Temperature Dependency of Net Water Drag Coefficient in Polymer Electrolyte Fuel Cells

A single cell was used to measure the $i$−${{\alpha }}_{{\rm{NWD}}}$ characteristics under various operating conditions. The cell used in this study was identical to those used in our previous studies ^42,43 and had an electrode area of 25 cm² (50 × 50 mm, square). The bipolar plates (separators) of both sides anode and cathode were made of graphite for high-temperature applications, and the geometry of the flow field was "serpentine-dual" with a channel and rib width of 1 mm and a channel depth of 0.5 mm. The flow direction of both the anode gas (H₂) and cathode gas (air) was set at a "counter-flow" configuration. The same commercial catalyst-coated membranes (CCMs) as in previous studies ^41,43 were applied in this study. The membrane used in the CCMs was made of perfluorosulfonic acid (PFSA) polymer and reinforced with expanded polytetrafluoroethylene (ePTFE). Two types of CCM with different membrane thicknesses (t_mem) were incorporated into the cell for the experiment, that is, 15 and 30 μm (for Cell-1 and Cell-2, respectively). Because both types of CCMs were obtained from the same vender, the catalyst layer specifications were the same for both CCMs, with a platinum (Pt) loading of 0.1 and 0.4 mg cm⁻² for the anode and cathode, respectively. For the gas diffusion layer (GDL), a Sigracet product (SGL28BC) with microporous layer coated on one side, was used for both sides of anode and cathode. The cell was assembled under compression of about 3 MPa with Teflon gaskets.

The objective of this study was to measure the water balance under gas supply conditions similar to those of a real PEFC system as presented in Fig. 1. However, in the present measurement system, neither an anode circulation line nor a cathode humidity exchanger was installed, and both anode and cathode gases (H₂ and air) were supplied in a one-way direction. Figure 2 shows a schematic of the measurement system used in this study. The flow rate of supplied dry gases (H₂/air) for each electrode (anode/cathode) (i.e., ${n}_{{{\rm{H}}}_{2}}^{{\rm{in}}}$ and ${n}_{{\rm{air}}}^{{\rm{in}}}$) was regulated by a digital flow controller, respectively. The dry gas (H₂ or air) was humidified to the target dew point by passing through a respective bubbling tank (humidifier) in which water temperature was regulated by the heater covering the tank. The dew point of each gas at the cell inlet (${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}$ and ${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{in}}}$) was continuously monitored by a mirror-type dew point meter (DPM) installed in each pipeline. In the experiment, the temperature of the pipeline from the tank to the cell was also carefully controlled by using a wrapping heater, so that ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}$ and ${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{in}}}$ were restrained within ±1 °C of the target value (the error of RH was approximately within ±1.5%). Target values for the humidifying gas dew point at each RH are summarized in Table SI. As for the dew point measurements at the outlet, our previous study using the same type of measurement system ⁴³ showed that due to the high content of water, the condensation of water vapor could not be avoided at the cathode outlet even when the pipeline was heated, and thus, the dew point of discharged air at cathode (${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{out}}}$) could not be measured properly. Therefore, in this experiment, a DPM was not installed at the cathode outlet, but only at the anode outlet to measure the dew point of discharged H₂ (${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$). The three DPMs (installed in the anode inlet/outlet and cathode inlet) used here were all capable of measuring dew points up to 120 °C (Optidew401, Michell Instruments). The pressures of inlet/outlet at anode and cathode (${p}_{{\rm{A}}}^{{\rm{in}}}$/${p}_{{\rm{A}}}^{{\rm{out}}}$ and ${p}_{{\rm{C}}}^{{\rm{in}}}$/${p}_{{\rm{C}}}^{{\rm{out}}}$) were continuously monitored by pressure transducers (HL, Sensez), and the outlet pressures of both the anode and cathode sides were controlled by a respective back pressure regulator installed at the ends of the outlet pipelines. The T_cell was controlled by plate heaters attached to both end plates.

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In this experiment, cell operation tests were conducted at T_cell = 80 °C, 100 °C, and 120 °C for both Cell-1 and Cell-2. The flow rates of supplied gas on both sides (H₂ at anode and air at cathode) were controlled at a constant stoichiometric ratio, that is, the stoichiometric ratio of H₂ at anode (${\gamma }_{{{\rm{H}}}_{2}}$) and that of air at cathode (${\gamma }_{{\rm{air}}}$) were set at 1.5. However, in order to verify the effect of ${\gamma }_{{{\rm{H}}}_{2}}$ on ${{\alpha }}_{{\rm{NWD}}},$ an additional test with ${\gamma }_{{{\rm{H}}}_{2}}$ = 2.0 was also performed with Cell-1 only at T_cell = 120 °C, whereas ${\gamma }_{{\rm{air}}}$ was kept at 1.5. In the experiments using Cell-1, the RH of supplied H₂ at the anode inlet (${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$) was set to 20, 30, and 40% at each T_cell, whereas the RH of supplied air at cathode inlet (${{\rm{RH}}}_{{\rm{C}}}^{{\rm{in}}}$) was set to 30%. Experiments using Cell-2 were conducted under conditions of 30% RH for both gas supplies (i.e., ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ and ${{\rm{RH}}}_{{\rm{C}}}^{{\rm{in}}}$) at each T_cell. All experiments were performed under the condition of 250 kPa (abs) of outlet pressure of the gas on both sides of anode and cathode. Table I summarizes the operating conditions applied here.

Table I. Operating conditions in the measurements of cell performance and water balance.

	Cell-1	Cell-2
	(${t}_{{\rm{mem}}}$ = 15 μm)	(${t}_{{\rm{mem}}}$ = 30 μm)
Cell temperature (${T}_{{\rm{cell}}}$)	80 °C, 100 °C, 120 °C	80 °C, 100 °C, 120 °C
Stoichiometric ratio of H2 (${{\gamma }}_{{{\rm{H}}}_{2}}$) at anode	1.5 a)	1.5
Stoichiometric ratio of air (${{\gamma }}_{{\rm{air}}}$) at cathode	1.5	1.5
Relative humidity at anode inlet (${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$)	20, 30, 40%	30%
Relative humidity at cathode inlet (${{\rm{RH}}}_{{\rm{C}}}^{{\rm{in}}}$)	30%	30%
Total pressure at anode outlet (${p}_{{\rm{A}}}^{{\rm{out}}}$)	250 kPa (abs)	250 kPa (abs)
Total pressure at cathode outlet (${p}_{{\rm{C}}}^{{\rm{out}}}$)	250 kPa (abs)	250 kPa (abs)

^a)Tests were also conducted at ${{\gamma }}_{{{\rm{H}}}_{2}}$ = 2.0 only when ${T}_{{\rm{cell}}}$ = 120 °C and ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ = 20%.

In order to verify the $i$ dependence of ${{\alpha }}_{{\rm{NWD}}},$ the measurement of $i-{\alpha }_{{\rm{NWD}}}$ characteristics was carried out at the same time as the $i$–${V}_{{\rm{cell}}}$ characteristics. The $i$ was controlled with an electrical load (As-510, NF Corporation), and kept constant for at least 5 min at each measurement. The cell resistance (R_cell) during operation was monitored using an impedance meter (3566, Tsuruga) at a constant frequency of 1 kHz.

The definition and the method of calculation of ${{\alpha }}_{{\rm{NWD}}}$ was the same as those in our previous studies. ^41–43 Table II summarizes the parameters and equations used in calculating ${{\alpha }}_{{\rm{NWD}}}.$ As described in the previous subsection of "Measurements of cell performance and water balance," the flow rates of supplied dry gases (H₂/air) for each electrode (${n}_{{{\rm{H}}}_{2}}^{{\rm{in}}}$ and ${n}_{{\rm{air}}}^{{\rm{in}}}$) were regulated by respective digital flow meters. The total pressure in the pipeline was measured at the inlet and outlet of each side (${p}_{{\rm{A}}}^{{\rm{in}}},$ ${p}_{{\rm{A}}}^{{\rm{out}}},$ ${p}_{{\rm{C}}}^{{\rm{in}}},$ and ${p}_{{\rm{C}}}^{{\rm{out}}}$) by respective pressure gauges. The dew point in the pipeline was measured at the inlet and outlet of the anode and at the inlet of the cathode (${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}},$ ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}},$ and ${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{in}}}$) by dew point meters, and then the vapor pressure was equal to the saturated vapor pressure derived from the measured dew point, that is, ${p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}\right),$ ${p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}\right),$ and ${p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{in}}}\right).$ The rate of charged and discharged amount of water accompanied by gas flow at each side (${n}_{{\rm{W}}\_{\rm{A}}}^{{\rm{in}}},$ ${n}_{{\rm{W}}\_{\rm{A}}}^{{\rm{out}}},$ and ${n}_{{\rm{W}}\_{\rm{C}}}^{{\rm{in}}}$) was then calculated by using the measured gas flow rates, total pressures, and dew points as presented in Table II. At steady state, the rate of water amount is balanced between charged, generated and discharged water from the cell as follows:

$$\begin{eqnarray}&&{n}_{{\rm{W}}\_{\rm{A}}}^{{\rm{in}}}+{n}_{{\rm{W}}\_{\rm{C}}}^{{\rm{in}}}+{n}_{{\rm{W}}}^{{\rm{gen}}}={n}_{{\rm{W}}\_{\rm{A}}}^{{\rm{out}}}+{n}_{{\rm{W}}\_{\rm{C}}}^{{\rm{out}}}\end{eqnarray} \tag{ 1 }$$

where ${n}_{{\rm{W}}}^{{\rm{gen}}}$ denotes the water production rate and can be expressed as

$$\begin{eqnarray}&&{n}_{{\rm{W}}}^{{\rm{gen}}}=\displaystyle \frac{iA}{2F}\end{eqnarray} \tag{ 2 }$$

The ${{\alpha }}_{{\rm{NWD}}}$ can be calculated independently from the respective water balances of the anode and cathode. The net water drag coefficient based on the water balance of charged and discharged water at the anode (${{\alpha }}_{{\rm{NWD}}\_{\rm{A}}}$) is calculated by using the following equation.

$$\begin{eqnarray}&&{\alpha }_{{\rm{NWD}}\_{\rm{A}}}=\displaystyle \frac{{n}_{{\rm{W}}\_{\rm{A}}}^{{\rm{in}}}-{n}_{{\rm{W}}\_{\rm{A}}}^{{\rm{out}}}}{iA/F}\end{eqnarray} \tag{ 3 }$$

Similarly, ${{\alpha }}_{{\rm{NWD}}}$ obtained from the cathode side (${{\alpha }}_{{\rm{NWD}}\_{\rm{C}}}$) is expressed by the following equation.

$$\begin{eqnarray}&&{\alpha }_{{\rm{NWD}}\_{\rm{C}}}=\displaystyle \frac{{n}_{{\rm{W}}\_{\rm{C}}}^{{\rm{out}}}-{n}_{{\rm{W}}\_{\rm{C}}}^{{\rm{in}}}-{n}_{{\rm{W}}}^{{\rm{gen}}}}{iA/F}\end{eqnarray} \tag{ 4 }$$

When the equality of Eq. 1 holds true, ${{\alpha }}_{{\rm{NWD}}\_{\rm{A}}}$ can be assumed to be equal to ${{\alpha }}_{{\rm{NWD}}\_{\rm{C}}}.$ In our previous studies, ^41,42 when ${{\gamma }}_{{\rm{air}}}$ was set high (>2.0), the dew point of discharged air at the cathode outlet (${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{out}}}$) could also be measured stably, and the balance of Eq. 1 was confirmed to be valid within 5% error directly from the dew point results at four locations (inlet and outlet at cathode/anode). However, when ${{\gamma }}_{{\rm{air}}}$ was set low as 1.5, as in the present study, it was difficult to measure ${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{out}}},$ as mentioned above. ⁴³ Because ${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{out}}}$ was not measured in this experiment, it was not possible to confirm the balance in Eq. 1. Instead, the dew points of H₂ at the anode inlet and outlet (${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}$ and ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$) were measured simultaneously and accurately to calculate the value of ${\alpha }_{{\rm{NWD}}\_{\rm{A}}}$ from Eq. 3, which was considered here to be ${{\alpha }}_{{\rm{NWD}}}.$ The dew point of air at the cathode inlet (${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{in}}}$) was also measured and carefully controlled so that air with the target ${{\rm{RH}}}_{{\rm{C}}}^{{\rm{in}}}$ was supplied to the cathode.

Table II. Parameters in water balance calculation.

		Anode (H2)	Cathode (air)
Dry gas flow rate [mol s−1] a)	Inlet	${n}_{{{\rm{H}}}_{2}}^{{\rm{in}}}\left(={{\gamma }}_{{{\rm{H}}}_{2}}\displaystyle \frac{iA}{2F}\right)$	${n}_{{\rm{air}}}^{{\rm{in}}}\left(=\displaystyle \frac{{{\gamma }}_{{\rm{air}}}}{{x}_{{{\rm{O}}}_{2}}}\displaystyle \frac{iA}{4F}\right)$
	Outlet	${n}_{{{\rm{H}}}_{2}}^{{\rm{out}}}\left(=\left({{\gamma }}_{{{\rm{H}}}_{2}}-1\right)\displaystyle \frac{iA}{2F}\right)$	${n}_{{\rm{air}}}^{{\rm{out}}}\left(=\left({{\gamma }}_{{\rm{air}}}/{x}_{{{\rm{O}}}_{2}}-1\right)\displaystyle \frac{iA}{4F}\right)$
Total gas pressure [Pa (abs)]	Inlet	${p}_{{\rm{A}}}^{{\rm{in}}}$	${p}_{{\rm{C}}}^{{\rm{in}}}$
	Outlet	${p}_{{\rm{A}}}^{{\rm{out}}}$	${p}_{{\rm{C}}}^{{\rm{out}}}$
Dew point of gas [K (°C)]	Inlet	${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}$	${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{in}}}$
	Outlet	${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$	—
Vapor pressure [Pa (abs)] b	Inlet	${p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}\right)$	${p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{in}}}\right)$
	Outlet	${p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}\right)$	—
Water amount accompanied by gas flow [mol s−1] b	Inlet	${n}_{W\_A}^{in}=\displaystyle \frac{{p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}\right)}{{p}_{{\rm{A}}}^{{\rm{in}}}-{p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}\right)}{n}_{{{\rm{H}}}_{2}}^{{\rm{in}}}$	${n}_{W\_{\rm{C}}}^{in}=\displaystyle \frac{{p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{in}}}\right)}{{p}_{{\rm{C}}}^{{\rm{in}}}-{p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{in}}}\right)}{n}_{{\rm{air}}}^{{\rm{in}}}$
	Outlet	${n}_{{\rm{W}}\_{\rm{A}}}^{{\rm{out}}}=\displaystyle \frac{{p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}\right)}{{p}_{{\rm{A}}}^{{\rm{out}}}-{p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}\right)}{n}_{{{\rm{H}}}_{2}}^{{\rm{out}}}$	—
Relative humidity (RH) b	Inlet	${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}=\displaystyle \frac{{p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}\right)}{{p}_{{\rm{sat}}}\left({T}_{{\rm{cell}}}\right)}$	${{\rm{RH}}}_{{\rm{C}}}^{{\rm{in}}}=\displaystyle \frac{{p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{in}}}\right)}{{p}_{{\rm{sat}}}\left({T}_{{\rm{cell}}}\right)}$
	Outlet	${{\rm{RH}}}_{{\rm{A}}}^{{\rm{out}}}=\displaystyle \frac{{p}_{{\rm{sat}}}\left({T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}\right)}{{p}_{{\rm{sat}}}\left({T}_{{\rm{cell}}}\right)}$	—

^a) $i$ is current density, $A$ is electrode active area, and $F$ is the Faraday constant. ${{\gamma }}_{{{\rm{H}}}_{2}}$ and ${{\gamma }}_{{\rm{air}}}$ are the stoichiometric ratio of supplied gas at the inlet of the anode and cathode, respectively, and ${x}_{{{\rm{O}}}_{2}}$ is the fraction of oxygen (O₂) in air (i.e., 0.21). ^b) p_sat(T) represents the saturation pressure of water vapor at temperature T.

Calculation of the amount of water carried along with the gas required measuring not only the saturated vapor pressure based on the gas dew point but also the total gas pressure (Table II). The total pressure of both inlet and outlet at both the cathode and anode (${p}_{{\rm{A}}}^{{\rm{in}}},$ ${p}_{{\rm{A}}}^{{\rm{out}}},$ ${p}_{{\rm{C}}}^{{\rm{in}}},$ and ${p}_{{\rm{C}}}^{{\rm{out}}}$) were measured with the pressure gauges during the cell operation. Dependency of these pressures on $i$ during the measurements of $i-{V}_{{\rm{cell}}}$ (and $i-{\alpha }_{{\rm{NWD}}}$) characteristics under different conditions is shown in Fig. S1. The back pressure of both sides anode and cathode of the cell was set at around 250 kPa (abs) by using back-pressure regulators. However, the increase in gas flow rate (${n}_{{{\rm{H}}}_{2}}^{{\rm{in}}}$ and ${n}_{{\rm{air}}}^{{\rm{in}}}$) with increasing $i$ under constant stoichiometric ratio conditions resulted in an increase in the outlet pressure (${p}_{{\rm{A}}}^{{\rm{out}}}$ and ${p}_{{\rm{C}}}^{{\rm{out}}}$) as well as the inlet pressure (${p}_{{\rm{A}}}^{{\rm{in}}}$ and ${p}_{{\rm{C}}}^{{\rm{in}}}$).

As for the anode H₂, as shown in Fig. S1, under the same ${\gamma }_{{{\rm{H}}}_{2}}$ conditions, the behaviors of ${p}_{{\rm{A}}}^{{\rm{in}}}$ and ${p}_{{\rm{A}}}^{{\rm{out}}}$ with respect to $i$ were almost the same regardless of T_cell, ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ and ${t}_{{\rm{mem}}}.$ When ${\gamma }_{{{\rm{H}}}_{2}}$ = 1.5, the pressure difference between ${p}_{{\rm{A}}}^{{\rm{in}}}$ and ${p}_{{\rm{A}}}^{{\rm{out}}}$ was approximately 3 kPa at $i$ = 1.4 A cm⁻². The experiments with ${\gamma }_{{{\rm{H}}}_{2}}$ = 2.0 was also carried out at T_cell = 120 °C and ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ = 20%, and the pressure difference was increased to about 5 kPa.

As for the cathode, air supply conditions were the same for all experiments with ${\gamma }_{{{\rm{H}}}_{2}}$ = 1.5 and ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ = 30%. Because ${n}_{{\rm{air}}}^{{\rm{in}}}$ was about five times higher than ${n}_{{{\rm{H}}}_{2}}^{{\rm{in}}}$ even when ${{\gamma }}_{{{\rm{H}}}_{2}}$ = ${{\gamma }}_{{\rm{air}}}$ = 1.5, the increase in ${p}_{{\rm{C}}}^{{\rm{in}}}$ and ${p}_{{\rm{C}}}^{{\rm{out}}}$ with respect to the increase in $i$ was greater than that for anode H₂ as seen in Fig. S1. The behaviors of ${p}_{{\rm{C}}}^{{\rm{in}}}$ and ${p}_{{\rm{C}}}^{{\rm{out}}}$ versus $i$ at each T_cell were almost the same regardless of the change in anode gas supply conditions, though the pressure fluctuations were relatively large due to the high water uptake in the cell. When T_cell = 80 °C or 100 °C, the pressure difference between ${p}_{{\rm{C}}}^{{\rm{in}}}$ and ${p}_{{\rm{C}}}^{{\rm{out}}}$ ranged from 15 to 20 kPa at $i$ = 1.4 A cm⁻². However, when T_cell = 120 °C, the pressure differences increased to nearly 30 kPa at the same $i.$ The ${\gamma }_{{{\rm{H}}}_{2}}$ and ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ were the same at all temperatures, and the reason for the pressure differences is not well understood at present.

In the region of high $i$ (c.a., > 1.0 A cm⁻²), a pressure difference of about 20 − 30 kPa between the anode and cathode should have been generated locally near the cathode gas inlet. However, our previous studies ^41,43 showed that the effect of the gas pressure difference on water transport through the membrane was fairly limited. In any case, the measured total pressures here were directly used in the calculations of ${{\alpha }}_{{\rm{NWD}}}.$

The $i-{V}_{{\rm{cell}}}$ characteristics of the cells with CCMs of different ${t}_{{\rm{mem}}}$ (15 and 30 μm) were compared at ${T}_{{\rm{cell}}}$ = 80 °C, 100 °C, and 120 °C. Figure 3 shows this comparison and the $i-{R}_{{\rm{cell}}}$ characteristics. As listed in Table I, in the case of Cell-1 (${t}_{{\rm{mem}}}$ = 15 μm), the $i-{V}_{{\rm{cell}}}$ characteristics were measured under different ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ conditions (20%, 30%, and 40%) at ${{\gamma }}_{{{\rm{H}}}_{2}}$ = 1.5, whereas ${{\gamma }}_{{\rm{air}}}$ and ${{\rm{RH}}}_{{\rm{C}}}^{{\rm{in}}}$ were fixed at 1.5 and 30% respectively for all measurements. In the case of Cell-2 (${t}_{{\rm{mem}}}$ = 30 μm), tests were conducted under fixed ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ of 30% at each temperature. Note that the cell behavior was often unstable when $i$ = 0.1 A cm⁻², probably due to the small gas flow rate. For this reason, data of ${V}_{{\rm{cell}}}$ and ${R}_{{\rm{cell}}}$ at $i$ = 0.1 A cm⁻² were omitted from the graphs shown in Fig. 3.

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There is a possibility that cell operation at T_cell above 100 °C causes degradation of the membrane structure in a proton exchange membrane (PEM). A series of experiments were conducted here in consecutive order of T_cell at 80, 100, and 120 °C, and finally again at 120 °C. The results confirmed that there was almost no change in the $i-{V}_{{\rm{cell}}}$ characteristics at T_cell = 120 °C, that is, the change in ${V}_{{\rm{cell}}}$ was about 15 mV at $i$ = 1.4 A cm⁻². Therefore, no significant membrane degradation occurred during this operation time (several hours) even when T_cell was 120 °C.

The experiments at T_cell = 80 °C were also conducted in our previous study using cells with the same specifications (Cell-1 and Cell-2) under the same gas supply conditions for both the anode and cathode. ⁴³ The $i-{V}_{{\rm{cell}}}$ characteristics obtained in the present study were in good agreement with previous data; that is, the ${V}_{{\rm{cell}}}$ difference at $i$ = 1.4 A cm⁻² was about 6 mV and 12 mV with Cell-1 (${t}_{{\rm{mem}}}$ = 15 μm) and Cell-2 (${t}_{{\rm{mem}}}$ = 30 μm), respectively. However, there was a significant difference in ${R}_{{\rm{cell}}}$ between the present data and the previous data. In a previous study using a cell with the same specifications as Cell-1, ⁴³ ${R}_{{\rm{cell}}}$ was stable at around 0.032 Ω cm² in the $i$ range of 0.5 to 1.4 A cm⁻², whereas in the present study, ${R}_{{\rm{cell}}}$ showed a downward trend with increasing $i,$ ranging from 0.05 Ω cm² at $i$ = 0.5 A cm⁻² to 0.035 at 1.4 A cm⁻² (Fig. 3a). Similar differences in ${R}_{{\rm{cell}}}$ data were also observed in Cell-2. In our previous study, ⁴³ ${R}_{{\rm{cell}}}$ was measured at 10 kHz for each $i$ by using a frequency response analyzer in combination with an electrical load. In contrast, in the present experiment, ${R}_{{\rm{cell}}}$ was measured simply and constantly monitored at 1 kHz by using a impedance meter. The accuracy of the ${R}_{{\rm{cell}}}$ measurement was supposed to be higher in the previous data ⁴³ than in the present data. However, we determined that the present ${R}_{{\rm{cell}}}$ data provided qualitative insights of the temperature dependence of ${R}_{{\rm{cell}}}$ and the water content in the membrane.

The $i-{V}_{{\rm{cell}}}$ characteristics of Cell-1 in Fig. 3 show that the $i-{V}_{{\rm{cell}}}$ characteristics were relatively unaffected by changes in ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ at any T_cell. In Cell-1, not only the $i-{V}_{{\rm{cell}}}$ characteristics but also $i-{R}_{{\rm{cell}}}$ characteristics were almost the same at T_cell = 80 °C and 100 °C, whereas those at 120 °C were significantly degraded. Because the ${R}_{{\rm{cell}}}$ of Cell-1 at 120 °C was certainly higher than that at 80 and 100 °C, the performance degradation at T_cell = 120 °C was considered to be mainly due to the high ${R}_{{\rm{cell}}}.$ On the other hand, the difference in ${t}_{{\rm{mem}}}$ of the CCM was evident in the difference in ${R}_{{\rm{cell}}}.$ The difference in $i-{V}_{{\rm{cell}}}$ performance between Cell-1 and Cell-2 could be attributed to the difference in ${R}_{{\rm{cell}}}.$ In particular, at T_cell = 120 °C, the ${R}_{{\rm{cell}}}$ of Cell-2 was significantly higher than that of Cell-1, and the cell performance was also severely degraded. This result suggests that the membrane in Cell-2 was significantly dry during the operation at 120 °C.

Net water drag coefficient (${{\alpha }}_{{\rm{NWD}}}$) at each $i$ was obtained by measuring the pressures and dew points of gases at the inlet/outlet of both sides of anode and cathode as described in the Experimental section above. Measurement of the gas dew point is crucial in the calculation of ${{\alpha }}_{{\rm{NWD}}}.$ When water droplets adhered to the mirror surface of a mirror-type dew point meter, the dew point fluctuated severely, thus making it difficult to accurately measure the dew point. Our previous studies ⁴³ observed dew point fluctuations at low $i$ ≈ 0.3 A cm⁻² at the cathode outlet. Therefore, in the present experiment, the measurement of ${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{out}}}$ was omitted. In our present measurements of not only ${T}_{{\rm{dew}}\_{\rm{C}}}^{{\rm{out}}}$ but also ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}},$ the dew point fluctuations possibly increased with $i.$ For the ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}},$ only data that could be measured stably for more than 2 min were adopted and plotted in the graphs.

Figure 4 shows the $i-{T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ and $i-{\alpha }_{{\rm{NWD}}}$ characteristics obtained for Cell-1 (${t}_{{\rm{mem}}}$ = 15 μm) under different T_cell (80 °C, 100 °C, and 120 °C) and ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ (20, 30, and 40%), at ${{\gamma }}_{{{\rm{H}}}_{2}}$ = ${{\gamma }}_{{\rm{air}}}$ = 1.5 and ${{\rm{RH}}}_{{\rm{C}}}^{{\rm{in}}}$ = 30%. Figure 4a shows that at T_cell = 80 °C, ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ was constant regardless of $i$ and was almost the same temperature as T_cell (i.e., ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{iout}}}$ ≈ 100%), although data could only be obtained up to i = 0.6 A cm⁻². The effect of ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ on $i-{T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ characteristics was negligible. The ${{\alpha }}_{{\rm{NWD}}}$ calculated based on this ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ data decreased with decreasing ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}},$ and ${{\alpha }}_{{\rm{NWD}}}$ was negative when ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ ≤ 30% as shown in Fig. 4d. The present data for ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ and ${{\alpha }}_{{\rm{NWD}}}$ at T_cell = 80 °C agreed well with our previous data measured under the same gas conditions using a cell with the same specifications. ⁴³ Interestingly, the $i$ range in which ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ could be measured stably was also consistent with previous data. The $i-{T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ characteristics at T_cell = 100 °C (Fig. 4b) showed that ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ increased with increasing $i$ and stabilized at approximately $i$ = 1.0 A cm⁻². Again, the effect of ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ on ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ was small, and ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ in the stable region range was 96 °C to 97 °C regardless of ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ (i.e., ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{out}}}$ = 90%-93%). The $i-{\alpha }_{{\rm{NWD}}}$ characteristics at T_cell of 100 °C (Fig. 4e) show that ${{\alpha }}_{{\rm{NWD}}}$ was decreased with increasing $i,$ and stabilized at approximately $i$ = 1.0 A cm⁻². The same as the case of T_cell = 80 °C, ${{\alpha }}_{{\rm{NWD}}}$ decreased with decreasing ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ at T_cell = 100 °C, and was negative region over almost the entire $i$ range at ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ of 20%. In the $i-{T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ characteristics at T_cell = 120 °C (Fig. 4c), ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ increased with increasing $i$ and stabilized at approximately $i$= 0.8 A cm⁻², similar to the characteristics at 100 °C. At this T_cell = 120 °C, ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ in the stable region ranged from 96 °C to 98 °C regardless of ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}},$ which corresponded to the fact that ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{out}}}$ ranged from 45 to 48%. These results reveal that the anode side of the cell became considerably dryer at T_cell = 120 °C than at T_cell = 80 and 100 °C. It is reasonable to assume that this was the cause of the high ${R}_{{\rm{cell}}}$ at T_cell = 120 °C (Fig. 3c). Interestingly, ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ in the stable region at T_cell = 100 °C and 120 °C was almost identical, but the reason for this is not clear at this time. The $i-{\alpha }_{{\rm{NWD}}}$ characteristics at T_cell = 120 °C (Fig. 4f) show that the effect of the ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ decrease on the ${{\alpha }}_{{\rm{NWD}}}$ decrease became more significant as the increase of T_cell. However, even at ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ = 20%, ${{\alpha }}_{{\rm{NWD}}}$ barely entered the negative region.

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To verify the effect of ${t}_{{\rm{mem}}}$ on the $i-{T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ and $i-{\alpha }_{{\rm{NWD}}}$ characteristics, a comparison of both characteristics obtained with Cell-1 (${t}_{{\rm{mem}}}$ = 15 μm) and Cell-2 (${t}_{{\rm{mem}}}$ = 30 μm) is shown in Fig. 5, at ${{\gamma }}_{{{\rm{H}}}_{2}}$ = ${{\gamma }}_{{\rm{air}}}$ = 1.5 and ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ = ${{\rm{RH}}}_{{\rm{C}}}^{{\rm{in}}}$ = 30%. A similar comparison of $i-{\alpha }_{{\rm{NWD}}}$ characteristics at T_cell = 80 °C has been reported in our previous paper. ⁴³ The data obtained in the present study were in good agreement with the data in that previous study, and the ${{\alpha }}_{{\rm{NWD}}}$ values of Cell-1 and Cell-2 were almost the same at $i$ > 0.4 A cm⁻² as shown in Fig. 5d. This is because ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ was the same as T_cell in both cells in this $i$ range (Fig. 5a). The fact that ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ was equal to T_cell (i.e., ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{out}}}$ = 100%) regardless of ${t}_{{\rm{mem}}}$ suggests that at T_cell = 80 °C, almost the entire area of membrane was fully hydrated regardless of ${t}_{{\rm{mem}}},$ and that the effect of back diffusion on ${{\alpha }}_{{\rm{NWD}}}$ did not appear in either cell.

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Comparison of $i-{T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ characteristics at T_cell = 100 °C (Fig. 5b) shows that ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ increased with the increase in $i$ in both cells and stabilized when $i$ exceeded approximately 1.0 A cm⁻², but there was a clear difference between the ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ values of the two cells. There was also a difference in ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ in the stable region, when ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ with Cell-1 was about 96 °C, whereas that with Cell-2 was about 90 °C. This difference in $i-{T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ characteristics was reflected in the $i-{\alpha }_{{\rm{NWD}}}$ characteristics (Fig. 5e). As ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ increased, the $i-{\alpha }_{{\rm{NWD}}}$ characteristics reveal that ${{\alpha }}_{{\rm{NWD}}}$ decreased with the increase in $i$ and then stabilized when $i$ exceeded approximately 1.0 A cm⁻² with both cells. However, in Cell-1, ${{\alpha }}_{{\rm{NWD}}}$ entered a negative region when $i$ > 0.9 A cm⁻², whereas in Cell-2, ${{\alpha }}_{{\rm{NWD}}}$ remained in a positive region even in the stable region of$i$> 1.0 A cm⁻². According to Fick's law, for a given water concentration gradient, the diffusion flux is inversely proportional to the diffusion length. As for the back-diffusion of water through the membrane, the diffusion length is nearly equal to ${t}_{{\rm{mem}}}.$ The difference observed between Cell-1 and Cell-2 in the $i-{\alpha }_{{\rm{NWD}}}$ characteristics was thought to be due to the difference in back-diffusion flux caused by the difference in ${t}_{{\rm{mem}}},$ that is, the membrane was not fully hydrated, but a water concentration gradient appeared in the through-plane direction of the membrane. Note that ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ tended to increase in both cells at $i$ < 1.0 A cm⁻², suggesting that the humidification of the membrane progressed gradually with the increase in $i.$ In addition, unlike the case of T_cell = 80 °C, ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ did not reach T_cell in the stable region of $i$ > 1.0 A cm⁻² in Cell-1 as well as Cell-2 at T_cell = 100 °C. This suggests that even in this $i$ region, the entire area of the membrane was not fully hydrated for either cell.

Comparison of the $i-{T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ characteristics of both cells at T_cell = 120 °C (Fig. 5c), reveals extraordinary behavior in Cell-2, that is, ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ of Cell-2 decreased with the increase in $i.$ Because ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}$ in this condition (T_cell = 120 °C, ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ = 30%) was set at 86.0 °C, ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ was lower than ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{in}}}$ in the region of $i$ > 0.4 A cm⁻², and water was thus drawn up into the cell from the anode. According to the decrease in ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}},$ ${{\alpha }}_{{\rm{NWD}}}$ increased with the increase in $i$ (Fig. 5f). It is known that the diffusion coefficient of water in PEM depends on the water content in the membrane, and that the diffusion coefficient decreases significantly when the water content is small. Therefore, the flux of back-diffusion in Cell-2 must be significantly small, and the amount of water transported from the cathode through the membrane was considered to be restrained. As a result, drying of the membrane progressed from the anode side, resulting in performance degradation. For this reason, ${R}_{{\rm{cell}}}$ was considered to be very high in Cell 2 as seen in Fig. 3c. In conclusion, operation of Cell-2 (${t}_{{\rm{mem}}}$ = 30 μm) is very difficult under gas supply conditions similar to a real system at T_cell = 120 °C.

As mentioned in the Introduction section, ${{\alpha }}_{{\rm{NWD}}}$ must be negative in a stand-alone PEFC system. However, as shown in Fig. 4f, at T_cell = 120 °C, ${{\alpha }}_{{\rm{NWD}}}$ did not enter the negative region even when ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ was lowered to 20%. On the other hand, the flow conditions of anode H₂ were expected to be more flexible than those of cathode air in real system operation. Furthermore, our previous results obtained at T_cell = 80 °C ⁴³ revealed that increasing ${\gamma }_{{{\rm{H}}}_{2}}$ is effective in lowering ${{\alpha }}_{{\rm{NWD}}}.$ An additional experiment was thus conducted with ${\gamma }_{{{\rm{H}}}_{2}}$ being increased from 1.5 to 2.0 under the conditions of T_cell = 120 °C and ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ = 20%. The $i-{T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ and $i-{\alpha }_{{\rm{NWD}}}$ characteristics obtained from this additional experiment are shown in Fig. 6. Comparison of ${\gamma }_{{{\rm{H}}}_{2}}$ at 1.5 and 2.0 in the $i-{T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ characteristics (Fig. 6a) reveal that ${T}_{{\rm{dew}}\_{\rm{A}}}^{{\rm{out}}}$ with ${\gamma }_{{{\rm{H}}}_{2}}$ = 2.0 was a slightly higher than that with ${\gamma }_{{{\rm{H}}}_{2}}$ = 1.5 when $i$ < 0.5 A cm⁻², but were almost identical in the region above 0.6 A cm⁻². On the other hand, the difference between the $i-{\alpha }_{{\rm{NWD}}}$ characteristics (Fig. 6b) at ${\gamma }_{{{\rm{H}}}_{2}}$= 1.5 and 2.0 was significant due to the increase in flow rate of H₂ (i.e., ${n}_{{{\rm{H}}}_{2}}^{{\rm{in}}}$ and ${n}_{{{\rm{H}}}_{2}}^{{\rm{out}}}$), and furthermore, ${{\alpha }}_{{\rm{NWD}}}$ was negative over the entire $i$ range when ${\gamma }_{{{\rm{H}}}_{2}}$ = 2.0. Note that there was no significant difference in the $i-{V}_{{\rm{cell}}}$ and $i-{R}_{{\rm{cell}}}$ characteristics (Fig. S2). These results indicate that the $i-{V}_{{\rm{cell}}}$ characteristic was more insensitive to water transport in the cell than the $i-{\alpha }_{{\rm{NWD}}}$ characteristic; although an increase in ${\gamma }_{{{\rm{H}}}_{2}}$ increased the amount of water transported into the anode, the change in water transport had little effect on cell performance. As mentioned in the introduction section, ${\gamma }_{{{\rm{H}}}_{2}}$ and ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ are not independently controllable in a real system. However, the results confirmed that changes in ${\gamma }_{{{\rm{H}}}_{2}}$ have a greater effect on ${{\alpha }}_{{\rm{NWD}}}$ than changes in ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}.$ In real system operation, ${\gamma }_{{{\rm{H}}}_{2}}$ and ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ would be closely related, and an increase in ${\gamma }_{{{\rm{H}}}_{2}}$ is likely to result in a decrease in ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}.$ Both the increase in ${\gamma }_{{{\rm{H}}}_{2}}$ and the decrease in ${{\rm{RH}}}_{{\rm{A}}}^{{\rm{in}}}$ were advantageous in terms of lowering ${{\alpha }}_{{\rm{NWD}}}.$ Therefore, this result indicates that increasing ${\gamma }_{{{\rm{H}}}_{2}}$ was an effective means of making ${{\alpha }}_{{\rm{NWD}}}$ negative even in high-temperature operation above 100 °C, though there was concern about performance degradation due to drying of the membrane.

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In real systems, change in ${\gamma }_{{{\rm{H}}}_{2}}$ could be achieved relatively easily by the power control of the H₂ circulation pump (Fig. 1). It should be noted, however, that increasing ${\gamma }_{{{\rm{H}}}_{2}}$ would reduce the fuel utilization efficiency of FCVs. To optimize water management during high-temperature operation above 100 °C, further thinning of the PEM or sophisticated flow channel design would be required to ensure the water transport to the anodes through the membrane.