This study has developed a two-dimensional, two-phase transport model to investigate the transport characteristics in direct methanol fuel cells (DMFCs) using platinum group metal (PGM)-free cathode catalysts. The model considered anisotropic properties of the gas diffusion layer (GDL) caused by current collector’s mechanical compression, the interfacial mass transfer of water and methanol between liquid and vapor, and unique properties of the cathode PGM-free catalyst layer. Results showed that the liquid methanol solution from the anode could provide sufficient water to hydrate the proton exchange membrane (PEM), and the relative humidity of the cathode air did not impact the membrane hydration. Fully hydrating the cathode air may deteriorate the fuel cell performance, especially when the operating temperature is close to 100 °C because the exponential increase of the saturated water pressure with temperature decreased the partial pressure of oxygen. The optimized operating temperature increased with the increase of air pressure and was about 80 °C at 1.5 atm cathode pressure. To achieve the US Department of Energy’s performance target of 300 mW/cm2 peak power density, catalytic activities of both the anode and cathode catalysts need to be improved by one order of magnitude compared with the state-of-the-art commercial catalysts.
Compared with hydrogen, liquid methanol has a much higher volumetric energy density than hydrogen, is easy to handle, and has a much low cost per unit of energy. The advance of the DMFC technology and the deployments of the DMFC systems, however, have been suffocated by methanol crossover and high catalyst loading [3–5]. Methanol crossover (methanol diffusing from the anode to the cathode through the membrane) is caused by the inherent permeability of the Nafion® membrane (the most widely used proton exchange membrane) and the miscibility of methanol and water. Methanol crossover wasted the fuel and degraded fuel cell power and efficiency due to mixed potential from MOR and ORR and catalyst poisoning. Traditional DMFCs cannot be fed with high-concentration methanol solutions and typically require dilute methanol solutions (1.0 M or ∼3 wt% in water) to alleviate methanol crossover [6,7]. The use of high-concentration methanol solutions causes high methanol crossover rates, decreases fuel efficiency, and severely degrades fuel cell performance. However, dilute methanol solutions used to address this issue reduces the energy density of the fuel.
Besides the design of various fuel delivery systems and fuel cell structures to reduce methanol crossover [8–10], significant efforts have been carried out to design and synthesize platinum group metal (PGM)-free cathode catalysts [11–13]. Karim and Kamarudin  overviewed the PGM-free cathode catalysts for DMFC such as the macrocyclic molecules, transition metal oxides and sulfides, amorphous transition metal sulfides, and transition metal-based catalysts, and pointed out that the Ag- and Tungsten-based catalysts and nitrogen-doped carbon black and carbon nanotubes are potentially useful cathode catalysts for DMFCs. Advanced PGM-free catalysts have not only high ORR activity but also high methanol tolerance. The cathode PGM-free catalyst is inert to the cross-over methanol and has no MOR activity [15–17]. Therefore, DMFCs using PGM-free catalysts can obtain decent performance even with high-concentration methanol solutions with concentrations up to 17 M . The advance and application of PGM-free catalysts in DMFCs promote a new research direction to significantly reduce the cost and improve the performance. This study aims to develop a liquid–vapor two-phase model for DMFCs using PGM-free cathode catalysts to quantitatively investigate the mass transfer coupled with electrochemical reaction within the membrane electrode assembly (MEA).
There has been a tremendous amount of model studies to understand the liquid–vapor two-phase mass transfer within DMFCs. Many of the liquid–vapor two-phase DMFC models [18–20] stem from Wang and his research group’s widely used two-phase models applied to proton exchange membrane fuel cells (PEMFCs) . The two-phase model simulates the species transfer within liquid and vapor phases separately and couples the two phases using empirical correlations between the capillary pressure and liquid saturation. The models from one-dimensional to three-dimensional have been developed. The one-dimensional models [22,23] only consider the transport phenomena along the through-plane direction of the MEA and are likely to obtain the analytical solution. The three-dimensional models [19,24,25] are the most complicated. It can simulate the single cell or the fuel cell stack. The 2D models can be implemented for the domain on both the longitudinal section and cross section according to the concerns of the transport processes. The two-dimensional (2D) models are the most frequently used model as the model complexity, and the computational requirement can be properly balanced. He et al.  proposed a 2D liquid–vapor model along the longitudinal section considering the fact that the liquid and gas phases transfer within the porous components of DMFCs: liquid water and methanol are consumed and CO2 gas is generated in the anode catalyst layer (CL) and liquid water is generated and O2 gas is consumed in the cathode CL. Miao et al.  has developed a two-dimensional DMFC model along the cross section to consider the anisotropic properties of the gas diffusion layer (GDL) due to the inherent anisotropy of the GDL and compression by the bipolar plate. In addition, several recent DMFC model studies consider the detailed structure (scaffold-like or fibrous electrodes) of the fuel cell electrodes [28,29]. The liquid water and oxygen transfer characteristics of the electrode structure and approaches to improve transport properties and electrochemical performance have been proposed and quantitatively studied using these models.
Although models of DMFCs using PGM catalysts have been developed, the authors are not aware of models that focus on DMFCs with PGM-free catalysts. Because PGM-free catalysts have much lower mass density and require higher loading than PGM catalysts, the cathode catalyst layer of a PGM-free DMFC is much thicker than a traditional PGM DMFC. A recent experimental study of PEMFCs with PGM-free cathode catalyst illustrated the importance of the gas transport properties of bulk-electrode on the fuel cell performance . The design criterion of DMFCs with PGM-free cathode, such as wettability of MEA components, flowrates, and relative humidity of the air, is also different from that of DMFCs with PGM cathode. Therefore, this study developed a liquid–vapor two-phase model to simulate the heat and mass transfer of reactants and products, coupled with electrochemical reactions, within the porous materials of direct methanol fuel cells using both Pt-based and PGM-free cathode catalysts. Quantitative analyses of operating parameters and fuel cell components design parameters using this model lead to tangible plans to develop high-performance DMFCs using PGM-free catalysts that can obtain ∼300 mW/cm2 peak power density. Model results and new design criteria have enabled the research team to develop fuel cells with unprecedented performance .
2 Model Description
2.1 Computational Domain.
Figure 1 shows the two-dimensional physical domains of a typical MEA, which consists of a pair of GDLs, microporous layers (MPLs), and CLs on both sides of a PEM. The MEA is sandwiched between two parallel flow fields, represented in Fig. 1 by a half rib and a half channel. During the assembly, the deformation of the GDLs can be observed due to the compression of the ribs. A liquid–vapor two-phase mass transport model was developed to investigate the multi-physics phenomena in the MEA. The anisotropy of the GDL, including the inherent anisotropy and deformation of the GDL was taken into account in this model, similar to the approach applied in the study by Miao et al. [27,32]. The geometric dimensions and some model parameters of the DMFC are listed in Table 1. The supporting material of the PGM-free catalyst is the activated carbon. Because PGM-free catalysts have much lower mass density and require higher loading than PGM catalysts, the cathode catalyst layer of a PGM-free DMFC is set as five times thicker than a traditional PGM DMFC.
2.2 Governing Equations
2.2.1 Mass and Heat Transport in Porous Media.
2.2.2 Water and Methanol Crossover Through the Membrane.
2.2.3 Electrochemical Kinetics and Charge Transport.
All the governing equations have been presented. Detailed expressions of the anisotropic coefficients are listed in Table 2. These expressions are obtained from the literature [41,42] and modified according to the geometries of the modeled DMFC in the present work. The source terms in the governing equations are presented in Table 3.
2.2.4 Current Balance and Cell Voltage.
Hence, the cell output current density and cell voltage can be determined by
Note that the parasitic current density due to methanol crossover, given as Ip = 6FNM for the catalyst based on platinum group metals, equals to zero for the PGM-free cathode in the present study.
2.3 Boundary Conditions.
All the aforementioned governing equations were solved under the given boundary conditions for the 12 interfaces marked with Arabic numerals in Fig. 1.
Boundaries 1 and 5 represent the interface between the channels and the GDLs. At these two boundaries, the conditions were specified according to the operating conditions. For the mass and species transport, these two interfaces were set as the first type boundary condition by giving the pressures and concentration, while the second type boundary condition with zero flux was applied for the heat and charge transport equations.
Boundaries 2 and 4 were the interface between the ribs and the GDLs. At these two boundaries, the cell temperature and electric potential were set for the heat and charge transport equations. The second type boundary condition with zero flux was applied for the mass and species transport equations.
Boundaries 3 and 6: The symmetrical conditions for all variables were specified at these two boundaries as the computational domain was a periodic unit of the entire cell.
Boundaries 7–12 are the internal interfaces between adjacent components of the MEA. Boundary conditions were specified based on the continuity principle and flux balance of mass, charges, and heat.
Detailed information about these boundary conditions can be found in our former work .
3 Model Validations
All the governing equations were numerically solved using a developed fortran computer code based on the finite volume method. Physicochemical properties and parameters used in the model are presented in Table 4. Some parameters are from the openly published works [43,44]. The model was validated by the experimental data of anode and cathode overpotentials measured with the help of a hydrogen reference electrode . In the test, the anode was fed with 3 M liquid methanol solution at 0.1 mL/min flowrate, while the cathode was supplied with three different oxidants at 0.1 L/min flowrate and 100% relative humidity (RH): 1.0 atm air, 1.5 atm air, and 1.5 atm O2. The corresponding oxygen supply rates were calculated to be 3.86, 7.48, and 35.63 mol/m3, respectively. The polarization curve and the anode and cathode overpotentials were recorded at the cell temperature of 80 °C.
As shown in Fig. 2, the modeling results agreed well with the tested data under all three cathode feeding conditions. It can be seen that the cathode feeding condition had a significant effect on cell performance. The limit cell current density increased from about 570 mA/cm2 to 710 mA/cm2 with the cathode feeding pressure of air increased from 1 atm to 1.5 atm. When the 1.5 atm air was changed to 1.5 atm O2, the cell current density at a specific cell voltage increase significantly, and no concentration polarization occurred. This indicates that the oxygen transport in the cathode porous media may be a limiting factor on cell performance as the methanol concentration was relatively high, and humidification of the cathode feeding air reduces the concentration of oxygen. The model was then used to investigate the transport mechanisms through the MEA and predict cell performance based on several optimization measures.
4 Results and Discussion
4.1 Methanol Crossover.
One of the advantages of the PGM-free catalyst is the inertia to the MOR. In this study, we modeled the cell performance using traditional PGM catalysts (with Icross) and the PGM-free catalyst (without Icross). Also, methanol and water crossover still occur in fuel cells with PGM-free catalyst, but the crossover current, Icross, is zero because the PGM-free catalyst has no MOR activity. It is shown in Fig. 3 that the cell with PGM-free catalyst showed much better performance than the cell with Icross, especially at relatively low cathode oxygen concentration. The methanol and water crossover rates were higher at lower current density; therefore, the impact of the crossover was more significant when the cathode oxygen concentration was low. Besides, no anode concentration polarization appeared on the polarization curve, even up to a cell current density of 1200 mA/cm2, which indicates that the 3 M methanol solution fed to the anode can supply sufficient methanol. Even though Icross was set as zero in the PGM-free catalyst, the crossover methanol solution increased the liquid saturation in the cathode CL and GDL and increased the oxygen transfer resistance. Therefore, the RH of the cathode flow is important to regulate the mass transfer and maximize the peak power density of the fuel cell.
4.2 Transport of Oxygen and Methanol.
The effect of anode methanol feeding concentration on cell performance with different cathode feeding conditions was modeled and shown in Fig. 4. When the cathode oxygen feeding concentration was low, as shown in Fig. 4(a), the cell with 1–3 M methanol solution had almost identical polarization curves, and the limiting current densities were less than 500 mA/cm2. It indicates that even 1 M methanol solution was sufficient for the anode MOR. This phenomenon was quite different from that in the DMFC with the traditional PGM catalyst cathode. The parasitic current Icross on the PGM catalyst reduced the cathode overpotential, consequently decreased cell performance. Hence, 3 M methanol feed concentration always leads to lower cell performance than 1 M [46,47]. As the oxygen feeding concentration was increased, shown in Figs. 4(b) and 4(c), the limiting current density and the peak power density increased significantly. The polarization curves of 1 M and 2 M methanol solution clearly showed the concentration polarization region. Results in Fig. 4 show that the insufficient oxygen supply and transport at the cathode electrode was one of the key issues limiting cell performance. Operating fuel cells with pure oxygen is not practical in real applications, but it is common practice to pressurize air up to 1.5 atm for improved performance . Thus, the model used the 3 M methanol solution and 1.5 atm air as the basic case to analyze the transport phenomena in the MEA and proposed several measures to optimize the cell performance.
Figure 5 shows the species transport of methanol, methanol vapor, and oxygen in the MEA at the cell voltage of 0.15 V. It is seen that the deformation of the GDL made it harder for the species to transfer from the channel to the area under the rib. However, it has limited effects on the liquid methanol and methanol vapor transport as 3 M methanol solution can provide sufficient methanol. The reference methanol concentration in the anode MOR dynamic equation was 100 mol/m3. Model results show that even the lowest methanol concentration at the anode CL was much higher than 100 mol/m3. Compared to the anode species transport, the cathode oxygen supply was insufficient. The lowest concentration of oxygen at the cathode CL (lower left corner) approached zero. Due to the lower mass density and higher loading of the PGM-free catalyst, the thickness of the cathode CL was five times larger than the traditional CL with the PGM catalyst. It is clear that the enhancement of oxygen transport in the cathode electrode can probably improve cell performance.
4.3 Anode and Cathode Microporous Layerss.
Figure 6 shows the distribution of liquid saturation in anode and cathode electrodes and the water content in the electrolyte. Compare to GDLs and CLs, MPLs have larger contact angles that lead to much lower liquid saturation. The anode MPL reduces the water and methanol crossover. The cathode MPL keeps more water in the cathode CL to avoid membrane drying and excessive electrolyte resistance. In the present study, the 100% RH was adopted for the cathode air supply. It is shown in Fig. 6(c) that the water content in the electrolyte was pretty high, thanks to the supply of the liquid methanol solution to the anode. This implies that the cathode air or oxygen supply does not need to be fully hydrated to reduce the complexity and improve the reliability of the balance of the plant. Further experiments tested with 1 and 3 M methanol and air with 0% and 100% relative humidity at 80 and 90 °C have proven the results. Experimental results will be published soon.
In the following sections, operating parameters and cell geometries were investigated to optimize the cell performance and maximize the peak power density: catalyst activity, wettability of the cathode catalyst layer, and cell temperature.
4.4 Catalytic Activities.
The activity of the anode and cathode catalysts is the primary barrier to performance improvement and commercialization. Hence, the effect of the catalyst activity was first modeled, and the predicted cell performance is shown in Fig. 7. Comparing Figs. 7(a) and 7(b), it is seen that the increase in the anode catalyst activity led to a more significant increase in the cell current density at a specific cell voltage compared to the cathode catalyst. This is because the insufficient supply of oxygen to the cathode CL limited the improvement of the cathode ORR dynamics. In addition, the increase in the catalyst activity can significantly improve cell performance. As the anode and cathode activities were increased to ten times as high as the basic case, the cell current density at 0.15 V increased from 700 mA/cm2 to about 960 mA/cm2, and the peak power density increased from 120 mW/cm2 to 254 mW/cm2.
4.5 Porosity and Wettability of the Cathode Catalyst Layer.
The change of the cell structure will significantly impact the mass transport of oxygen in the cathode electrode. The predicted cell performance with different porosity and wettability values of the cathode CL is shown in Fig. 8. The sensitive analysis of the parameters relative to the mass transport resistance of oxygen was carried out. It is seen that the increase in the porosity of the cathode CL from 0.2 to 0.4 can increase the peak power density from 254 mW/cm2 to 281 mW/cm2 due to the increased oxygen diffusivity. The increase in the contact angle of the cathode CL led to lower liquid saturation and consequently a higher oxygen diffusivity. However, the modeling results in Fig. 8 show that the contact angle of the cathode CL had very limited effect on cell performance. At the same time, the reduction of the cathode CL width and the removal of the cathode MPL can significantly reduce the mass transfer resistance of oxygen. It can further increase the highest cell power density from 281 mW/cm2 to about 311 mW/cm2. It should be noted that all results shown in Fig. 8 were based on the assumption that the catalytic activities of the anode and cathode catalysts could be improved by ten times compared with catalytic activities of state-of-the-art commercial catalysts, which is the goal of the ongoing project to design and develop high-performance PGM-free catalysts.
4.6 Operating Temperature and Backpressure.
The heat transfer in the MEA was considered in the model, and the temperature distribution in the MEA is shown in Fig. 9. It is seen that the temperature distribution was relatively uniform. The temperature difference across the MEA was less than 2 °C. The cell performance is very sensitive to the cell temperature. The higher the temperature is, the higher reaction dynamics and species transport coefficients would be. At the same time, the saturated pressure of water vapor increases very quickly with temperature: from 0.31 atm at 70 °C, to 0.47 atm at 80 °C, and to 0.69 atm at 90 °C. The molar fractions of water vapor in fully hydrated air supplies (100% RH) are very significant given the total air pressure of 1.5 atm. The increase in the operating temperature will increase the partial pressure of water vapor and decrease the partial pressure of oxygen. Thus, the cell temperature should be investigated to optimize the cell performance.
As the effect of the temperature is a trade-off among the increased reaction dynamic, species diffusivity, and the reduced oxygen supply concentration, two parameters were considered in the modeling: the cell temperature and the (absolute) pressure of the cathode channel. Figure 10 shows that the cell power density was very sensitive to the cell temperature and the backpressure. At the cell temperature of 70 °C and backpressure of 1.0 atm, the highest power density was 232 mW/cm2. When the cell temperature and backpressure are increased to 90 °C and 2.5 atm, the highest peak power density could achieve 442 mW/cm2. Results also show that higher cathode backpressure can benefit cell performance at all cell temperatures due to the higher oxygen concentration supplied. However, for a specific cathode back pressure, there is an optimal cell temperature for the highest peak power density. At 1.0 atm backpressure, the optimal cell temperature was low, 70 °C. With the increase in the backpressure, the optimal cell temperature also increased. In the benchmark case of the present work, 1.5 atm air pressure, the optimal cell temperature was 80 °C. If the backpressure of air was further increased, the optimal cell temperature could be increased to up to 90 °C.
This study developed a two-dimensional and two-phase computational fluid dynamics model to investigate the heat and mass transfer in DMFCs using PGM-free cathode catalysts. The design criteria of DMFCs with PGM-free cathode catalyst are slightly different from DMFCs with the Pt cathode catalyst due to different electrochemical and physical properties of the catalysts. The following conclusions could be made based on the model results:
The compression of GDL by the rib of the current collector increased the mass transfer resistance.
Even though PGM-free cathode catalysts have no MOR activity, the crossover methanol solution increased the oxygen transfer resistance in the cathode and negatively impacted the cell performance slightly.
The cathode air or oxygen flow may not need to be fully hydrated, and the cathode MPL was less critical for water management since the liquid water supplied from the anode methanol solution could hydrate the PEM.
The cathode overpotential was higher than the anode overpotential. To enable DMFCs to achieve 300 mW/cm2 peak power density, catalytic activities of both the anode and cathode catalysts need to be improved by one order of magnitude comparing with the state-of-the-art commercial catalysts.
Even if the PEM is fully hydrated, increasing the operating temperature may result in lower peak power density because the increased partial pressure of water vapor with temperature will reduce the partial pressure (concentration) of oxygen in the cathode. The preferred operating temperature of DMFCs was about 80 °C when the pressure of the fully hydrated air is 1.5 atm in the cathode.
Z. M. and X. L. highly appreciate the support by the US Department of Energy’s Office of Energy Efficiency and Renewable Energy (EERE) under the Fuel Cell Technologies Office Award Number DE−0008440. Z. M., X. L., Y.-L. H., and J. X. acknowledge the support from National Natural Science Foundation of China (Grant No. 51776064).
Conflict of Interest
There are no conflicts of interest.
Data Availability Statement
The authors attest that all data for this study are included in the paper. Data provided by a third party listed in Acknowledgment.
- i =
electrochemical reaction rate (A/m3)
- m =
source terms in mass conservation equations (kg/(m3 · s))
- p =
- q =
- s =
- u =
superficial velocity vector (m/s)
- A =
specific area in the catalyst layer (m2/m3)
- C =
- D =
- F =
faraday constant, 96485 C/mol
- I =
current density (A/m3)
- I =
current vector (A/m3)
- K =
absolute permeability of porous media (m2)
- L =
length of the channel (m)
- M =
molecular weight (kg/mol)
- N =
molar flux (mol/(m2 · s))
- R =
gas constant (J/(mol · K))
- R =
source term in species conservation equations (mol/(m3 · s))
- T =
- kc =
condensation rate of water (1/s)
- ke =
evaporation rate of water (1/(atm · s))
- kH =
Henry’s law constant
- krg =
relative permeability of gas phase
- krl =
relative permeability of liquid phase
- nd =
electro-osmotic drag coefficient
- pc =
capillary pressure (pa)
- RW =
interfacial transfer rate of water (mol/(m3 · s))
- V0 =
thermodynamic equilibrium voltage (V)
- VCell =
cell voltage (V)