# On the Main Factors Limiting the Performance of State-of-the-Art Polymer Electrolyte Membrane Fuel Cells in the 90-100 °C Temperature Range

G Etienne, A Ouhammi, Assma El Kaddouri, J Mainka, J Dillet, A Morin, M Chatenet, Olivier Lottin

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G Etienne, A Ouhammi, Assma El Kaddouri, J Mainka, J Dillet, et al.. On the Main Factors Limiting the Performance of State-of-the-Art Polymer Electrolyte Membrane Fuel Cells in the 90-100 °C Temperature Range. Electrochimica Acta, 2025, 10.1016/j.electacta.2025.147320. hal-05262865

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# On the main factors limiting the performance of state-of-the-art polymer electrolyte membrane fuel cells in the 90–100 °C temperature range

G. Etienne<sup>a, ID</sup>, A. Ouhammi<sup>a</sup>, Assma El Kaddouri<sup>a, ID</sup>, J. Mainka<sup>a, ID</sup>, J. Dillet<sup>a</sup>, A. Morin<sup>c, ID</sup>, M. Chatenet<sup>b, ID</sup>, O. Lottin<sup>a, *, ID</sup>

## ARTICLE INFO

**Keywords:**

IT-PEMFC

90–100 °C

Perfluorosulfonic acid membrane

LSC-PFSA

Performance limitations

High-frequency resistance

High current densities

## ABSTRACT

This study investigates the performance limitations of state-of-the-art PEMFC operating in the 90–100 °C temperature range under low to moderate RH conditions, i.e. close to those encountered in automotive applications. Using a commercial MEA based on a 12 µm thick LSC-PFSA membrane, a comprehensive performance mapping was conducted across various operating parameters including temperature, pressure, RH, and air stoichiometry. Results show that elevated temperature negatively impacts performance, especially at high current densities, primarily due to MEA dehydration. Electrochemical Impedance Spectroscopy (EIS) revealed that the cell high-frequency resistance ($R_{hf}$) increases sharply with current density at high temperatures, highlighting hydration as a dominant limiting factor. Accelerated stress tests confirmed that heat generation was the primary driver of MEA dehydration under these conditions, rather than electro-osmotic drag. While increasing gas RH improves hydration and performance, a threshold (~40% RH) was identified, beyond which gains are offset by increased oxygen dilution and mass transport limitations. iR-corrected polarization curves also showed residual voltage losses at high temperatures, attributed to reduced oxygen partial pressure due to increased water vapor content. Impedance spectra confirmed no significant increase in mass transport resistance at high temperature, suggesting that oxygen dilution and MEA dehydration are the primary causes of performance degradation. These findings underscore the critical importance of water management at elevated temperatures and provide a foundation for future work on optimized materials and operating strategies for intermediate temperature PEMFC.

## 1. Introduction

Thanks to their high-power density, rapid start-up and shutdown, and good efficiency, PEMFC are suitable for many applications, particularly in heavy transport [1]. PEMFC are divided into several categories: low temperature (LT-PEMFC) below 90 °C, intermediate temperature (IT-PEMFC) above 80 °C/90 °C but still using PFSA (PerFluoroSulfonic Acid) or more generally ionomer membranes, and high temperature (HT-PEMFC) above 120 °C using PBI membranes. During operation, hydrogen undergoes oxidation on the anode side while oxygen undergoes reduction at the cathode. This results in the production of electrical work, water, and heat which must be removed by an external cooling system. Increasing the temperature of the Fuel Cell (FC) can therefore reduce the size of the cooling system, which is advantageous when space is limited, as is often the case in many transport

applications. In addition, increasing cell temperature is believed to improve half-reactions kinetics and thus electrodes tolerance to platinum poisoning by gases such as carbon monoxide or sulphur compounds [2,3]. Most studies deal with LT-PEMFC but some works considered HT-PEMFC because of their better tolerance to hydrogen impurities [4,5], easier water management with suitable materials [6] to prevent flooding and better thermal management [7,8]. However, performance and durability remain major obstacles due to high corrosion of bipolar plates and severe degradation of electrodes and membranes [6,9, 10]. IT-PEMFC share some advantages with HT-PEMFC, such as tolerance to catalyst poisoning and improved thermal management, while also offering good performance and relying on well-known PFSA membranes as in LT-PEMFC, with the added benefit of interesting durability: up to several tens of thousands of operating hours.

IT-PEMFC operating conditions generally correspond to

<footnote><sup>a</sup> LEMTA, CNRS, Université de Lorraine, Nancy, France</footnote>

<footnote><sup>b</sup> Univ. Grenoble Alpes, Univ. Savoie Mont Blanc, CNRS, Grenoble INP, LEPMI, Grenoble, France</footnote>

<footnote><sup>c</sup> Univ. Grenoble Alpes, CEA, LITEN, Grenoble, France</footnote>

<footnote>* Corresponding author.</footnote>

<footnote>E-mail address: olivier.lottin@univ-lorraine.fr (O. Lottin).</footnote>
temperatures between 90 and 120 °C and low relative humidity. Consequently, a key parameter of the system is MEA hydration. Long-side-chain PFSA polymer is known to perform well at low temperatures but suffers from dehydration at high temperatures and low RH, leading to an increase in membrane resistance and therefore to a decrease in proton conductivity [11–14] and performance. Short-side-chain PFSA have been developed as electrolyte membranes and as ionomers in electrodes due to their superior water retention capacity at high temperatures [15,16]. Particularly at intermediate temperature, membranes and catalyst layers made with SSC-PFSA perform better than when using LSC-PFSA [17,18]. Stassi et al. [19] for instance reported better performances of SSC-PFSA at 130 °C, 100% RH, 3 bars compared with LSC-PFSA, while Zhao et al. [20] observed significantly better performances of SSC-based MEA at 95 °C, particularly with gas inlet RH equal to 30%. Several authors carried out electrochemical impedance spectroscopy measurements at different temperature and RH, observing a lower high frequency resistance ($R_{hf}$) with the SSC-PFSA membrane than with the LSC-PFSA membrane, which is explained by greater water uptake at high temperature and low RH [19,20]. Using molecular simulations, other studies report a better connectivity and a more homogeneous distribution of water cluster at intermediate hydration state for SSC than LSC, which implies a higher proton conductivity of the membrane and therefore better performances [21–23]. In parallel, several groups have developed membranes based on hydrocarbon ionomer, which are mechanically more stable, cheaper and fluorine-free [24–26], but with performance that highly depend on the gas inlet RH [27].

One way to improve FC operation at intermediate temperatures, especially under dry conditions, consists in adapting the FC materials, such as the type of ionomer for the membrane and electrodes or the ionomer/carbon ratio in the electrodes. Another way consists of applying intermediate conditions such as low relative humidity and a temperature below 100 °C, while adapting the operating conditions when needed to allow the use of well-established materials as in the LT-PEMFC. Hickner et al. [28] studied the water content inside an operating PEMFC as a function of current density and cell temperature under fully humidified conditions: for cell temperatures between 40 and 80 °C and a constant air stoichiometry equal to 2, they noted a decrease in the water content of the cell with temperature, which was more pronounced at higher current density. Indeed, higher fuel cell temperature improves the water removal capacity through the gas flow. The problems of dehydration of the MEA induced by the operating temperature of the fuel cell could therefore be compensated by appropriately choosing the operating point in terms of air stoichiometry and gas inlet RH.

Several groups studied how air stoichiometry [29,30] and/or current density [31] governed the MEA hydration. Kim et al. observed that stable performance at 70 °C was linked to precise air stoichiometry as a function of the current density [32]. Cho et al. [33] considered the impact of the air flow rate on the cathode side at 120 °C and several RH (10 to 35%) for different current densities: they observed that a low air flow rate implies a lack of reactant while a high flow rate induces dehydration of the MEA by excessive water removal, leading to voltage drops. For catalyst layers, Cho et al. [33] observed that a high ionomer binder content implies slightly better performance at low and medium current densities, but lower performance at high current density where mass transport problems may occur, including flooding. Also at 10% RH, they observed that the FC high-frequency resistance firstly decreases with increasing current density and thus water production, before a sharp increase at 0.2 A·cm⁻² due to the dehydration of the MEA, which they justify by the electro-osmosis flux becoming more important than water back-diffusion from the cathode to the anode, as has been observed in several studies [34,35]. Such a membrane drying phenomenon is expected to happen at significantly higher current densities with state-of-the-art components.

Several works investigated the behaviour of fuel cells at different current densities using impedance spectroscopy, mainly to separate the

voltage drop associated with charge transfer, mass transfer and membrane ionic resistance, i.e. high frequency resistance. These phenomena were then related to the characteristics of the membrane and electrodes to provide a better understanding of fuel cell operation, depending on the operating point. Many focused on a small range of current densities: for example, Reshetenko et al. [36] observed significant variations in the parameters of the catalytic layer between 50 and 400 mA/cm² at 80 °C. A large increase in proton conductivity in the catalytic layer was also observed when the current density increases while the double layer capacity decreases, which can be explained respectively by a higher water content and better proton transport. Tang et al. [13] studied the evolution of the voltage drop due to charge transfer, membrane resistance and mass transport between 0.1 and 1.9 A/cm² at 100 % RH, 80 and 120 °C. For both temperatures, they observed that the charge transfer resistance, mainly responsible for the voltage drop at low current densities, decreases as current density increases in accordance with the impedance theory. In parallel, the high frequency resistance, assumed to be governed mainly by the membrane, decreases very slightly, or even remains constant, with increasing current density. They also reported better mass transfer parameters with increasing temperature, especially at high current densities, which they did not explain.

Although these studies provide detailed data on FC operation under various conditions, they primarily focus on high relative humidity and/or typical operating temperatures (Table 1), which differ significantly from the conditions that are targeted in heavy mobility. In addition, in most cases the MEA materials used in the above-mentioned studies are neither recent nor representative of the present state of the art; nowadays thinner membranes and more optimised ink deposition processes are the norm. The observations and conclusions are therefore difficult to compare with those of previous studies, which reinforced our motivation to consider the impact of conditions close to those for heavy transport systems - i.e. 95 °C, our reference temperature, and low relative humidity - on the performance of state-of-the-art MEA.

Although SSC-PFSA is generally considered the better candidate in the literature for IT-PEMFC, this study investigates the feasibility of using LSC-PFSA at intermediate temperatures and aims to clarify the phenomena that limit its performance under such conditions. To this end, we operated a commercial MEA at temperatures up to 105 °C, taking 95 °C and 70 °C as the reference cases. The gas inlet relative humidity (RH) was maintained at low to moderate levels (i.e. 20 to 50% RH) to simulate conditions like those encountered in automotive applications. Electrochemical impedance spectroscopy was performed to study the evolution of the high frequency resistance $R_{hf}$, as a marker of MEA hydration, as well as the parameters representative of oxygen transport & cathode kinetics. This work was done using state of the art 12 µm thick LSC-PFSA membrane and electrode materials. Particularly, we were interested in performance limitations and focused on high current densities, where mass transfer resistance and the lack of reactants are usually considered as the main phenomena responsible for voltage drop at usual operating temperatures. However, it was observed that depending on the operating conditions, MEA dehydration could become a significant factor limiting performance, since low gas relative humidity combined with high cell temperature may affect the membrane hydration state [47]. In addition, high current densities can lead to local membrane heating, further contributing to its drying out [40]. As a result, the phenomena limiting cell performance under these conditions may differ from those typically observed at standard operating temperatures.

## 2. Materials and methods

### 2.1. MEA and break-in protocol

MEA performances were mostly measured using a single cell with 50 straight parallel channels 0.15 mm deep at the anode and 0.25 mm deep at the cathode (Fig. 1(a)). Another cell was also used, in occasions,
<caption>**Table 1**</caption>

Non-exhaustive list of current density, operating conditions and materials in various literature studies.

<table><thead><tr><th rowspan="2">Cell T (°C)</th><th rowspan="2">i range (A/cm²)</th><th colspan="2">Air/cathode</th><th colspan="2">Hydrogen/anode</th><th colspan="2">Membrane</th><th rowspan="2">Authors</th><th rowspan="2">Ref.</th></tr><tr><th>Stoichiometry/ flowrate</th><th>RH (%)</th><th>Stoichiometry/ flowrate</th><th>RH (%)</th><th>Type</th><th>Thickness (μm)</th></tr></thead><tbody><tr><td>40–60–80</td><td>0–1.5</td><td>2</td><td>100</td><td>90 L/h</td><td>100</td><td>Nafion 112</td><td>50</td><td>Hickner et al.</td><td>[28]</td></tr><tr><td>60</td><td>0.5–1.5</td><td>2, 4, 6</td><td></td><td></td><td></td><td>Aquivion</td><td>30</td><td>Cho et al.</td><td>[33]</td></tr><tr><td>120</td><td>0.05–0.38</td><td>4.2 to 14.7 (L/h)</td><td>10.0–35.0</td><td>2.58 (L/h)</td><td>10.0–35.0</td><td>Nafion 115</td><td>100</td><td>Mérida et al.</td><td>[37]</td></tr><tr><td>70</td><td>0.1–0.5</td><td>0–4</td><td>0–100</td><td>2</td><td>100</td><td>Not disclosed</td><td></td><td>Moçotéguy et al.</td><td>[38]</td></tr><tr><td>49–57</td><td>0.15–0.4</td><td>1.6</td><td>25–122</td><td>1.3</td><td>25–122</td><td></td><td></td><td>Malevich et al.</td><td>[39]</td></tr><tr><td>60</td><td>0.3–0.8</td><td>3</td><td>100</td><td>1,4</td><td>100</td><td>Nafion 112</td><td>50</td><td></td><td></td></tr><tr><td>80</td><td>0.05–0.4</td><td>9.5</td><td>50</td><td>2</td><td>100</td><td>Gore</td><td>16–18</td><td>Reshetenko et al.</td><td>[36]</td></tr><tr><td>80–120</td><td>0.1–1.9</td><td>60 (L/h)</td><td>100</td><td>18 (L/h)</td><td>100</td><td>Nafion 112</td><td>50</td><td>Tang et al.</td><td>[13]</td></tr><tr><td>68</td><td>0–3</td><td>60 (L/h)</td><td>50–100</td><td>60 (L/h)</td><td>50–100</td><td>Not disclosed</td><td></td><td>Ge et al.</td><td>[40]</td></tr><tr><td>52</td><td>0.05–0.4</td><td>4</td><td>Dry to humidification (lower than 100%)</td><td>Not disclosed</td><td>Dry to humidification (lower than 100%)</td><td>Nafion</td><td>30</td><td>Ciureanu et al.</td><td>[41]</td></tr><tr><td>60</td><td>0.2–1.2</td><td>2.5–3.5</td><td>40–100</td><td>1.5</td><td>40–100</td><td>Not disclosed</td><td>15</td><td>Miao et al.</td><td>[42]</td></tr><tr><td>80</td><td>0.1–1.5</td><td>4.0–8.0</td><td>50–100</td><td>2.0–3.0</td><td>30–100</td><td>Nafion XL</td><td>27.5</td><td>Najafi et al.</td><td>[43]</td></tr><tr><td>80</td><td>0.05–0.9</td><td>>10 (O2)</td><td>30–70</td><td>>10</td><td>30–70</td><td>Not disclosed</td><td></td><td>Schiefer et al.</td><td>[44]</td></tr><tr><td>70</td><td>0–2</td><td>30 (L/h)</td><td>40–80</td><td>90 (L/h)</td><td>40–80</td><td>Not disclosed</td><td>15</td><td>Xia et al.</td><td>[45]</td></tr><tr><td>120</td><td>0.1–1.5</td><td>45 (L/h)</td><td>25–100</td><td>60 (L/h)</td><td>25–100</td><td>Nafion 112</td><td>50</td><td>Zhang et al.</td><td>[46]</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>**Fig. 1.** Straight parallel channels (a) and serpentine channels (b) bipolar plates.</figcaption></figure>

corresponding to earlier designs (e.g. serpentine channels, Fig. 1(b)). In both cases, the plates were made of gold-coated 316 L stainless steel.

The cell was operated in counter-flow, its temperature being imposed thanks to an oil circulation loop. For every experiment, 25 cm² commercial MEA were used, consisting of:

* Anode: Pt/HSAC 50 wt% (Tanaka TKK TEC10E50E) - 0.1 mg/cm²

* Cathode: Pt/HSAC 50 wt% (Tanaka TKK TEC10E50E) - 0.3 mg/cm²

* Ionomer binder: Nafion® D2020CS for both anode and cathode side with an ionomer/carbon ratio equal to 0.8

* Ionomer membrane: Gore 788.12

* Gas diffusion layer (GDL): Freudenberg H14CX653

A 25 % compression rate was applied to each GDL using two 100 µm PTFE gaskets and one 23 µm polyethylene naphthalate (PEN) film. Before any performance characterization, each MEA was subjected to

a conditioning (break-in) protocol, consisting of potentiostatic steps at OCV (30 s), 0.6 V (45 s) and 0.3 V (60 s) for about 2 h. The cell temperature was set to 70 °C, gas pressure and relative humidity (RH) were imposed at 1 bar and 50% RH; the stoichiometry was set to 1.5 for hydrogen and 3 for air, calculated on the measured current density at each imposed voltage. External parameters such as cell temperature, gas RH, pressure and stoichiometries were controlled.

For performance mapping, all the external parameters were varied, except for the hydrogen stoichiometry, which was deliberately set to a low value (1.25) to approach real-life operating conditions. After the performance mapping, the gas pressure and air stoichiometry were fixed to the values giving the best performances (i.e. reference conditions: 3 bar and an air stoichiometry equal to 3), so that only the gas RH and cell temperature were varied.
## 2.2. Polarisation curves and electrochemical impedance spectroscopy

### 2.2.1. Polarization curves with imposed current density (galvanostatic mode)

Firstly, performance mapping was done by measuring the polarisation curves in galvanostatic mode, i.e. by imposing the current density. Each polarization curve was recorded after a 30 min constant current stage (1 A/cm²) to begin from an identical starting point. The current density was then varied in 100 s steps, starting from OCV (Open Circuit Voltage), until the FC voltage dropped below 0.3 V. Then, the current density was decreased following the same protocol, i.e. by 100 s steps, up to OCV. The average voltage value corresponding to each current density value was then calculated by considering the last 50 s of the increasing and decreasing steps. The cell temperature, air stoichiometry, pressure and gas RH are specified in each case.

However, although similar to what we had done in previous works [26,48,49] this way of measuring the polarisation curves resulted in serious voltage instabilities at high current density, especially at high temperature (i.e. 95 °C) and low gas inlet RH, as illustrated in Fig. 2(a). Similarly, it was not possible to perform Electrochemical Impedance Spectroscopy (EIS) in galvanostatic mode in the high current density region of the polarisation curves, because of sudden voltage drops; consequently, it was not possible to study the cause of that voltage drop.

### 2.2.2. Polarization curves and EIS in potentiostatic mode

Since measuring the polarisation curves and performing EIS in galvanostatic mode proved difficult at high current density, i.e. near unstable operating points, the MEA behaviour was instead studied in potentiostatic mode. In this approach, EIS was performed simultaneously with the recording of the polarisation curves, rather than separately in galvanostatic mode. EIS was used to evaluate the high-frequency resistance $R_{hf}$ as well as other impedance parameters and thus assess the hydration state of the MEA and/or the oxygen transport impedance.

* Before measuring each point on the polarisation curve, a 30 min, 1.5 A/cm², constant current step was performed to avoid any discrepancies linked to the FC hydration history. The polarisation curves were measured by decreasing the FC voltage from approximately 0.8 V (maximum value corresponding to about 0.25 A/cm²) down to 0.2 V. Each step lasted 30 min to ensure that the current density value reading corresponded to a stable operating point. Hydrogen and air flow rates had to be adjusted several times to achieve a stoichiometry of 1.25 and 3 based on the measured current density (i.e. reference conditions, as mentioned at the end of the previous section).

* EIS measurements were carried out at the end of each constant voltage steps. A small sinusoidal disturbance was imposed on the voltage setpoint, and the current density response was recorded simultaneously. For full-spectrum measurements, the frequency range was from 25 kHz to 0.02 Hz. When $R_{hf}$ values only were needed, the minimum frequency was increased to 500 Hz to save time. In both cases, the amplitude of the disturbance was set between ± 10 to 4% of the voltage measurement. At low voltage, the disturbance was reduced to the minimum value to avoid altering the state of the MEA. However, our tests showed that at high current density and low voltage, there was no significant effect of the amplitude of the disturbance, especially at high frequency, at least in the tested range (± 2 to 10%).

## 2.3. Accelerated stress test (AST)

The accelerated stress test used in this study was introduced in previous works [48,50–53]. It does not target one specific component of the MEA but is designed to induce a global ageing, including a decrease in the electrode surface area, chemical and mechanical stress to the membrane and ionomer. Such an AST was chosen because of its ability to combine stress factors that induce coupled mechanical and chemical degradation of the membrane and the electrodes. Its effectiveness has been demonstrated in previous works on MEA durability, showing a significant decrease in performance due to ECSA degradation and, in some cases, membrane breaking [48–53]. It consists of the repetition of a 60 s sequence (Fig. 3) that is divided into two parts while the gas flow rates are kept constant, based on a stoichiometry of 1.25/3 (i.e. our reference conditions) when the current density is the highest:

* A 43s load cycling stage between a current density value corresponding to 0.55 V for the pristine MEA-for 3s- and Open Circuit Voltage (OCV) -for 2s. This load, i.e. potential, cycling stage is well-known to induce ageing of the Catalyst Layer (CL) [54,55]; in addition, one can also observe a FC voltage undershoot in Fig. 3 when the current density increases, which may be the marker of membrane and/or CL drying. Note that in our case, the current density was equal to about 2.2 A/cm² at 0.55 V, with 30% inlet RH and 3 bar operation pressure.

* A 17s OCV stage to induce chemical ageing of the membrane and ionomer in the electrodes [56,57], as well as MEA drying, due to relatively low gas inlet RH (30%) and thus a mechanical ageing due to swelling and contraction cycling [52]. As mentioned above, the FC voltage undershoot observed in Fig. 3 when the current density increases is a key indicator of membrane and/or catalyst layer drying; such drying may also occur during load cycling due to the low thickness of the membrane.

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** Polarization curve in galvanostatic mode (a) and in potentiostatic mode (b); potentiostatic polarization curves prove more stable at high current density and this makes it possible to perform EIS simultaneously.</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Representation of the accelerated stress test used with the presentation of the repeated 60 s cycle divided in three parts: load cycle (yellow) for electrodes ageing, OCV (red) for chemical ageing, and hydration/dehydration cycle (dark and light blue) for mechanical ageing.</figcaption></figure>

The cell temperature was set to 95 °C and the relative humidity of the gas at 30%. AST periods of 2 days were applied to the MEA, between which performance and state of the MEA were characterised using polarisation curves and impedance spectroscopy at imposed voltage, as described above.

A total of four two-day periods of AST and characterisation were conducted to determine whether electroosmotic drag or heat generation primarily governs membrane drying at high current densities. The investigation was motivated by the fact that ageing affects the current density at a given fuel cell voltage, thereby influencing both electroosmotic water flux through the membrane and heat production. This point is treated in Section 3.4.

## 3. Performance mapping

### 3.1. Impact of operating conditions on PEMFC performance

The research data repository contains all the data presented in this article [58].

Performance mapping was carried out to identify the operating conditions that yield the best performance, as well as the situations where voltage instabilities may occur at high temperature. In parallel (see below), this also helped us select the most suitable cell geometry (Fig. 1). PEMFC temperature, as well as gas relative humidity, pressure and air stoichiometry were varied to optimize operating conditions and

<table><caption>**Table 2**
Range of operating condition tested for performance mapping.</caption><thead><tr><th>T (°C)</th><th>RH (%)</th><th>P (bar)</th><th>St (air)</th></tr></thead><tbody><tr><td rowspan="3">70</td><td rowspan="2">50</td><td>1</td><td>2-2.5-3-4-5</td></tr><tr><td>2-3</td><td>2-2.5-3</td></tr><tr><td>80</td><td>1</td><td>2-2.5-3-4-5</td></tr><tr><td rowspan="5">95</td><td rowspan="3">30</td><td>2-3</td><td>2-2.5-3</td></tr><tr><td>1-2-3</td><td>2-2.5-3-4-5</td></tr><tr><td>2-3</td><td>2-2.5-3</td></tr><tr><td>50</td><td>1</td><td>2-2.5-3-4-5</td></tr><tr><td>2-3</td><td>2-2.5-3</td></tr></tbody></table>

to investigate the impact of a higher temperature. A total of 44 different cases has been tested (Table 2) while, as mentioned above, the hydrogen stoichiometry was always maintained at 1.25.

These experiments were performed using the five-channel serpentine cell (Fig. 1(b)) and the parallel-channel cell (Fig. 1(a)). Since the performance was lower and the observations and conclusions were similar, we chose, for the sake of simplicity, to present only the results obtained with the straight parallel channel cell.

The polarization curves in galvanostatic mode (Fig. 4) include error bars representing the difference between measurements taken during increasing and decreasing current density (see Section 2.a). Large vertical error bars, such as those observed at high current densities -particularly at 95 °C- indicate significant hysteresis between the forward and backward current scans, and instabilities. The horizontal error bars (i.e., those on the current density values) reflect unstable operating conditions that prevent precise control of the setpoint.

Not all of data are presented here, as the volume of data was too large to be displayed in full without impacting clarity. Nevertheless, the complete dataset allowed us to highlight the following trends:

* As expected, increasing the FC operating pressure enhances performance, particularly at high current densities. Lu et al. [59] reported that the primary benefit of increased back pressure in PEMFC arises from improved membrane hydration, which leads to higher membrane conductivity. In contrast, the associated increase in reactant partial pressure contributes only marginally to the cell voltage. Furthermore, the influence of operating pressure on FC performance is most pronounced under conditions of low gas inlet RH [60]. These findings agree with our $R_{hf}$ measurements (Table 4), for both temperature and at all current densities that were tested. There was a more pronounced decrease in $R_{hf}$ with increasing gas pressure at 20% RH. A similar trend was observed at 95 °C, however, the impact of RH on this trend could not be verified for all current densities, as certain operating conditions did not allow operation at certain specific current densities.

The operating pressure is beneficial for the hydration of the membrane and the catalyst layers [61], but it also leads to a decrease in the diffusivity of oxygen and water vapour [59]. The cathode compartment environment is a multi-species system containing liquid water, water vapor, oxygen, and nitrogen, which makes it challenging to calculate a global diffusion coefficient for a single component. However, the interdiffusion $D_{AB}$ between two gases components can be calculated, using the molar mass, critical pressure and critical temperature of the two components, as well as the operating pressure and temperature [62]:

$$ \frac{PD_{AB}}{(P_{cA}P_{cB})^{1/3}(T_{cA}T_{cB})^{5/12}(1/M_{A} + 1/M_{B})^{1/2}} = a \left( \frac{T}{\sqrt{T_{cA}T_{cB}}} \right)^{b} \quad (1) $$

Where a and b are dimensionless constants, P and T are the temperature and pressure of the system. $P_{cA}$, $T_{cA}$ and $M_{A}$ (respectively $P_{cB}$, $T_{cB}$ and $M_{B}$) are the critical pressure, critical temperature and molar mass of species A (respectively species B).

The values in Table 3 show that increasing the operating pressure significantly reduces interdiffusion for any gas pair. For example, increasing the pressure from 1 to 3 bar results in a threefold decrease in all the interdiffusion coefficients. In that regard, one might be tempted to attribute the instabilities observed at high temperature and high current density in Fig. 4 to limitations in oxygen diffusion. However, oxygen diffusion alone cannot explain the sudden instabilities and hysteresis observed at high current densities, which result in large error bars on the polarization curves. Oxygen diffusion
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Polarization curves in galvanostatic mode: impact of temperature and air stoichiometry at 3 bar/50% RH and St(H₂) = 1.25 (a) and impact of gas pressure and relative humidity at 95 °C and StH₂/air = 1.25/3 (b).</figcaption></figure>

<table><caption>**Table 3**
interdiffusion coefficient for several pair of gases.</caption><caption>D (cm²/s)</caption><thead><tr><th rowspan="2">Species<br>P (bar)<br>T (°C)</th><th colspan="2">O₂/N₂</th><th colspan="2">O₂/H₂O</th><th colspan="2">H₂O/ N₂</th></tr><tr><th>1</th><th>3</th><th>1</th><th>3</th><th>1</th><th>3</th></tr></thead><tbody><tr><td>25</td><td>0.208</td><td>0.069</td><td>0.254</td><td>0.085</td><td>0.266</td><td>0.089</td></tr><tr><td>40</td><td>0.228</td><td>0.076</td><td>0.285</td><td>0.095</td><td>0.298</td><td>0.099</td></tr><tr><td>50</td><td>0.241</td><td>0.080</td><td>0.307</td><td>0.102</td><td>0.321</td><td>0.107</td></tr><tr><td>60</td><td>0.255</td><td>0.085</td><td>0.329</td><td>0.110</td><td>0.344</td><td>0.115</td></tr><tr><td>70</td><td>0.269</td><td>0.090</td><td>0.353</td><td>0.118</td><td>0.369</td><td>0.123</td></tr><tr><td>80</td><td>0.284</td><td>0.095</td><td>0.377</td><td>0.126</td><td>0.394</td><td>0.131</td></tr><tr><td>90</td><td>0.299</td><td>0.100</td><td>0.403</td><td>0.134</td><td>0.421</td><td>0.140</td></tr><tr><td>95</td><td>0.306</td><td>0.102</td><td>0.416</td><td>0.139</td><td>0.435</td><td>0.145</td></tr><tr><td>100</td><td>0.314</td><td>0.105</td><td>0.429</td><td>0.143</td><td>0.449</td><td>0.150</td></tr></tbody></table>

limitations usually develop more gradually with increasing current density and do not cause hysteresis. This suggests that a more detailed analysis of the experimental results is required.

* Increasing the gas inlet RH up to 50% (at 95 °C) or 80% (at 70 °C) also improves the FC performances. Zhang et al. [46] observed an approximately five-fold decrease in membrane resistance (from approximately 700 to 140 mΩ·cm²) when the relative humidity at the gas inlet increased from 25 to 100% at 120 °C. They associated this result with an increase in membrane water content and thus, in ionic conductivity. This is confirmed by our R<sub>hf</sub> measurements, which show a substantial decrease between 20 and 50% RH across all current densities and pressures at 95 °C. For example, at 3 bar and 1.5 A/cm², R<sub>hf</sub> drops from 87 to 41 mΩ·cm². A similar trend is observed at 70 °C, although it is significantly less pronounced—for instance, R<sub>hf</sub> decreases only slightly, from 35 to 32 mΩ·cm² at 1.5 A/cm². However, these results are only valid through the range of parameters tested: Xu et al. [63] came to a different conclusion when increasing the gas inlet RH from 50 to 90% RH at 90 °C and 1.5 atm: despite the decrease in membrane resistance, the performance were lower at 90% RH due to a higher resistance to oxygen transport. This was explained by the greater amount of water brought in by the gases and produced by the electrochemical reaction, hindering oxygen diffusion. Indeed, the oxygen inlet molar fraction decreases from 14.8 to 10.5% when the gas inlet RH increases from 50 to 90% at 1.5 atm, while the water molar fraction increases from 29.6 to 49.9%.

* Increasing the air stoichiometry increases the performance, especially at high current densities. At 3 bars, the increase in performances is mainly noticeable at high current densities, contrary to 1 and 2 bar where the gain in voltage can be observed over a larger current density range. Wang et al. observed that the optimal air

stoichiometry value was depending on the operating point [64]: high current densities require a higher air stoichiometry to avoid gas starvation [7] and to evacuate the excess water produced; however, a higher air stoichiometry can also entail MEA dehydration, especially for dry conditions, leading to a decrease in the membrane's water content and therefore proton conductivity, resulting in a sometimes severe drop in performance. This finding is in line with our measurements, which demonstrate that at 95 °C, 30% RH (rather dry conditions), there is no observed increase in performance with increasing air stoichiometry. Further characterisation revealed that a sharper decrease in performance is observed in drier conditions, for example at temperatures of 95 °C and relative humidity levels of 20%.

* Increasing the FC temperature while keeping all other parameters constant negatively impacts performance. Notably, this decline is observed across the entire polarization curve (see Fig. 4) and attempts to optimize operating conditions—such as adjusting air stoichiometry, gas inlet relative humidity, and back pressure—failed to compensate for the performance loss.

Although catalyst activity and proton conductivity are generally enhanced by elevated temperatures [65–68], several studies also suggest that higher temperatures, especially under low humidity conditions, increase the rate of water evaporation [69–71]. This results in reduced membrane hydration, which significantly lowers proton conductivity and FC efficiency [17,72,73]. For instance, Wu et al. [74] observed an increase in proton conductivity from 0.079 S/cm at 20 °C to 0.210 S/cm at 60 °C, followed by a decline at higher temperatures; similarly, Jeon et al. reported that raising the operating temperature at constant relative humidity (RH) increases both R<sub>hf</sub>, —which reflects membrane hydration—and the charge transfer resistance [18]. In addition, the positive effect of temperature increase on the reaction kinetics can be balanced by detrimental mass transfer effects (e.g. decrease of the oxygen solubility) [75]. For all the current densities and RH tested (Table 4), we observed similar trends, i.e. much higher R<sub>hf</sub> values at 95 °C than at 70 °C, particularly at 1 and 2 bar. At 3 bar and 50% RH, the variation in R<sub>hf</sub> between 70 and 95 °C is much smaller, indicating that the effect of temperature on hydration is more significant at low RH and low pressure.

Note that the R<sub>hf</sub> values reported in Table 4 were measured in galvanostatic mode (see section 2.2.1, which could only be applied at relatively low current densities due to the current/voltage instabilities observed in Fig. 4. The slight general decrease in R<sub>hf</sub> from 1 to 2 A/cm² aligns with trends reported in the literature [13,33,38,40,41,73,76] and suggests progressive membrane hydration in the low-current-density region of the polarization curve [77]. However, the significantly
<caption>**Table 4**</caption>

R<sub>hf</sub> measurements with imposed current density at different current densities and for various temperature, pressure and gas inlet RH.

<table><thead><tr><th colspan="11">R<sub>hf</sub> (Ohm.cm<sup>2</sup>)</th></tr><tr><th rowspan="2">i (A/cm<sup>2</sup>)</th><th rowspan="2">T (°C)</th><th colspan="3">Gas inlet RH: 20%</th><th colspan="3">Gas inlet RH: 30%</th><th colspan="3">Gas inlet RH: 50%</th></tr><tr><th>1 bar</th><th>2 bar</th><th>3 bar</th><th>1 bar</th><th>2 bar</th><th>3 bar</th><th>1 bar</th><th>2 bar</th><th>3 bar</th></tr></thead><tbody><tr><td rowspan="2">1</td><td>70</td><td>0.097</td><td>0.045</td><td>0.036</td><td>0.072</td><td>0.039</td><td>0.034</td><td>0.050</td><td>0.035</td><td>0.033</td></tr><tr><td>95</td><td>-</td><td>0.177</td><td>0.094</td><td>0.168</td><td>0.096</td><td>0.066</td><td>0.070</td><td>0.054</td><td>0.043</td></tr><tr><td rowspan="2">1.5</td><td>70</td><td>-</td><td>0.103</td><td>0.042</td><td>0.070</td><td>0.037</td><td>0.033</td><td>0.049</td><td>0.033</td><td>0.032</td></tr><tr><td>95</td><td>-</td><td>-</td><td>0.087</td><td>-</td><td>0.099</td><td>0.059</td><td>0.081</td><td>0.053</td><td>0.041</td></tr><tr><td rowspan="2">2</td><td>70</td><td>-</td><td>0.040</td><td>0.032</td><td>0.085</td><td>0.037</td><td>0.031</td><td>0.054</td><td>0.033</td><td>0.031</td></tr><tr><td>95</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.057</td><td>0.104</td><td>0.056</td><td>0.041</td></tr></tbody></table>

higher R<sub>hf</sub> values at 95 °C compared to 70 °C—particularly at 1 and 2 bar—may indicate membrane hydration challenges at elevated temperatures. Additionally, the increased hysteresis between the forward and backward current scans in the polarization curves at high current densities under high-temperature, low-RH conditions (Fig. 4) further supports the possibility of membrane and ionomer hydration issues. While some of the hysteresis may be due to the formation/reduction of platinum oxides, the process being dependent on temperature and humidification [77,78], it is likely that the increase in error bars at high current densities is mainly related to hydration of the MEA.

To conclude and summarize this section, performance mapping shows that high air stoichiometry and gas humidification generally improve performance, while low humidity and high temperature lead to voltage instabilities. These instabilities may be linked to water management issues and/or mass transport limitations. Based on these initial observations, we further investigated the impact of gas inlet relative humidity (RH) at high temperature (i.e. 95 °C) to better understand the primary cause of the voltage drop observed at high current densities. For simplicity, the results presented below were performed under reference conditions: a gas back pressure of 3 bar, with hydrogen and air stoichiometries set to 1.25 and 3, respectively. These conditions corresponded to the best performance observed.

### 3.2. Impact of relative humidity at 95 °C – possible issues with membrane hydration and oxygen diffusion

To gain a deeper understanding of the MEA behaviour at 95 °C, performance tests were carried out with various gas inlet relative humidities, in the reference conditions defined above. Note that, unless otherwise stated, we always considered identical RH values on the hydrogen side and on the oxygen (air) side. According to the literature, an increase in RH induces a decrease in the cell resistance, usually associated with a better hydration of the membrane and possibly the ionomer in the CL, resulting in higher proton conductivity [40,79–81] and better performances [40,82]. Indeed, we observed an increase in performances at 95 °C with relative humidity from 20 to 40%, which is in line with the quoted literature (Fig. 5). However, there was no significant increase in performance at 70 °C between 20% RH and 50% RH and above 40% RH at 95 °C, although the studies cited above report an increase in the ionomer proton conductivity with relative humidity, up to 100% RH. Therefore, there must be at least one additional phenomenon in competition with the increase in proton conductivity: possibly, as mentioned in the previous section, some difficulties in oxygen diffusion [63].

In addition, low gas inlet RH leads to severe current and voltage instabilities, as evidenced by the large error bars in Fig. 5. These large error bars arise from both a significant voltage drop at high current densities and strong hysteresis between the forward and backward current scans: the lower the gas inlet RH, the more pronounced these instabilities. Impedance spectroscopy was performed at 95 °C and at several RH and current density values to better capture the MEA behaviour (Fig. 6).

#### 3.2.1. Impact of gas inlet RH

As expected, we observed a decrease in R<sub>hf</sub> with increasing relative humidity across all the current density tested (1, 1.5 and 2.5 A/cm<sup>2</sup>, see Fig. 6(a–c)) reflecting improved hydration of both the membrane and the ionomer. However, at the highest current densities –2.5 A/cm<sup>2</sup>, Fig. 6(c) – an increase in the mass transfer (low-frequency) loop is also observed, possibly indicating higher resistance to oxygen diffusion. This behaviour may be attributed to oxygen dilution and/or reactant starvation, potentially caused by the combined effects of increased RH and the higher water production by the fuel cell. Overall, it appears there is a trade-off between the performance gains from enhanced MEA hydration and the losses due to increased mass transport resistance. This trade-off could explain the absence of significant performance improvement above 40% RH at 95 °C.

#### 3.2.2. Impact of current density

Paradoxically, increasing the current density to 2.5 A/cm<sup>2</sup> has a negative impact on R<sub>hf</sub>, which increases despite the higher water production (Fig. 6(d)). This effect is observed across the entire tested range of relative humidity (20% to 70%) and has also been observed by Vandenberghe at al [77,78]. Instead of enhancing membrane and ionomer hydration—and thereby improving proton conductivity—there seems to be a net dehydration of the MEA at high current density. One possible explanation is the increased electro-osmotic drag of water from the anode to the cathode, which can deplete water from the anode compartment [83–85] and lead to significant membrane dehydration on that side [86,87]. Another potential cause is membrane and/or electrode drying induced by the heat generated during the electrochemical half-reactions. This heat can produce substantial temperature gradients between the MEA and the bipolar plates, particularly under high current densities. Some studies suggest that, under saturated vapor conditions, such temperature gradients lead to gradients in saturated water vapor pressure, driving water toward the cathode-side bipolar plate and further drying the membrane. This phenomenon is known as the heat pipe effect [88–92].

### 3.3. Origin of voltage drop at 95 °C

Section 3.2 confirmed that water management, rather than mass transport, is the dominant factor behind the voltage drop and instabilities observed at high temperature.<fnref n="1" /> However, although Fig. 6(d) shows an increase in R<sub>hf</sub> with current density, it does not clarify whether the steep FC voltage drops or instabilities observed at 95 °C are actually due to membrane dehydration (whether driven by electro-osmotic drag, thermal effects, or both) or to increased oxygen transport limitations, as is typically expected and accepted at lower temperatures [93,94]. A deep understanding of these mechanisms required EIS measurements conducted near the inflection point of the polarization curves. Since this

<footnote n="1">¹ This conclusion applies to the materials used here, i.e., conventional Pt/C electrocatalysts. With Pt-free electrocatalysts, for instance, oxygen transport limitations would likely be more significant.</footnote>
<figure><img src="image_7.png" /><figcaption>Fig. 5. Polarization curves in reference conditions (StH₂/air = 1.25/3, P = 3 bar, symmetrical RH) at various RH at 95 °C (a) and 70 °C (b).</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Fig. 6. impedance spectra in galvanostatic mode at different relative humidities at 95 °C and 1 A/cm² (a), 1.5 A/cm² (b), 2.5 A/cm² (c), R<sub>hf</sub> measurements at different current density for different relative humidities (d).</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Fig. 7. polarization curves and thermal power with 20, 30 and 50% gas RH at 95 °C (a) and 70 °C (b).</figcaption></figure>

was not feasible in galvanostatic mode (see section 2.2.1) due to the instability of the fuel cell voltage, we switched to potentiostatic mode for both the polarization curve and EIS measurements. Our focus was

primarily on the high-frequency range, and we did not always record the full EIS spectra to enable rapid measurements and minimize changes in the MEA state.
<table><caption>**Table 5**
Voltage, current density and thermal power at the current density limit.</caption><thead><tr><th rowspan="2">RH (%)</th><th colspan="3">95 °C</th><th colspan="3">70 °C</th></tr><tr><th>U (V)</th><th>i (A/cm<fnref n="2" />)</th><th>P<sub>th</sub> (W/cm<fnref n="2" />)</th><th>U (V)</th><th>i (A/cm<fnref n="2" />)</th><th>P<sub>th</sub> (W/cm<fnref n="2" />)</th></tr></thead><tbody><tr><td>20</td><td>0.4</td><td>2.31</td><td>1.91</td><td>0.39</td><td>3.72</td><td>3.13</td></tr><tr><td>30</td><td>0.36</td><td>2.95</td><td>2.56</td><td>0.36</td><td>3.72</td><td>3.24</td></tr><tr><td>50</td><td>0.27</td><td>3.23</td><td>3.10</td><td>0.3</td><td>3.66</td><td>3.29</td></tr></tbody></table>

Typical polarization curves measured with imposed voltage are presented at 70 and 95 °C with 20, 30 and 50% gas inlet RH, at 3 bar and stoichiometry of 1.25/3 in hydrogen/air (Fig. 7).

An unusual but normal behaviour, compared to galvanostatic measurements, is the presence of a reversal point in the curves, corresponding to a maximum current density that cannot be exceeded. This reversal point is observed at both temperatures, but exhibits a much stronger dependence on the gas inlet RH at 95 °C. At 95 °C, the maximum current density increases significantly with RH, reaching 2.31, 2.95, and 3.23 A/cm<fnref n="2" /> for 20, 30, and 50% RH, respectively. In contrast, at 70 °C, the maximum current density shows almost no variation, ranging between 3.66 to 3.72 A/cm<fnref n="2" /> (Table 5).

Fig. 7 and Table 5 also present the evolution and the value at $i_{max}$ of the thermal power that results from the voltage losses, estimated as $P_{th} = (U_{rev} - U) \times j$, with $U_{rev}$, the thermodynamic (reversible) FC voltage<fnref n="2" />

A striking result in Fig. 7 is the differing impact of RH at 95 and 70 °C. At 95 °C, increasing the gas inlet RH has a strong effect on the fuel cell voltage across the entire current density range. Both the maximum current density and thermal power increase significantly. In contrast, at 70 °C, neither the current density values nor the thermal power appear to be strongly dependent on the gas inlet RH. This suggests that the voltage drop observed at high current densities in Figs. 4, 5 and 7 may stem from different causes at 70 and 95 °C. At the very least, it indicates that membrane and/or ionomer-related issues may play a significantly greater role in the voltage drop at 95 than at 70 °C. To confirm this point, high-frequency resistance values were extracted from EIS measurements. The results show that at 95 °C, increasing the gas inlet RH significantly affects $R_{hf}$ across the entire polarization curve (Fig. 8(a)). Notably, $R_{hf}$ is nearly halved between 20 and 50% RH at intermediate current densities, dropping from approximately 75 mΩ·cm<fnref n="2" /> (20% RH) to 41 mΩ·cm<fnref n="2" /> (50% RH) at 1.9 A/cm<fnref n="2" />. This reduction indicates that higher gas inlet RH improves the membrane-electrode assembly (MEA)

$$U_{\text{rev}} = 1.184 - 2.3 \times 10^{-4}(T - T_0) + 4.3085 \times 10^{-5}T \left[ \ln \left( \frac{p_{\text{H}_2} \times P_{\text{O}_2}^{1/2}}{p_{\text{H}_2\text{O}} \times P_0^{1/2}} \right) \right] \quad (2)$$

The gas composition within the cell is uniform and equal to that at gas inlets since the Nernst voltage is obtained at open circuit. The reversible voltage decreases slightly with the temperature: this is because the gas inlet RH stays identical at 70 and 95 °C, resulting in a decrease in the reactant partial pressure. Nernst voltage depending on operating temperature, gas pressure and relative humidity.

<table><thead><tr><th>RH (%)</th><th>P (bar)</th><th>U<sub>Nernst</sub> (V)</th></tr></thead><tbody><tr><td rowspan="2">70</td><td>1</td><td>1.22</td></tr><tr><td>3</td><td>1.25</td></tr><tr><td rowspan="2">95</td><td>1</td><td>1.20</td></tr><tr><td>3</td><td>1.23</td></tr></tbody></table>

hydration, thereby enhancing proton conductivity and overall fuel cell performance. Interestingly, this behaviour is not observed at 70 °C, as shown in the $R_{hf}$ versus voltage plot in Fig. 8(b). In contrast to the results at 95 °C, the $R_{hf}$ curves at 70 °C remain closely aligned regardless of the gas inlet RH, indicating a much weaker influence of humidity under these conditions.

Fig. 8(a) also reveals a steep and sudden increase in $R_{hf}$ near the maximum current density, reflecting most probably a rapid membrane dehydration. This may contribute to the increased instability of the operating point observed during polarization curve measurements in galvanostatic mode (Fig. 5) at 95 °C. The increase in $R_{hf}$ becomes less abrupt as the gas inlet RH rises, confirming that the phenomenon is related to water management issues. In contrast, at 70 °C, no such increase is observed: the estimated $R_{hf}$ values remain consistently close (around 35 mΩ·cm<fnref n="2" />), regardless of the gas inlet RH. The slight $R_{hf}$ increase of about 10 mΩ/cm<fnref n="2" /> observed at low voltages (i.e., high currents) at 70 °C is minor compared to the behaviour at 95 °C, indicating that water management is not an issue at the lower temperature (Table 6).

### 3.4. $R_{hf}$ measurements during the AST

As highlighted in the preceding sections, the water management issues observed at high current densities and elevated temperatures may stem from two main causes: the so-called heat pipe effect [90–92], driven solely by thermal gradients within the MEA, and localized drying on the anode side of the MEA due to electro-osmotic drag [34,35,83–85]. Electro-osmosis is driven solely by the current density and is independent on the fuel cell’s electrochemical efficiency; in other words, it does not depend on the amount of heat generated by the MEA during operation. Naturally, both mechanisms may occur simultaneously, and their effects can be additive. To clarify this point, we performed an AST over eight days (see section 2.3) measuring the current density and the high frequency resistance across a voltage range from approximately 0.8 to 0.2 V (Fig. 9(a)) every 48 h. As shown in Fig. 9(a), the AST leads -as expected- to a decline in FC efficiency and voltage, thereby increasing the heat generated by the MEA at a given current density. Simultaneously, the maximum current density reached in potentiostatic mode tends to decrease and the associated rise in $R_{hf}$ also tends to occur earlier. Interestingly, the $R_{hf}$ values at low FC voltage remain of the same order of magnitude: approximately 100 mΩ/cm<fnref n="2" /> at 0.2 V. This suggests that heat generation (and related membrane drying) is most likely the primary factor driving the increase in $R_{hf}$ at high current density, and consequently, the voltage drop. Indeed, if electro-osmotic drag were the dominant mechanism, the increase in high-frequency resistance and the associated voltage drop would be expected to occur at the same current density, regardless of the amount of heat generated, i.e. independently on the MEA material degradation over the course of the AST.

To confirm the minor role played by electro-osmotic drag in the observed increase of $R_{hf}$, we repeated the voltage and $R_{hf}$ vs. current density measurements with an asymmetric gas inlet RH case, specifically 20% inlet RH on the hydrogen side and 50% on the air side, instead of 50% on both sides. Fig. 9(b) clearly shows that this change has no significant effect on either the polarization curves or the estimated high frequency resistance values. If electro-osmosis was the cause of membrane dehydration, the reduction in anode humidification would have led to an increase in $R_{hf}$ at a lower current density, as this effect dries out the membrane on the anode side. Consequently, membrane drying observed in the present conditions is primarily due to a thermal phenomenon that occurs at high current density, i.e. the so-called heat pipe effect mentioned and discussed above, rather than electroosmosis drag.

### 3.5. $R_{hf}$ measurements at intermediate temperature

In real life, the operating temperature of PEMFCs may vary depending on a variety of factors. For instance, Wang et al. [95] used a numerical model to assess the temperature field gradient within a stack

<footnote n="2">² The reversible cell voltage $U_{rev}$ was estimated using the following pseudo-Nernst equation, where $p_i$ denotes the partial pressure of component i and $P_0$ the standard (reference) pressure (1 atm); $T_0$ stands for the standard temperature (298.15 K). The values of $U_{rev}$ are given, for illustration, in the table below (with the cell temperature in °C for convenience).</footnote>
<figure><img src="image_10.png" /><figcaption>Fig. 8. $R_{hf}$ and U evolution at 95 °C (a) and $R_{hf}$ evolution as a function of voltage at different RH and temperatures (b).</figcaption></figure>

<table><caption>**Table 6**
$R_{hf}$ values at 95 and 70 °C and different voltages.</caption><thead><tr><th rowspan="2">RH (%)</th><th colspan="2">95 °C</th><th colspan="2">70 °C</th></tr><tr><th>U (V)</th><th>R<sub>hf</sub> (mΩ/cm²)</th><th>U (V)</th><th>R<sub>hf</sub> (mΩ/cm²)</th></tr></thead><tbody><tr><td rowspan="2">20</td><td>0.54</td><td>74</td><td>0.52</td><td>34</td></tr><tr><td>0.2</td><td>159</td><td>0.2</td><td>44</td></tr><tr><td rowspan="2">30</td><td>0.52</td><td>54</td><td>0.52</td><td>33</td></tr><tr><td>0.2</td><td>103</td><td>0.2</td><td>45</td></tr><tr><td rowspan="2">50</td><td>0.54</td><td>41</td><td>0.54</td><td>34</td></tr><tr><td>0.22</td><td>69</td><td>0.22</td><td>40</td></tr></tbody></table>

with different cooling plate geometries. They found a significant temperature disparity between the membrane and the surface of the outmost cooling plate, depending on the current density (less than 3 °C at low current density versus more than 18 °C at high current density), as seen in others studies [96,97]. We therefore measured $R_{hf}$ in a temperature range between 70 and 95 °C at 20 and 50% relative humidity. To save time, measurements were only made between 0.48 and 0.2 V to observe whether the increase in MEA dehydration begins at a specific temperature (only three voltage values are shown, see Table 7). Usual temperatures, such as 70–80 °C, do not show a very significant increase in $R_{hf}$, which demonstrates that there are no major problems with MEA hydration at high current densities with the present MEA materials. However, a more significant increase in $R_{hf}$ is observed at 85 °C, with a

<figure><img src="image_11.png" /><figcaption>Fig. 9. polarization curves and $R_{hf}$ values: during AST (a) and for asymmetrical (20/50%) vs symmetrical (50/50%) RH case (b).</figcaption></figure>
<table><caption>**Table 7**
R<sub>hf</sub> measurements in potentiostatic mode at intermediate temperatures.</caption><thead><tr><th rowspan="2">T (°C)</th><th rowspan="2">RH (%)</th><th colspan="3">R<sub>hf</sub> (Ohm.cm<sup>2</sup>)</th></tr><tr><th>U (V)</th><th></th><th></th></tr><tr><th></th><th></th><th>0.48</th><th>0.3</th><th>0.2</th></tr></thead><tbody><tr><td rowspan="2">70</td><td>20</td><td>0.034</td><td>0.039</td><td>0.044</td></tr><tr><td>50</td><td>0.039</td><td>0.033</td><td>0.033</td></tr><tr><td rowspan="2">75</td><td>20</td><td>0.038</td><td>0.047</td><td>0.050</td></tr><tr><td>50</td><td>0.032</td><td>0.039</td><td>0.038</td></tr><tr><td rowspan="2">80</td><td>20</td><td>0.042</td><td>0.052</td><td>0.066</td></tr><tr><td>50</td><td>0.035</td><td>0.044</td><td>0.048</td></tr><tr><td rowspan="2">85</td><td>20</td><td>0.067</td><td>0.075</td><td>0.095</td></tr><tr><td>50</td><td>0.040</td><td>0.054</td><td>0.054</td></tr><tr><td rowspan="2">90</td><td>20</td><td>0.056</td><td>0.084</td><td>0.108</td></tr><tr><td>50</td><td>0.044</td><td>0.059</td><td>0.067</td></tr><tr><td rowspan="2">95</td><td>20</td><td>0.078</td><td>0.118</td><td>0.159</td></tr><tr><td>50</td><td>0.043</td><td>0.062</td><td>0.069</td></tr></tbody></table>

value of 95 mΩ.cm² at 0.2 V and 20% relative humidity: the increase in MEA dehydration with current density is a gradual phenomenon, accentuated by the operating temperature. However, it can be counterbalanced with adequate gas RH, as the increase in R<sub>hf</sub> is less significant at high RH.

## 4. Discussion: on the main factors limiting the FC performance in the 90 °C–100 °C temperature range

Raising the cell operating temperature from standard (70–80 °C) to higher levels under automotive conditions, i.e. relatively dry conditions with low gas RH, alters the factors limiting fuel cell performance. While no increase in cell voltage is observed in the kinetics region, the voltage decreases in the ohmic region, and drops more significantly at high current densities (Fig. 4(a)), where voltage instabilities emerge, becoming more pronounced as the gas inlet RH is low (Fig. 5(a)). R<sub>hf</sub> measurements across the entire polarization curve demonstrate that MEA hydration is responsible for that decline in performance at high current density. Similar trends have already been reported by Cho et al. at 120 °C and 10% RH with SSC-PFSA ionomer [33]. Additional R<sub>hf</sub> measurements taken during AST, as well as under reference conditions with asymmetric RH, support the conclusion that the heat flux generated by electrochemical reactions, rather than electro-osmotic drag, is the primary driver of MEA dehydration at 95 °C and low gas RH. Complementary R<sub>hf</sub> measurements, carried out to cover the full temperature range from 70 to 95 °C in 5 °C increments, demonstrated that this limiting factor is highly correlated with operating temperature and gas

relative humidity (Table 7); however, 85 °C could be a critical operating point above which, MEA dehydration becomes a significant issue, at least in our operating conditions.

In addition, although, MEA dehydration can be counterbalanced by a higher gas RH, the increase in water content may create other issues that could become again the main limiting factor: actually, a threshold in gas inlet RH (app. 40%) was identified, above which no significant performance improvement was observed (Fig. 5(a)), suggesting that a trade-off exists between enhanced MEA hydration and the negative effects of oxygen dilution and/or increased mass transport resistance, as previously noted by Xu et al. [63]. Indeed, the iR-corrected polarization curves for 20, 30, and 50% inlet RH at fuel cell temperatures of 70 and 95 °C (Fig. 10) confirm that the increase in R<sub>hf</sub> at 95 °C alone does not fully account for the lower performance compared to 70 °C. A voltage difference of about 30 to 50 mV remains at low to moderate current densities (up to ~1.8–2.0 A/cm²), and this difference increases at higher current densities. Impedance spectroscopy in galvanostatic mode has been carried out in the same conditions at 1 and 2 A/cm² (only 30 and 50% RH are represented in Fig. 11). For both applied current density and relative humidity (RH), the mass transport loop appears to be equivalent or smaller at 95 than 70 °C, which suggests that larger mass transport limitations are unlikely at higher operating temperatures, at least within the low to mid-current density range. As mentioned above, the increase in water concentration with temperature (and constant RH) may be offset by a higher overall interdiffusion coefficient (see Table 3 and [62]). Therefore, the lower fuel cell voltage observed at 95 °C is most likely due to the reduced oxygen partial pressure, resulting from the higher water vapor partial pressure. In addition, the results of the pseudo-Nernst equation (equation 2)² are in favour of that interpretation: for example, at 50% gas inlet RH and 3 bar, the oxygen inlet partial pressure diminishes from 0.6 to 0.54 bar when the temperature goes from 70 °C to 95 °C. This explains the app. 24 mV difference in Nernst voltage.

Butori et al. [98] reached similar conclusions after observing differences in iR-corrected polarisation curves under varying temperature conditions at constant gas RH. In a subsequent experiment, they kept the gas RH and the oxygen partial pressure constant and found a good match between the iR-corrected polarization curves. This indicated that the increase in R<sub>hf</sub> and the decrease in oxygen partial pressure jointly contribute to the voltage drop with increasing temperature. Saleh et al. [99] measured polarization curves at 70 and 90 °C with various gas RH and concluded that FC operation at 70 °C and high current densities is limited by oxygen transport, while MEA hydration becomes a major issue above 90 °C as they observed that gas inlet RH is an essential

<figure><img src="image_12.png" /><figcaption>**Fig. 10.** iR<sub>hf</sub>-corrected polarization curves for 20, 30 & 50% inlet RH gases and 70 °C and 95 °C FC temperature.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>Fig. 11. EIS spectra at 70–95 °C and 1–2.5 A/cm² for RH = 30% (a) and 50% (b).</figcaption></figure>

<figure><img src="image_14.png" /></figure>

parameter to control fuel cell performance; their current density range (0–1.4 A/cm²) was smaller than ours. The hypothesis that oxygen dilution is the main factor responsible for the remaining discrepancies between iR<sub>hf</sub>-corrected polarization curves could potentially be validated through impedance spectrum modelling and the determination of the cathode charge transfer resistance; however, this is out of the scope of this work. Considering only experimental results, and to summarize this discussion, four key observations lead to the conclusion that oxygen diffusion is not a performance-limiting factor at high temperature:

* Membrane drying at high temperature occurs at current densities that are usually much lower than those at which oxygen diffusion limitations appear at lower temperatures. For instance, with 20% RH inlet gases, the FC voltage drops to 0.4 V at a current density of 2.3 A/cm² at 95 °C, vs. 3.7 A/cm² at 70 °C (see Table 5). In addition, increasing the gas inlet RH at high temperature improves the current density limit, without any oxygen diffusion issue.

* Gas-phase interdiffusion coefficients improve with temperature: they are about 10 to 15% higher at 95 than at 70 °C.

* All other conditions kept equal, EIS spectra do not show a larger diffusion loop at higher temperatures.

* Discrepancies between iR<sub>hf</sub>-corrected polarization curves are observed over the entire current density range, including at very low current density. This suggests that the remaining phenomena (other than the increase in R<sub>hf</sub>) explaining the drop in performance at high temperature are not governed by oxygen diffusion. They could possibly be driven by oxygen dilution.

**Table 8**

current density, fuel cell voltage and R<sub>hf</sub> measurements at usual operating points and different operating temperature.

<table><thead><tr><th colspan="5">Gas inlet RH: 20%</th></tr><tr><th>T (°C)</th><th>U (V)<br>@ i = 1.5 A/cm²</th><th>R<sub>hf</sub> (Ω.cm²)<br>@ i = 1.5 A/cm²</th><th>i (A/cm²)<br>@ U = 0.7 V</th><th>R<sub>hf</sub> (Ω.cm²)<br>@ U = 0.7 V</th></tr></thead><tbody><tr><td>70</td><td>0.71</td><td>0.033</td><td>1.708</td><td>0.032</td></tr><tr><td>75</td><td>0.7</td><td>0.033</td><td>1.616</td><td>0.033</td></tr><tr><td>80</td><td>0.71</td><td>0.035</td><td>1.568</td><td>0.035</td></tr><tr><td>85</td><td>0.7</td><td>0.044</td><td>1.476</td><td>0.043</td></tr><tr><td>90</td><td>0.67</td><td>0.058</td><td>1.124</td><td>0.063</td></tr><tr><td>95</td><td>0.62</td><td>0.079</td><td>0.748</td><td>0.087</td></tr><tr><td>100</td><td>0.59</td><td>0.096</td><td>0.748</td><td>0.097</td></tr><tr><td>105</td><td>—</td><td>—</td><td>0.624</td><td>0.108</td></tr></tbody></table><table><thead><tr><th colspan="5">Gas inlet RH: 50%</th></tr><tr><th>T (°C)</th><th>U (V)<br>@ i = 1.5 A/cm²</th><th>R<sub>hf</sub> (Ω.cm²)<br>@ i = 1.5 A/cm²</th><th>i (A/cm²)<br>@ U = 0.7 V</th><th>R<sub>hf</sub> (Ω.cm²)<br>@ U = 0.7 V</th></tr></thead><tbody><tr><td>70</td><td>0.73</td><td>0.030</td><td>1.844</td><td>0.029</td></tr><tr><td>75</td><td>0.72</td><td>0.030</td><td>1.8</td><td>0.029</td></tr><tr><td>80</td><td>0.72</td><td>0.030</td><td>1.772</td><td>0.029</td></tr><tr><td>85</td><td>0.7</td><td>0.032</td><td>1.552</td><td>0.033</td></tr><tr><td>90</td><td>0.68</td><td>0.036</td><td>1.528</td><td>0.035</td></tr><tr><td>95</td><td>0.71</td><td>0.040</td><td>1.492</td><td>0.040</td></tr><tr><td>100</td><td>0.7</td><td>0.044</td><td>1.4</td><td>0.043</td></tr></tbody></table>

Setting aside the sudden increase in R<sub>hf</sub> at high current density, it should be noted that there is already a significant difference in MEA hydration between different operating temperatures at low and medium current densities, affecting performance. In Table 8, fuel cell voltage and current densities measurements reveal slight voltage differences at 1.5 A/cm² from 70 to 90 °C (a 40 mV drop with 20% RH inlet gases and a 50 mV drop with 50% inlet RH gases) while current densities at 0.7 V show more pronounced variations, mainly due to the increase in R<sub>hf</sub>. This trend is confirmed above 90 °C (Table 8), although the FC voltage at 1.5 A/cm² is less sensitive to temperature with 50% gas inlet RH.<fnref n="3" /> On the other hand, increasing the temperature above 90 °C under 20% inlet RH considerably accentuates the current density drop at 0.7 V, with only 0.624 A/cm² at 105 °C, while R<sub>hf</sub> increases up to 0.108 Ω.cm².

## 5. Conclusion

We conducted extensive performance mapping using a commercial, state-of-the-art PEMFC MEA featuring a 12 µm thick LSC-PFSA membrane. The study was carried out over a temperature range of 70 to 105 °C and under low to moderate gas inlet relative humidity (i.e., 20 to 50% RH), representative of conditions encountered in automotive applications. Initial investigations examined the impact of external parameters, including gas relative humidity and pressure, cell temperature, and air stoichiometry. Within the tested range, results indicated that increasing gas pressure and relative humidity enhances the cell performance thanks to a higher MEA hydration, hence a smaller high frequency resistance. Additionally, an increase in air stoichiometry is beneficial, particularly at high current densities if the relative humidity of the gas is sufficient; otherwise, a drop in performance is observed due to MEA dehydration. However, although the performances remain satisfactory - which was not guaranteed with a LSC-PFSA membrane - increasing the cell temperature was found to negatively affect them. The effect is particularly pronounced under low or moderate RH, where a sudden voltage drop occurs at high current densities. Therefore, a second round of investigations was focused on the region of high current densities, where performance is typically limited by mass transport and reactant availability at standard temperatures. At 95 °C, our results indicate that MEA dehydration becomes the dominant limiting factor, as low RH and elevated temperature significantly reduce membrane hydration and, consequently, proton conductivity. This was evidenced mostly through a sharp increase in the FC high frequency resistance. Additional measurements performed during an AST, i.e. with a performance degradation over time, showed that membrane dehydration was most probably linked to the heat generated by the electrochemical reaction rather than by electro-osmotic drag; indeed, this was supported by the absence of

<footnote n="3">³ Measurements between 95 and 105 °C were carried out with a fresh MEA, which explains the increase in voltage observed between 90 and 95 °C at 1.5 A/cm² with 50% inlet RH humidity gases. Nevertheless, this does not alter the overall trend in R<sub>hf</sub> and current density at 0.7 V.</footnote>
significant difference in the performance measured with symmetric gas
inlet condition (same inlet RH on the anode and cathode side: 50%) than
with a lower inlet RH at the hydrogen inlet (20%) than at the air inlet
(50%).

Although membrane dehydration is a major limiting factor at high temperatures, it only happens in dry conditions and non-usual operating points, i.e. high current densities. Nevertheless, FC performance decreases across the entire current density range as temperature increases, mostly due to the rise in R<sub>hf</sub>. However, iR-corrected polarization curves reveal that MEA hydration does not fully account for the lower performance of PEMFC when all other parameters (gas stoichiometry, pressure, and inlet RH) are held constant. We observed a residual 40 to 50 mV voltage difference up to ~1.8–2.0 A/cm<sup>2</sup>, with the discrepancy increasing significantly at higher current densities. Impedance spectroscopy in the low-to-moderate current density range showed no substantial differences in the mass transport loop between 70 and 95 °C, suggesting that larger mass transport limitations at elevated temperatures are unlikely. This led us to the conclusion that oxygen dilution due to a higher water vapor concentration, was the most probable origin of the remaining voltage losses.

Finally, it should be emphasized that these findings are specific to the
operating conditions, materials, and cell geometry used in this work.
The optimisation of both the cell geometry and MEA materials may
enable improved performance at high temperature in the future.

Future work will first focus on modelling the impedance spectra to accurately extract key parameters, particularly the cathode charge transfer resistance. This will enable a more precise assessment of the impact of oxygen dilution on fuel cell performance. In parallel, we plan to repeat this performance mapping using a segmented cell, to investigate the local effects of membrane and MEA dehydration on performance, impedance, and electrode potentials.

CRediT authorship contribution statement

G. Etienne: Writing – review & editing, Writing – original draft, Visualization, Methodology, Formal analysis, Data curation, Conceptualization. A. Ouhammi: Data curation. Assma El Kaddouri: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Methodology, Formal analysis, Conceptualization. J. Mainka: Writing – review & editing, Methodology, Investigation, Formal analysis, Conceptualization. J. Dillet: Writing – review & editing, Visualization, Validation, Supervision, Software, Methodology, Investigation. A. Morin: Writing – review & editing, Methodology, Investigation, Formal analysis. M. Chatenet: Writing – review & editing, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization. O. Lottin: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial
interests or personal relationships that could have appeared to influence
the work reported in this paper.

Acknowledgments

This study was carried out within the framework of the PEMFC95
project. The PEMFC95 project was funded by "France 2030" operated by
the French National Research Agency (grant ANR-22-PEHY-0005).

The authors also thank Kévin Mozet from Métro'NRJ - LEMTA
(Université de Lorraine-CNRS - https://lemta.univ-lorraine.fr/).

Data availability

The data are available via a DOI link in the manuscript. Published on
Recherche Data Gouv: DOI: 10.57745/6K5UR2 https://entrepot.
recherche.data.gouv.fr/dataset.xhtml?
persistentId=doi:10.57745/6K5UR2.

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