Numerical Analysis on Impact of Thickness of PEM and GDL with and without MPL on Coupling Phenomena in PEFC Operated at Higher Temperature Such as 363 K and 373 K

Abstract

The aim of this study is to clarify the impact of the thickness of a gas diffusion layer (GDL) and a micro porous layer (MPL) on the distributions of gas, H₂O, and current density in a polymer electrolyte fuel cell (PEFC) which is operated at 363 K and 373 K and with various thicknesses of polymer electrolyte membrane (PEM) as well as a relative humidity (RH) of supply gas. These investigations are carried out by numerical simulation using the 3D model with COMSOL Multiphysics. In the case of Nafion 115, which is the thicker PEM, the change in the molar concentration of H₂O from the inlet to the outlet with MPL is larger than that without MPL irrespective of the thickness of GDL, T_ini and RH condition. In the case of Nafion NRE-212, which is the thinner PEM, the change in the molar concentration of H₂O from the inlet to the outlet is larger with MPL than that without MPL in the case of TGP-H-060 (the thicker commercial GDL), while that is smaller with MPL than that without MPL in the case of TGP-H-030 (the thinner commercial GDL). These results exhibit the same tendency as the results of the numerical simulation on the current density.

1. Introduction

In Japan, it is required that a polymer electrolyte fuel cell (PEFC) is operated at 363 K and 373 K for the application of stationary and mobility usage, respectively, for the duration from 2020 to 2025 according to the Japanese New Energy and Industry Technology Development Organization (NEDO) road map 2017 [1]. However, the PEFC using Nafion membrane as a polymer electrolyte membrane (PEM) is generally operated below 353 K [2,3,4]. There are several merits when the PEFC system is operated at higher temperatures, such as 363 K and 373 K, including: (i) improvement of the kinetics of electrode, (ii) small size effect of the cooling system due to the increase in the temperature difference between the PEFC stack and the coolant, and (iii) endurance improvement to CO which includes the H₂ reformed from hydrocarbon [5]. However, the following demerits have to be overcome related to the operation of PEFC at a higher temperature: (i) deterioration of PEM; (ii) electrode erosion; (iii) non-uniform distribution of gases flow, pressure, temperature, voltage, and current in PEFC [6]. Moreover, it is thought that the uniform distributions of gas, H₂O, and current density would be required to obtain the higher power generation performance as well as extend the operation time when operating at higher temperatures [6,7].

We can classify the recent research on high temperature PEFC (HTPEFC) into the target component of PEFC.

As to PEM, some research focuses on new materials which are available for high temperature operation. Phosphoric acid-doped polybenzimidazole (PA-PBI) membranes [8] and bulky basic group grafted ether-free poly (terphenyl piperidinium) membranes [9] have been reported. However, the stability has not been confirmed.

Regarding catalyst layer, the catalyst layer with different microstructures and Pt, which was blade-coated, was prepared by mixing Pt/C, PTFE solution, and ethanol-H₂O solution [10]. Although the electrode with less cracks and optimum pore structure shows the better cell performance, the effect of microstructures of catalyst layers on cell performance decreases with the increase in Pt loading.

As to micro porous layer (MPL), the numerical analysis using a 3D model has been conducted to clarify the impact of MPL on in-plane temperature distribution in PEM and cathode GDL and through-plane temperature distribution [11]. In addition, it has also clarified the impact of MPL on through-plane distributions of H₂, O₂ and H₂O mass fraction. According to this reference, the MPL reduces the local temperature and helps to obtain a more uniform in-plane temperature distribution, and thus to increase the proton conductivity of PEM. In addition, the polarization curve without MPL has shown the superiority to that with MPL, which indicates that MPL is not necessary for high-temperature operation. However, the thickness of PEM and GDL was fixed. The impact of MPL changing the thickness of PEM and GDL has not been investigated in this reference. In addition, the impact of MPL changing the relative humidity (RH) of supply gas has not been investigated in this reference, either. The other study developing MPL experimentally has reported that the reticulated polyaniline nanowires as a cathode MPL improves the power generation performance at 443 K [12], improving the higher power density by 36% compared with that using a conventional MPL. However, the effect of the developed MPL on mass and heat transfer phenomena in the cell as well as the effect of thickness of GDL on the performance of MPL has not been investigated.

Regarding GDL, the structure such as porosity distribution and thickness [13,14] has been investigated numerically. The impact of them on distributions of O₂, H₂, and H₂O in the cell as well as the power generation performance has been investigated. When the porosity in GDL is uniform, the O₂ concentration decreases, and the H₂O concentration increases gradually along the gas channel [13]. The distribution uniformity of H₂ and O₂ in the catalyst layer is more uniform with the increase in the thickness of GDL [14]. It has been revealed that the optimum thickness of GDL at anode and cathode is 100 μm and 150 μm, respectively, from the viewpoint of improving the power generation performance. However, the thickness of PEM was fixed in these references. In addition, the impact of MPL and the RH of supply gas changing the thickness of GDL has not been investigated yet.

The other research on GDL has conducted the numerical simulation to clarify the distributions of O₂, H₂O, and current density in MPL and GDL [15,16]. Xu et al. [15] has also investigated the temperature distribution changing the RH. In the case of low RH conditions, reducing water saturation on the interface between catalyst layer and GDL at cathode provides better power generation performance due to the higher O₂ mole fraction at the reaction sites. When the operation temperature increases from 323.15 K to 363.15 K, the capillary-driven flow is the dominant factor for the water transfer in MPL. Zhang et al. [16] has also investigated the impact of assembly force on the distributions of O₂, H₂O and current density. The porosity distribution of GDL is influenced by the assembly force. High assembly force leads to wider in-plane distributions of O₂ and H₂O concentration in GDL, which provides the wider in-plane distribution of current. However, the impact of MPL and the RH of supply gas changing the thickness of GDL has not been investigated yet.

The impact of the thickness of PEM, GDL and MPL on the temperature distribution on separator back of PEFC operated at 363 K and 373 K has been investigated experimentally by the authors [17,18,19]. In addition, the authors have reported that the impact of the thickness of PEM, GDL and MPL on the temperature distribution on the interface between PEM and the catalyst layer at cathode of PEFC operated at 363 K and 373 K which was evaluated by the 1D heat transfer model [20,21,22]. It was concluded that the combination of thinner PEM and thinner GDL without MPL provided the highest power generation performance and a uniform temperature distribution. The numerical simulation with the 3D isothermal model on coupling phenomena in a cell of HTPEFC at 363 K and 373 K has also been conducted by the authors [23]. The effect of the thickness of PEM on mass and current density distributions on the interface between PEM and the catalyst layer at anode and cathode has been investigated, indicating the thinner PEM with well-humidified conditions is more desirable to attain a higher power generation and a uniform distribution of current density. However, the impacts of MPL and the thickness of GDL on distributions of gas, H₂O, and current density on the interface between PEM and catalyst layer at anode and cathode in PEFC operated at 363 K and 373 K changing the thickness of PEM and the RH of supply gas have not been investigated yet.

Therefore, the aim of this study is to clarify these impacts, which have not been studied so far. This study carries out a numerical simulation using a 3D model with COMSOL Multiphysics composed of multi-physics simulation codes. The thickness of PEM changed from 127 μm and 51 μm, which is simulated for Nafion 115 and Nafion NRE-212, respectively. The thickness of GDL is changed from 190 μm and 110 μm, which is simulated for TGP-H-060 and TGP-H-030, respectively. The operation temperature is changed from 353 K to 373 K. The RH of supply gas at anode of 80%RH and cathode of 80%RH (A80%RH, C80%RH) and that at anode of 40%RH and cathode of 40%RH (A40%RH, C40%RH) is also investigated in both well-humidified conditions and dry conditions, respectively. These simulations are also compared among the conditions with and without MPL.

2. Numerical Simulation Procedure

Governing Equations in 3D Numerical Simulation Model

In this study, a numerical simulation has been conducted using a multi-physics simulation software COMSOL Multiphysics. This software has the simulation code for PEFC composed of the continuity equation, the Brinkman equation for a momentum transfer, the Maxwell–Stefan equation for a diffusion transfer and Butler–Volmer equation for an electrochemical reaction. This simulation code for PEFC has been validated well by many previous studies [24,25,26,27].

At first, the continuity equation which considers the gas species in porous media, e.g., catalyst layer, MPL, and GDL as well as the gas channel is expressed as follows:

$$\frac{\partial }{\partial t}\left({\epsilon }_p\rho \right)+\nabla ·\left(\rho \overrightarrow{u}\right)=Q_m$$

(1)

where ε_p indicates the porosity (-), ρ indicates the density (kg/m³), u indicates the velocity vector (m/s), Q_m indicates the mass source term (kg/(m³·s)), and t indicates the time (s). The Brinkmann equation considering the relationship between the pressure and gas flow velocity, which is solved in porous media, e.g., catalyst layer, MPL, and GDL as well as in the gas channel, is expressed as follows:

$$\frac{\rho }{{\epsilon }_p}\left(\frac{\partial \overrightarrow{u}}{\partial t}+\left(\overrightarrow{u}·\nabla \right)\frac{\overrightarrow{u}}{{\epsilon }_p}\right)$$

$$=-\nabla p+\nabla ·\left[\frac{1}{{\epsilon }_p}\left\{\mu \left(\nabla \overrightarrow{u}+{\left(\nabla \overrightarrow{u}\right)}^T\right)-\frac{2}{3}\mu \left(\nabla ·\overrightarrow{u}\right)\overrightarrow{I}\right\}\right]-\left({\kappa }^{-1}\mu +\frac{Q_m}{{\epsilon }_p^2}\right)\overrightarrow{u}+\overrightarrow{F}$$

(2)

where p indicates the pressure (Pa), μ indicates the viscosity (Pa·s), I indicates the unit vector (-), κ indicates the permeability (m²), and F indicates the force vector (kg/(m²·s²)), e.g., gravity.

The Maxwell–Stefan equation which considers the mass transfer such as the diffusion, ion transfer, and convection transfer is expressed as follows:

$$\overrightarrow{N_i}=-D_i\nabla C_i-z_i{u}_{m,i}F{C}_i\nabla {\phi }_l+C_i\overrightarrow{u}=\overrightarrow{J_i}+C_i\overrightarrow{u}$$

(3)

$$\frac{\partial C_i}{\partial t}+\nabla ·\overrightarrow{N_i}=R_{i,tot}$$

(4)

where N_i indicates the vector molar flow rate on the interface between PEM and electrode (mol/(m²·s)), D_i indicates the diffusion coefficient (m²/s), C_i indicates the concentration of ion i (mol/m³), z_i indicates the valence of ion (-), u_m,i indicates the mobility of ion i ((s·mol)/kg), F indicates the Faraday constant (C/mol), φ_l indicates the electrical potential of liquid [28] (V), J indicates the molar flow rate of the convection transfer (mol/(m·s)), and R_i,tot indicates the reaction rate of species (mol/(m³·s)).

The Butler–Volmer equation calculates the electrochemical reaction as follows:

$$i=i_0\left\{\exp \left(\frac{{\alpha }_{a}F\eta }{RT}\right)-\exp \left(\frac{-{\alpha }_{c}F\eta }{RT}\right)\right\}$$

(5)

$$\eta ={\phi }_s-{\phi }_l-E_{eq}$$

(6)

where i indicates the current density (A/m²), i₀ indicates the exchange current density (A/m²), α_a indicates the charge transfer coefficient at anode (-), η indicates the activation over-potential [28] (V), R indicates the gas constant (J/(mol·K)), T indicates the temperature (K), α_c indicates the charge transfer coefficient at cathode (-), φ_s indicates the electrical potential of solid [28] (V), E_eq indicates the equilibrium electric potential [28] (V).

The 3D model of single cell of PEFC for the numerical simulation used in this study is the same as the authors’ previous study [24]. This structure follows the commercial single cell used in the experimental studies carried out by the authors [18,19]. The outside of the roof of the gas separator at anode and cathode sides is omitted in this model. The cell has a gas separator with a serpentine flow channel consisting of five gas channels with the width of 1.0 mm and depth of 1.0 mm as well as a width of 1.0 mm.

Table 1. Geometrical parameters of 3D model adopted for the numerical simulation in this study [14,29,30,31,32].

Components of Cell	Size	Characteristics
PEM	50.0 mm × 50.0 mm × 0.127 mm (for Nafion 115) and 0.051 mm (for Nafion NRE-212)	Nafion 115 and Nafion NRE-212 (manufactured by Du Pont Corp.)
Catalyst layer	50.0 mm × 50.0 mm × 0.01 mm	Pt/C (Pt: 20 wt%)
MPL	50.0 mm × 50.0 mm × 0.003 mm	PTFE + carbon black
GDL	50.0 mm × 50.0 mm × 0.19 mm (for TGP-H-060) and 0.11 mm (for TGP-H-030)	TGP-H-060 and TGP-H-030 (manufactured by Toray Corp.)
Gas separator	50.0 mm × 50.0 mm × 2.00 mm (thickness of rib: 1.00 mm) (width of gas channel and rib: 1.0 mm, thickness of gas channel: 1.0 mm)	Carbon graphite, serpentine

lists the geometrical parameters of the 3D model. As to PEM, Nafion 115 and Nafion NRE-212 with a thickness of 127 μm and 51 μm, respectively, have been adopted to investigate the effect of thickness of PEM on the distributions of H₂, O₂, and H₂O concentrations and the current density. In addition, TGP-H-060 and TGP-H-030 with the thickness of 190 μm and 110 μm, respectively, have been adopted to investigate the effect of the thickness of GDL on the distributions of H₂, O₂, and H₂O concentrations and the current density.

Table 2. Physical parameters adopted for the numerical simulation in this study.

Parameter	Value
Density of H2 [kg/m3]	7.10 × 10−2 (353 K), 6.89 × 10−2 (363 K), 6.69 × 10−2 (373 K) [33]
Density of O2 [kg/m3]	1.11 (353 K), 1.08 (363 K), 1.05 (373 K) [33]
Density of H2O [kg/m3]	2.95 × 10−1 (353 K), 4.26 × 10−1 (363 K), 6.01 × 10−1 (373 K) [33]
Viscosity of H2 [Pa·s]	9.96 × 10−6 (353 K), 1.02 × 10−5 (363 K), 1.03 × 10−5 (373 K) [33]
Viscosity of O2 [Pa·s]	2.35 × 10−5 (353 K), 2.40 × 10−5 (363 K), 2.45 × 10−5 (373 K) [33]
Viscosity of H2O [Pa·s]	1.16 × 10−5 (353 K), 1.19 × 10−5 (363 K), 1.23 × 10−5 (373 K) [33]
Binary diffusion coefficient between H2 and H2O [m2/s]	9.27 × 10−5 [34]
Binary diffusion coefficient between O2 and H2O [m2/s]	3.57 × 10−5 [34]
Porosity of catalyst layer [-]	0.78 [14,22,30,31,32]
Permeability of catalyst layer [m2]	8.69 × 10−12 [14,22,30,31,32]
Porosity of MPL [-]	0.60 [14,22,30,31,32]
Permeability of MPL [m2]	1.00 × 10−13 [14,22,30,31,32]
Porosity of GDL [-]	0.78 [14,22,30,31,32]
Permeability of GDL [m2]	8.69 × 10−12 [14,22,30,31,32]
Conductivity of PEM [S/m]	10 [35]
Conductivity of catalyst layer [S/m]	53 [36]
Conductivity of MPL [S/m]	1000 [37]
Conductivity of GDL [S/m]	1250 [38]
Anode reference equilibrium potential [V]	0
Cathode reference equilibrium potential [V]	1.229
Anode reference exchange current density [A/m2]	1000 [39]
Cathode reference exchange current density [A/m2]	1 [39]
Anode charge transfer coefficient [-]	0.5 [40]
Cathode charge transfer coefficient [-]	0.5 [41]

and

Table 3. Operation conditions adopted for the numerical simulation in this study.

Condition	Value
The initial temperature of cell (Tini) [K]	353, 363, 373
Cell voltage [V]	Experimental data are applied [18,19]
Supply gas condition	Anode	Cathode
Gas type	H2	O2
Temperature of supply gas at inlet [K]	353, 363, 373	353, 363, 373
RH of supply gas [%RH]	40, 80	40, 80
Pressure of supply gas at inlet (absolute) [MPa]	0.4	0.4
Flow rate of supply gas at inlet [NL/min] (Stoichiometric ratio [-])	0.210 (1.5)	0.105 (1.5)

list physical parameters and operation conditions, respectively. The initial operation temperature of cell (T_ini) is changed from 353 K to 373 K. As to 353 K, this study has selected it to exhibit the characteristics at a standard operation temperature comparing the characteristics at a higher temperature. The RH of supply gases for A80%RH, C80%RH and A40%RH, C40%RH have been investigated as a well-humidified condition and a dry condition, 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 the cathode is 0.210 NL/min and 0.105 NL/min, respectively. The stoichiometric ratio of 1.0, which indicates the flow rate of supply gas, can be defined by Equation (7).

$$C_{H2}=\frac{I}{n_{H2}F}$$

(7)

where C_H2 indicates the molar flow rate of consumed H₂ (mol/s), I indicates the loaded current (A) and n_H2 indicates the electrons moles exchanged in the reaction (=2) (-), C_H2 indicates the molar flow rate corresponding to the stoichiometric ratio of 1.0. The C_O2 indicates the molar flow rate of consumed O₂ (mol/s), which is the half of C_H2 (which can be defined by Equation (8)).

H₂ + 1/2 O₂ = H₂O

(8)

It can be expected that H₂, which is produced from a renewable energy via H₂O electrolyzer, will be used as a fuel for PEFC in order to realize a zero-CO₂-emission society in the near future. When H₂ is produced by H₂O electrolysis, O₂ is also produced as a by-product. This study suggests that not only H₂ but also O₂ produced from H₂O electrolysis can be used for PEFC. This study also proposes that the total system consisting of renewable energy, H₂O electrolyzer, and PEFC system can be operated using H₂ and O₂ produced by the H₂O electrolyzer. Therefore, in this study, O₂ is adopted as the cathode gas for the numerical simulation. If O₂ was adopted as a cathode gas, a higher current density on the interface between PEM and the catalyst layer could be expected, especially under the rib, compared with the case using air [29].

The assumptions set in this study are the same as the authors’ previous study [24]. When PEFC is operated at higher temperatures, such as 363 K and 373 K, it is easy to dehydrate PEM and the catalyst layer due to the exponential increase in the saturation of H₂O vapor with temperature [42]. The performance of O₂ reduction reaction occurring at the cathode is influenced by the hydration of ionomer in the catalyst layer using the H₂O [41]. Therefore, this study focuses on distributions of O₂, H₂O, and current density on the interface between PEM and catalyst layer at cathode which indicates the performance of O₂ reduction reaction and shows the results.

3. Results and Discussion

3.1. In-Plane Distribution of O₂, H₂O and Current Density on the Interface between PEM and Cathode Catalyst Layer

Figure 1 and Figure 2 show the comparison of the in-plane molar concentration distribution of O₂ on the interface between PEM and catalyst layer at cathode among different PEM, GDL, and T_ini with and without MPL, respectively. Figure 3 and Figure 4 show the comparison of the in-plane molar concentration distribution of H₂O on the interface between PEM and catalyst layer at cathode among different PEM, GDL, and T_ini with and without MPL, respectively. Figure 5 and Figure 6 show the comparison of the in-plane current density distribution on the interface between PEM and catalyst layer at cathode among different PEM, GDL, and T_ini with and without MPL, respectively. In these figures, the RH of supply gas is A80%RH, C80%RH.

According to Figure 1, it is found that the molar concentration of O₂ decreases along with the gas flow through the gas channel irrespective of the thickness of PEM and GDL as well as T_ini. In addition, it is confirmed that the amount of O₂ consumption from the inlet to the outlet is the smallest at T_ini = 373 K irrespective of thickness of PEM and GDL. The kinetics of catalyst layer are faster with the increase in temperature [41]. According to the previous studies [43,44], the proton conductivity of PEM increases with the increase in temperature as well as the increase in RH. The saturation pressure of H₂O vapor increases with the temperature exponentially [42], with the result that it is easy to dehydrate PEM at T_ini = 373 K compared with T_ini = 353 K. The proton conductivity of PEM decreases at T_ini = 373 K. If the proton conductivity of PEM decreases, the performance of the O₂ reduction reaction drops by the lack of proton. Moreover, the hydration of PEM is not enough at T_ini = 373 K, with the result that the high O₂ partial pressure is needed to progress the O₂ reduction reaction [42]. Therefore, it is thought that the amount of O₂ consumption decreases at T_ini = 373 K. In addition, it is seen that the decrease in concentration of O₂ from the inlet to the outlet using the thin PEM, i.e., Nafion NRE-212 is larger than that using the thick PEM, i.e., Nafion 115 irrespective of the thickness of GDL. When the thickness of PEM decreases, the proton conductivity of PEM increases [45]. Since the amount of proton which is transported to the catalyst layer at cathode via PEM is larger, the O₂ reduction reaction is conducted well. As a result, the amount of O₂ consumption from the inlet to the outlet is larger when using the thin PEM, i.e., Nafion NRE-212.

According to Figure 2, it is found that the change in the concentration of O₂ from the inlet to the outlet in the case of Nafion NRE-212 is larger compared with that of Nafion 115 when using the thick GDL, i.e., TGP-H-060, which is the same tendency as the results with MPL shown in Figure 1. As discussed above, when the thickness of PEM decreases, the proton conductivity of PEM increases [45]. Since the amount of proton which is transported to the catalyst layer at cathode via PEM is larger, the O₂ reduction reaction is conducted well. As a result, the amount of O₂ consumption from the inlet to the outlet is larger when using the thin PEM, i.e., Nafion NRE-212. On the other hand, it is seen that the amount of O₂ consumption from the inlet to the outlet in the case of Nafion NRE-212 is almost the same as that of Nafion 115 when using the thin GDL, i.e., TGP-H-030, which shows the different tendency compared with the results with MPL shown in Figure 1. Since the RH of supply gas is A80%RH, C80%RH, which is a well-humidified condition, it is thought that the discharge of H₂O from the catalyst layer is not well conducted without MPL. As a result, the supplied O₂ is not consumed well, the change in the concentration of O₂, i.e., the amount of O₂ consumption, from the inlet to the outlet in the case of Nafion NRE-212 is almost the same as that of Nafion 115 when using the thin GDL, i.e., TGP-H-030.

It is seen from Figure 3 that the molar concentration of H₂O increases along with the gas flow through the gas channel irrespective of the thickness of PEM and GDL as well as T_ini. This result matches with Figure 1 from the viewpoint of progress on the O₂ reduction reaction which produces H₂O at the cathode. In addition, it is observed that the amount of H₂O produced from the inlet to the outlet is the smallest at T_ini = 373 K, irrespective of the thickness of PEM and GDL. It can also be explained by the above discussion conducted for Figure 1. Moreover, it is revealed from Figure 3 that the increase in the concentration of H₂O from the inlet to the outlet using thin PEM, i.e., Nafion NRE-212 is larger than that using the thick PEM, i.e., Nafion 115, irrespective of the thickness of GDL. When the thickness of PEM decreases, the proton conductivity of PEM increases [45]. Since the amount of proton which is transported to the catalyst layer at cathode via PEM increases, the O₂ reduction reaction is conducted well. As a result, the amount of H₂O produced from the O₂ reduction reaction increases.

According to Figure 4, it is observed that the molar concentration of H₂O increases along with the gas flow through the gas channel irrespective of the thickness of PEM and GDL as well as T_ini which is the same as the results with MPL shown in Figure 3. In addition, it is observed that the amount of H₂O produced from the inlet to the outlet is the smallest at T_ini = 373 K irrespective of the thickness of PEM and GDL, which is the same tendency as the results with MPL shown in Figure 3. Moreover, it is revealed that the increase in the concentration of H₂O from the inlet to the outlet using the thin PEM, i.e., Nafion NRE-212 is larger than that using the thick PEM, i.e., Nafion 115 irrespective of the thickness of GDL, which is the same as the results with MPL shown in Figure 3.

It is observed from Figure 5 that the current density decreases with the increase in T_ini. Some previous experimental studies have reported that the current density increases with the increase in T_ini. However, they are the reported results using the new materials which are available for high temperature operation, e.g., bulky N-heterocyclic group functionalized poly (terphenyl piperidinium) membranes [9] and PBI-based membranes [45]. The authors selected the Nafion membrane which is a popular membrane used under low temperature operation conditions, e.g., below 353 K. According to the reference using the Nafion membrane such as Nafion NRE-211 experimentally [43], the power generation performance declines with the increase in T_ini. The previous study has reported that the operation using Nafion membrane at higher temperatures results in a poor power generation performance due to the low proton conductivity of Nafion membrane under a dry condition [8]. In addition, the other study has suggested preparing the new material which can conduct protons independent of H₂O [45]. Therefore, it can be thought that the Nafion membrane is influenced by a humidification condition easily at higher temperatures. The saturation pressure of H₂O vapor increases with temperature exponentially [42]. Therefore, it is easy to dehydrate PEM at higher temperatures when using the Nafion membrane. The proton conductivity of PEM decreases at T_ini = 373 K. If the proton conductivity of PEM decreases, the performance of O₂ reduction reaction drops due to the lack of proton. Moreover, the hydration of PEM is not enough at T_ini = 373 K, resulting that the high O₂ partial pressure is needed to progress the O₂ reduction reaction [42]. Consequently, the current density decreases with the increase in T_ini due to the increase in ohmic over-potential and concentration over-potential [42]. In addition, it is seen from Figure 5 that the current density in the case of the thin PEM, i.e., Nafion NRE-212 is higher than that of the thick PEM, i.e., Nafion 115 irrespective of the thickness of GDL and T_ini. When the thickness of PEM decreases, the proton conductivity of PEM increases [45]. Since the amount of proton which is transported to the catalyst layer at cathode via PEM increases, the O₂ reduction reaction is conducted well. As a result, the current density is higher when using the thin PEM such as Nafion NRE-212. Moreover, it is observed that the current density in the case of the thick GDL, i.e., TGP-H-060 is higher than that of the thin GDL, i.e., TGP-H-030 irrespective of T_ini. Since the performance of mass and O₂ transportation in GDL is lower in the case of the thick GDL, it is believed that the function of MPL such as (i) reduction of ohmic losses due to enhancing the hydration of PEM [46], (ii) O₂ diffusion in the catalyst layer due to discharging H₂O [47], and (iii) back diffusion from the cathode to the anode caused by the increase in the H₂O vaporized due to the increase in the temperature of the catalyst layer at cathode [48], which plays an important role in the PEFC, would work well.

According to Figure 6, it is found that the current density decreases with the increase in T_ini, which exhibits the same tendency as the results with MPL shown in Figure 5. The reason for this phenomenon has been already discussed above. Additionally, it is observed that the current density in the case of the thin PEM, i.e., Nafion NRE-212 is larger than that of Nafion 115 when using the thin GDL, i.e., TGP-H030. This tendency is more remarkable compared with using the thick GDL, i.e., TGP-H-060. Since the RH of supply gas is A80%RH, C80%RH, which is a well-humidified condition, it is thought that the discharge of H₂O from the catalyst layer is not well without MPL. Therefore, it is thought that the combination of thin PEM and thin GDP is effective to promote H₂O transfer as well as O₂ transfer. The electro-osmotic drag which decides the H₂O flux in PEM decreases with the decrease in the thickness of PEM [49] and the mass transfer resistance decreases with the decrease in the thickness of GDL due to the promotion of discharging H₂O [19]. Consequently, the higher current density is obtained for the thin PEM, i.e., Nafion NRE-212 compared with the thick PEM, i.e., Nafion 115 when using the thin GDL, i.e., TGP-H-030.

3.2. Analysis on Distribution of O₂, H₂O and Current Density along with the Gas Flow through the Gas Channel

This study has selected the analysis points from A to K, which are the same as the authors’ previous study [24], to investigate the impact of the thickness of GDL and MPL changing the thickness of PEM on distributions of O₂, H₂O, and current density. In this analysis, the average value on the cross-sectional area of the interface between PEM and catalyst layer at the cathode at each point, which covers both part under gas channel and that under rib, has been estimated.

Figure 7 and Figure 8 show comparisons of molar concentration of O₂ along with the gas flow through the gas channel on the interface between PEM and catalyst layer at cathode among different RH, GDL and T_ini with and without MPL in the case of Nafion 115, respectively. The results of A80%RH, C80%RH and A40%RH, C40%RH are shown in Figure 7 and Figure 8, respectively. In addition, the data at T_ini = 373 K as well as that of TGP-H-060 without MPL are not shown in Figure 8 since the total voltage obtained at the load current of 0.80 A/cm², whose data are used for the initial condition in this numerical simulation, could not be carried out due to dry conditions.

According to Figure 7 and Figure 8, it is seen the molar concentration of O₂ decreases along with the gas flow through the gas channel irrespective of the thickness of GDL and T_ini with and without MPL. It can be understood that the O₂ reduction reaction is progressed along with the gas flow through the gas channel. In particular, it is revealed that the change in the molar concentration of O₂ from the inlet to the outlet is larger with MPL than that without MPL. Due to the function of MPL which exhausts H₂O, it is thought that the mass transfer is promoted, resulting that the O₂ reduction reaction is progressed well. The effect of MPL on the promotion of O₂ reduction reaction in the case of TGP-H-060 is larger compared with that in the case of TGP-H-030. When the thickness of GDL is larger, the performance of O₂ and H₂O transfer is lower. Therefore, the function of MPL which exhausts H₂O becomes more effective. In addition, the change in the concentration of O₂ from the inlet to the outlet decreases with the increase in T_ini with and without MPL. It is known from the previous studies [43,44] that the proton conductivity of PEM increases with the increase in temperature as well as the increase in RH. Since the saturation pressure of H₂O vapor increases with temperature exponentially [42], it is easy to dehydrate PEM at higher temperature. The proton conductivity of PEM decreases at higher temperature. If the proton conductivity of PEM decreases, the performance of O₂ reduction reaction drops due to the lack of proton. Since the hydration of PEM is not enough at T_ini = 373 K, the high O₂ partial pressure is needed to progress the O₂ reduction reaction [42]. Consequently, it is thought that the change in the concentration of O₂ from the inlet to the outlet decreases with the increase in T_ini. Moreover, it is found that the change in the concentration of O₂ from the inlet to the outlet for A40%RH, C40%RH is smaller compared with that for A80%RH, C80%RH. Since A40%RH, C40%RH is the dry condition, PEM and the catalyst layer are dehydrated easily [50,51]. The proton conductivity of PEM is smaller under a dry condition [49] and the RH influences the performance of the O₂ reduction reaction occurring on the ionomer in the catalyst layer at cathode [41]. There is the optimum H₂O saturation for ionomer in the catalyst layer at cathode [23]. Due to these reasons, the change in the concentration of O₂ from the inlet to the outlet for A40%RH, C40%RH is smaller compared with that for A80%RH, C80%RH.

Figure 9 and Figure 10 show comparisons of molar concentration of O₂ along with the gas flow through the gas channel on the interface between PEM and catalyst layer at cathode among different RH, GDL and T_ini with and without MPL in the case of Nafion NRE-212, respectively. The results of A80%RH, C80%RH and A40%RH, C40%RH are shown in Figure 9 and Figure 10, respectively. In addition, the data at T_ini = 373 K as well as that in the case of TGP-H-060 without MPL are not shown in Figure 10 since the total voltage could not be obtained at the load current of 0.80 A/cm² used for the initial condition in this numerical simulation due to the dry condition.

According to Figure 9 and Figure 10, it is seen the molar concentration of O₂ decreases along with the gas flow through the gas channel irrespective of the thickness of GDL and T_ini with and without MPL, which is the same tendency as the results for Nafion 115. It can be understood that the O₂ reduction reaction is progressed along with the gas flow through the gas channel. Especially, it is revealed that the change in the molar concentration of O₂ from the inlet to the outlet is larger with MPL than that without MPL, which shows the same tendency as the results for Nafion 115. Due to the function of MPL which exhausts H₂O, it is thought that the mass transfer is promoted, resulting that the O₂ reduction reaction is progressed well. The effect of MPL on the promotion of O₂ reduction reaction in the case of TGP-H-060 is larger compared with that in the case of TGP-H-030. When the thickness of GDL is larger, the performance of O₂ and H₂O transfer is lower. Therefore, the function of MPL which exhausts H₂O becomes more effective. In addition, the change in the concentration of O₂ from the inlet to the outlet decreases with the increase in T_ini with and without MPL, which can be explained by the discussion conducted for Figure 7 and Figure 8. Additionally, it is observed that the change in the concentration of O₂ from the inlet to the outlet for A40%RH, C40%RH is smaller compared with that for A80%RH, C80%RH, which is the same tendency as the results for Nafion 115. The reason for this phenomenon is the same as described above, resulting that the trend of change in the molar concentration of O₂ along with the gas flow through the gas channel on the interface between PEM and catalyst layer at cathode among different RH, GDL and T_ini with and without MPL in the case of Nafion NRE-212 is similar to that in the case of Nafion 115.

Figure 11 and Figure 12 show comparisons of molar concentration of H₂O along with the gas flow through the gas channel on the interface between PEM and catalyst layer at cathode among different RH, GDL and T_ini with and without MPL in the case of Nafion 115, respectively. The results of A80%RH, C80%RH and A40%RH, C40%RH are shown in Figure 11 and Figure 12, respectively. In addition, the data at T_ini = 373 K as well as that of TGP-H-060 without MPL are not shown in Figure 12 since the total voltage could not be obtained at the load current of 0.80 A/cm² used for the initial condition in this numerical simulation due to the dry conditions.

According to Figure 11 and Figure 12, it is seen the molar concentration of H₂O increases along with the gas flow through the gas channel irrespective of the thickness of GDL and T_ini with and without MPL. It can be understood that the O₂ reduction reaction, which produces H₂O, is progressed along with the gas flow through the gas channel. It is also revealed that the change in the molar concentration of H₂O from the inlet to the outlet is larger with MPL than that without MPL irrespective of the thickness of GDL, T_ini, and RH condition. Due to the function of MPL which exhausts H₂O, it is thought that the mass transfer is promoted. As a result, it is thought that the O₂ reduction reaction producing H₂O is progressed well. Additionally, the change in the concentration of H₂O from the inlet to the outlet decreases with the increase in T_ini with and without MPL. According to the previous studies [43,44], the proton conductivity of PEM increases with not only the increase in temperature but also the increase in RH. Due to the exponential increase in the saturation pressure of H₂O vapor with temperature [42], it is easy to dehydrate PEM at higher temperature. As a result, the proton conductivity of PEM decreases at higher temperature. If the proton conductivity of PEM decreases, the performance of O₂ reduction reaction drops due to the lack of proton. The hydration of PEM is not enough at higher temperatures, with the result that the high O₂ partial pressure is needed to progress the O₂ reduction reaction [42]. Consequently, it is thought that the change in the concentration of H₂O from the inlet to the outlet, i.e., the amount of produced H₂O from the inlet to the outlet, decreases with the increase in T_ini. Furthermore, it is confirmed that the change in the concentration of H₂O from the inlet to the outlet for A40%RH, C40%RH is smaller compared with that for A80%RH, C80%RH. Since A40%RH, C40%RH is the dry condition, PEM and catalyst layer are dehydrated easily [50]. The proton conductivity of PEM is smaller under a dry condition [49]. In addition, the RH influences the performance of the O₂ reduction reaction occurring on the ionomer in the catalyst layer at the cathode [41]. There is the optimum H₂O saturation for ionomer in the catalyst layer at cathode [23], which indicates the O₂ reduction performance producing H₂O is lower for A40%RH, C40%RH. Consequently, it can be claimed that the change in the concentration of H₂O from the inlet to the outlet for A40%RH, C40%RH is smaller compared with that for A80%RH, C80%RH.

Figure 13 and Figure 14 show comparisons of molar concentration of H₂O along with the gas flow through the gas channel on the interface between PEM and catalyst layer at cathode among different RH, GDL and T_ini with and without MPL in the case of Nafion NRE-212, respectively. The results of A80%RH, C80%RH and A40%RH, C40%RH are shown in Figure 13 and Figure 14, respectively. In addition, the data at T_ini = 373 K as well as that in the case of TGP-H-060 without MPL are not shown in Figure 14 since the total voltage could not be obtained at the load current of 0.80 A/cm² used for the initial condition in this numerical simulation due to the dry condition.

According to Figure 13 and Figure 14, it is seen the molar concentration of H₂O increases along with the gas flow through the gas channel irrespective of the thickness of GDL and T_ini with and without MPL. It can be understood that the O₂ reduction reaction, which produces H₂O, is progressed along with the gas flow through the gas channel. It is also revealed that the change in the molar concentration of H₂O from the inlet to the outlet is larger with MPL than that without MPL in the case of TGP-H-060, while that is smaller with MPL than that without MPL at 353 K and 363 K in the case of TGP-H-030 as shown in Figure 13. Regarding TGP-H-060, which is a thick GDL, the performance of O₂ and H₂O transfer is lower. Therefore, the function of MPL which exhausts H₂O becomes more effective as discussed above. On the other hand, in the case of TGP-H-030 which is the thin GDL, it is thought that the performance of O₂ and H₂O transfer is higher even when the RH condition is A80%RH, C80%RH. In addition, Nafion NRE-212, which is the thin PEM is used in Figure 13 and Figure 14, resulting that the performance of proton and H₂O transfer is better. Although it is believed that the actual RH in cell increases with the decrease in T_ini due to the exponential increase in the saturation pressure of H₂O vapor with temperature [42], the function of MPL which exhausts H₂O works well. As a result, it is thought that the change in the molar concentration of H₂O from the inlet to the outlet is smaller with MPL than that without MPL at 353 K and 363 K in the case of TGP-H-030. In addition, the change in the concentration of H₂O from the inlet to the outlet decreases with the increase in T_ini with and without MPL. The reason for this phenomenon is the same as explained for Figure 11 and Figure 12. Moreover, it is confirmed that the change in the concentration of H₂O from the inlet to the outlet for A40%RH, C40%RH is smaller compared with that for A80%RH, C80%RH. Since A40%RH, C40%RH is the dry condition, PEM and catalyst layer are dehydrated easily [50,51]. The reason for this phenomenon is the same as explained for Figure 11 and Figure 12, which can be discussed irrespective of the thickness of PEM.

In this numerical simulation, the H₂O is treated as a vapor, in other words, the phase change of H₂O is not neglected. To validate this assumption, this study examines the saturation of H₂O obtained by the numerical simulation. According to the estimation of saturation of H₂O for all conditions investigated in this study, it is revealed that all of them are lower than 1.0, which indicates the H₂O is a vapor. Consequently, it is proved that this assumption is reasonable for the investigated conditions in this study.

Figure 15 and Figure 16 show comparisons of current density along with the gas flow through the gas channel on the interface between PEM and catalyst layer at cathode among different RH, GDL and T_ini with and without MPL in the case of Nafion 115, respectively. The results of A80%RH, C80%RH and A40%RH, C40%RH are shown in Figure 15 and Figure 16, respectively. In addition, the data at T_ini = 373 K as well as that in the case of TGP-H-060 without MPL are not shown in Figure 16 since the total voltage could not be obtained at the load current of 0.80 A/cm² used for the initial condition in this numerical simulation due to a dry condition.

According to Figure 15 and Figure 16, it is observed that the current density with MPL is larger than that without MPL, irrespective of the thickness of GDL, T_ini, and RH condition. Since the thickness of PEM is large, the proton conductivity of PEM is smaller [45]. Therefore, it is believed that the function of MPL such as (i) reduction of ohmic losses due to enhancing the hydration of PEM [46], (ii) O₂ diffusion in the catalyst layer due to discharging H₂O [47], and (iii) back diffusion from the cathode to the anode caused by the increase in the H₂O vaporized due to the increase in the temperature of the catalyst layer at the cathode [48] can work well. As a result, it is claimed that the current density with MPL is larger than that without MPL. In particular, this tendency is remarkable for the thicker GDL, i.e., TGP-H-060. Since the mass transfer performance in GDL is worse with the increase in thickness of GDL, it is thought that the function of MPL as described above works well. In addition, it is found that the current density decreases with the increase in T_ini. Since the saturation pressure of H₂O vapor increases with temperature exponentially [42], it is easy to dehydrate PEM at higher temperatures. The proton conductivity of PEM decreases with the increase in T_ini, with the result that the performance of O₂ reduction reaction drops due to the lack of proton. Moreover, since the hydration of PEM is not enough at higher temperatures, the high O₂ partial pressure is needed to progress the O₂ reduction reaction [42]. Consequently, the current density decreases with the increase in T_ini due to the increase in ohmic over-potential and concentration over-potential [42].

To compare the simulation results with the experimental results, Figure 17 and Figure 18 show the polarization curve with and without MPL in the case of Nafion 115 at T_ini = 353 K and 363 K [18,19], respectively. The results of A80%RH, C80%RH are shown in Figure 17 and Figure 18. According to Figure 17 and Figure 18, it is observed that the total voltage with MPL is larger, especially at high current density, than that without MPL irrespective of the thickness of GDL and T_ini. In addition, this tendency is remarkable for the thicker GDL, i.e., TGP-H-060. This study has conducted the numerical simulation assumed to operate at the current density of 0.80 A/cm², which follows the experimental condition [18,19]. These experimental results match the simulation results obtained by this study. Consequently, it is claimed that the simulation results obtained by this study can predict the experimental results.

Figure 19 and Figure 20 show comparisons of molar concentration of H₂O along with the gas flow through the gas channel on the interface between PEM and catalyst layer at cathode among different RH, GDL and T_ini with and without MPL in the case of Nafion NRE-212, respectively. The results of A80%RH, C80%RH and A40%RH, C40%RH are shown in Figure 19 and Figure 20, respectively. In addition, the data at T_ini = 373 K as well as that of TGP-H-060 without MPL are not shown in Figure 18 since the total voltage could not be obtained at the load current of 0.80 A/cm² used for the initial condition in this numerical simulation due to the dry condition.

According to Figure 19 and Figure 20, it is observed that the current density with MPL is larger than that without MPL in the case of TGP-H-060, while that with MPL is smaller than that without MPL at 353 K and 363 K in the case of TGP-H-030 as shown in Figure 20. This tendency matches that discussed for Figure 13 and Figure 14. Regarding TGP-H-060, which is the thick GDL, the performance of O₂ and H₂O transfer is lower. Therefore, the function of MPL which exhausts H₂O becomes more effective as discussed above. As a result, the O₂ reduction reaction is progressed, which provides the better power generation. On the other hand, in the case of TGP-H-030 which is the thin GDL, it is thought that the performance of O₂ and H₂O transfer is higher even the RH condition of A80%RH, C80%RH. In addition, Nafion NRE-211 which is the thin PEM is used in Figure 19 and Figure 20, resulting that the performance of proton and H₂O transfer is better. Although it is believed that the actual RH in cell increases with the decrease in T_ini due to the exponential increase in saturation pressure of H₂O vapor with temperature [42], the function of MPL which exhausts H₂O works well. As a result, it is thought that the change in the molar concentration of H₂O, i.e., the amount of produced H₂O, from the inlet to the outlet is smaller with MPL than that without MPL at 353 K and 363 K in the case of TGP-H-030. Since the actual RH is lower with MPL due to the small amount of H₂O, the ohmic loss is larger. Therefore, the current density with MPL is smaller compared with that without MPL.

It is also seen from Figure 19 and Figure 20 that the current density for A80%RH, C80%RH is larger than that for A40%RH, C40%RH irrespective of T_ini. High RH of supply gas provides the hydration of PEM and the increase in the H₂O diffusivity through PEM as well as the decrease in the ohmic loss, resulting in higher current density [52,53].

From the above results and discussion, it is not easy to obtain high power generation performance by changing the thickness of PEM and GDL as well as using MPL at higher temperature such as 363 K and 373 K. Though the current density under the high RH condition exhibits the larger value compared with that under the low RH condition, it is necessary to investigate the procedure in order to improve the power generation performance more. The authors of this study think the reason why the power generation performance is lower at higher temperatures such as 363 K and 373 K is the dehydration of PEM and catalyst layer. In this study, it is confirmed that the amount of O₂ consumption as well as the amount of H₂O produced by the O₂ reduction reaction is smaller at higher temperature such as 363 K and 373 K. Therefore, it can be suggested that the equipment to humidify the gas is added to the cell of PEFC, e.g., installment into the gas channel of separator. Or, the design and control of thermal properties, e.g., thermal conductivity and heat capacity, of MPL, catalyst layer, GDL, and separator are effective to remove the heat generated from power generation. If the heat is removed smoothly, the dehydration of PEM and catalyst layer can be prevented.

As to the degradation of PEM operated at high temperatures, the authors had conducted the experimental investigation using a Nafion membrane which seems to be degraded easily at higher temperatures such as 363 K and 373 K [19]. In this experiment, it was confirmed that the Nafion membrane could maintain the performance over the power generation operation of 200 h. However, it is necessary to study the characteristics of Nafion membranes operated for longer operation times, e.g., 90,000 h (=10 years), which is the target operation time according to NEDO road map 2010 in Japan [54], for the practical application of the PEFC system. The authors would like to conduct the stability and repetition tests in the near future.

4. Conclusions

The impact of the thickness of GDL and MPL on distributions of gas, H₂O, and current density on the interface between PEM and catalyst layer in a single cell of PEFC operated from 353 K to 373 K have been investigated changing the thickness of PEM. The 3D numerical simulation model to estimate the above-described distributions has been developed in this study. The RH of supply gas has been also changed to clarify the characteristics under a well-humidified condition and a dry condition. From the investigation, the following conclusions have been obtained:

(i)

The molar concentration of O₂ decreases along the gas channel with and without MPL irrespective of the thickness of PEM and GDL as well as T_ini. The change in the molar concentration of O₂ from the inlet to the outlet is larger with MPL than that without MPL. In addition, the change in the concentration of O₂ from the inlet to the outlet for A40%RH, C40%RH is smaller compared with that for A80%RH, C80%RH irrespective of the thickness of PEM and GDL and T_ini.

(ii)

The molar concentration of H₂O increases along the gas channel irrespective of the thickness of PEM, GDL and T_ini with and without MPL, which follows the progress of the O₂ reduction reaction.

(iii)

In the case of Nafion 115 which is the thick PEM, the change in the molar concentration of H₂O along the gas channel is larger with MPL than that without MPL irrespective of the thickness of GDL, T_ini and RH condition.

(iv)

In the case of Nafion NRE-212 which is the thin PEM, the change in the molar concentration of H₂O along the gas channel is larger with MPL than that without MPL in the case of TGP-H-060, while that is smaller with MPL than that without MPL at 363 K and 363 K in the case of TGP-H-030. Although it is believed that the actual RH in cell increases with the decrease in T_ini due to the exponential increase in the saturation pressure of H₂O vapor with the temperature, the function of MPL which exhausts H₂O works well when using thin PEM and GDL. As a result, the change in the molar concentration of H₂O from the inlet to the outlet is smaller with MPL than that without MPL at 353 K and 363 K in the case of TGP-H-030.

(v)

The change in the concentration of H₂O along the gas channel decreases with the increase in T_ini with and without MPL, irrespective of the thickness of PEM and GDL as well as the RH condition.

(vi)

The change in the concentration of H₂O along the gas channel for A40%RH, C40%RH is smaller compared with that for A80%RH, C80%RH with and without MPL, irrespective of the thickness of PEM and GDL.

(vii)

In the case of Nafion 115 which is the thick PEM, the current density with MPL is larger than that without MPL irrespective of the thickness of GDL, T_ini and RH condition. Since the proton conductivity of PEM is smaller due to the thick PEM, the function of MPL works well.

(viii)

In the case of Nafion NRE-212 which is the thin PEM, the current density with MPL is larger than that without MPL in the case of TGP-H-060, while that with MPL is smaller than that without MPL at 353 K and 363 K in the case of TGP-H-030. Although it is believed that the actual RH in cell increases with the decrease in T_ini due to the exponential increase in the saturation pressure of H₂O vapor with temperature, the function of MPL which exhausts H₂O works well when using the thin PEM and GDL. Since the actual RH is lower with MPL due to the small amount of H₂O, the ohmic loss is larger. Therefore, the current density with MPL is smaller compared with that without MPL.

(ix)

As it is important to prevent the dehydration of PEM and catalyst layer in order to attain the higher power generation performance at higher temperature such as 363 K and 373 K, it is suggested that the equipment to humidify the gas is added to the cell of PEFC as well as the humidifier pre-installed for the gas supplied to the cell, e.g., installing it into the gas channel of the separator. Additionally, the smoothly removal of the heat generated from power generation by means of carefully designing and controlling the thermal properties of MPL, catalyst layer, GDL, and separator is also important.