Numerical Simulation on Impacts of Thickness of Nafion Series Membranes and Relative Humidity on PEMFC Operated at 363 K and 373 K

The purpose of this study is to understand the impact of the thickness of Nafion membrane, which is a typical polymer electrolyte membrane (PEM) in Polymer Electrolyte Membrane Fuel Cells (PEMFCs), and relative humidity of supply gas on the distributions of H2, O2, H2O concentration and current density on the interface between a Nafion membrane and anode catalyst layer or the interface between a Nafion membrane and cathode catalyst layer. The effect of the initial temperature of the cell (Tini) is also investigated by the numerical simulation using the 3D model by COMSOL Multiphysics. As a result, the current density decreases along with the gas flow through the gas channel irrespective of the Nafion membrane thickness and Tini, which can be explained by the concentration distribution of H2 and O2 consumed by electrochemical reaction. The molar concentration of H2O decreases when the thickness of Nafion membrane increases, irrespective of Tini and the relative humidity of the supply gas. The current density increases with the increase in relative humidity of the supply gas, irrespective of the Nafion membrane thickness and Tini. This study recommends that a thinner Nafion membrane with well-humidified supply gas would promote high power generation at the target temperature of 363 K and 373 K.


Introduction
The polymer electrolyte membrane fuel cell (PEMFC) is one of the promising fuel cell technologies which can use H 2 as a fuel for co-generation system and vehicles. Recently, it has been conceived that H 2 could be one procedure to realize the target of zero CO 2 emissions by 2050 in Japan. Therefore, it is important to develop the efficient PEMFC system by 2050. It is important to develop the efficient PEMFC system as well as green H 2 production in order to achieve the net target, i.e., a virtually zero CO 2 emission in Japan by 2050. According to the Japanese New Energy and Industry Technology Development Organization (NEDO) road map 2017 [1], a PEMFC system is required to be operated at 363 K and 373 K for stationary and mobility applications, respectively, from 2020 to 2025. However, the normal PEMFC, which uses a Nafion membrane, is usually operated within a lower temperature range, between 333 K and 353 K [2,3]. If PEMFC is operated at a higher temperature than usual, the following advantages can be obtained: (1) promoting electrochemical kinetics in both electrodes, (2) reducing the cooling system for automobile applications due to an increase in the temperature difference between the PEMFC stack and coolant, and (3) endurance enhancement to CO in lower quality reformed H 2 [4]. However, operating the PEMFC system at a higher temperature would present challenges, including: (1) degradation of Nafion membranes; (2) catalyst elution; (3) uneven distributions of gas flow, pressure, temperature, voltage and current in a cell of PEMFC. It is necessary to solve them in order to commercialize the PEMFC system operated at a higher temperature [5]. In addition, it is also believed that the temperature distribution influences the phase change of H 2 O and can influence the performance of the polymer electrolyte membrane (PEM), fuel and oxidant flows in gas diffusion layer (GDL) and catalyst layer at high temperatures. Consequently, it is necessary to analyze the heat and mass transfer mechanism in a cell of PEMFC in order to improve the power generation performance and achieve a longer operation time.
According to the literature on high-temperature PEMFC operated over 373 K, newly developed membranes which can be used at a high temperature include polybenzimidazolebased membrane [6] and bulky N-heterocyclic group functionalized poly (terphenyl piperidinium) membrane [7]. Regarding the development of new electrode, polytetrafluoroethylene (PTFE) binder dispersion [8] and 3D numerical simulation for the optimization of electrode thickness [9] have been reported. In addition, the optimization of the flow channel of a gas separator [10] and multi-objective optimization of operating conditions [11] are popular topics being studied. Mass transport phenomena in a cell such as distributions of H 2 , O 2 , and H 2 O concentration are also being investigated [12][13][14]. The temperature distribution on the back of the separator and the interface between PEM and the cathode catalyst layer has been investigated experimentally [15,16] and numerically [17,18], respectively, by the authors. Though the current density and temperature distribution were studied experimentally [19] and numerically [20] at the same time, there have been no reports investigating the distribution of H 2 , O 2 , H 2 O concentration and current density on the interface between PEM and the anode catalyst layer, where the H 2 oxidation reaction occurs or the interface between PEM and the cathode catalyst layer where the O 2 reduction reaction occurs. In addition, the previous numerical research [12][13][14] used the contour figure qualitatively. It is not enough to understand the mechanism of electrochemical reaction deciding the power generation performance of PEMFC. It is important to understand the characteristics on the interface between PEM and the anode catalyst layer where the H 2 oxidization reaction occurs and the interface between PEM and the cathode catalyst layer where the O 2 reduction reaction occurs quantitatively. Therefore, the analysis of these distributions is important to understand the electrochemical reaction and power generation characteristics of PEMFC. Therefore, the purpose of this study is to clarify the distributions of H 2 , O 2 , H 2 O concentration and the current density on the interface between the Nafion membrane, which is used as a typical PEM, and the anode catalyst layer or the interface between the Nafion membrane and cathode catalyst layer under a higher-temperature operation condition than usual. Some new membranes, e.g., polybenzimidazole-based membrane [6], have recently been developed for the high-temperature operation of PEMFC. However, it is easy to apply and commercialize the PEMFC system if the Nafion membrane can be used at a high temperature such as 363 K and 373 K. Numerical simulation using a 3D model by multi-physics simulation software COMSOL Multiphysics has also been carried out to achieve the aim of this study. In addition, the impact of the Nafion membrane thickness on these distributions has also been investigated. When the thinner Nafion membrane is used, lower Ohmic resistance as well as a higher proton flux ratio and back diffusion can be obtained [21][22][23]. Therefore, it is also important to investigate the effect of the Nafion membrane thickness on the distributions of H 2 , O 2 , and H 2 O concentration and current density on the interface between the Nafion membrane and anode catalyst layer or the interface between the Nafion membrane and cathode catalyst layer.

Model Description and Governing Equations
This study has conducted the numerical analysis using a 3D model by multi-physics simulation software COMSOL Multiphysics. It has the simulation code for PEMFC composed of a continuity equation, the Brinkmann equation, considering the momentum transfer; the Maxwell-Stefan equation, considering the diffusion transfer; and the Butler- Volmer equation, considering the electrochemical reaction. This simulation code has been validated well by many previous studies [12,[24][25][26].
The continuity equation considering the gas species in porous media such as the catalyst layer, micro porous layer (MPL), and GDL as well as in the gas channel is expressed as follows: where ε p is the porosity ( ), ρ is the density (kg/m 3 ), → u is the velocity vector (m/s), Q m is the mass source term (kg/(m 3 s)), and t is the time (s). The relationship between the pressure and gas flow velocity, which is solved in porous media such as the catalyst layer, MPL, and GDL, as well as in the gas channel, can be expressed by the following Brinkmann equation: where p is the pressure (Pa), µ is the viscosity (Pa s), → I is the unit vector( ), κ is the permeability (m 2 ), and → F is the force vector (kg/(m 2 ·s 2 )), e.g., gravity. Mass transfer considering the diffusion, ion transfer, and convection transfer can be expressed by the following Maxwell-Stefan equation: where → N i is the vector of the molar flow rate on the interface between PEM and electrode (mol/(m 2 s)), D i is the diffusion coefficient (m 2 /s), C i is the concentration of ion i (mol/m 3 ), z i is the valence of ion ( ), u m,i is the mobility of ion i ((s mol)/kg), F is the Faraday constant (C/mol), ϕ l is the electrical potential of liquid [27] (V), → J is the molar flow rate of the convection transfer (mol/(m 2 s)), and R i,tot is the reaction rate of species (mol/(m 3 s)).
The electrochemical reaction is calculated following Butler-Volmer equation: where i is the current density (A/m 2 ), i 0 is the exchange current density (A/m 2 ), α a is the charge transfer coefficient at anode ( ), η is the activation over-potential [27] (V), R is the gas constant (J/(mol K)), T is the temperature (K), α c is the charge transfer coefficient at cathode ( ), ϕ s is the electrical potential of solid [27] (V), E eq is the equilibrium electric potential [27] (V). Figure 1 illustrates 3D model of single cell of PEMFC. This structure follows the commercialized single cell used in the previous experimental study [16]. In this model, the outside of the roof of gas separator at anode and cathode sides are omitted. This single cell has a gas separator having a serpentine flow channel which consists not only of five gas channels with the width of 1.0 mm and depth of 1.0 mm but also a rib with a width of 1.0 mm. Table 1 lists the geometrical parameters of the 3D model used in this study. Nafion 115, Nafion NRE-212, and Nafion NRE-211, whose thicknesses are 127 µm, 51 µm, and 25 µm, respectively, have been investigated to assess the impact of the thickness of the Nafion membrane on the distributions of H 2 , O 2 , and H 2 O concentrations and the current density. Physical parameters and operation conditions for numerical simulation in this study are listed in Tables 2 and 3, respectively. T ini is changed by 353 K, 363 K, and 373 K. This study has conducted the numerical simulation at T ini = 353 K showing the characteristics at a standard operation temperature to compare the characteristics at a higher temperature. The relative humidity of supply gas at the anode and cathode is changed by 40%RH and 80%RH, respectively. The flow rate of supply gas is set at the stoichiometric ratio of 1.5, where the volume flow rate of supply gas at the anode and cathode is 0.210 NL/min and 0.105 NL/min, respectively. The stoichiometric ratio of 1.0 for the flow rate of supply gas can be defined by Equation (7).
where C H2 is the molar flow rate of consumed H 2 (mol/s), I is the loaded current (A) and z H2 is the electrons moles exchanged in the reaction (=2) ( ). C H2 is the molar flow rate corresponding to the stoichiometric ratio of 1.0. The C O2 is the molar flow rate of consumed O 2 (mol/s), which is a half of C H2 (which can be defined by Equation (8)).
cell has a gas separator having a serpentine flow channel which consists not only of five gas channels with the width of 1.0 mm and depth of 1.0 mm but also a rib with a width of 1.0 mm. Table 1 lists the geometrical parameters of the 3D model used in this study. Nafion 115, Nafion NRE-212, and Nafion NRE-211, whose thicknesses are 127 μm, 51 μm, and 25 μm, respectively, have been investigated to assess the impact of the thickness of the Nafion membrane on the distributions of H2, O2, and H2O concentrations and the current density. Physical parameters and operation conditions for numerical simulation in this study are listed in Tables 2 and 3, respectively. Tini is changed by 353 K, 363 K, and 373 K. This study has conducted the numerical simulation at Tini = 353 K showing the characteristics at a standard operation temperature to compare the characteristics at a higher temperature. The relative humidity of supply gas at the anode and cathode is changed by 40%RH and 80%RH, respectively. The flow rate of supply gas is set at the stoichiometric ratio of 1.5, where the volume flow rate of supply gas at the anode and cathode is 0.210 NL/min and 0.105 NL/min, respectively. The stoichiometric ratio of 1.0 for the flow rate of supply gas can be defined by Equation (7).
where CH2 is the molar flow rate of consumed H2 (mol/s), I is the loaded current (A) and zH2 is the electrons moles exchanged in the reaction (=2) ( ). CH2 is the molar flow rate corresponding to the stoichiometric ratio of 1.0. The CO2 is the molar flow rate of consumed O2 (mol/s), which is a half of CH2 (which can be defined by Equation (8)).
H2 + 1/2 O2 = H2O (8)      In this study, O 2 is adopted as the cathode gas. In the near future, it can be expected that H 2 will be produced from renewable energy via H 2 O electrolyzer mainly in order to realize a zero-CO 2 -emission society. After the production of H 2 by H 2 O electrolysis, O 2 is also produced as a by-product. This study suggests that not only H 2 but also O 2 produced from H 2 O electrolysis are used for PEMFC. The total system consisting of renewable energy, H 2 O electrolyzer, and PEMFC can be operated effectively by using O 2 . In addition, if we use O 2 as a cathode gas, we can obtain a higher current density on the interface between PEM and the catalyst layer, especially under the rib, compared to the case using air [28]. This is due to the decrease in over-potential by the increase in the concentration of O 2 . Therefore, it can be expected that higher power generation performance is obtained by using O 2 . They are the reasons why this study adopts pure O 2 instead of air.

Model Assumption
This study considers the following assumptions:  (vii) The cell temperature is uniform and the outside boundary of the 3D model is set at T ini . (viii) The effective porosity and the permeability of the porous media are isotropic. The conductivity in the porous media is also isotropic.
The impact of the Nafion membrane thickness, T ini , and relative humidity of the supply gas on the distributions of the molar concentration of H 2 , O 2 , and H 2 O and current the density on the interface between the Nafion membrane and anode catalyst layer or the interface between the Nafion membrane and cathode catalyst layer has been investigated, considering the above-described equations and parameters as well as the assumptions.

Results and Discussion
3.1. In-Plane Distribution of Mass and Current Density on the Interface between Nafion Membrane and Anode Catalyst Layer or the Interface between Nafion Membrane and Cathode Catalyst Layer Figure 2 shows the comparison of the in-plane molar concentration distribution of H 2 on the interface between the Nafion membrane and anode catalyst layer with a different Nafion membrane and T ini for the relative humidity of the supply gas of the anode of 80%RH and cathode of 80%RH (A80%RH&C80%RH).        According to Figure 2, it is found that the molar concentration of H2 decreases along with the gas flow through the gas channel irrespective of the Nafion membrane thickness and Tini due to the uniform consumption rate of H2 caused by the high permeability through porous media [12]. In addition, it is known that the molar concentration of H2 decreases more with the increase in Tini, irrespective of the Nafion membrane thickness. The molar concentration is defined by dividing the molar quantity of gas species by its volume. Since the gas volume increases when Tini increases, the molar concentration of H2 would decrease with the increase in Tini.
It is seen from Figure 3 that the molar concentration of O2 decreases along with the gas flow through the gas channel irrespective of the Nafion membrane thickness and Tini. It is found that the O2 reduction reaction progresses along with the gas flow through the gas channel. According to Figure 3, the amount of O2 consumption from the inlet to the outlet is the largest at Tini = 353 K, irrespective of the Nafion membrane thickness. The According to Figure 2, it is found that the molar concentration of H 2 decreases along with the gas flow through the gas channel irrespective of the Nafion membrane thickness and T ini due to the uniform consumption rate of H 2 caused by the high permeability through porous media [12]. In addition, it is known that the molar concentration of H 2 decreases more with the increase in T ini , irrespective of the Nafion membrane thickness. The molar concentration is defined by dividing the molar quantity of gas species by its volume. Since the gas volume increases when T ini increases, the molar concentration of H 2 would decrease with the increase in T ini . It is seen from Figure 3 that the molar concentration of O 2 decreases along with the gas flow through the gas channel irrespective of the Nafion membrane thickness and T ini . It is found that the O 2 reduction reaction progresses along with the gas flow through the gas channel. According to Figure 3, the amount of O 2 consumption from the inlet to the outlet is the largest at T ini = 353 K, irrespective of the Nafion membrane thickness. The kinetics of the catalyst are faster with the increase in temperature, while the relative humidity influences the performance of the O 2 reduction reaction occurring on the ionomer in the cathode catalyst layer [40]. There is the optimum H 2 O saturation of ionomer in the cathode catalyst layer. On the other hand, the proton conductivity of the Nafion membrane is influenced by the temperature and relative humidity. According to the literature [41,42], the proton conductivity of the Nafion membrane increases with the increase in temperature as well as the increase in relative humidity. Since the saturation pressure of H 2 O vapor increases with the temperature exponentially [43], it is easy to dehydrate the Nafion membrane at T ini = 373 K compared to T ini = 353 K, resulting in the proton conductivity of the Nafion membrane decreasing at T ini = 373 K. If the proton conductivity of the Nafion membrane decreases, the performance of the O 2 reduction reaction drops due to a lack of proton. In addition, since the hydration of the Nafion membrane is not enough at T ini = 373 K, the high O 2 partial pressure is needed to progress the O 2 reduction reaction [43]. Consequently, it is thought that the amount of O 2 consumption decreases at T ini = 373 K. The proton conductivity of the Nafion membrane increases when the temperature increases, even at a temperature above 373 K [40]. However, we have to consider the degradation of the Nafion membrane under the dehydrated condition [44]. Therefore, it is a challenging issue to control the humidification of the Nafion membrane at a temperature above 373 K.
It is seen from Figure 4 that the molar concentration of H 2 O increases along with the gas flow through the gas channel, irrespective of the Nafion membrane thickness and T ini . This result matches with Figure 3 from the viewpoint of the O 2 reduction reaction which produces H 2 O at the cathode. According to Figure 4, the amount of H 2 O produced from the inlet to the outlet is the largest at T ini = 353 K, irrespective of the Nafion membrane thickness. The reason why this result is obtained can be explained by the above discussion in Figure 3.
According to Figure 5, the current density decreases along with the gas flow through the gas channel, irrespective of the Nafion membrane thickness and T ini . The molar concentrations of H 2 and O 2 are the highest at the inlet, respectively, and they decrease along with the gas flow through the gas channel, as shown in Figures 2 and 3, indicating that the electrochemical reaction progresses along with the gas flow through the gas channel. In addition, the current density is the largest at T ini = 353 K among different T ini . Moreover, it is evident that the current density decreases with an increase in the thickness of the Nafion membrane. The authors of this study argue that we have to consider the kinetics of catalyst as well as proton conductivity of Nafion membrane for the discussion of this phenomena. The kinetics of the catalyst are faster with an increase in temperature, while the relative humidity influences the performance of the O 2 reduction reaction occurring on the ionomer in the cathode catalyst layer [40]. There is an optimum H 2 O saturation of ionomer in the cathode catalyst layer. On the other hand, the proton conductivity of the Nafion membrane is influenced by the temperature and relative humidity. According to the literature [41,42], the proton conductivity of the Nafion membrane increases with the increase in temperature as well as the increase in relative humidity. Since the saturation pressure of H 2 O vapor exponentially increases with the temperature [43], it is easy to dehydrate the Nafion membrane at T ini = 373 K compared to T ini = 353 K, resulting in the proton conductivity of the Nafion membrane decreasing at T ini = 373 K. If the proton conductivity of the Nafion membrane decreases, the performance of the O 2 reduction reaction drops due to a lack of proton. In addition, since the hydration of the Nafion membrane is not enough at T ini = 373 K, the high O 2 partial pressure is needed to progress the O 2 reduction reaction [43]. As a result, it is thought that the amount of O 2 consumption decreases at T ini = 373 K. The concentration over-potential increases with a decrease in the O 2 consumption, resulting in the current density decreasing as T ini = 373 K. In addition, the ohmic loss due to the proton conductivity of the Nafion membrane increases when thickness of the Nafion membrane increases [45]. Consequently, the current density in the case with Nafion 115 at T ini = 373 K is smaller compared to the other conditions.

Quantitative Evaluation along with the Gas Flow through the Gas Channel on Mass and Current Density on the Interface between Nafion Membrane and Cathode Catalyst Layer
In order to investigate the effect of the Nafion membrane and T ini on the molar concentration distribution of H 2 O and the distribution of the current density, which can quantitatively indicate the performance of the electrochemical reaction in PEMFC, this study selected the analysis points of A to K, as shown in Figure 6. The average value on the cross sectional area of the interface between the Nafion membrane and cathode catalyst layer at each point, which covers both part under gas channel and that under rib, has been calculated.    Figures 7-10, the molar concentration of H2O increases along with the gas flow through the gas channel, irrespective of the Nafion membrane thickness, Tini, and relative humidity of the supply gas. Since the O2 reduction reaction progresses along with the gas flow through the gas channel, H2O, which is a product of the O2 reduction reaction, increases as expected. In addition, the molar concentration of H2O is the highest at Tini = 353 K among different Tini, irrespective of the Nafion membrane thickness and relative humidity of the supply gas. As described above, Tini = 353 K is the most humidified condition among different Tini, irrespective of the Nafion membrane thickness and relative humidity of the supply gas, resulting in the proton conductivity of the Nafion membrane and the performance of O2 reduction reaction at cathode being the best. Consequently, the molar concentration of H2O is the highest at Tini = 353 K among the investigated Tini. Regarding the impact of the relative humidity of the supply gas, the molar concentration of H2O increases when the relative humidity of the supply gas increases, irrespective of the Nafion membrane thickness and Tini. The largest molar concentration of H2O is confirmed with A80%RH&C80%RH, while the smallest molar concentration of H2O is confirmed with an anode of 40%RH and cathode of 40%RH (A40%RH&C40%RH). Generally speaking, the increase in humidification enhances the performance of PEMFC, which promotes the proton conductivity of the Nafion mem-   Figures 7-10 to compare quantitatively, respectively. According to Figures 7-10, the molar concentration of H 2 O increases along with the gas flow through the gas channel, irrespective of the Nafion membrane thickness, T ini , and relative humidity of the supply gas. Since the O 2 reduction reaction progresses along with the gas flow through the gas channel, H 2 O, which is a product of the O 2 reduction reaction, increases as expected. In addition, the molar concentration of H 2 O is the highest at T ini = 353 K among different T ini , irrespective of the Nafion membrane thickness and relative humidity of the supply gas. As described above, T ini = 353 K is the most humidified condition among different T ini , irrespective of the Nafion membrane thickness and relative humidity of the supply gas, resulting in the proton conductivity of the Nafion membrane and the performance of O 2 reduction reaction at cathode being the best. Consequently, the molar concentration of H 2 O is the highest at T ini = 353 K among the investigated T ini . Regarding the impact of the relative humidity of the supply gas, the molar concentration of H 2 O increases when the relative humidity of the supply gas increases, irrespective of the Nafion membrane thickness and T ini . The largest molar concentration of H 2 O is confirmed with A80%RH&C80%RH, while the smallest molar concentration of H 2 O is confirmed with an anode of 40%RH and cathode of 40%RH (A40%RH&C40%RH). Generally speaking, the increase in humidification enhances the performance of PEMFC, which promotes the proton conductivity of the Nafion membrane, while the decrease in proton conductivity of Nafion membrane causes higher ohmic losses [22,46]. As discussed above, with the low relative humidity, the ionomer in the cathode catalyst layer is hard to be saturated by the H 2 O migrated through the Nafion membrane from the anode to the cathode, deciding the performance of the O 2 reduction reaction at the cathode, which produces H 2 O [40]. Consequently, it is obtained that the molar concentration of H 2 O is the largest with A80%RH&C80%RH, while it is the smallest with A40%RH&C40%RH. Comparing the thickness of the Nafion membrane, the molar concentration of H 2 O decreases when the thickness of the Nafion membrane increases, irrespective of T ini and the relative humidity of the supply gas. In particular, the molar concentration of H 2 O for Nafion 115 is much smaller than that for the other Nafion membranes. H 2 O flux of PEM as well as the conductivity of the Nafion membrane is promoted when the thickness of the Nafion membrane decreases, particularly below 50 µm [21,47,48], which corresponds to Nafion NRE-212 and Nafion NRE-211 in this study. In addition, the ohmic loss due to proton conductivity of Nafion membrane decreases when the thickness of Nafion membrane [49] decreases. Since the proton conductivity and H 2 O flux of Nafion membrane are low for a thick Nafion membrane, the performance of O 2 reduction reaction, which produces H 2 O at the cathode, declines. Consequently, it is thought that the molar concentration of H 2 O decreases when the thickness of the Nafion membrane increases, especially for Nafion 115. Summarizing the above discussion, the largest molar concentration of H 2 O, which is 15.1 mol/m 3 , is obtained at the position K in the case of using Nafion NRE-211 at T ini = 353 K with A80%RH&C80%RH according to Tables 4-8. In this study, it is assumed that H 2 O is treated as a vapor. To validate this assumption, the saturation of H 2 O calculated by the numerical simulation of this study is confirmed. The saturation of H 2 O is defined by dividing a partial pressure of H 2 O vapor by a saturation H 2 O vapor pressure. Figure 11 shows a comparison of the saturation of H 2 O along with the gas flow through the gas channel among different Nafion membranes at T ini = 353 K with A80%RH&C80%RH. It is seen from Figure 11 that the saturation of H 2 O is lower than 1.0 even the case of Nafion NRE-211 near the outlet. When the saturation of H 2 O is lower than 1.0, it means that H 2 O exists as a vapor. The molar concentration of H 2 O is the largest in the case of Nafion NRE-211 under the condition that T ini = 353 K with A80%RH&C80%RH among conditions investigated in this study. Therefore, it can be argued that H 2 O can be treated as a vapor under the conditions investigated in this study. at Tini = 353 K with A80%RH&C80%RH. It is seen from Figure 11 that the saturation of H2O is lower than 1.0 even the case of Nafion NRE-211 near the outlet. When the saturation of H2O is lower than 1.0, it means that H2O exists as a vapor. The molar concentration of H2O is the largest in the case of Nafion NRE-211 under the condition that Tini = 353 K with A80%RH&C80%RH among conditions investigated in this study. Therefore, it can be argued that H2O can be treated as a vapor under the conditions investigated in this study.             Table 8. Comparison of current density along with the gas flow through the gas channel on the interface between Nafion membranes and cathode catalyst layer among different Nafion membranes and T ini (unit: A/mm 2 ; A80%H&C80%RH).  Figures 12-15 show comparisons of current density along with the gas flow through the gas channel on the interface between the Nafion membrane and cathode catalyst layer changing the relative humidity of the supply gas among different Nafion membranes and Tini, respectively. Tables 8-12 list the values shown in Figures 12-15 to compare quantitatively, respectively. In addition, Table 12 summarizes the relationship between the current and voltage to compare the cell performance under the conditions investigated in this study. In this study, the data of the voltage, which were obtained at the constant current of 20 A under all conditions investigated in this study by the power generation experiment, were used as the initial condition for numerical simulation. Table 12 lists these data, which follow the tendencies shown in Figures 12-15. It is seen from Figures 12-15, since H2 and O2 are consumed along with the gas flow through the gas channel, the current density decreases along with the gas flow through the gas channel. With the decrease in the molar concentration of H2 and O2, i.e., the partial pressure of H2 and O2, the gas diffusion from gas channel to the interface between Nafion membrane and cathode catalyst Figure 11. Comparison of saturation of H 2 O along with the gas flow through the gas channel among different Nafion membranes at T ini = 353 K with A80%RH&C80%RH. Figures 12-15 show comparisons of current density along with the gas flow through the gas channel on the interface between the Nafion membrane and cathode catalyst layer changing the relative humidity of the supply gas among different Nafion membranes and T ini , respectively. Tables 8-12 list the values shown in Figures 12-15 to compare quantitatively, respectively. In addition, Table 12 summarizes the relationship between the current and voltage to compare the cell performance under the conditions investigated in this study. In this study, the data of the voltage, which were obtained at the constant current of 20 A under all conditions investigated in this study by the power generation experiment, were used as the initial condition for numerical simulation. Table 12 lists these data, which follow the tendencies shown in Figures 12-15. It is seen from Figures 12-15, since H 2 and O 2 are consumed along with the gas flow through the gas channel, the current density decreases along with the gas flow through the gas channel. With the decrease in the molar concentration of H 2 and O 2 , i.e., the partial pressure of H 2 and O 2 , the gas diffusion from gas channel to the interface between Nafion membrane and cathode catalyst layer declines, resulting in the increase in the concentration over-potential [50]. In addition, it is seen from these figures that the current density is higher with the decrease in T ini . As discussed above, a higher relative humidity increases the current density [40]. Since the actual relative humidity of gas in the cell is the highest at T ini = 353 K among the investigated T ini , resulting in the current density being the highest at T ini = 353 K. As to the impact of the relative humidity of the supply gas, the current density increases when the relative humidity of the supply gas increases, irrespective of the Nafion membrane thickness and T ini . The largest current density is confirmed with A80%RH&C80%RH, while the smallest current density is confirmed with A40%RH&C40%RH. The performance of PEMFC is enhanced with the increase in humidification by the promotion of proton conductivity of Nafion membrane, resulting in lower ohmic losses [22,46]. Therefore, it was revealed that the current density is the largest with A80%RH&C80%RH, while it is the smallest with A40%RH&C40%RH. According to Figures 12-15, it is known that the current density increases when the thickness of the Nafion membrane decreases. The thinner Nafion membrane provides lower ohmic losses, indicating that the proton transfers with a shorter distance to reach the cathode and the H 2 O produced in the cathode catalyst layer reaches the anode faster [49]. In addition, H 2 O flux of Nafion membrane as well as the conductivity of the Nafion membrane is promoted when the thickness of the Nafion membrane decreases, especially below 50 µm [21,47,48], which corresponds to Nafion NRE-212 and Nafion NRE-211 in this study. Therefore, it is revealed that the current density increases when the thickness of Nafion membrane decreases, especially for Nafion NRE-212 and Nafion NRE-211. Summarizing the above discussion, the largest current density of 0.336 A/mm 2 is obtained at the position A in the case of using Nafion NRE-211 at T ini = 353 K with A80%RH&C80%RH according to Tables 8-12. rent density increases when the thickness of the Nafion membrane decreases. The thinner Nafion membrane provides lower ohmic losses, indicating that the proton transfers with a shorter distance to reach the cathode and the H2O produced in the cathode catalyst layer reaches the anode faster [49]. In addition, H2O flux of Nafion membrane as well as the conductivity of the Nafion membrane is promoted when the thickness of the Nafion membrane decreases, especially below 50 μm [21,47,48], which corresponds to Nafion NRE-212 and Nafion NRE-211 in this study. Therefore, it is revealed that the current density increases when the thickness of Nafion membrane decreases, especially for Nafion NRE-212 and Nafion NRE-211. Summarizing the above discussion, the largest current density of 0.336 A/mm 2 is obtained at the position A in the case of using Nafion NRE-211 at Tini = 353 K with A80%RH&C80%RH according to Tables 8-12 Table 9. Comparison of current density along with the gas flow through the gas channel. on the interface between Nafion membranes and cathode catalyst layer among different Nafion membranes and T ini (unit: A/mm 2 ; A80%H&C40%RH).         Table 11. Comparison of current density along with the gas flow through the gas channel on the interface between Nafion membrane and cathode catalyst layer among different Nafion membranes and T ini (unit: A/mm 2 ; A40%RH&C40%RH).     Considering the above results and discussion, this study can suggest that the thinner Nafion membrane under well-humidified conditions is desirable in order to obtain a higher power generation performance operated at higher temperatures such as 363 K and 373 K. In addition, the uniform distribution of the current density along with the gas flow through the gas channel is obtained by using the thinner Nafion membrane according to Figures 12-15. However, the value of current density is still low at high temperatures such as 363 K and 373 K, even using a thinner Nafion membrane. According to Tables 8-12, the current density is 0.237 A/mm 2 and 0.107 A/mm 2 at the position A in the case of using Nafion NRE-211 at T ini = 363 K and 373 K with A80%RH&C80%RH, respectively. To increase the current density in the case of a thinner Nafion membrane, this study suggests the optimization of the catalyst layer [9], MPL [45], and gas channel flow of the gas separator [10], not only in order to control the mass and heat transfer phenomena but also to improve the electrochemical reaction. We have to consider the degradation of the Nafion membrane if we operate PEMFC at a higher temperature than usual. This study conducted the experimental investigation using a thin Nafion membrane at higher temperatures such as 363 K and 373 K [16]. In this experiment, it was confirmed that the thin Nafion membrane kept the performance over the power generation operation of 200 h. However, it is necessary to investigate the characteristics of a thin Nafion membrane by operating for a longer time, e.g., 90,000 h ( 10 years), which is the target time according to the NEDO road map 2010 in Japan for the practical application of a PEMFC system.

Conclusions
The numerical simulation using a 3D model by multi-physics simulation software COMSOL Multiphysics has been conducted in order to investigate distributions of H 2 , O 2 , and H 2 O concentration and current density on the interface between Nafion the membrane and anode catalyst layer, and the interface between the Nafion membrane and cathode catalyst layer when operated at higher temperatures. The impacts of the Nafion membrane thickness, T ini , and relative humidity of the supply gas on these distributions have been investigated. The conclusions have been drawn as follows: (i). The molar concentration of H 2 and O 2 decreases along with the gas flow through the gas channel, irrespective of the Nafion membrane thickness and T ini . (ii). The O 2 consumption in the fuel cell is the largest at T ini = 353 K, irrespective of Nafion membrane thickness. (iii). The molar concentration of H 2 O increases along with the gas flow through the gas channel, irrespective of the Nafion membrane thickness and T ini , which can be explained by the O 2 reduction reaction at cathode. (iv). The current density decreases along with the gas flow through the gas channel, irrespective of Nafion membrane thickness and T ini . The current density is the largest at T ini = 353 K, irrespective of the Nafion membrane thickness. (v). The molar concentration of H 2 O increases when the relative humidity of the supply gas increases, irrespective of the Nafion membrane thickness and T ini . The molar concentration of H 2 O is the largest with A80%RH&C80% RH, while it is the smallest with A40%RH&C40%RH. (vi). The molar concentration of H 2 O generally decreases when the thickness of the Nafion membrane increases. The molar concentration of H 2 O for Nafion 115, whose thickness is 127 µm, is much smaller than that for the other thin Nafion membranes. (vii). It is revealed that the largest molar concentration of H 2 O is 15.1 mol/m 3 near the outlet in the case of using Nafion NRE-211 at T ini = 353 K with A80%RH&C80%RH among the conditions investigated in this study. (viii).The current density is the highest at T ini = 353 K. (ix). The current density increases when the relative humidity of the supply gas increases, irrespective of the Nafion membrane thickness and Tini, which indicates that the