Structure, Property, and Performance of Catalyst Layers in Proton Exchange Membrane Fuel Cells

Electrochemical Energy Reviews - Tập 6 - Trang 1-61 - 2023
Jian Zhao1, Huiyuan Liu1, Xianguo Li1
1Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Canada

Tóm tắt

Catalyst layer (CL) is the core component of proton exchange membrane (PEM) fuel cells, which determines the performance, durability, and cost. However, difficulties remain for a thorough understanding of the CLs’ inhomogeneous structure, and its impact on the physicochemical and electrochemical properties, operating performance, and durability. The inhomogeneous structure of the CLs is formed during the manufacturing process, which is sensitive to the associated materials, composition, fabrication methods, procedures, and conditions. The state-of-the-art visualization and characterization techniques are crucial to examine the CL structure. The structure-dependent physicochemical and electrochemical properties are then thoroughly scrutinized in terms of fundamental concepts, theories, and recent progress in advanced experimental techniques. The relation between the CL structure and the associated effective properties is also examined based on experimental and theoretical findings. Recent studies indicated that the CL inhomogeneous structure also strongly affects the performance and degradation of the whole fuel cell, and thus, the interconnection between the fuel cell performance, failure modes, and CL structure is comprehensively reviewed. An analytical model is established to understand the effect of the CL structure on the effective properties, performance, and durability of the PEM fuel cells. Finally, the challenges and prospects of the CL structure-associated studies are highlighted for the development of high-performing PEM fuel cells.

Tài liệu tham khảo

U.S. Department of Energy Hydrogen and Fuel Cells Program: Record 17007: Fuel Cell System Cost-2017 (2017) Holton, O., Stevenson, J.: The role of platinum in proton exchange membrane fuel cells. Platin. Met. Rev. 57, 259–271 (2013). https://doi.org/10.1595/147106713X671222 Zhang, J.J.: PEM Fuel Cell Electrocatalysts and Catalyst Layers: Fundamentals and Applications. Springer, London (2008). https://doi.org/10.1007/978-1-84800-936-3 Zhao, J., Li, X.G.: Oxygen transport in polymer electrolyte membrane fuel cells based on measured electrode pore structure and mass transport properties. Energy Convers. Manag. 186, 570–585 (2019). https://doi.org/10.1016/j.enconman.2019.02.042 Li, X.G.: Principles of Fuel Cells. CRC Press, Boca Raton (2005). https://doi.org/10.1201/9780203942338 Nørskov, J.K., Rossmeisl, J., Logadottir, A., et al.: Origin of the overpotential for oxygen reduction at a fuel-cell cathode. J. Phys. Chem. B 108, 17886–17892 (2004). https://doi.org/10.1021/jp047349j10.1021/jp047349j Yin, Y., Liu, J., Chang, Y.F., et al.: Design of Pt–C/Fe–N–S–C cathode dual catalyst layers for proton exchange membrane fuel cells under low humidity. Electrochim. Acta 296, 450–457 (2019). https://doi.org/10.1016/j.electacta.2018.11 Fan, J.T., Chen, M., Zhao, Z.L., et al.: Bridging the gap between highly active oxygen reduction reaction catalysts and effective catalyst layers for proton exchange membrane fuel cells. Nat. Energy 6, 475–486 (2021). https://doi.org/10.1038/s41560-021-00824-7 Neergat, M., Rahul, R.: Unsupported Cu–Pt core–shell nanoparticles: oxygen reduction reaction (ORR) catalyst with better activity and reduced precious metal content. J. Electrochem. Soc. 159, F234–F241 (2012). https://doi.org/10.1149/2.039207jes Ding, Y., Chen, M.W., Erlebacher, J.: Metallic mesoporous nanocomposites for electrocatalysis. J. Am. Chem. Soc. 126, 6876–6877 (2004). https://doi.org/10.1021/ja0320119 Chen, Z.W., Higgins, D., Yu, A.P., et al.: A review on non-precious metal electrocatalysts for PEM fuel cells. Energy Environ. Sci. 4, 3167–3192 (2011). https://doi.org/10.1039/c0ee00558d Higgins, D.C., Chen, Z.W.: Recent progress in non-precious metal catalysts for PEM fuel cell applications. Can. J. Chem. Eng. 91, 1881–1895 (2013). https://doi.org/10.1002/cjce.21884 Zamani, P., Higgins, D.C., Hassan, F.M., et al.: Highly active and porous graphene encapsulating carbon nanotubes as a non-precious oxygen reduction electrocatalyst for hydrogen-air fuel cells. Nano Energy 26, 267–275 (2016). https://doi.org/10.1016/j.nanoen.2016.05.035 Fu, X.G., Hassan, F.M., Zamani, P., et al.: Engineered architecture of nitrogenous graphene encapsulating porous carbon with nano-channel reactors enhancing the PEM fuel cell performance. Nano Energy 42, 249–256 (2017). https://doi.org/10.1016/j.nanoen.2017.10.051 Zhu, J.B., Xiao, M.L., Song, P., et al.: Highly polarized carbon nano-architecture as robust metal-free catalyst for oxygen reduction in polymer electrolyte membrane fuel cells. Nano Energy 49, 23–30 (2018). https://doi.org/10.1016/j.nanoen.2018.04.021 Tabe, Y., Saito, M., Fukui, K.R., et al.: Cold start characteristics and freezing mechanism dependence on start-up temperature in a polymer electrolyte membrane fuel cell. J. Power Sources 208, 366–373 (2012). https://doi.org/10.1016/j.jpowsour.2012.02.052 Xie, J., Garzon, F., Zawodzinski, T., et al.: Ionomer segregation in composite MEAs and its effect on polymer electrolyte fuel cell performance. J. Electrochem. Soc. 151, A1084 (2004). https://doi.org/10.1149/1.1756887 Gao, Y.: Using MRT lattice Boltzmann method to simulate gas flow in simplified catalyst layer for different inlet-outlet pressure ratio. Int. J. Heat Mass Transf. 88, 122–132 (2015). https://doi.org/10.1016/j.ijheatmasstransfer.2015.04.031 Jhong, H.R., Brushett, F.R., Kenis, P.J.A.: The effects of catalyst layer deposition methodology on electrode performance. Adv. Energy Mater. 3, 589–599 (2013). https://doi.org/10.1002/aenm.201200759 Hitchcock, A.P., Johansson, G.A., Mitchell, G.E., et al.: 3-D chemical imaging using angle-scan nanotomography in a soft X-ray scanning transmission X-ray microscope. Appl. Phys. A 92, 447–452 (2008). https://doi.org/10.1007/s00339-008-4588-x Kim, S., Mench, M.M.: Physical degradation of membrane electrode assemblies undergoing freeze/thaw cycling: micro-structure effects. J. Power Sources 179, 140–146 (2008). https://doi.org/10.1016/j.jpowsour.2007.12.114 More, K., Borup, R., Reeves, K.: Identifying contributing degradation phenomena in PEM fuel cell membrane electride assemblies via electron microscopy. ECS Trans. 3, 717–733 (2006). https://doi.org/10.1149/1.2356192 Gode, P., Jaouen, F., Lindbergh, G., et al.: Influence of the composition on the structure and electrochemical characteristics of the PEFC cathode. Electrochim. Acta 48, 4175–4187 (2003). https://doi.org/10.1016/S0013-4686(03)00603-0 Pollet, B.G., Goh, J.T.E.: The importance of ultrasonic parameters in the preparation of fuel cell catalyst inks. Electrochim. Acta 128, 292–303 (2014). https://doi.org/10.1016/j.electacta.2013.09.160 Bonifácio, R.N., Paschoal, J.O.A., Linardi, M., et al.: Catalyst layer optimization by surface tension control during ink formulation of membrane electrode assemblies in proton exchange membrane fuel cell. J. Power Sources 196, 4680–4685 (2011). https://doi.org/10.1016/j.jpowsour.2011.01.010 Litster, S., McLean, G.: PEM fuel cell electrodes. J. Power Sources 130, 61–76 (2004). https://doi.org/10.1016/j.jpowsour.2003.12.055 Wolf, G.: Modification of chemical properties of materials by ion beam mixing and ion beam assisted deposition. J. Vac. Sci. Technol. A Vac. Surf. Films A10, 1757–1764 (1992). https://doi.org/10.1116/1.577743 George, S.M.: Atomic layer deposition: an overview. Chem. Rev. 110, 111–131 (2010). https://doi.org/10.1021/cr900056b Niedrach, L.W., Alford, H.R.: Polytetrafluoroethylene Coated and Bonded Cell Structures. US Patent 3,432,355 (1969) Wilson, M.S., Gottesfeld, S.: Thin-film catalyst layers for polymer electrolyte fuel cell electrodes. J. Appl. Electrochem. 22, 1–7 (1992). https://doi.org/10.1007/BF01093004 Wee, J.H., Lee, K.Y., Kim, S.H.: Fabrication methods for low-Pt-loading electrocatalysts in proton exchange membrane fuel cell systems. J. Power Sources 165, 667–677 (2007). https://doi.org/10.1016/j.jpowsour.2006.12.051 Ticianelli, E.A., Derouin, C.R., Redondo, A., et al.: Methods to advance technology of proton exchange membrane fuel cells. J. Electrochem. Soc. 135, 2209–2214 (1988). https://doi.org/10.1149/1.2096240 Alvar, E.N., Zhou, B., Eichhorn, S.H.: Carbon-embedded mesoporous Nb-doped TiO2 nanofibers as catalyst support for the oxygen reduction reaction in PEM fuel cells. J. Mater. Chem. A 4, 6540–6552 (2016). https://doi.org/10.1039/c5ta08801a Mukherjee, S., Bates, A., Lee, S.C., et al.: A review of the application of CNTs in PEM fuel cells. Int. J. Green Energy 12, 787–809 (2015). https://doi.org/10.1080/15435075.2013.867270 Fraser, A., Zhang, Z.S., Merle, G.E., et al.: Composite carbon nanotube microsphere coatings for use as electrode supports. Adv. Funct. Mater 28, 1803713 (2018). https://doi.org/10.1002/adfm.201803713 Ozden, A., Shahgaldi, S., Zhao, J., et al.: Degradations in porous components of a proton exchange membrane fuel cell under freeze-thaw cycles: morphology and microstructure effects. Int. J. Hydrog. Energy 45, 3618–3631 (2020). https://doi.org/10.1016/j.ijhydene.2018.10.209 Navaei Alvar, E., Zhou, B., Eichhorn, S.H.: Composite-supported Pt catalyst and electrosprayed cathode catalyst layer for polymer electrolyte membrane fuel cell. Int. J. Energy Res. 41, 1626–1641 (2017). https://doi.org/10.1002/er.3746 Raistrick, I.D.: Electrode Assembly for Use in a Solid Polymer Electrolyte Fuel Cell. US Patent 4,876,115 (1989) Wilson, M.S.: Membrane Catalyst Layer for Fuel Cells. US Patent 5,234,777 (1993) Wu, J.F., Yuan, X.Z., Martin, J.J., et al.: A review of PEM fuel cell durability: degradation mechanisms and mitigation strategies. J. Power Sources 184, 104–119 (2008). https://doi.org/10.1016/j.jpowsour.2008.06.006 Shahgaldi, S., Zhao, J., Alaefour, I., et al.: Investigation of catalytic vs reactant transport effect of catalyst layers on proton exchange membrane fuel cell performance. Fuel 208, 321–328 (2017). https://doi.org/10.1016/j.fuel.2017.07.035 Zhao, J., Shahgaldi, S., Ozden, A., et al.: Effect of catalyst deposition on electrode structure, mass transport and performance of polymer electrolyte membrane fuel cells. Appl. Energy 255, 113802 (2019). https://doi.org/10.1016/j.apenergy.2019.113802 Hwang, D.S., Park, C.H., Yi, S.C., et al.: Optimal catalyst layer structure of polymer electrolyte membrane fuel cell. Int. J. Hydrog. Energy 36, 9876–9885 (2011). https://doi.org/10.1016/j.ijhydene.2011.05.073 Shahgaldi, S., Alaefour, I., Zhao, J., et al.: Impact of ionomer in the catalyst layers on proton exchange membrane fuel cell performance under different reactant flows and pressures. Fuel 227, 35–41 (2018). https://doi.org/10.1016/j.fuel.2018.04.076 Shahgaldi, S., Alaefour, I., Unsworth, G., et al.: Development of a low temperature decal transfer method for the fabrication of proton exchange membrane fuel cells. Int. J. Hydrog. Energy 42, 11813–11822 (2017). https://doi.org/10.1016/j.ijhydene.2017.02.127 Strong, A., Thornberry, C., Beattie, S., et al.: Depositing catalyst layers in polymer electrolyte membrane fuel cells: a review. J. Fuel Cell Sci. Technol. 12, 064001 (2015). https://doi.org/10.1115/1.403196110.1115/1.4031961 Therdthianwong, A., Ekdharmasuit, P., Therdthianwong, S.: Fabrication and performance of membrane electrode assembly prepared by a catalyst-coated membrane method: effect of solvents used in a catalyst ink mixture. Energy Fuels 24, 1191–1196 (2010). https://doi.org/10.1021/ef901105k10.1021/ef901105k Zhao, J.: Catalyst Layers in Polymer Electrolyte Membrane Fuel Cells: Formation, Characterization and Performance. Dissertation, University of Waterloo (2019). https://uwspace.uwaterloo.ca/handle/10012/14425 Huang, D.C., Yu, P.J., Liu, F.J., et al.: Effect of dispersion solvent in catalyst ink on proton exchange membrane fuel cell performance. Int. J. Electrochem. Sci. 6, 2551–2565 (2011) Jeon, S., Lee, J.S., Rios, G.M., et al.: Effect of ionomer content and relative humidity on polymer electrolyte membrane fuel cell (PEMFC) performance of membrane-electrode assemblies (MEAs) prepared by decal transfer method. Int. J. Hydrog. Energy 35, 9678–9686 (2010). https://doi.org/10.1016/j.ijhydene.2010.06.044 Harris, T.A.L., Walczyk, D.F.: Development of a casting technique for membrane material used in high-temperature PEM fuel cells. J. Manuf. Process. 8, 8–20 (2006). https://doi.org/10.1016/S1526-6125(06)70097-4 Peng, X., Omasta, T., Rigdon, W., et al.: Fabrication of high performing PEMFC catalyst-coated membranes with a low cost air-assisted cylindrical liquid jets spraying system. J. Electrochem. Soc. 163, E407–E413 (2016). https://doi.org/10.1149/2.0981614jes Zhao, J., Ozden, A., Shahgaldi, S., et al.: Effect of Pt loading and catalyst type on the pore structure of porous electrodes in polymer electrolyte membrane (PEM) fuel cells. Energy 150, 69–76 (2018). https://doi.org/10.1016/j.energy.2018.02.134 Wu, S.D., Chou, C.P., Peng, R.G., et al.: A novel scrape-applied method for the manufacture of the membrane–electrode assembly of the fuel–cell system. Acta Mech. Sin. 25, 831–837 (2009). https://doi.org/10.1007/s10409-009-0261-7 Rajalakshmi, N., Dhathathreyan, K.S.: Catalyst layer in PEMFC electrodes: fabrication, characterisation and analysis. Chem. Eng. J. 129, 31–40 (2007). https://doi.org/10.1016/j.cej.2006.10.035 Wang, W.T., Chen, S.Q., Li, J.J., et al.: Fabrication of catalyst coated membrane with screen printing method in a proton exchange membrane fuel cell. Int. J. Hydrog. Energy 40, 4649–4658 (2015). https://doi.org/10.1016/j.ijhydene.2015.02.027 Shukla, S., Domican, K., Karan, K., et al.: Analysis of low platinum loading thin polymer electrolyte fuel cell electrodes prepared by inkjet printing. Electrochim. Acta 156, 289–300 (2015). https://doi.org/10.1016/j.electacta.2015.01.028 Millington, B., Whipple, V., Pollet, B.G.: A novel method for preparing proton exchange membrane fuel cell electrodes by the ultrasonic-spray technique. J. Power Sources 196, 8500–8508 (2011). https://doi.org/10.1016/j.jpowsour.2011.06.024 Vilambi Reddy, N.R.K., Anderson, E.B., Taylor, E.J.: High Utilization Supported Catalytic Metal-Containing Gas-Diffusion Electrode, Process for Making it, and Cells Utilizing it. US Patent 5,084,144 (1992) Chaparro, A.M., Ferreira-Aparicio, P., Folgado, M.A., et al.: Catalyst layers for proton exchange membrane fuel cells prepared by electrospray deposition on Nafion membrane. J. Power Sources 196, 4200–4208 (2011). https://doi.org/10.1016/j.jpowsour.2010.09.096 Chaparro, A.M., Gallardo, B., Folgado, M.A., et al.: PEMFC electrode preparation by electrospray: optimization of catalyst load and ionomer content. Catal. Today 143, 237–241 (2009). https://doi.org/10.1016/j.cattod.2008.12.003 Umeda, M., Kawaguchi, S., Uchida, I.: Characterization of membrane electrode assembly for fuel cells prepared by electrostatic spray deposition. Jpn. J. Appl. Phys. 45, 6049–6054 (2006). https://doi.org/10.1143/jjap.45.6049 Wang, X.H., Richey, F.W., Wujcik, K.H., et al.: Ultra-low platinum loadings in polymer electrolyte membrane fuel cell electrodes fabricated via simultaneous electrospinning/electrospraying method. J. Power Sources 264, 42–48 (2014). https://doi.org/10.1016/j.jpowsour.2014.04.052 Huang, J., Li, Z., Zhang, J.B.: Review of characterization and modeling of polymer electrolyte fuel cell catalyst layer: the blessing and curse of ionomer. Front. Energy 11, 334–364 (2017). https://doi.org/10.1007/s11708-017-0490-6 de las Heras, A., Vivas, F.J., Segura, F., et al.: From the cell to the stack. A chronological walk through the techniques to manufacture the PEFCs core. Renew. Sustain. Energy Rev. 96, 29–45 (2018). https://doi.org/10.1016/j.rser.2018.07.036 Gruber, D., Ponath, N., Müller, J., et al.: Sputter-deposited ultra-low catalyst loadings for PEM fuel cells. J. Power Sources 150, 67–72 (2005). https://doi.org/10.1016/j.jpowsour.2005.02.076 Caillard, A., Charles, C., Boswell, R., et al.: Improvement of the sputtered platinum utilization in proton exchange membrane fuel cells using plasma-based carbon nanofibres. J. Phys. D Appl. Phys. 41, 185307 (2008). https://doi.org/10.1088/0022-3727/41/18/185307 Saha, M.S., Gullá, A.F., Allen, R.J., et al.: High performance polymer electrolyte fuel cells with ultra-low Pt loading electrodes prepared by dual ion-beam assisted deposition. Electrochim. Acta 51, 4680–4692 (2006). https://doi.org/10.1016/j.electacta.2006.01.006 Fernandes, M.G., Thompson, D.A., Smeltzer, W.W., et al.: Electrocatalysis of Pt–Fe alloys produced by ion beam mixing. J. Mater. Res. 5, 98–108 (1990). https://doi.org/10.1557/jmr.1990.0098 Gullá, A.F., Saha, M.S., Allen, R.J., et al.: Dual ion-beam-assisted deposition as a method to obtain low loading-high performance electrodes for PEMFCs. Electrochem. Solid-State Lett. 8, A504–A508 (2005). https://doi.org/10.1149/1.2008887 Song, Z.X., Banis, M.N., Zhang, L., et al.: Origin of achieving the enhanced activity and stability of Pt electrocatalysts with strong metal-support interactions via atomic layer deposition. Nano Energy 53, 716–725 (2018). https://doi.org/10.1016/j.nanoen.2018.09.008 Cheng, N.C., Shao, Y.Y., Liu, J., et al.: Electrocatalysts by atomic layer deposition for fuel cell applications. Nano Energy 29, 220–242 (2016). https://doi.org/10.1016/j.nanoen.2016.01.016 Cheng, N.C., Liu, J., Banis, M.N., et al.: High stability and activity of Pt electrocatalyst on atomic layer deposited metal oxide/nitrogen-doped graphene hybrid support. Int. J. Hydrog. Energy 39, 15967–15974 (2014). https://doi.org/10.1016/j.ijhydene.2014.01.202 Zhang, L., Doyle-Davis, K., Sun, X.L.: Pt-Based electrocatalysts with high atom utilization efficiency: from nanostructures to single atoms. Energy Environ. Sci. 12, 492–517 (2019). https://doi.org/10.1039/c8ee02939c Yao, D.W., Yu, H.M., Song, W., et al.: Porous Pt–Ni nanobelt arrays with superior performance in H2/air atmosphere for proton exchange membrane fuel cells. ACS Appl. Energy Mater. 4, 10703–10712 (2021). https://doi.org/10.1021/acsaem.1c01432 Ozkan, S., Valle, F., Mazare, A., et al.: Optimized polymer electrolyte membrane fuel cell electrode using TiO2 nanotube arrays with well-defined spacing. ACS Appl. Nano Mater. 3, 4157–4170 (2020). https://doi.org/10.1021/acsanm.0c00325 Murata, S., Imanishi, M., Hasegawa, S., et al.: Vertically aligned carbon nanotube electrodes for high current density operating proton exchange membrane fuel cells. J. Power Sources 253, 104–113 (2014). https://doi.org/10.1016/j.jpowsour.2013.11.073 Kongkanand, A., Zhang, J.X., Liu, Z.Y., et al.: Degradation of PEMFC observed on NSTF electrodes. J. Electrochem. Soc. 161, F744–F753 (2014). https://doi.org/10.1149/2.074406jes Kongkanand, A., Owejan, J.E., Moose, S., et al.: Development of dispersed-catalyst/NSTF hybrid electrode. J. Electrochem. Soc. 159, F676–F682 (2012). https://doi.org/10.1149/2.023211jes Debe, M.K.: Tutorial on the fundamental characteristics and practical properties of nanostructured thin film (NSTF) catalysts. J. Electrochem. Soc. 160, F522–F534 (2013). https://doi.org/10.1149/2.049306jes Jiao, K., Li, X.G.: Water transport in polymer electrolyte membrane fuel cells. Prog. Energy Combust. Sci. 37, 221–291 (2011). https://doi.org/10.1016/j.pecs.2010.06.002 Dobson, P., Lei, C., Navessin, T., et al.: Characterization of the PEM fuel cell catalyst layer microstructure by nonlinear least-squares parameter estimation. J. Electrochem. Soc. 159, B514–B523 (2012). https://doi.org/10.1149/2.041205jes Yu, H.M., Schumacher, J.O., Zobel, M., et al.: Analysis of membrane electrode assembly (MEA) by environmental scanning electron microscope (ESEM). J. Power Sources 145, 216–222 (2005). https://doi.org/10.1016/j.jpowsour.2004.12.069 Inaba, M., Yamada, H., Tokunaga, J., et al.: Hydrogen peroxide formation as a degradation factor of polymer electrolyte fuel cells. ECS Trans. 1, 315–322 (2006). https://doi.org/10.1149/1.2214564 Roane, T.M., Pepper, I.L.: Microscopic techniques. In: Pepper, I.L., Gerba, C.P., Gentry, T.J. (eds.) Environmental Microbiology, pp. 177–193. Elsevier, Amsterdam (2015). https://doi.org/10.1016/B978-0-12-394626-3.00009-0 Zhao, J., Shahgaldi, S., Li, X.G., et al.: Experimental observations of microstructure changes in the catalyst layers of proton exchange membrane fuel cells under wet-dry cycles. J. Electrochem. Soc. 165, F3337–F3345 (2018). https://doi.org/10.1149/2.0391806jes Ozden, A., Shahgaldi, S., Zhao, J., et al.: Assessment of graphene as an alternative microporous layer material for proton exchange membrane fuel cells. Fuel 215, 726–734 (2018). https://doi.org/10.1016/j.fuel.2017.11.109 Park, Y.C., Tokiwa, H., Kakinuma, K., et al.: Effects of carbon supports on Pt distribution, ionomer coverage and cathode performance for polymer electrolyte fuel cells. J. Power Sources 315, 179–191 (2016). https://doi.org/10.1016/j.jpowsour.2016.02.091 Xu, L.C., Siedlecki, C.A.: Atomic force microscopy. In: Ducheyne, P. (ed.) Comprehensive Biomaterials, pp. 23–35. Elsevier, Amsterdam (2011). https://doi.org/10.1016/b978-0-08-055294-1.00083-0 Morawietz, T., Handl, M., Oldani, C., et al.: Quantitative in situ analysis of ionomer structure in fuel cell catalytic layers. ACS Appl. Mater. Interfaces 8, 27044–27054 (2016). https://doi.org/10.1021/acsami.6b07188 Zhang, X.X., Gao, Y., Ostadi, H., et al.: Modelling water intrusion and oxygen diffusion in a reconstructed microporous layer of PEM fuel cells. Int. J. Hydrog. Energy 39, 17222–17230 (2014). https://doi.org/10.1016/j.ijhydene.2014.08.027 Sabharwal, M., Pant, L.M., Putz, A., et al.: Analysis of catalyst layer microstructures: from imaging to performance. Fuel Cells 16, 734–753 (2016). https://doi.org/10.1002/fuce.201600008 Inoue, G., Yokoyama, K., Ooyama, J., et al.: Theoretical examination of effective oxygen diffusion coefficient and electrical conductivity of polymer electrolyte fuel cell porous components. J. Power Sources 327, 610–621 (2016). https://doi.org/10.1016/j.jpowsour.2016.07.107 Miller, B.D., Gan, J., Madden, J., et al.: Advantages and disadvantages of using a focused ion beam to prepare TEM samples from irradiated U–10Mo monolithic nuclear fuel. J. Nucl. Mater. 424, 38–42 (2012). https://doi.org/10.1016/j.jnucmat.2012.01.022 Moreno-Atanasio, R., Williams, R.A., Jia, X.D.: Combining X-ray microtomography with computer simulation for analysis of granular and porous materials. Particuology 8, 81–99 (2010). https://doi.org/10.1016/j.partic.2010.01.001 Hack, J., Heenan, T.M.M., Iacoviello, F., et al.: A structure and durability comparison of membrane electrode assembly fabrication methods: self-assembled versus hot-pressed. J. Electrochem. Soc. 165, F3045–F3052 (2018). https://doi.org/10.1149/2.0051806jes Epting, W.K., Gelb, J., Litster, S.: Resolving the three-dimensional microstructure of polymer electrolyte fuel cell electrodes using nanometer-scale X-ray computed tomography. Adv. Funct. Mater. 22, 555–560 (2012). https://doi.org/10.1002/adfm.201101525 Wu, J., Melo, L.G.A., Zhu, X.H., et al.: 4D imaging of polymer electrolyte membrane fuel cell catalyst layers by soft X-ray spectro-tomography. J. Power Sources 381, 72–83 (2018). https://doi.org/10.1016/j.jpowsour.2018.01.074 Anand, A., Savery, D., Hall, C.: Three-dimensional spatial and temporal temperature imaging in gel phantoms using backscattered ultrasound. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54, 23–31 (2007). https://doi.org/10.1109/TUFFC.2007.208 Lockwood, G.R., Talman, J.R., Brunke, S.S.: Real-time 3-D ultrasound imaging using sparse synthetic aperture beamforming. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 45, 980–988 (1998). https://doi.org/10.1109/58.710573 Takeuchi, M., Nishikage, T., Mor-Avi, V., et al.: Measurement of left ventricular mass by real-time three-dimensional echocardiography: validation against magnetic resonance and comparison with two-dimensional and M-mode measurements. J. Am. Soc. Echocardiogr. 21, 1001–1005 (2008). https://doi.org/10.1016/j.echo.2008.07.008 Zewail, A.H.: Four-dimensional electron microscopy. Science 328, 187–193 (2010). https://doi.org/10.1126/science.1166135 Campbell, S.: 4D, or not 4D: that is the question. Ultrasound Obstet. Gynecol. 19, 1–4 (2002). https://doi.org/10.1046/j.0960-7692.2002.00625.x Saida, T., Sekizawa, O., Ishiguro, N., et al.: 4D visualization of a cathode catalyst layer in a polymer electrolyte fuel cell by 3D laminography-XAFS. Angew. Chem. Int. Ed. 51, 10311–10314 (2012). https://doi.org/10.1002/anie.201204478 Singh, Y., White, R.T., Najm, M., et al.: Tracking the evolution of mechanical degradation in fuel cell membranes using 4D in situ visualization. J. Power Sources 412, 224–237 (2019). https://doi.org/10.1016/j.jpowsour.2018.11.049 White, R.T., Wu, A., Najm, M., et al.: 4D in situ visualization of electrode morphology changes during accelerated degradation in fuel cells by X-ray computed tomography. J. Power Sources 350, 94–102 (2017). https://doi.org/10.1016/j.jpowsour.2017.03.058 Giesche, H.: Mercury porosimetry: a general (practical) overview. Part. Part. Syst. Charact. 23, 9–19 (2006). https://doi.org/10.1002/ppsc.200601009 Rouquerol, J., Fairbridge, C., Everett, D., et al.: Recommendations for the characterization of porous solids. Pure Appl. Chem. 66, 1739–1958 (1994). https://doi.org/10.1351/pac199466081739 Lastoskie, C., Gubbins, K.E., Quirke, N.: Pore size distribution analysis of microporous carbons: a density functional theory approach. J. Phys. Chem. 97, 4786–4796 (1993). https://doi.org/10.1021/j100120a035 Yu, Z., Carter, R.N., Zhang, J.: Measurements of pore size distribution, porosity, effective oxygen diffusivity, and tortuosity of PEM fuel cell electrodes. Fuel Cells 12, 557–565 (2012). https://doi.org/10.1002/fuce.201200017 Shukla, S., Wei, F., Mandal, M., et al.: Determination of PEFC gas diffusion layer and catalyst layer porosity utilizing Archimedes principle. J. Electrochem. Soc. 166, F1142–F1147 (2019). https://doi.org/10.1149/2.0251915jes Yu, H.R., Roller, J.M., Mustain, W.E., et al.: Influence of the ionomer/carbon ratio for low-Pt loading catalyst layer prepared by reactive spray deposition technology. J. Power Sources 283, 84–94 (2015). https://doi.org/10.1016/j.jpowsour.2015.02.101 Zhao, J., Shahgaldi, S., Ozden, A., et al.: Geometric pore surface area and fractal dimension of catalyzed electrodes in polymer electrolyte membrane fuel cells. Int. J. Energy Res. 43, 3011–3019 (2019). https://doi.org/10.1002/er.4260 Rootare, H.M., Prenzlow, C.F.: Surface areas from mercury porosimeter measurements. J. Phys. Chem. 71, 2733–2736 (1967). https://doi.org/10.1021/j100867a057 Dullien, F.A.L.: Porous Media: Fluid Transport and Pore Structure. Academic Press, California (1979) Malekian, A., Salari, S., Tam, M., et al.: Compressive behaviour of thin catalyst layers. Part II - model development and validation. Int. J. Hydrog. Energy 44, 18461–18471 (2019). https://doi.org/10.1016/j.ijhydene.2019.04.135 Li, A.D., Han, M., Chan, S.H., et al.: Effects of hydrophobicity of the cathode catalyst layer on the performance of a PEM fuel cell. Electrochim. Acta 55, 2706–2711 (2010). https://doi.org/10.1016/j.electacta.2009.12.048 Volfkovich, Y.M., Bagotzky, V.S.: The method of standard porosimetry. 1. Principles and possibilities. J. Power Sources 48, 327–338 (1994). https://doi.org/10.1016/0378-7753(94)80029-4 Yu, H.M., Ziegler, C., Oszcipok, M., et al.: Hydrophilicity and hydrophobicity study of catalyst layers in proton exchange membrane fuel cells. Electrochim. Acta 51, 1199–1207 (2006). https://doi.org/10.1016/j.electacta.2005.06.036 Volfkovich, Y.M., Bagotzky, V.S.: The method of standard porosimetry. 2. Investigation of the formation of porous structures. J. Power Sources 48, 339–348 (1994). https://doi.org/10.1016/0378-7753(94)80030-8 Morrow, N.R., Harris, C.C.: Capillary equilibrium in porous materials. Soc. Pet. Eng. J. 5, 15–24 (1965). https://doi.org/10.2118/1011-pa Volfkovich, Y.M., Sakars, A.V., Volinsky, A.A.: Application of the standard porosimetry method for nanomaterials. Int. J. Nanotechnol. 2, 292–302 (2005). https://doi.org/10.1504/ijnt.2005.008066 Zhao, J., Shahgaldi, S., Alaefour, I., et al.: Pore structure and effective diffusion coefficient of catalyzed electrodes in polymer electrolyte membrane fuel cells. Int. J. Hydrog. Energy 43, 3776–3785 (2018). https://doi.org/10.1016/j.ijhydene.2018.01.019 Volfkovich, Y.M., Sosenkin, V.E., Bagotsky, V.S.: Structural and wetting properties of fuel cell components. J. Power Sources 195, 5429–5441 (2010). https://doi.org/10.1016/j.jpowsour.2010.03.002 Park, S., Popov, B.N.: Effect of cathode GDL characteristics on mass transport in PEM fuel cells. Fuel 88, 2068–2073 (2009). https://doi.org/10.1016/j.fuel.2009.06.020 Bonifácio, R.N., Neto, A.O., Linardi, M.: Influence of the relative volumes between catalyst and Nafion ionomer in the catalyst layer efficiency. Int. J. Hydrog. Energy 39, 14680–14689 (2014). https://doi.org/10.1016/j.ijhydene.2014.07.004 Fairweather, J.D., Cheung, P., St-Pierre, J., et al.: A microfluidic approach for measuring capillary pressure in PEMFC gas diffusion layers. Electrochem. Commun. 9, 2340–2345 (2007). https://doi.org/10.1016/j.elecom.2007.06.042 Brunauer, S., Emmett, P.H., Teller, E.: Adsorption of gases in multimolecular layers. J. Am. Chem. Soc. 60, 309–319 (1938). https://doi.org/10.1021/ja01269a023 von Kraemer, S., Puchner, M., Jannasch, P., et al.: Gas diffusion electrodes and membrane electrode assemblies based on a sulfonated polysulfone for high-temperature PEMFC. J. Electrochem. Soc. 153, A2077–A2084 (2006). https://doi.org/10.1149/1.2335979 Giesche, H., Unger, K.K., Müller, U., et al.: Hysteresis in nitrogen sorption and mercury porosimetry on mesoporous model adsorbents made of aggregated monodisperse silica spheres. Colloids Surf. 37, 93–113 (1989). https://doi.org/10.1016/0166-6622(89)80109-X Rashapov, R.R., Unno, J., Gostick, J.T.: Characterization of PEMFC gas diffusion layer porosity. J. Electrochem. Soc. 162, F603–F612 (2015). https://doi.org/10.1149/2.0921506jes Drake, L.C.: Pore-size distribution in porous materials. Ind. Eng. Chem. 41, 780–785 (1949). https://doi.org/10.1021/ie50472a024 Abell, A.B., Willis, K.L., Lange, D.A.: Mercury intrusion porosimetry and image analysis of cement-based materials. J. Colloid Interface Sci. 211, 39–44 (1999). https://doi.org/10.1006/jcis.1998.5986 Yan, Z., Chen, C., Fan, P.X., et al.: Pore structure characterization of ten typical rocks in China. Electron. J. Geotech. Eng. 20, 479–494 (2015) Gregg, S.J., Sing, K.S.W., Salzberg, H.W.: Adsorption surface area and porosity. J. Electrochem. Soc. 114, 279C (1967). https://doi.org/10.1149/1.2426447 Lee, Y., Jeong, J., Youn, I.J., et al.: Modified liquid displacement method for determination of pore size distribution in porous membranes. J. Membr. Sci. 130, 149–156 (1997). https://doi.org/10.1016/S0376-7388(97)00017-3 Dubinin, M.M., Plavnik, G.M.: Microporous structures of carbonaceous adsorbents. Carbon 6, 183–192 (1968). https://doi.org/10.1016/0008-6223(68)90302-3 Anovitz, L.M., Cole, D.R.: Characterization and analysis of porosity and pore structures. Rev. Mineral. Geochem. 80, 61–164 (2015). https://doi.org/10.2138/rmg.2015.80.04 Mezedur, M.M., Kaviany, M., Moore, W.: Effect of pore structure, randomness and size on effective mass diffusivity. Aiche J. 48, 15–24 (2002). https://doi.org/10.1002/aic.690480104 Yu, K., Groom, D.J., Wang, X., et al.: Degradation mechanisms of platinum nanoparticle catalysts in proton exchange membrane fuel cells: the role of particle size. Chem. Mat. 26, 5540–5548 (2014). https://doi.org/10.1021/cm501867c Neimark, A.V., Ravikovitch, P.I.: Capillary condensation in MMS and pore structure characterization. Microporous Mesoporous Mater. 44, 697–707 (2001). https://doi.org/10.1016/S1387-1811(01)00251-7 Majlan, E.H., Rohendi, D., Daud, W.R.W., et al.: Electrode for proton exchange membrane fuel cells: a review. Renew. Sustain. Energy Rev. 89, 117–134 (2018). https://doi.org/10.1016/j.rser.2018.03.007 Bock, C., Blakely, M.A., MacDougall, B.: Characteristics of adsorbed CO and CH3OH oxidation reactions for complex Pt/Ru catalyst systems. Electrochim. Acta 50, 2401–2414 (2005). https://doi.org/10.1016/j.electacta.2004.10.057 Shao, Y.Y., Yin, G.P., Gao, Y.Z.: Understanding and approaches for the durability issues of Pt-based catalysts for PEM fuel cell. J. Power Sources 171, 558–566 (2007). https://doi.org/10.1016/j.jpowsour.2007.07.004 Bi, W., Fuller, T.F.: Temperature effects on PEM fuel cells Pt/C catalyst degradation. J. Electrochem. Soc. 155, B215–B221 (2008). https://doi.org/10.1149/1.2819680 Kusoglu, A., Weber, A.Z.: New insights into perfluorinated sulfonic-acid ionomers. Chem. Rev. 117, 987–1104 (2017). https://doi.org/10.1021/acs.chemrev.6b00159 Rahnavard, A., Rowshanzamir, S., Parnian, M.J., et al.: The effect of sulfonated poly (ether ether ketone) as the electrode ionomer for self-humidifying nanocomposite proton exchange membrane fuel cells. Energy 82, 746–757 (2015). https://doi.org/10.1016/j.energy.2015.01.086 Chung, C.G., Kim, L., Sung, Y.W., et al.: Degradation mechanism of electrocatalyst during long-term operation of PEMFC. Int. J. Hydrog. Energy 34, 8974–8981 (2009). https://doi.org/10.1016/j.ijhydene.2009.08.094 He, M.S., Liu, B.L., Chernov, A.I., et al.: Growth mechanism of single-walled carbon nanotubes on iron–copper catalyst and chirality studies by electron diffraction. Chem. Mater. 24, 1796–1801 (2012). https://doi.org/10.1021/cm300308k Sharabi, R., Wijsboom, Y.H., Borchtchoukova, N., et al.: Methodology for the design of accelerated stress tests for non-precious metal catalysts in fuel cell cathodes. J. Power Sources 335, 56–64 (2016). https://doi.org/10.1016/j.jpowsour.2016.10.032 Coats, A.W., Redfern, J.P.: Thermogravimetric analysis. A Rev. Anal. 88, 906–924 (1963). https://doi.org/10.1039/an9638800906 Baturina, O.A., Aubuchon, S.R., Wynne, K.J.: Thermal stability in air of Pt/C catalysts and PEM fuel cell catalyst layers. Chem. Mater. 18, 1498–1504 (2006). https://doi.org/10.1021/cm052660e Woo, Y., Oh, S.Y., Kang, Y.S., et al.: Synthesis and characterization of sulfonated polyimide membranes for direct methanol fuel cell. J. Membr. Sci. 220, 31–45 (2003). https://doi.org/10.1016/S0376-7388(03)00185-6 Daş, E., Alkan Gürsel, S., Işıkel Şanlı, L., et al.: Thermodynamically controlled Pt deposition over graphene nanoplatelets: effect of Pt loading on PEM fuel cell performance. Int. J. Hydrog. Energy 42, 19246–19256 (2017). https://doi.org/10.1016/j.ijhydene.2017.06.108 Huang, C.D., Seng Tan, K., Lin, J.Y., et al.: XRD and XPS analysis of the degradation of the polymer electrolyte in H2–O2 fuel cell. Chem. Phys. Lett. 371, 80–85 (2003). https://doi.org/10.1016/S0009-2614(03)00259-8 Goodenough, J.B., Hamnett, A., Kennedy, B.J., et al.: XPS investigation of platinized carbon electrodes for the direct methanol air fuel cell. Electrochim. Acta 32, 1233–1238 (1987). https://doi.org/10.1016/0013-4686(87)80041-5 Ye, L.C., Gao, Y., Zhu, S.Y., et al.: A Pt content and pore structure gradient distributed catalyst layer to improve the PEMFC performance. Int. J. Hydrog. Energy 42, 7241–7245 (2017). https://doi.org/10.1016/j.ijhydene.2016.11.002 Ponomarev, I.I., Zhigalina, O.M., Skupov, K.M., et al.: Preparation and thermal treatment influence on Pt-decorated electrospun carbon nanofiber electrocatalysts. RSC Adv. 9, 27406–27418 (2019). https://doi.org/10.1039/C9RA05910E Niu, Z.Q., Becknell, N., Yu, Y., et al.: Anisotropic phase segregation and migration of Pt in nanocrystals en route to nanoframe catalysts. Nat. Mater. 15, 1188–1194 (2016). https://doi.org/10.1038/nmat4724 Zamel, N., Li, X.G.: Effect of contaminants on polymer electrolyte membrane fuel cells. Prog. Energy Combust. Sci. 37, 292–329 (2011). https://doi.org/10.1016/j.pecs.2010.06.003 Zhao, J., Shahgaldi, S., Alaefour, I., et al.: Gas permeability of catalyzed electrodes in polymer electrolyte membrane fuel cells. Appl. Energy 209, 203–210 (2018). https://doi.org/10.1016/j.apenergy.2017.10.087 Chapman, S., Cowling, T.G., Park, D.: The mathematical theory of non-uniform gases. Am. J. Phys. 30, 389 (1962). https://doi.org/10.1119/1.1942035 Crank, J.: The Mathematics of Diffusion. Oxford University Press, New York (1979) Cussler, E.L.: Multicomponent Diffusion. Elsevier, Amsterdam (1976) Wu, H., Li, X.G., Berg, P.: Numerical analysis of dynamic processes in fully humidified PEM fuel cells. Int. J. Hydrog. Energy 32, 2022–2031 (2007). https://doi.org/10.1016/j.ijhydene.2006.09.046 Kim, Y., Gostick, J.T.: Measuring effective diffusivity in porous media with a gasket-free, radial arrangement. Int. J. Heat Mass Transf. 129, 1023–1030 (2019). https://doi.org/10.1016/j.ijheatmasstransfer.2018.10.054 Mangal, P., Pant, L.M., Carrigy, N., et al.: Experimental study of mass transport in PEMFCs: through plane permeability and molecular diffusivity in GDLs. Electrochim. Acta 167, 160–171 (2015). https://doi.org/10.1016/j.electacta.2015.03.100 Shen, J., Zhou, J.Q., Astrath, N.G.C., et al.: Measurement of effective gas diffusion coefficients of catalyst layers of PEM fuel cells with a Loschmidt diffusion cell. J. Power Sources 196, 674–678 (2011). https://doi.org/10.1016/j.jpowsour.2010.07.086 Pant, L.M., Mitra, S.K., Secanell, M.: Absolute permeability and Knudsen diffusivity measurements in PEMFC gas diffusion layers and micro porous layers. J. Power Sources 206, 153–160 (2012). https://doi.org/10.1016/j.jpowsour.2012.01.099 Xue, Q., Zhang, R.F., Yang, D.J., et al.: Effect of ionomer content on cathode catalyst layer for PEMFC via molecular dynamics simulations and experiments. Int. J. Hydrog. Energy 47, 23335–23347 (2022). https://doi.org/10.1016/j.ijhydene.2022.05.122 Choo, M.J., Oh, K.H., Park, J.K., et al.: Analysis of oxygen transport in cathode catalyst layer of low-Pt-loaded fuel cells. ChemElectroChem 2, 382–388 (2015). https://doi.org/10.1002/celc.201402354 Nonoyama, N., Okazaki, S., Weber, A.Z., et al.: Analysis of oxygen-transport diffusion resistance in proton-exchange-membrane fuel cells. J. Electrochem. Soc. 158, B416 (2011). https://doi.org/10.1149/1.3546038 Andisheh-Tadbir, M., El Hannach, M., Kjeang, E., et al.: An analytical relationship for calculating the effective diffusivity of micro-porous layers. Int. J. Hydrog. Energy 40, 10242–10250 (2015). https://doi.org/10.1016/j.ijhydene.2015.06.067 Satterfield, C.N., Sherwood, T.K.: The Role of Diffusion in Catalysis. Addison-Wesley, Massachusetts (1963) Dong, L.: Accuracy Improvement for Measurement of Gas Diffusivity Through Thin Porous Media. Dissertation, University of Waterloo (2012). https://uwspace.uwaterloo.ca/handle/10012/6967 Bruggeman, D.A.G.: Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen. III. Die elastischen Konstanten der quasiisotropen Mischkörper aus isotropen Substanzen. Ann. Phys. 421, 160–178 (1937). https://doi.org/10.1002/andp.19374210205 Zamel, N., Li, X.G., Shen, J.: Correlation for the effective gas diffusion coefficient in carbon paper diffusion media. Energy Fuels 23, 6070–6078 (2009). https://doi.org/10.1021/ef900653x Neale, G.H., Nader, W.K.: Prediction of transport processes within porous media: diffusive flow processes within an homogeneous swarm of spherical particles. AIChE J. 19, 112–119 (1973). https://doi.org/10.1002/aic.690190116 Tomadakis, M.M., Sotirchos, S.V.: Ordinary and transition regime diffusion in random fiber structures. Aiche J. 39, 397–412 (1993). https://doi.org/10.1002/aic.690390304 Das, P.K., Li, X.G., Liu, Z.S.: Effective transport coefficients in PEM fuel cell catalyst and gas diffusion layers: beyond Bruggeman approximation. Appl. Energy 87, 2785–2796 (2010). https://doi.org/10.1016/j.apenergy.2009.05.006 Mitani, M.: Geometric factor for diffusion in porous media. J. Chem. Eng. Jpn. 17, 441–443 (1984). https://doi.org/10.1252/jcej.17.441 Zamel, N., Li, X.G.: Effective transport properties for polymer electrolyte membrane fuel cells: with a focus on the gas diffusion layer. Prog. Energy Combust. Sci. 39, 111–146 (2013). https://doi.org/10.1016/j.pecs.2012.07.002 Hussaini, I.S., Wang, C.Y.: Measurement of relative permeability of fuel cell diffusion media. J. Power Sources 195, 3830–3840 (2010). https://doi.org/10.1016/j.jpowsour.2009.12.105 Taira, H., Liu, H.T.: In-situ measurements of GDL effective permeability and under-land cross-flow in a PEM fuel cell. Int. J. Hydrog. Energy 37, 13725–13730 (2012). https://doi.org/10.1016/j.ijhydene.2012.03.030 Ismail, M.S., Damjanovic, T., Hughes, K., et al.: Through-plane permeability for untreated and PTFE-treated gas diffusion layers in proton exchange membrane fuel cells. J. Fuel Cell Sci. Technol. 7, 051016 (2010). https://doi.org/10.1115/1.4000685 Tomadakis, M.M., Robertson, T.J.: Viscous permeability of random fiber structures: comparison of electrical and diffusional estimates with experimental and analytical results. J. Compos. Mater. 39, 163–188 (2005). https://doi.org/10.1177/0021998305046438 Ismail, M.S., Hughes, K.J., Ingham, D.B., et al.: Effects of anisotropic permeability and electrical conductivity of gas diffusion layers on the performance of proton exchange membrane fuel cells. Appl. Energy 95, 50–63 (2012). https://doi.org/10.1016/j.apenergy.2012.02.003 Springer, D.S., Loaiciga, H.A., Cullen, S.J., et al.: Air permeability of porous materials under controlled laboratory conditions. Groundwater 36, 558–565 (1998). https://doi.org/10.1111/j.1745-6584.1998.tb02829.x Klinkenberg, L.J., Shell, D.C.: The permeability of porous media to liquids and gases. Drill. Prod. Pract. (2012). https://doi.org/10.5510/ogp20120200114 Chen, Y.P., Shen, C.Q., Lu, P.F., et al.: Role of pore structure on liquid flow behaviors in porous media characterized by fractal geometry. Chem. Eng. Process. Process. Intensif. 87, 75–80 (2015). https://doi.org/10.1016/j.cep.2014.11.014 Yuan, W., Tang, Y., Yang, X.J., et al.: Porous metal materials for polymer electrolyte membrane fuel cells: a review. Appl. Energy 94, 309–329 (2012). https://doi.org/10.1016/j.apenergy.2012.01.073 Gostick, J.T., Fowler, M.W., Pritzker, M.D., et al.: In-plane and through-plane gas permeability of carbon fiber electrode backing layers. J. Power Sources 162, 228–238 (2006). https://doi.org/10.1016/j.jpowsour.2006.06.096 Feser, J.P., Prasad, A.K., Advani, S.G.: Experimental characterization of in-plane permeability of gas diffusion layers. J. Power Sources 162, 1226–1231 (2006). https://doi.org/10.1016/j.jpowsour.2006.07.058 Kim, G.S., Sui, P.C., Shah, A.A., et al.: Reduced-dimensional models for straight-channel proton exchange membrane fuel cells. J. Power Sources 195, 3240–3249 (2010). https://doi.org/10.1016/j.jpowsour.2009.11.110 Li, Y.B., Zhou, Z.F., Liu, X.L., et al.: Modeling of PEM fuel cell with thin MEA under low humidity operating condition. Appl. Energy 242, 1513–1527 (2019). https://doi.org/10.1016/j.apenergy.2019.03.189 Vasile, N.S., Monteverde Videla, A.H.A., Specchia, S.: Effects of the current density distribution on a single-cell DMFC by tuning the anode catalyst in layers of gradual loadings: modelling and experimental approach. Chem. Eng. J. 322, 722–741 (2017). https://doi.org/10.1016/j.cej.2017.04.060 Zhang, G.B., Fan, L.H., Sun, J., et al.: A 3D model of PEMFC considering detailed multiphase flow and anisotropic transport properties. Int. J. Heat Mass Transf. 115, 714–724 (2017). https://doi.org/10.1016/j.ijheatmasstransfer.2017.07.102 Raj, A., Shamim, T.: Investigation of the effect of multidimensionality in PEM fuel cells. Energy Convers. Manag. 86, 443–452 (2014). https://doi.org/10.1016/j.enconman.2014.04.088 Tomadakis, M.M., Sotirchos, S.V.: Effective Kundsen diffusivities in structures of randomly overlapping fibers. Aiche J. 37, 74–86 (1991). https://doi.org/10.1002/aic.690370107 Tomadakis, M.M., Sotirchos, S.V.: Knudsen diffusivities and properties of structures of unidirectional fibers. Aiche J. 37, 1175–1186 (1991). https://doi.org/10.1002/aic.690370807 Bird, R.B.: Transport phenomena. Appl. Mech. Rev. 55, R1–R4 (2002). https://doi.org/10.1115/1.1424298 Rumpf, H.C.H., Gupte, A.R.: Einflüsse der porosität und korngrößenverteilung im widerstandsgesetz der porenströmung. Chem. Ing. Techn. 43, 367–375 (1971). https://doi.org/10.1002/cite.330430610 Zamora, H., Cañizares, P., Rodrigo, M.A., et al.: Improving of micro porous layer based on advanced carbon materials for high temperature proton exchange membrane fuel cell electrodes. Fuel Cells 15, 375–383 (2015). https://doi.org/10.1002/fuce.201400139 Honarpour, M.M.: Relative Permeability of Petroleum Reservoirs. CRC Press, Boca Raton (2017). https://doi.org/10.1201/9781351076326 Ye, Q., Nguyen, T.V.: Three-dimensional simulation of liquid water distribution in a PEMFC with experimentally measured capillary functions. J. Electrochem. Soc. 154, B1242 (2007). https://doi.org/10.1149/1.2783775 Gostick, J.T., Fowler, M.W., Ioannidis, M.A., et al.: Capillary pressure and hydrophilic porosity in gas diffusion layers for polymer electrolyte fuel cells. J. Power Sources 156, 375–387 (2006). https://doi.org/10.1016/j.jpowsour.2005.05.086 Leverett, M.C.: Capillary behavior in porous solids. Trans. AIME 142, 152–169 (1941). https://doi.org/10.2118/941152-g Wang, Y., Chen, K.S., Mishler, J., et al.: A review of polymer electrolyte membrane fuel cells: technology, applications, and needs on fundamental research. Appl. Energy 88, 981–1007 (2011). https://doi.org/10.1016/j.apenergy.2010.09.030 Kumbur, E.C., Sharp, K.V., Mench, M.M.: Validated leverett approach for multiphase flow in PEFC diffusion media. J. Electrochem. Soc. 154, B1315 (2007). https://doi.org/10.1149/1.2784286 Park, J.: Serial Compression Effects on Porosity, Diffusion, Permeability, and Water Droplet Contact Angle of the Gas Diffusion Layer in Polymer Electrolyte Membrane Fuel Cells. Dissertation, University of Waterloo (2020). Ma, L., Liu, Z.S., Huang, C., et al.: Microstructure changes induced by capillary condensation in catalyst layers of PEM fuel cells. Int. J. Hydrog. Energy 35, 12182–12190 (2010). https://doi.org/10.1016/j.ijhydene.2010.08.072 Wood, D.L., Rulison, C., Borup, R.L.: Surface properties of PEMFC gas diffusion layers. J. Electrochem. Soc. 157, B195–B206 (2010). https://doi.org/10.1149/1.3261850 Arvay, A., Yli-Rantala, E., Liu, C.H., et al.: Characterization techniques for gas diffusion layers for proton exchange membrane fuel cells: a review. J. Power Sources 213, 317–337 (2012). https://doi.org/10.1016/j.jpowsour.2012.04.026 Bazylak, A.: Liquid water visualization in PEM fuel cells: a review. Int. J. Hydrog. Energy 34, 3845–3857 (2009). https://doi.org/10.1016/j.ijhydene.2009.02.084 Abbou, S., Tajiri, K., Alofari, K.T., et al.: Capillary penetration method for measuring wetting properties of carbon ionomer films for proton exchange membrane fuel cell (PEMFC) applications. J. Electrochem. Soc. 166, F3227–F3233 (2019). https://doi.org/10.1149/2.0271907jes Wang, M., Chen, M., Yang, Z.Y., et al.: High-performance and durable cathode catalyst layer with hydrophobic C@PTFE particles for low-Pt loading membrane assembly electrode of PEMFC. Energy Convers. Manag. 191, 132–140 (2019). https://doi.org/10.1016/j.enconman.2019.04.014 Liu, G.C., Ye, F., Xiong, L.Y., et al.: Cathode catalyst layer with nanofiber microstructure for direct methanol fuel cells. Energy Convers. Manag. 218, 113013 (2020). https://doi.org/10.1016/j.enconman.2020.113013 Fang, S.Y., Teoh, L.G., Huang, R.H., et al.: Effect of adding zinc oxide particles to the anode catalyst layer on the performance of a proton-exchange membrane fuel cell. J. Electron. Mater. 43, 3601–3610 (2014). https://doi.org/10.1007/s11664-014-3246-7 Wenzel, R.N.: Resistance of solid surfaces to wetting by water. Ind. Eng. Chem. 28, 988–994 (1936). https://doi.org/10.1021/ie50320a024 Cassie, A.B.D., Baxter, S.: Wettability of porous surfaces. Trans. Faraday Soc. 40, 546–551 (1944). https://doi.org/10.1039/tf9444000546 Bock, R., Karoliussen, H., Pollet, B.G., et al.: The influence of graphitization on the thermal conductivity of catalyst layers and temperature gradients in proton exchange membrane fuel cells. Int. J. Hydrog. Energy 45, 1335–1342 (2020). https://doi.org/10.1016/j.ijhydene.2018.10.221 Khandelwal, M., Mench, M.M.: Direct measurement of through-plane thermal conductivity and contact resistance in fuel cell materials. J. Power Sources 161, 1106–1115 (2006). https://doi.org/10.1016/j.jpowsour.2006.06.092 Ahadi, M., Tam, M., Saha, M.S., et al.: Thermal conductivity of catalyst layer of polymer electrolyte membrane fuel cells. Part 1. Experimental study. J. Power Sources 354, 207–214 (2017). https://doi.org/10.1016/j.jpowsour.2017.02.016 Burheim, O.S., Su, H.N., Hauge, H.H., et al.: Study of thermal conductivity of PEM fuel cell catalyst layers. Int. J. Hydrog. Energy 39, 9397–9408 (2014). https://doi.org/10.1016/j.ijhydene.2014.03.206 Astrath, N.G.C., Astrath, F.B.G., Shen, J., et al.: An open-photoacoustic-cell method for thermal characterization of a two-layer system. J. Appl. Phys. 107, 043514 (2010). https://doi.org/10.1063/1.3310319 Rowe, A., Li, X.G.: Mathematical modeling of proton exchange membrane fuel cells. J. Power Sources 102, 82–96 (2001). https://doi.org/10.1016/S0378-7753(01)00798-4 Wu, H., Li, X.G., Berg, P.: On the modeling of water transport in polymer electrolyte membrane fuel cells. Electrochim. Acta 54, 6913–6927 (2009). https://doi.org/10.1016/j.electacta.2009.06.070 Weber, A.Z., Newman, J.: Modeling transport in polymer-electrolyte fuel cells. Chem. Rev. 104, 4679–4726 (2004). https://doi.org/10.1021/cr020729l Pant, L.M., Gerhardt, M.R., Macauley, N., et al.: Along-the-channel modeling and analysis of PEFCs at low stoichiometry: development of a 1+2D model. Electrochim. Acta 326, 134963 (2019). https://doi.org/10.1016/j.electacta.2019.134963 Gurau, V., Liu, H.T., Kakaç, S.: Two-dimensional model for proton exchange membrane fuel cells. Aiche J. 44, 2410–2422 (1998). https://doi.org/10.1002/aic.690441109 Barbir, F.: Fuel cell electrochemistry. In: Barbir, F. (ed.) PEM Fuel Cells: Theory and Practice, pp. 33–72. Elsevier, Amsterdam (2005). https://doi.org/10.1016/b978-012078142-3/50004-5 Wilberforce, T., El-Hassan, Z., Khatib, F.N., et al.: Modelling and simulation of proton exchange membrane fuel cell with serpentine bipolar plate using MATLAB. Int. J. Hydrog. Energy 42, 25639–25662 (2017). https://doi.org/10.1016/j.ijhydene.2017.06.091 Guidelli, R., Compton, R.G., Feliu, J.M., et al.: Definition of the transfer coefficient in electrochemistry (IUPAC recommendations 2014). Pure Appl. Chem. 86, 259–262 (2014). https://doi.org/10.1515/pac-2014-5025 Springer, T.E., Zawodzinski, T.A., Gottesfeld, S.: Polymer electrolyte fuel cell model. J. Electrochem. Soc. 138, 2334–2342 (1991). https://doi.org/10.1149/1.2085971 Um, S., Wang, C.Y., Chen, K.S.: Computational fluid dynamics modeling of proton exchange membrane fuel cells. J. Electrochem. Soc. 147, 4485–4493 (2000). https://doi.org/10.1149/1.1394090 Li, G.C., Pickup, P.G.: Ionic conductivity of PEMFC electrodes. J. Electrochem. Soc. 150, C745–C752 (2003). https://doi.org/10.1149/1.1611493 Haghayegh, M., Eikani, M.H., Rowshanzamir, S.: Modeling and simulation of a proton exchange membrane fuel cell using computational fluid dynamics. Int. J. Hydrog. Energy 42, 21944–21954 (2017). https://doi.org/10.1016/j.ijhydene.2017.07.098 Goshtasbi, A., Pence, B.L., Ersal, T.: A real-time pseudo-2D bi-domain model of PEM fuel cells for automotive applications. In: ASME 2017 dynamic systems and control conference, Tysons, Virginia (2017). Doi:https://doi.org/10.1115/DSCC2017-5053 Jiang, Y., Yang, Z.R., Jiao, K., et al.: Sensitivity analysis of uncertain parameters based on an improved proton exchange membrane fuel cell analytical model. Energy Convers. Manag. 164, 639–654 (2018). https://doi.org/10.1016/j.enconman.2018.03.002 Parsons, R.: Electrode reaction orders, transfer coefficients and rate constants: amplification of definitions and recommendations for publication of parameters. Electrochim. Acta 26, 1869–1874 (1981). https://doi.org/10.1016/0013-4686(81)85177-8 Kulikovsky, A.A., Divisek, J., Kornyshev, A.A.: Modeling the cathode compartment of polymer electrolyte fuel cells: dead and active reaction zones. J. Electrochem. Soc. 146, 3981–3991 (1999). https://doi.org/10.1149/1.1392580 Le, A.D., Zhou, B.: A general model of proton exchange membrane fuel cell. J. Power Sources 182, 197–222 (2008). https://doi.org/10.1016/j.jpowsour.2008.03.047 Garrick, T.R., Moylan, T., Carpenter, M., et al.: Electrochemically active surface area measurement of aged Pt alloy catalysts in PEM fuel cells by CO stripping. J. Electrochem. Soc. 164, F55–F59 (2017). https://doi.org/10.1149/2.0381702jes Kneer, A., Jankovic, J., Susac, D., et al.: Correlation of changes in electrochemical and structural parameters due to voltage cycling induced degradation in PEM fuel cells. J. Electrochem. Soc. 165, F3241–F3250 (2018). https://doi.org/10.1149/2.0271806jes Migliardini, F., Corbo, P.: CV and EIS study of hydrogen fuel cell durability in automotive applications. Int. J. Electrochem. Sci. 8, 11033–11047 (2013) Savinell, R.F., Zeller, R.L., Adams, J.A.: Electrochemically active surface area: voltammetric charge correlations for ruthenium and iridium dioxide electrodes. J. Electrochem. Soc. 137, 489–494 (1990). https://doi.org/10.1149/1.2086468 Elgrishi, N., Rountree, K.J., McCarthy, B.D., et al.: A practical beginner’s guide to cyclic voltammetry. J. Chem. Educ. 95, 197–206 (2018). https://doi.org/10.1021/acs.jchemed.7b00361 Mayrhofer, K.J.J., Strmcnik, D., Blizanac, B.B., et al.: Measurement of oxygen reduction activities via the rotating disc electrode method: from Pt model surfaces to carbon-supported high surface area catalysts. Electrochim. Acta 53, 3181–3188 (2008). https://doi.org/10.1016/j.electacta.2007.11.057 Park, Y.C., Kakinuma, K., Uchida, M., et al.: Deleterious effects of interim cyclic voltammetry on Pt/carbon black catalyst degradation during start-up/shutdown cycling evaluation. Electrochim. Acta 123, 84–92 (2014). https://doi.org/10.1016/j.electacta.2013.12.120 Koponen, U., Kumpulainen, H., Bergelin, M., et al.: Characterization of Pt-based catalyst materials by voltammetric techniques. J. Power Sources 118, 325–333 (2003). https://doi.org/10.1016/S0378-7753(03)00079-X Iden, H., Ohma, A.: An in situ technique for analyzing ionomer coverage in catalyst layers. J. Electroanal. Chem. 693, 34–41 (2013). https://doi.org/10.1016/j.jelechem.2013.01.026 Reid, O., Saleh, F.S., Easton, E.B.: Determining electrochemically active surface area in PEM fuel cell electrodes with electrochemical impedance spectroscopy and its application to catalyst durability. Electrochim. Acta 114, 278–284 (2013). https://doi.org/10.1016/j.electacta.2013.10.050 Badduri, S.R., Srinivasulu, G.N., Rao, S.S.: Experimental analysis of PEM fuel cell performance using lung channel design bipolar plate. Int. J. Green Energy 16, 1591–1601 (2019). https://doi.org/10.1080/15435075.2019.1677238 Ismail, M.S., Damjanovic, T., Ingham, D.B., et al.: Effect of polytetrafluoroethylene-treatment and microporous layer-coating on the electrical conductivity of gas diffusion layers used in proton exchange membrane fuel cells. J. Power Sources 195, 2700–2708 (2010). https://doi.org/10.1016/j.jpowsour.2009.11.069 Tranter, T.G., Tam, M., Gostick, J.T.: The effect of cracks on the in-plane electrical conductivity of PEFC catalyst layers. Electroanalysis 31, 619–623 (2019). https://doi.org/10.1002/elan.201800553 Pauw, I.J.V.D.: A method of measuring specific resistivity and Hall effect of discs of arbitrary shape. Philips Res. Rep.174–182 (1991). https://aki.issp.u-tokyo.ac.jp/okano/WalWiki/etc/VDP_PRR_13_1.pdf Sadeghifar, H.: In-plane and through-plane electrical conductivities and contact resistances of a Mercedes-Benz catalyst-coated membrane, gas diffusion and micro-porous layers and a Ballard graphite bipolar plate: impact of humidity, compressive load and polytetrafluoroethylene. Energy Convers. Manag. 154, 191–202 (2017). https://doi.org/10.1016/j.enconman.2017.10.060 Suzuki, T., Murata, H., Hatanaka, T., et al.: Analysis of the catalyst layer of polymer electrolyte fuel cells. R&D Rev. Toyota CRDL 39, 33–38 (2003) Li, C.H., Liu, J.H., Guan, R., et al.: Effect of heating and stretching membrane on ionic conductivity of sulfonated poly(phenylene oxide). J. Membr. Sci. 287, 180–186 (2007). https://doi.org/10.1016/j.memsci.2006.10.015 Kuwertz, R., Kirstein, C., Turek, T., et al.: Influence of acid pretreatment on ionic conductivity of Nafion® membranes. J. Membr. Sci. 500, 225–235 (2016). https://doi.org/10.1016/j.memsci.2015.11.022 Zhai, Y.F., Ge, J.J., St-Pierre, J.: The ionic conductivity and catalyst activity effects of acetonitrile on proton exchange membrane fuel cells. Electrochem. Commun. 66, 49–52 (2016). https://doi.org/10.1016/j.elecom.2016.02.024 Lee, C.H., Park, H.B., Lee, Y.M., et al.: Importance of proton conductivity measurement in polymer electrolyte membrane for fuel cell application. Ind. Eng. Chem. Res. 44, 7617–7626 (2005). https://doi.org/10.1021/ie0501172 Yuan, X.Z., Song, C.J., Wang, H.J., et al.: Electrochemical Impedance Spectroscopy in PEM Fuel Cells. Springer, London (2010). https://doi.org/10.1007/978-1-84882-846-9 Yuan, X.Z., Wang, H.J., Colin Sun, J., et al.: AC impedance technique in PEM fuel cell diagnosis: a review. Int. J. Hydrog. Energy 32, 4365–4380 (2007). https://doi.org/10.1016/j.ijhydene.2007.05.036 Qi, Y.Z., Liu, J.J., Sabarirajan, D.C., et al.: Interpreting ionic conductivity for polymer electrolyte fuel cell catalyst layers with electrochemical impedance spectroscopy and transmission line modeling. J. Electrochem. Soc. 168, 054502 (2021). https://doi.org/10.1149/1945-7111/abf96d Boyer, C., Gamburzev, S., Velev, O., et al.: Measurements of proton conductivity in the active layer of PEM fuel cell gas diffusion electrodes. Electrochim. Acta 43, 3703–3709 (1998). https://doi.org/10.1016/S0013-4686(98)00128-5 Sone, Y., Ekdunge, P., Simonsson, D.: Proton conductivity of Nafion 117 as measured by a four-electrode AC impedance method. J. Electrochem. Soc. 143, 1254–1259 (1996). https://doi.org/10.1149/1.1836625 Weber, A.Z., Borup, R.L., Darling, R.M., et al.: A critical review of modeling transport phenomena in polymer-electrolyte fuel cells. J. Electrochem. Soc. 161, F1254–F1299 (2014). https://doi.org/10.1149/2.0751412jes Mittal, V.O., Kunz, H.R., Fenton, J.M.: Membrane degradation mechanisms in PEMFCs. J. Electrochem. Soc. 154, B652–B656 (2007). https://doi.org/10.1149/1.2734869 Mond, L., Langer, C.: A new form of gas battery. Proc. R. Soc. London 46, 296–304 (1889). https://doi.org/10.1098/rspl.1889.0036 Chong, L., Wen, J., Kubal, J., et al.: Ultralow-loading platinum-cobalt fuel cell catalysts derived from imidazolate frameworks. Science 362, 1276–1281 (2018). https://doi.org/10.1126/science.aau0630 Wang, C., Zhao, Q., Zhou, X.W., et al.: Degradation characteristics of membrane electrode assembly under drive cycle test protocol. Int. J. Green Energy 16, 789–795 (2019). https://doi.org/10.1080/15435075.2019.1641712 Hansen, T.W., Delariva, A.T., Challa, S.R., et al.: Sintering of catalytic nanoparticles: particle migration or Ostwald ripening? Acc. Chem. Res. 46, 1720–1730 (2013). https://doi.org/10.1021/ar3002427 Mayrhofer, K.J.J., Meier, J.C., Ashton, S.J., et al.: Fuel cell catalyst degradation on the nanoscale. Electrochem. Commun. 10, 1144–1147 (2008). https://doi.org/10.1016/j.elecom.2008.05.032 Pizzutilo, E., Geiger, S., Grote, J.P., et al.: On the need of improved accelerated degradation protocols (ADPs): examination of platinum dissolution and carbon corrosion in half-cell tests. J. Electrochem. Soc. 163, F1510–F1514 (2016). https://doi.org/10.1149/2.0731614jes Ye, S.Y., Hall, M., Cao, H., et al.: Degradation resistant cathodes in polymer electrolyte membrane fuel cells. ECS Trans. 3, 657–666 (2006). https://doi.org/10.1149/1.2356186 Li, Y.B., Moriyama, K., Gu, W.B., et al.: A one-dimensional Pt degradation model for polymer electrolyte fuel cells. J. Electrochem. Soc. 162, F834–F842 (2015). https://doi.org/10.1149/2.0101508jes Ren, P., Pei, P.C., Li, Y.H., et al.: Degradation mechanisms of proton exchange membrane fuel cell under typical automotive operating conditions. Prog. Energy Combust. Sci. 80, 100859 (2020). https://doi.org/10.1016/j.pecs.2020.100859 de Bruijn, F.A., Dam, V.A.T., Janssen, G.J.M.: Review: durability and degradation issues of PEM fuel cell components. Fuel Cells 8, 3–22 (2008). https://doi.org/10.1002/fuce.200700053 Macauley, N., Wong, K.H., Watson, M., et al.: Favorable effect of in situ generated platinum in the membrane on fuel cell membrane durability. J. Power Sources 299, 139–148 (2015). https://doi.org/10.1016/j.jpowsour.2015.08.096 MacAuley, N., Papadias, D.D., Fairweather, J., et al.: Carbon corrosion in PEM fuel cells and the development of accelerated stress tests. J. Electrochem. Soc. 165, F3148–F3160 (2018). https://doi.org/10.1149/2.0061806jes Castanheira, L., Silva, W.O., Lima, F.H.B., et al.: Carbon corrosion in proton-exchange membrane fuel cells: effect of the carbon structure, the degradation protocol, and the gas atmosphere. ACS Catal. 5, 2184–2194 (2015). https://doi.org/10.1021/cs501973j Healy, J., Hayden, C., Xie, T., et al.: Aspects of the chemical degradation of PFSA ionomers used in PEM fuel cells. Fuel Cells 5, 302–308 (2005). https://doi.org/10.1002/fuce.200400050 Zhao, J., Li, X.G.: A review of polymer electrolyte membrane fuel cell durability for vehicular applications: degradation modes and experimental techniques. Energy Convers. Manag. 199, 112022 (2019). https://doi.org/10.1016/j.enconman.2019.112022 Novotny, P., Tomas, M., Nemec, T., et al.: On/off cycling test of low-temperature PEM fuel cell at fully humidified conditions. Int. J. Green Energy 16, 1189–1195 (2019). https://doi.org/10.1080/15435075.2019.1671394 Kim, S., Mench, M.M.: Physical degradation of membrane electrode assemblies undergoing freeze/thaw cycling: micro-structure effects. J. Power Sources 174, 206–220 (2007). https://doi.org/10.1016/j.jpowsour.2007.08.111 Sobolyeva, T.: On the Microstructure of PEM Fuel Cell Catalyst Layers. Dissertation, Simon Fraser University (2010). https://summit.sfu.ca/item/11450 Liu, Y.W., Wu, S.Y., Qin, Y.Z., et al.: Mass transport and performance of proton exchange membrane fuel cell considering the influence of porosity distribution of gas diffusion layer. Int. J. Green Energy (2021). https://doi.org/10.1080/15435075.2021.2007389 Khan, S.S., Shareef, H., Mutlag, A.H.: Dynamic temperature model for proton exchange membrane fuel cell using online variations in load current and ambient temperature. Int. J. Green Energy 16, 361–370 (2019). https://doi.org/10.1080/15435075.2018.1564141 Rong, F., Huang, C., Liu, Z.S., et al.: Microstructure changes in the catalyst layers of PEM fuel cells induced by load cycling. Part I. Mechanical model. J. Power Sources 175, 699–711 (2008). https://doi.org/10.1016/j.jpowsour.2007.10.006 Rong, F., Huang, C., Liu, Z.S., et al.: Microstructure changes in the catalyst layers of PEM fuel cells induced by load cycling. Part II. Simulation and understanding. J. Power Sources 175, 712–723 (2008). https://doi.org/10.1016/j.jpowsour.2007.10.007 Pan, M.Z., Meng, X.P., Li, C., et al.: Impact of nonuniform reactant flow rate on the performance of proton exchange membrane fuel cell stacks. Int. J. Green Energy 17, 603–616 (2020). https://doi.org/10.1080/15435075.2020.1761812