Summary of Material science doctoral thesis: Fabrication and investigation of influence of technological parameters on performance of proton exchange membrane fuel cell

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In Vietnam, currently the study of fuel cells is almost neglected and there is very little fundamental research on this issue. The research on fuel cells of our country is at innitial stage, mainly researching catalytic material in the laboratory and almost has not research in the technology of manufacturing fuel cell (stack).

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Nội dung Text: Summary of Material science doctoral thesis: Fabrication and investigation of influence of technological parameters on performance of proton exchange membrane fuel cell

MINISTRY OF EDUCATION AND VIETNAM ACADEMY OF SCIENCE TRAINING AND TECHNOLOGY GRADUATE UNIVERSITY SCIENCE AND TECHNOLOGY ----------------------------- GIANG HONG THAI FABRICATION AND EVALUATION OF INFLUENCE OF TECHNOLOGICAL PARAMETERS ON PERFORMANCE OF PROTON EXCHANGE MEMBRANE FUEL CELL Major: Metal Science Code: 9.44.01.29 SUMMARY OF MATERIAL SCIENCE DOCTORAL THESIS Hanoi – 2020
The work was completed at: Graduate University Science and Technology – Vietnam Academy of Science and Technology Advisors: 1. Dr. Pham Thi San 2. Prof. Dr. Vu Dinh Lam Reviewer 1: Dr. Nguyen Van Nghia Reviewer 2: Prof. Dr. Nguyen Huy Dan Reviewer 3: Dr. Dang Quoc Khanh The thesis will be protected before the doctoral dissertation thesis, meeting at the Academy of Science and Technology - Vietnam Academy of Science and Technology at ... hour...' date ... month ... 2020 The thesis can be found at: - Library of the Academy of Science and Technology - National Library of Vietnam
PREFACE 1. Urgency of thesis Economic development lead to increases of demand for energy in the world. Currently, energies derived from fossil energy such as oil, natural gas, coal ..., are gradually depleting and causing environmental pollution as well as global warming. The challenges of energy demand and sustainable development have prompted scientists around the world to focus their research on finding new and renewable sources of energy. Among all selectable renewable energy sources such as: solar, wind, hydro, nuclear, geothermal, tidal, etc., the promising renewable energy source is hydrogen fuel which is considered as a bright candidate for the future. Proton exchange membrane fuel cells (PEMFC) using hydrogen fuel have been the most interested in scientists around the world for three decades due to the advantages: light weight, compact size, high power, high stability, low emission, no noise, no pollution to the environment… Fuel cells with flexible output power should be widely applied to electronic devices, telephones, computers, vehicles, space stations, power stations... Performance and applicability of fuel cells depend very strongly on the process of manufacturing fuel cells. Therefore, research and development of fuel cell technology are also strongly invested by scientists and companies around the world. Companies and research facilities are extremely secretive about technology copyrights which keeps its own technical know-how and does not spread outside. Therefore, in order to develop fuel cell in Vietnam, we need to invest in researching and developing our own technology and core technologies in manufacturing fuel cells as an initial step as a prerequisite for the next development of fuel cell application. In Vietnam, currently the study of fuel cells is almost neglected and there is very little fundamental research on this issue. The research on fuel cells of our country is at innitial stage, mainly researching catalytic material in the laboratory and almost has not research in the technology of manufacturing fuel cell (stack). From the above reasons, the group of instructors and graduate students choose the research topic:“Fabrication and investigation of influence of technological parameters on performance of proton exchange membrane fuel cell”. 2. Scope of thesis 1
- Study on fabrication proton exchange membrane fuel cell (PEMFC). - Characteristics and selection of the optimal catalyst material and composition for the catalyst layer in membrane electrodes assembly (MEA) and to evaluate influence of manufacturing technological parameters on MEA properties and from that basis master core technology to develop MEA manufacturing process. - Building a model and explaining the mechanism of the process of converting energy into electricity in MEA. - Design, manufacture and operate a complete stack of PEMFC fuel cells with a power of ~ 100 W. 3. Main contents of thesis - Research, evaluate and select catalyst ink components of electrode catalyst formation: Pt/C catalyst materials, nafion content (proton conductor)... - Research, manufacture and evaluate MEA by the following techniques: CCS, DTM and hot pressing process to fabricate MEA and study on influence of technological parameters on MEA quality and optimum of MEA manufacturing process with the best quality. - Research, design, manufacture a complete PEMFC stack with a power of ~ 100 W and investigate the influence of technological parameters on the properties of the stack and give optimal operating conditions. CHAPTER 1. INTRODUCTION 1.1. Introduction of fuel cells A fuel cell is a device that converts chemical potential energy into electrical energy. A Proton Exchange Membrane cell uses hydrogen gas (H2) and oxygen gas (O2) as fuel. 1.2. Introduction of proton exchange membrane fuel cell 1.2.1. Operational principles of PEMFC The equations for the chemical reactions at the electrodes of a PEMFC are as follows: Reaction on anode: 2H 2  4H   4e  (1.1) Reaction oncathode: O2  4H   4e   2H 2 O (1.2) 2
Total: 2H 2  O2  2H 2 O + Electricity + Heat (1.3) 1.2.2. Structure of PEMFC The basic structure of a proton exchange membrane fuel cell is shown in Fig. 1.4 including the components: Fig. 1.4. Structure of PEMFC Fig. 1.2 Principle of PEMFC Membrane electrodes assembly (MEA) The most important part in a PEMFC is the membrane electrode assembly (MEA). MEA is composed of two layers of electrode catalyst material, anode and cathode, which are symmetrically placed through a nafion film that acts as an electrolyte medium to transport protons from the anode to the cathode. Catalytic layers in MEA The catalyst layer has a thickness of 5-100 µm with a porosity of about 40-70% and is dispersed by metallic Pt catalyst particles with size of 1-10 nm. MEA fabrication hot pressing technique Hot pressing technique is an important step to link the components of MEA. The three main parameters of hot pressing process including temperature, pressing pressure and pressing time need to be optimized. CHAPTER 2. EXPERIMENTAL AND RESEARCH METHOD 2.1. Chemicals and materials 2.2. Experimental 2.2.1. Characteristics of Pt/C electrocatalyst materials The four types of commercial catalyst materials are Pt/C 20%wt., 30% wt. of Fuelearth; and Pt/C 20 %wt., 40%wt. of Jonshon Mathey was selected and evaluated. 3
2.2.2. Fabrication of MEA 2.2.2.1. Fabrication of MEA by CCS method - Creating a catalyst layer in fabrication of membrane electrodes of PEMFC by sweep on sample with size (5x5) cm2. Figure 2.1. Process of MEA’s fabrication by CCS method 2.2.2.2. The effect of Nafion content in catalyst ink on MEA’s properties The catalyst layer with varying Nafion content of 20, 30, 40 and 50% of the solid weight of catalyst ink was studied. The material used is 40% Pt/C catalyst (HiSPEC, Johns Matthey, USA) with Pt catalyst loading on the membrane electrode kept fixed at 0.4 mg Pt /cm2 and Nafion solution 5% (Dupont's D520). The quality of MEAs is evaluated by the polarization curve U-I. 2.2.2.3. Fabrication of MEA by DTM method Figure 2.2. Process of MEA’s fabrication by DTM method 2.2.3. Design and manufacture of 100W PEMFC fuel cell 2.3.Equipment and materials 2.4. Research methods 4
2.4.1. The physical characteristic methods The surface morphology and particle size of the catalysts materials was examined by scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Energy-dispersive X-ray spectroscopy (EDX) is used to determine the composition of the catalyst mixture. 2.4.2. The physical electrochemical methods Cyclic Voltammetry measurements are measured to determination of catalytic activation and electrochemical processes on catalytic surface and catalytic degradation. Measurements were performed in 0.5 M H2SO4 solution and the electrochemical device used was PARSTAT2273 (EG&G –USA) with specialized software. Electrochemical impedance spectroscopy: frequency range is varied between 100 kHz and 10 mHz and the used AC voltage is 10 mV. Chapter III. RESEACH, FABRICATE AND EVALUATE OF MEA ELECTRODE 3.1. Evaluation of properties and selection of Pt/C catalyst materials used in fuel cells (PEMFC) 3.1.1. Evaluation of electrochemical properties of Pt/C catalyst materials The most important properties of a catalyst material in a fuel cell are the catalytic activity and durability of the catalyst in operation environment. Therefore, the evaluation of these properties determines the type of catalyst to be used in subsequent studies. 3.1.1.1. Evaluation ofactivityof Pt/C catalyst materials Fig. 3.2 shows the CV graph of carbon Vulcan XC-72 and Pt/C of FE and JM samples with loading of 0.4 mg/cm2 Pt in 0.5 M H2SO4 solution. The ESA values were calculated from H2 adsorption peaks in the potential range of 0-0.4 V. The ESA area values of the catalyst samples are summarized in Table 3.1. The JM’s catalysts have a higher ESAvalue than those of the FE’scatalysts. Thus, JM’s catalyst samples had higher catalytic activity and reached the highest ESA value with the JM-40 catalyst samples up to about 74.91 m2/g. 5
Table 3.1. The value of ESA (electrochemical activation area) of Pt/ C of FE and JM Material catalyst No FE-20 FE-30 JM-20 JM-40 ESA 56.99 62.88 64.91 74.91 (m2/g) Fig. 3.2. CV of Vulcan-72 and Pt/C of FE and JM in H2SO4 0.5M 3.1.1.2. Evaluation ofdurabilityof Pt/C catalyst materials Figure 3.4 shows a CV graph of the FE-30 catalyst sample measuring 1000 cycles in the stability test. After every 200 CV cycles, ESA values were measured and presented in Tables 3.2 and 3.5. The JM’s catalyst samples had a lower decrease of ESA value than the FE’s catalyst samples and the JM-40 sample reached the lowest decrease value of 29.95%. The degradation phenomenon of Pt/C catalyst is caused by: Firstly, Pt particles will be dissolved into ions according to the equations: Pt → Pt2+ + 2e (3.3) PtO + 2H+ → Pt2+ + H2O (3.4) Secondly, carbon corrosion will separate a small fraction of Pt-catalyst carbon particles. In addition, corrosion of carbon base may cause catalytic poisoning due to the formation of CO. Table.3.2. The change in ESA value after 1000 cycle durability test of Pt/C catalyst samples Catalyst samples FE-20 FE-30 JM-20 JM-40 The change in 34.0 35.7 32.3 29.9 Fig. 3.3. The model illustrates the ESA (%) processes affecting the durability of Pt/C catalyst 6
Fig. 3.4. CV graph evaluating durability in Fig. 3.5. The graph shows the change in 1000 cycles of FE-30 catalyst in 0.5M H2SO4 ESA value of different catalyst samples after 1000 cycle durability test Thus, the JM-40 catalyst exhibits best activity and durability and is selected for use in subsequent studies. 3.1.2. Evaluation of physical properties of Pt/C catalyst materials TEM images of the four catalysts show the common Pt particle size in the range of 3-4 nm. Figures 3.9, 3.10; 3.11; 3.12 present TEM images and particle size distribution graph of Pt/C catalyst samples. Compared to FE’s catalysts, the JM’s catalysts appear to be smaller in size and have a more uniform distribution. The results are shown in Table 3.3. Figure 3.9. TEM image and particle size Figure 3.10. TEM image and particle size distribution graph of FE-20 catalyst distribution graph of FE-30 catalyst Table 3.3. Average size of metal particles in Pt/C catalyst samples Catalyst samples FE-20 FE-30 JM-20 JM-40 Average size (nm) 3.6 3.5 3.1 3.2 7
Fig. 3.11. TEM image and particle size Hình 3.12. TEM image and particle size distribution graph of JM-20 catalyst distribution graph of JM-40 catalyst Thus, the catalyst Pt/C 40% of the weight of Johnson Matthey gave the best activity and durability and was selected as the catalyst in the next study. 3.2.Research and manufacture MEA by catalytic coating method on gas diffuse layer 3.2.1. The effect of hot pressing parameters on properties of MEA 3.2.1.1. The effect of hot pressing parameters onelectrical properties of MEA MEA is made fromdifferent pressure values: 17, 19, 21, 24, 28 kg.cm-2, T = 130 OC and pressing time 180 s. a. Evaluation of electrical properties of MEAs by the polarization curve U-I Fig. 3.13 is a graph of the U-I polarization curve of MEAs fabricated at different pressure values. With pressure values in the range of 17-21 kg.cm-2, the U-I curves gradually move to the left corresponding to the increase of current value at the same potential value. This indicates that the electrical properties of the MEA become better when the pressure value is increased within the study force range. In contrast, at higher pressure, MEA deteriorates. Fig. 3.13. Graph of the U-I polarization curve of MEAs fabricated at different pressure values: 17, 19, 21, 24, and 28kg.cm-2 8
Fig. 3.15 shows the maximum power density of the membrane fabricated at different pressure values. The highest Pmax values achieved were 365 and 374 mW.cm-2 of MEAs fabricated at pressure values of 21 and 19 kg.cm-2, respectively.. Fig. 3.15. Graph of changing the maximum power density value of Pmax of MEA fabricated at different pressure values Thus, by surveying the effect of pressure on MEA's properties, MEAs manufactured at pressurevalues of 19 and 21 kg.cm-2 will give the best electrical properties. b. Evaluation of open circuit voltage of MEA In theory, the standard voltage of a single fuel cell would be 1.23 V. However, in practice OCV of a single fuel cell will vary from 0.9 to 1.2 V. Fig. 3.16 is a graph of OCV of manufactured MEA at different pressure values. On the graph it can be seen that MEAs manufactured at higher values of pressure, the OCV decreases. Table 3.4. Change of open circuit voltage according to the pressure Pressure (kg.cm-2) 17 19 21 24 28 Fig. 3.16. The open circuit voltage (OCV) of OCV MEA fabricated at different pressure values: 920 955 965 960 946 (mV) 17, 19, 21, 24, 28 kg.cm-2 c. Evaluation of electrical properties of MEAs by EIS technique 9
Fig. 3.17 shows EIS graph of MEAs manufactured at different pressure values. The equivalent circuit of EIS graphs can be modeled as shown in Fig. 3.18 in which: Rs is the total Ohm resistor of the cell; L is an inductance that characterizes the effects created by the collector plates and all the metal components in the system. Rct is the charge transfer resistance of the cell. Table 3.5. The Rs and Rct values are extrapolated from the EIS of the MEAs fabricated at different pressure values. Pressure(kg.cm- Rs Rct 2 ) (Ω.cm2) (Ω.cm2) 17 0.215 5.739 19 0.241 3.015 21 0.425 18.806 Fig. 3.17. Nyquist graphs of MEAs fabricated 24 0.611 40.233 by the method of hot pressing at the values 28 0.824 76.737 17, 19, 21, 24 and 28kg.cm-2 Figure 3.18. Equivalent circuit model of EIS for a PEMFC From datas (Table 3.5) it can be seen that the resistance values of MEA are considerably influenced by the pressure values. When the pressure value exceeds of 24 kg.cm-2, the Rs value varies greatly, especially at the pressure of 28 kg.cm-2. MEA was fabricated at 19 kg.cm-2 hasthe smallest Rct value which due to the exposure of the catalyst layer to the nafion film when fabricated under this heat press condition to achieve the best efficiency so the electrical properties can be improved. 3.2.1.2. Effect of pressure on deformation of MEA From the measurements of the electrical properties of MEA fabricated at different pressures, we found that the electrical properties of MEA are best achieved between 19-21kg.cm-2. Thus, the pressure effect on the electrical properties of the 10
MEA may be predicted to be due to the change in geometric structure of MEA. The change in the pressure causes MEAs deformation showing the change in thickness (the results are summarized in Table 3.6). The mechanical deformation of the membrane electrode MEA is obsevered on figures 3.19, 3.20 and table 3.17. Table 3.6. The change in thickness of the MEA according to pressures Pressure(kg.cm-2) 17 19 21 24 28 Thicknees 671 662 663 618 614 Fig. 3.19. Typical images of MEAs fabricated (µm) at different pressures Table 3.7. Thickness and deformation of nafion membrane 212 in MEA fabricated by hot pressing method at different pressure values Pressure(kg.cm-2) 17 19 21 24 28 Fi g. 3.20. Graph of changing thickness of Thickness 48,3 45,7 42,1 33,7 30,8 MEAs at different pressure values: 17, 19, (µm) 21, 24, 28 kg.cm-2 Change thickness 3,2 8,9 15,4 25,5 46,8 (%) Fig. 3.21 and Fig. 3.22 are analytical results of a typical MEA cross- section fabricated at hot pressing conditions: 19 kg.cm-2, 130oC and 180 s. The EDX analysis results of the catalyst layer show that the composition of this layer consists of only Pt/C catalyst material surrounded by solid nafion ion conductors. Meanwhile, the component results of proton exchange membrane are mainly elements C, O and F.This confirms that the main composition of the membrane is nafion compound. It is the homogeneity of the use of nafion in the catalyst layer and the Nafion proton exchange membrane that will make the bond of these layers tighter and increase the properties of the membrane electrode. 11
Fig. 3.21. EDX analysis results of the cross Figure 3.22. EDX analysis results of the section of MEA at the catalyst site cross-section of MEA at the proton exchange membrane position From the EDX analysis results and based on some structural models of MEA, we have built a more specific model in order to explain the processes that affect properties of MEA. We built an additional model (Fig. 3.24) to fit the reaction process occurring in the anode and cathode region of the MEA. Based on the proposed model we apply to explain the mechanisms of technological process (Fig.. 3.25 to Fig. 3.28). Fig. 3.24. The model explains the reaction Fig. 3.25. Model of catalytic ink process in MEA manufacturing process Fig. 3.26. Model of catalytic layer creation process Fig. 3.27. Model of MEA’s structure on diffuse layer after hot pressing 12
a) Small pressure b. Medium pressure c) Great pressure Fig. 3.28. MEA structure model with different pressures 3.2.1.3. The effect of presing time and temperature on properties of MEA From above experiment, the pressure of 19 kg.cm-2 was selected and kept fixed in the next survey. Hot pressing temperature is chosen three values of 100oC, 130oC, and 140oC; The pressing times are changed to 90, 120, 180, 240, and 300 s respectively. The influence of time and temperature on the properties of MEAs is summarized in table 3.8 and is shown on the graph in fig. 3.31. Best results were obtained at 19 kg.cm-2,130oC, and 180s. This is the optimal parameter of the method of manufacturing MEA by CCS technique. Table 3.8. The change in capacity of MEA according to temperature and pressing time Pressing Max capacity (mW) time 100oC 130oC 140oC 90 s 266 329 283 120 s 273 351 292 180 s 280 369 306 240 s 278 363 298 Fig. 3.32. Powercapacity depend on the time and 300 s 268 355 289 temperature of pressing 13
3.2.2. Effect of nafion content in catalyst layer on properties of MEA The effect of nafion on MEA properties is carried out with the Nafion content varying from 20, 30, 40 and 50% of the catalyst ink. U-I and P-I polarization graphs (Fig. 3.34 and 3.35) show MEA with 40% Nafion content for best quality. Maximum power density achieved up to 751 mW.cm-2 as shown in Table 3.9. Table 3.9. Maximum power value at 0.4 V of MEA with different Nafion content % Nafion content(% k.lg) 20 30 40 50 Power density,Pmax (mW.cm-2) 196 355 751 680 Fig. 3.35. The P-I polarization curve of Fig. 3.34. The U-I polarization curve of MEAs MEAs with different Nafion content with different Nafion content 3.2.3. The manufacturing process of MEA by CCS method The manufacturingprocess of MEA by CCS method has been shown as in Fig. 3.37. 14
Figure 3.37. The manufacturing process of MEA by catalytic coating method directly on the diffusion layer 3.3. Research and manufacture MEA by decals method MEA fabrication by decals method (DTM) has been implemented. The properties of this MEA were evaluated and compared with MEAfabricated by CCS method. Fig. 3.39. SEM image of cross section of MEA Fig. 3.40. Polarization curves U-I and P-I of manufactured by decals (DTM) MEAs made by decals (DTM) and CCS method Table 3.10. Summary of power generation characteristics of MEAs manufactured by DTM and CCS methods OCV (V) I V (V) P max (W.cm-2) (A.cm-2) DTM 0.983 2.26 0.4 0.905 CCS 0.95 1.92 0.4 0.768 The maximum power of MEA manufactured by DTM method is 0.995 W.cm-2 which is about 18% higher than MEA manufactured by CCS method of 0.768W.cm-2. Thus, when using the decals (DTM) method, the electrical properties of MEA was improved by 18%. The reason for this quality is due to the thin, uniform catalyst ink and good bonding with the Nafion film. However, the decals method is relatively complicated and the catalytic loss rate is quite large. Moreover, using DTM method requires two steps hot pressing process and this can cause cracks and fractures in the catalytic layer which lead to distortion and reduction of the quality of the Nafion film meaning to reduce the quality and life of fuel cells. In our country, the DTM technique is not suitable and the research of this thesis still focuses on the traditional method of CCS and research on the operation of PEMFC. 15
Conclusion chapter III - The catalytic Pt/C 40% of the weight of Johnson Matthey has better performance than Pt/C commercial catalyst materials on the market and has been selected as a catalyst for this research. - Nafion content in the catalyst, an important factor affecting the properties of MEA, has also been studied. The appropriate Nafion content was found to be about 40% of the catalyst solid mass. - A suitable technological mode for making good quality MEA has been found. It is fabricated MEA with catalyst layer with composition of 60% Pt and 40% Nafion covered by brush and hot pressing technique with parameters: temperature of 130 oC, pressing time of 180 s and force pressed 19 kg.cm-2. - A model of structure and interaction of electrochemical reactions occurring in MEA was developed. This model has been used to explain the technological factors that affect the quality of MEA. Chapter IV: STUDY TO FABRICATE FUEL CELL STACK WITH POWER OF ~ 100W With the purpose of manufacturing a complete fuel cell stack with a power of ~ 100 W. The PEMFC stack consists of 10 single cell connected in series and each single cell has an active area of 25 cm2. 4.1. Study on fuel channel configuration on bipolar plate In this study, three channel configurations selected were: 1 groove, 3 grooves and 5 grooves in the folded structure designed and fabricated on bipolar plates with size of (5 x 5) cm2 and a wide and deep of groove about 1 mm. The design drawings were made by Autocard 2007 software. After that, the designs were transferred to CNC mechanical machines for processing. The material used to make bipolar plateis HK3 graphite sheet (Tokai, Japan) with dimensions of 130x1300x10 mm. Fig. 4.2; 4.4 and 4.6 are design drawings of channel configurations consisting of 1 groove, 3 grooves and 5 channels. Each single cell consists of a pair of bipolar plate. Fig. 4.3; 4.5 and 4.6 are photographs of manufactured bipolar plate. The results of U-I polarization measurements at the same operating parameters: temperature, 16
humidity, flow rate presented in Fig. 4.8 and 4.9. Fig. 4.2. Configuration design of Fig. 4.3. Photographs of manufactured bipolar bipolar platewith 1 kink groove plate with 1 kink groove Fig. 4.4. Configuration design of bipolar Fig. 4.3. Photographs of manufactured bipolar plate with 1 kink groove plate with 3 kink groove Fig. 4.6. Configuration design of Fig. 4.7. Photographs of manufactured bipolar bipolar plate with 5 kink groove plate with 5 kink groove The results of U-I and P-I polarization measurements at the same operating parameters such as temperature, humidity, flow rate are presented in Fig. 4.8 and 4.9. 17
Fig. 4.8. The polarization curve of bipolar Fig. 4.9. Power characteristics of bipolar plate has different channel configurations plates have different channel In range of current density from 0.3 A.cm-2to 0.9 A.cm-2, 5 grooves have better quality than grooves of 3 and 1. Because in this region, the voltage drop is almost linear with increase of the current density in the cell. This drop is mainly affected by the internal resistance of the battery. Because of the 5 grooves configuration for a more uniform gas distribution, the power output is greater. When the current density is higher than 0.9 A.cm-2, 5 and 3 grooves tends to be equal. In high current density, the main effects are the processes of transportation and control of mass transfer of fuel gas flow. The 5air grooves configuration has a lower pressure difference between the inlet and outlet of the gas, so water release capacity of this configuration is inferior to 3 air grooves and therefore may be due to inundation resulting in the quality of 5air grooves MEA decreased and the 3air grooves MEA increased. Because in the coupling of fuel cells, the quality of system is determined by the lowest quality single cell. Therefore we choose the 3 air grooves configuration for further studies. 4.2. Design and manufacture of PEMFC 4.2.1. Calculating, design choices for PEMFC The output power of the PEMFC is calculated by the formula: P = iA.nVcell 4.2.2.Design and manufacture of components of 100 W PEMFC With an output power requirement about 100 W, we chose a stack of 10 single- cell with active area of 25 cm2 that connect in series. The stack used the U-shaped fuel supply model. 18