioned downstream of the anode gas outlet or it is deposited on the backside of the PTL.³⁰ However, the former approach still leaves the risk of a small volume of potentially explosive gas within the catalyst layer, PTL, and flow-field. Another approach is the incorporation of a recombination catalyst into the membrane, either dispersed within a certain region of the membrane or introduced as an inter-layer, so that permeating H₂ and O₂ can recombine to water inside the membrane, which was shown to lead to a significant reduction of the H₂ in O₂ volume fraction in the anode compartment.^40–42 Of course, a recombination catalyst will only reduce the risk of the formation of an explosive gas mixture but will not improve the faradaic efficiency. However, as the analysis in Fig. 7b shows, a sufficient dynamic operating range at a high efficiency of ≥70% can be obtained despite of the faradaic losses. Consequently, the implementation of a recombination catalyst is currently the only approach to obtain a reasonable dynamic power operating range for a PEM-WE with PFSA membranes.

This section briefly explains the assumptions made to determine the measurement error of the H₂ permeation rate as displayed by the error bars in Fig. 3 and 4. Three main sources of measurement errors were considered to calculate the overall error of the H₂ permeation measurement: (i) For the mass spectrometer a total error ${\sigma }_{{\rm{MS}}}=3.2\, \%$ was determined based of the inaccuracy of the calibration curve and fluctuations of the measurement value over time; (ii) An overall error ${\sigma }_{{\rm{TS}}}=2.7\, \%$ was assumed for the components of the test station, i.e., for the inaccuracy of the gas flow determined by the mass flow controllers and the limited accuracy of temperature and pressure regulation; (iii) The largest error is related to an inaccuracy when determining the active area for H₂ permeation due to edge effects resulting from the assembly of the MEA along with gaskets and subgaskets in the cell hardware. A schematic drawing of the cell cross section is shown in Fig. A·1. The area of the electrodes, ${A}_{{\rm{E}}},$ is 5 cm² and is taken into account to calculate the area specific current density. However, to determine the area specific H₂ permeation rate an area of 5.76 cm² was assumed (corresponding to the size of the window in the subgasket, ${A}_{{\rm{SG}}},$ i.e., 24 × 24 mm) since H₂ permeation can in general occur through the entire subgasket window. If one assumes that the increase in H₂ permeation rate with current density is related to H₂ super saturation in the catalyst layer as discussed in the previous sections, this effect would of course only occur within the electrode area (5 cm²) and not at the edge between electrode and subgasket. Consequently, assuming an area of 5.76 cm² to determine the area specific H₂ permeation rate would lead to an underestimation of the real value, especially at high current densities where the effect of H₂ super saturation is most pronounced. The resulting error which is a function of the current density, i, can be calculated according to

$$\begin{eqnarray}&&{\sigma }_{{\rm{AA}},+}\left(i\right)=\displaystyle \frac{{A}_{{\rm{SG}}}-{A}_{{\rm{E}}}}{{A}_{{\rm{SG}}}}\cdot \displaystyle \frac{{n}_{{{\rm{H}}}_{2}}\left(i\right)-{n}_{{{\rm{H}}}_{2}}\left(i=0\right)}{{n}_{{{\rm{H}}}_{2}}\left(i\right)}\end{eqnarray} \tag{ A·1 }$$

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The first term in Eq. A·1 denotes the difference between the area of the subgasket window, ${A}_{{\rm{SG}}},$ and the electrode area, ${A}_{{\rm{E}}},$ normalized by ${A}_{{\rm{SG}}}.$ The second term accounts for the fraction of the H₂ permeation rate which is current dependent by subtracting the permeation rate at zero current, ${n}_{{{\rm{H}}}_{2}}(i=0),$ from the permeation rate at a certain current density, ${n}_{{{\rm{H}}}_{2}}(i),$ normalized by ${n}_{{{\rm{H}}}_{2}}(i).$ For the measured permeation rates shown in Fig. 3 this yields an error of ${\sigma }_{{\rm{AA}},+}\left(i\right)=0-11.9\, \%$ depending on current density and pressure. Since this effect would lead to an underestimation of the H₂ permeation rate, ${\sigma }_{{\rm{AA}},+}\left(i\right)$ will be considered to determine the error bars in positive direction in Figs. 3 and 4.

On the other hand, while the PTFE gaskets (thickness ≈300 μm) can be assumed as impermeable, the PTFE subgasket is only 10 μm thick and, hence, H₂ permeation through the subgasket is not negligible (cf red arrow in Fig. A·1). This additional permeation which is not accounted for in our measurement would lead to an overestimation of the area specific H₂ permeation rate. The permeation coefficient for PTFE is about ten times lower than for wet Nafion^®21 and the resulting error can be calculated as

$$\begin{eqnarray}&&{\sigma }_{{\rm{AA}},-}=\displaystyle \frac{{A}_{{\rm{G}}}-{A}_{{\rm{SG}}}}{{A}_{{\rm{SG}}}}\cdot \displaystyle \frac{{t}_{{\rm{memb}}}}{10\cdot {t}_{{\rm{SG}}}+{t}_{{\rm{memb}}}}\end{eqnarray} \tag{ A·2 }$$

Here, ${A}_{{\rm{G}}}$ is the area of the gasket window (27 × 27 mm, cf Fig. A·1) and ${A}_{{\rm{SG}}}$ is the area of the subgasket window while ${t}_{{\rm{memb}}}$ is the membrane thickness and ${t}_{{\rm{SG}}}$ the thickness of the subgasket. This yields an error ${\sigma }_{{\rm{AA}},-}=9.0 \%$ for the Nafion^® 212 membrane and an error ${\sigma }_{{\rm{AA}},-}=17.0 \%$ for the Nafion^® 117 membrane which will be considered to determine the error bars in negative direction in Figs. 3 and 4.

The total error for the H₂ permeation rate is then determined according to

$$\begin{eqnarray}&&{\sigma }_{{\rm{total}},\pm }=\sqrt{{\sigma }_{{\rm{MS}}}^{2}+{\sigma }_{{\rm{TS}}}^{2}+{\sigma }_{{\rm{AA}},\pm }^{2}}\end{eqnarray} \tag{ A·3 }$$

This yields total errors ${\sigma }_{{\rm{total}},+}=4.2-12.6\, \%$ and ${\sigma }_{{\rm{total}},-}=9.9/17.5\, \%$ (Nafion^® 212 / Nafion^® 117) for the H₂ permeation rates which is illustrated by the error bars in Fig. 3 and 4.

In order to verify that the permeation rate values for different MEAs shown in Fig. 3a and 3b are reproducible, we did conduct a limited number of repeat experiments. The permeation rates obtained from the repeat measurements (open symbols and dashed lines) are compared to the original data (full symbols and full lines) in Fig. A·2.

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