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Approaches for the Modeling of PBI/H3PO4 Based HT-PEM Fuel Cells

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Book cover High Temperature Polymer Electrolyte Membrane Fuel Cells
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Abstract

Modeling and simulation of all components of high temperature polymer electrolyte (HT-PEM) fuel cells are important tools to provide additional understanding of the operation behavior. The use of mathematical models is one possibility for analyzing species concentrations, temperature gradients, and pressure distributions for predicting the internal workings of HT-PEM fuel cells for different operating conditions and designs. This work reviews phosphoric acid fuel cell (PAFC) and HT-PEM fuel cell modeling and simulation activities since both technologies are very similar. The current state-of-the-art PAFC and HT-PEM fuel cell technology is overviewed. Selected literature is discussed and dedicated modeling equations listed. Next, electrolyte modeling and simulation possibilities are highlighted including the physicochemical properties of phosphoric acid (H3PO4), description of the vapor–liquid equilibrium (VLE), non-equilibrium effects at the interphase, and the coupling to electrochemistry and mass transport properties. Finally, numerical aspects are shortly presented, examples of practical implications given, and input parameters and experimental data for model validation listed.

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References

  1. Carter D, Wing J (2013) Fuel cell today—the fuel cell industry review 2013. Wonderberry UK Ltd, London

    Google Scholar 

  2. Costamagna P, Srinivasan S (2001) Quantum jumps in the PEMFC science and technology from the 1960s to the year 2000: part I. Fundamental scientific aspects. J Power Sources 102:242–252

    Article  Google Scholar 

  3. Costamagna P, Srinivasan S (2001) Quantum jumps in the PEMFC science and technology from the 1960s to the year 2000: part II. Engineering, technology development and application aspects. J Power Sources 102:253–269

    Article  Google Scholar 

  4. Weber AZ, Newman J (2004) Modeling transport in polymer-electrolyte fuel cells. Chem Rev 104:4679–4726

    Article  Google Scholar 

  5. Wang CY (2004) Fundamental models for fuel cell engineering. Chem Rev 104:4727–4766

    Article  Google Scholar 

  6. Haraldsson K, Wipke K (2004) Evaluating PEM fuel cell system models. J Power Sources 126:88–97

    Article  Google Scholar 

  7. Yao KZ, Karan K, McAuley KB et al (2004) A review of mathematical models for hydrogen and direct methanol polymer electrolyte membrane fuel cells. Fuel Cells 4:3–29

    Article  Google Scholar 

  8. Bıyıkoğlu A (2005) Review of proton exchange membrane fuel cell models. Int J Hydrogen Energy 30:1181–1212

    Article  Google Scholar 

  9. Faghri A, Guo Z (2005) Challenges and opportunities of thermal management issues related to fuel cell technology and modeling. Int J Heat Mass Transfer 48:3891–3920

    Article  Google Scholar 

  10. Cheddie D, Munroe N (2005) Review and comparison of approaches to proton exchange membrane fuel cell modeling. J Power Sources 147:72–84

    Article  Google Scholar 

  11. Tao WQ, Min CH, Liu XL et al (2006) Parameter sensitivity examination and discussion of PEM fuel cell simulation model validation: part I. Current status of modeling research and model development. J Power Sources 160:359–373

    Article  Google Scholar 

  12. Djilali N (2007) Computational modelling of polymer electrolyte membrane (PEM) fuel cells: challenges and opportunities. Energy 32:269–280

    Article  Google Scholar 

  13. Siegel C (2008) Review of computational heat and mass transfer modeling in polymer-electrolyte-membrane (PEM) fuel cells. Energy 33:1331–1352

    Article  Google Scholar 

  14. Kulikovsky AA (2010) Analytical modelling of fuel cells, 1st edn. Elsevier, Amsterdam

    Google Scholar 

  15. Mench MM (2010) Advanced modeling in fuel cell systems: a review of modeling approaches. In: Stolten D (ed) Hydrogen and fuel cells—fundamentals, technologies and application. Wiley-VCH, Weinheim, pp 89–118

    Google Scholar 

  16. Wannek C (2010) High-temperature PEM fuel cells: electrolytes, cells, and stacks. In: Stolten D (ed) Hydrogen and fuel cells—fundamentals, technologies and applications. Wiley-VCH, Weinheim, pp 17–40

    Google Scholar 

  17. Kulikovsky A (2012) Messages from analytical modeling of fuel cells. In: Stolten D, Emonts B (eds) Fuel cell science and engineering—materials, processes, systems and technology. Wiley-VCH, Weinheim, pp 647–668

    Google Scholar 

  18. Reimer U (2012) High-temperature polymer electrolyte fuel-cell modeling. In: Stolten D, Emonts B (eds) Fuel cell science and engineering—materials, processes, systems and technology. Wiley-VCH, Weinheim, pp 819–838

    Chapter  Google Scholar 

  19. Anahara R (1990) Fuji electric phosphoric acid fuel cell activities. J Power Sources 29:109–117

    Article  Google Scholar 

  20. Anahara R (1992) A perspective on PAFC commercialization by Fuji Electric. J Power Sources 37:119–131

    Article  Google Scholar 

  21. Shibata K, Watanabe K (1994) Philosophies and experiences of PAFC field trials. J Power Sources 49:77–102

    Article  Google Scholar 

  22. Nymoen H (1994) PAFC demonstration plants in Europe: first results. J Power Sources 49:63–76

    Article  Google Scholar 

  23. Hojo N, Okuda M, Nakamura M (1996) Phosphoric acid fuel cells in Japan. J Power Sources 61:73–77

    Article  Google Scholar 

  24. Vanhanen JP, Kauranen PS, Lund PD (1997) Operation experiences of a phosphoric acid fuel cell in a solar hydrogen energy system. Int J Hydrogen Energy 22:707–713

    Article  Google Scholar 

  25. Whitaker R (1998) Investment in volume building: the ‘virtuous cycle’ in PAFC. J Power Sources 71:71–74

    Article  Google Scholar 

  26. Kasahara K, Morioka M, Yoshida H et al (2000) PAFC operating performance verified by Japanese gas utilities. J Power Sources 86:298–301

    Article  Google Scholar 

  27. Spiegel RJ, Preston JL (2003) Technical assessment of fuel cell operation on anaerobic digester gas at the Yonkers, NY, wastewater treatment plant. Waste Manag 23:709–717

    Article  Google Scholar 

  28. Sammes N, Bove R, Stahl K (2004) Phosphoric acid fuel cells: fundamentals and applications. Curr Opin Solid State Mater Sci 8:372–378

    Article  Google Scholar 

  29. http://www.doosan.com/. Accessed Aug 2014

  30. http://www.fujielectric.com/. Accessed June 2014

  31. http://www.n2telligence.com/. Accessed June 2014

  32. Wainright JS, Wang JT, Weng D et al (1995) Acid-doped polybenzimidazoles: a new polymer electrolyte. J Electrochem Soc 142:L121–L123

    Article  Google Scholar 

  33. Samms SR, Wasmus S, Savinell RF (1996) Thermal stability of proton conducting acid doped polybenzimidazole in simulated fuel cell environments. J Electrochem Soc 143:1225–1232

    Article  Google Scholar 

  34. Wang JT, Savinell RF, Wainright JS et al (1996) A H2/O2 fuel cell using acid doped polybenzimidazole as a polymer electrolyte. Electrochim Acta 41:193–197

    Article  Google Scholar 

  35. http://www.fumatech.com. Accessed June 2014

  36. http://www.adventech.gr/ Accessed June 2014

  37. http://daposy.com/. Accessed June 2014

  38. http://serenergy.com/. Accessed June 2014

  39. http://www.elcore.com/. Accessed June 2014

  40. Li Q, He R, Jensen JO et al (2004) PBI-based polymer membranes for high temperature fuel cells—preparation, characterization and fuel cell operation. Fuel Cells 4:147–159

    Article  Google Scholar 

  41. Zhang J, Xie Z, Zhang J et al (2006) High temperature PEM fuel cells. J Power Sources 160:872–891

    Article  Google Scholar 

  42. Li QF, Rudbeck HC, Chromik A et al (2010) Properties, degradation and high temperature fuel cell test of different types of PBI and PBI blend membranes. J Membr Sci 347:260–270

    Article  Google Scholar 

  43. Aili D, Hansen MK, Pan C et al (2011) Phosphoric acid doped membranes based on Nafion®, PBI and their blends—membrane preparation, characterization and steam electrolysis testing. Int J Hydrogen Energy 36:6985–6993

    Article  Google Scholar 

  44. Bose S, Kuila T, Nguyen TXH et al (2011) Polymer membranes for high temperature proton exchange membrane fuel cell: recent advances and challenges. Prog Polym Sci 36:813–836

    Article  Google Scholar 

  45. Chandan A, Hattenberger M, El-kharouf A et al (2013) High temperature (HT) polymer electrolyte membrane fuel cells (PEMFC)—a review. J Power Sources 231:264–278

    Article  Google Scholar 

  46. Sugano N, Ishiwata T, Kawai S et al (1994) Investigation on dynamic characteristics of fuel cell stack cooling system. Trans Jpn Soc Mech Eng 60:1597–1601

    Article  Google Scholar 

  47. Miki H, Shimizu A (1998) Dynamic characteristics of phosphoric-acid fuel-cell stack cooling system. Appl Energy 61:41–56

    Article  Google Scholar 

  48. Kwak HY, Lee HS, Jung JY et al (2004) Exergetic and thermoeconomic analysis of a 200-kW phosphoric acid fuel cell plant. Fuel 83:2087–2094

    Article  Google Scholar 

  49. Zervas PL, Tatsis A, Sarimveis H et al (2008) Development of a novel computational tool for optimizing the operation of fuel cells systems: application for phosphoric acid fuel cells. J Power Sources 185:345–355

    Article  Google Scholar 

  50. Zhang H, Lin G, Chen J (2012) Multi-objective optimization analysis and load matching of a phosphoric acid fuel cell system. Int J Hydrogen Energy 37:3438–3446

    Article  Google Scholar 

  51. Tanni MA, Arifujjaman M, Iqbal T (2013) Dynamic modeling of a phosphoric acid fuel cell (PAFC) and its power conditioning system. J Clean Energy Technol 1:178–183

    Article  Google Scholar 

  52. Iczkowski RP, Cutlip MB (1980) Voltage losses in fuel cell cathodes. J Electrochem Soc 127:1433–1440

    Article  Google Scholar 

  53. Yang SC, Cutlip MB, Stonehart P (1990) Simulation and optimization of porous gas-diffusion electrodes used in hydrogen/oxygen phosphoric acid fuel cells. Electrochim Acta 35:869–878

    Article  Google Scholar 

  54. Yang SC (2000) Modeling and simulation of steady-state polarization and impedance response of phosphoric acid fuel-cell cathodes with catalyst-layer microstructure consideration. J Electrochem Soc 147:71–77

    Article  Google Scholar 

  55. Abdul-Aziz A, Alkasab KA (1994) Performance of serpentine passages in the cooling system of a phosphoric fuel cell stack. Exp Therm Fluid Sci 8:101–111

    Article  Google Scholar 

  56. Yoshioka S, Mitsuda K, Horiuchi H et al (1997) Mechanism of vaporization of phosphoric acid in a PAFC. Denki Kagaku 65:314–319

    Google Scholar 

  57. Yoshioka S, Mitsuda K, Horiuchi H et al (1998) Condensation of vaporized phosphoric acid in a PAFC cathode. Denki Kagaku 66:41–47

    Google Scholar 

  58. Yamashita K, Taniguchi T (1998) Agglomerate model for DC and AC response of phosphoric acid fuel cell cathode. J Electrochem Soc 145:45–49

    Article  Google Scholar 

  59. Maggio G (1999) Modelling of phosphoric acid fuel cell cathode behaviour. J Appl Electrochem 29:171–176

    Article  Google Scholar 

  60. Choudhury SR, Deshmukh MB, Rengaswamy R (2002) A two-dimensional steady-state model for phosphoric acid fuel cells (PAFC). J Power Sources 112:137–152

    Article  Google Scholar 

  61. Choudhury SR, Choudhury SR, Rangarajan J et al (2005) Step response analysis of phosphoric acid fuel cell (PAFC) cathode through a transient model. J Power Sources 140:274–279

    Article  Google Scholar 

  62. Psofogiannakis G, Bourgault Y, Conway BE et al (2006) Mathematical model for a direct propane phosphoric acid fuel cell. J Appl Electrochem 36:115–130

    Article  Google Scholar 

  63. Choudhury SR, Rengaswamy R (2006) Characterization and fault diagnosis of PAFC cathode by EIS technique and a novel mathematical model approach. J Power Sources 161:971–986

    Article  Google Scholar 

  64. Zervas PL, Koukou MK, Markatos NC (2006) Predicting the effects of process parameters on the performance of phosphoric acid fuel cells using a 3-D numerical approach. Energy Convers Manag 47:2883–2899

    Article  Google Scholar 

  65. Hirata H, Aoki T, Nakajima K (2011) Numerical study on the evaporative and condensational dissipation of phosphoric acid in PAFC. J Power Sources 196:8004–8011

    Article  Google Scholar 

  66. Hirata H, Aoki T, Nakajima K (2012) Liquid phase migration effects on the evaporative and condensational dissipation of phosphoric acid in phosphoric acid fuel cell. J Power Sources 199:110–116

    Article  Google Scholar 

  67. Paul T, Seal M, Banerjee D et al (2014) Analysis of drying and dilution in phosphoric acid fuel cell (PAFC) using galvanometric study and electrochemical impedance spectroscopy. J Fuel Cell Sci Technol 11:041001-1–041001-7

    Google Scholar 

  68. Korsgaard AR, Refshauge R, Nielsen MP et al (2006) Experimental characterization and modeling of commercial polybenzimidazole-based MEA performance. J Power Sources 162:239–245

    Article  Google Scholar 

  69. Zenith F, Seland F, Kongstein OE et al (2006) Control-oriented modelling and experimental study of the transient response of a high-temperature polymer fuel cell. J Power Sources 162:215–227

    Article  Google Scholar 

  70. Andreasen SJ, Kær SK (2008) Modelling and evaluation of heating strategies for high temperature polymer electrolyte membrane fuel cell stacks. Int J Hydrogen Energy 33:4655–4664

    Article  Google Scholar 

  71. Korsgaard AR, Nielsen MP, Kær SK (2008) Part one: a novel model of HT-based micro-combined heat and power fuel cell system. Int J Hydrogen Energy 33:1909–1920

    Article  Google Scholar 

  72. Korsgaard AR, Nielsen MP, Kær SK (2008) Part two: control of a novel HT-based micro combined heat and power fuel cell system. Int J Hydrogen Energy 33:1921–1931

    Article  Google Scholar 

  73. Arsalis A, Nielsen MP, Kær SK (2011) Modeling and parametric study of a 1 kWe HT-PEMFC-based residential micro-CHP system. Int J Hydrogen Energy 36:5010–5020

    Article  Google Scholar 

  74. Zuliani N, Taccani R (2012) Microcogeneration system based on HTPEM fuel cell fueled with natural gas: performance analysis. Appl Energy 97:802–808

    Article  Google Scholar 

  75. Romero-Pascual E, Soler J (2013) Modelling of an HT-based micro-combined heat and power fuel cell system with methanol. Int J Hydrogen Energy 39:4053–4059

    Article  Google Scholar 

  76. Arsalis A, Nielsen MP, Kær SK (2013) Application of an improved operational strategy on a PBI fuel cell-based residential system for Danish single-family households. Appl Therm Eng 50:704–713

    Article  Google Scholar 

  77. Authayanun S, Mamlouk M, Scott K et al (2013) Comparison of high-temperature and low-temperature polymer electrolyte membrane fuel cell systems with glycerol reforming process for stationary applications. Appl Energy 109:192–201

    Article  Google Scholar 

  78. Jannelli E, Minutillo M, Perna A (2013) Analyzing microcogeneration systems based on LT-PEMFC and HT-PEMFC by energy balances. Appl Energy 108:82–91

    Article  Google Scholar 

  79. Authayanun S, Saebea D, Patcharavorachot Y, Arpornwichanop A (2014) Effect of different fuel options on performance of high-temperature PEMFC (proton exchange membrane fuel cell) systems. Energy 68:989–997

    Article  Google Scholar 

  80. Park J, Min K (2014) Dynamic modeling of a high-temperature proton exchange membrane fuel cell with a fuel processor. Int J Hydrogen Energy 39:10683–10696

    Article  Google Scholar 

  81. Cheddie D, Munroe N (2006) Parametric model of an intermediate temperature PEMFC. J Power Sources 156:414–423

    Article  Google Scholar 

  82. Cheddie D, Munroe N (2006) Three dimensional modeling of high temperature PEM fuel cells. J Power Sources 160:215–223

    Article  Google Scholar 

  83. Cheddie D, Munroe N (2006) Mathematical model of a PEMFC using a PBI membrane. Energy Convers Manag 47:1490–1504

    Article  Google Scholar 

  84. Cheddie D, Munroe N (2007) A two-phase model of an intermediate temperature PEMFC. Int J Hydrogen Energy 32:832–841

    Article  Google Scholar 

  85. Cheddie DF, Munroe NDH (2008) Semi-analytical proton exchange membrane fuel cell modeling. J Power Sources 183:164–173

    Article  Google Scholar 

  86. Peng J, Lee SJ (2006) Numerical simulation of proton exchange membrane fuel cells at high operating temperature. J Power Sources 162:1182–1191

    Article  Google Scholar 

  87. Peng J, Lee SJ (2008) Transient response of high temperature PEM fuel cell. J Power Sources 179:220–231

    Article  Google Scholar 

  88. Wang CP, Chu HS, Yan YY et al (2007) Transient evolution of carbon monoxide poisoning effect of PBI membrane fuel cells. J Power Sources 170:235–241

    Article  Google Scholar 

  89. Scott K, Pilditch S, Mamlouk M (2007) Modelling and experimental validation of a high temperature polymer electrolyte fuel cell. J Appl Electrochem 37:1245–1259

    Article  Google Scholar 

  90. Siegel C, Bandlamudi G, Heinzel A (2007) Numerical simulation of a high-temperature PEM (HT) fuel cell. In: Proceedings of the European COMSOL conference, Grenoble

    Google Scholar 

  91. Siegel C, Bandlamudi G, Heinzel A (2008) Modeling polybenzimidazole/phosphoric acid membrane behaviour in a HTPEM fuel cell. In: Proceedings of the European COMSOL conference, Hannover

    Google Scholar 

  92. Siegel C, Bandlamudi G, van der Schoot N et al (2009) Large scale 3D flow distribution analysis in HTPEM fuel cells. In: Proceedings of the European COMSOL conference, Milan

    Google Scholar 

  93. Siegel C, Bandlamudi G, Heinzel A (2008) Evaluating the effects of stack compression on the physical characteristics of HT PEMFCs with CFD modelling software. In: Proceedings of the fuel cell science and technology conference, Copenhagen

    Google Scholar 

  94. Ubong EU, Shi Z, Wang X (2008) A-3D-modeling and experimental validation of a high temperature PBI based PEMFC. ECS Trans 16:79–90

    Article  Google Scholar 

  95. Schaar B (2008) Simulation einer Hochtemperatur-PEM-Brennstoffzelle. Dissertation, AutoUni - Schriftreihe, Logos Verlag, Berlin

    Google Scholar 

  96. Siegel C, Bandlamudi G, Beckhaus P et al (2009) Segmented current and temperature measurement in a HTPEM fuel cell. In: Proceedings of the 6th symposium on fuel cell modelling and experimental validation, Bad Herrenalb/Karlsruhe

    Google Scholar 

  97. Siegel C, Bandlamudi G, Heinzel A (2011) Locally resolved measurements in a segmented HTPEM fuel cell with straight flow-fields. Fuel Cells 11:489–500

    Article  Google Scholar 

  98. Andreasen SJ, Kær SK (2009) Dynamic model of the high temperature proton exchange membrane fuel cell stack temperature. J Fuel Cell Sci Technol 6:041006-1–041006-8

    Google Scholar 

  99. Scholta J, Messerschmidt M, Jörissen L et al (2009) Externally cooled high temperature polymer electrolyte membrane fuel cell stack. J Power Sources 190:83–85

    Article  Google Scholar 

  100. Scott K, Mamlouk M (2009) A cell voltage equation for an intermediate temperature proton exchange membrane fuel cell. Int J Hydrogen Energy 34:9195–9202

    Article  Google Scholar 

  101. Shamardina O, Chertovich A, Kulikovsky AA et al (2010) A simple model of a high temperature PEM fuel cell. Int J Hydrogen Energy 35:9954–9962

    Article  Google Scholar 

  102. Kulikovsky AA, Oetjen HF, Wannek C (2010) A simple and accurate method for high-temperature PEM fuel cell characterisation. Fuel Cells 10:363–368

    Article  Google Scholar 

  103. Sousa T, Mamlouk M, Scott K (2010) An isothermal model of a laboratory intermediate temperature fuel cell using PBI doped phosphoric acid membranes. Chem Eng Sci 65:2513–2530

    Article  Google Scholar 

  104. Bergmann A, Gerteisen D, Kurz T (2010) Modelling of CO poisoning and its dynamics in HTPEM fuel cells. Fuel Cells 10:278–287

    Article  Google Scholar 

  105. Sousa T, Mamlouk M, Scott K (2010) A non-isothermal model of a laboratory intermediate temperature fuel cell using PBI doped phosphoric acid membranes. Fuel Cells 10:993–1012

    Article  Google Scholar 

  106. Lobato J, Cãnizares P, Rodrigo MA et al (2010) Three-dimensional model of a 50 cm2 high temperature PEM fuel cell. Study of the flow channel geometry influence. Int J Hydrogen Energy 35:5510–5520

    Article  Google Scholar 

  107. Sousa T, Mamlouk M, Scott K (2010) A dynamic non-isothermal model of a laboratory intermediate temperature fuel cell using PBI doped phosphoric acid membranes. Int J Hydrogen Energy 35:12065–12080

    Article  Google Scholar 

  108. Lobato J, Cãnizares P, Rodrigo MA et al (2010) Direct and inverse neural networks modelling applied to study the influence of the gas diffusion layer properties on PBI-based PEM fuel cells. Int J Hydrogen Energy 35:7889–7897

    Article  Google Scholar 

  109. Jiao K, Li X (2010) A three-dimensional non-isothermal model of high temperature proton exchange membrane fuel cells with phosphoric acid doped polybenzimidazole membranes. Fuel Cells 10:351–362

    Article  Google Scholar 

  110. Jiao K, Alaefour IE, Li X (2011) Three-dimensional non-isothermal modeling of carbon monoxide poisoning in high temperature proton exchange membrane fuel cells with phosphoric acid doped polybenzimidazole membranes. Fuel 90:568–582

    Article  Google Scholar 

  111. Siegel C, Bandlamudi G, Heinzel A (2011) Systematic characterization of a PBI/H3PO4 sol-gel membrane—modeling and simulation. J Power Sources 196:2735–2749

    Article  Google Scholar 

  112. Doubek G, Robalinho E, Cunha EF et al (2011) Application of CFD techniques in the modelling and simulation of PBI PEMFC. Fuel Cells 11:764–774

    Article  Google Scholar 

  113. Mamlouk M, Sousa T, Scott K (2011) A high temperature polymer electrolyte membrane fuel cell model for reformate gas. Int J Electrochem, Article ID 520473:1–18

    Google Scholar 

  114. Kurz T (2011) Entwicklung und Charakterisierung eines portable Hochtemperatur-PEM-Brennstoffzellensystems. Dissertation, Fraunhofer Verlag, Stuttgart

    Google Scholar 

  115. Siegel C, Bandlamudi G, Heinzel A (2011) Solid-phase temperature measurements in a HTPEM fuel cell. Int J Hydrogen Energy 36:12977–12990

    Article  Google Scholar 

  116. Olapade PO, Meyers JP, Borup RL et al (2011) Parametric study of the morphological proprieties of HT-PEMFC components for effective membrane hydration. J Electrochem Soc 158:B639–B649

    Article  Google Scholar 

  117. Falcucci G, Jannelli E, Minutillo M et al (2012) Fluid dynamic investigation of channel design in high temperature PEM fuel cells. J Fuel Cell Sci Technol 9:021014-1–021014-10

    Google Scholar 

  118. Kvesić M, Reimer U, Froning D et al (2012) 3D modeling of a 200 cm2 HT-PEFC short stack. Int J Hydrogen Energy 37:2430–2450

    Article  Google Scholar 

  119. Kvesić M (2012) Modellierung und Simulation von Hochtemperatur-Polymerelektrolyt-Brennstoffzellen. Dissertation, Forschungszentrum Jülich GmbH, Zentralbibliothek Verlag, Jülich

    Google Scholar 

  120. Lüke L, Janßen H, Kvesić M et al (2012) Performance analysis of HT-PEFC stacks. Int J Hydrogen Energy 37:9171–9181

    Article  Google Scholar 

  121. Chippar P, Ju H (2012) Three-dimensional non-isothermal modeling of a phosphoric acid-doped polybenzimidazole (PBI) membrane fuel cell. Solid State Ion 225:30–39

    Article  Google Scholar 

  122. Park J, Min K (2012) A quasi-three-dimensional non-isothermal dynamic model of a high-temperature proton exchange membrane fuel cell. J Power Sources 216:152–161

    Article  Google Scholar 

  123. Reddy EH, Jayanti S (2012) Thermal management strategies for a 1 kWe stack of a high temperature proton exchange membrane fuel cell. Appl Therm Eng 48:465–475

    Article  Google Scholar 

  124. Sousa T, Mamlouk M, Scott K et al (2012) Three dimensional model of a high temperature PEMFC. Study of the flow field effect on performance. Fuel Cells 12:566–576

    Article  Google Scholar 

  125. Reddy EH, Monder DS, Jayanti S (2013) Parametric study of an external coolant system for a high temperature polymer electrolyte membrane fuel cell. Appl Therm Eng 58:155–164

    Article  Google Scholar 

  126. Jiao K, Zhou Y, Du Q et al (2013) Numerical simulations of carbon monoxide poisoning in high temperature proton exchange membrane fuel cells with various flow channel designs. Appl Energy 104:21–41

    Article  Google Scholar 

  127. Chippar P, Ju H (2013) Numerical modeling and investigation of gas crossover effects in high temperature proton exchange membrane (PEM) fuel cells. Int J Hydrogen Energy 38:7704–7714

    Article  Google Scholar 

  128. Chippar P, Oh K, Kim D et al (2013) Coupled mechanical stress and multi-dimensional CFD analysis for high temperature proton exchange membrane fuel cells (HT-PEMFCs). Int J Hydrogen Energy 38:7715–7724

    Article  Google Scholar 

  129. Supra J, Janßen H, Lehnert W et al (2013) Temperature distribution in a liquid cooled HT-PEFC stack. Int J Hydrogen Energy 38:1943–1951

    Article  Google Scholar 

  130. Grigoriev SA, Kalinnikov AA, Kuleshov NV et al (2013) Numerical optimization of bipolar plates and gas diffusion electrodes for PBI-based PEM fuel cells. Int J Hydrogen Energy 38:8557–8567

    Article  Google Scholar 

  131. Salomov RU, Chiavazzo E, Asinari P (2014) Pore-scale modeling of fluid flow through gas diffusion and catalyst layers for high temperature proton exchange membrane (HT-PEM) fuel cells. Comput Math Appl 67:393–411

    Article  Google Scholar 

  132. Bezmalinović D, Strahl S, Roda V et al (2014) Water transport study in a high temperature proton exchange membrane fuel cell stack. Water transport study in a high temperature proton exchange membrane fuel cell stack. Int J Hydrogen Energy 39:10627–10640

    Article  Google Scholar 

  133. Chippar P, Oh K, Kim WG et al (2014) Numerical analysis of effects of gas crossover through membrane pinholes in high-temperature proton exchange membrane fuel cells. Int J Hydrogen Energy 39:2863–2871

    Article  Google Scholar 

  134. Chippar P, Kang K, Lim YD et al (2014) Effects of inlet relative humidity (RH) on the performance of a high temperature-proton exchange membrane fuel cell (HT-PEMFC). Int J Hydrogen Energy 39:2767–2775

    Article  Google Scholar 

  135. Oh K, Chippar P, Ju H (2014) Numerical study of thermal stresses in high temperature proton exchange membrane fuel cell (HT-PEMFC). Int J Hydrogen Energy 39:2785–2794

    Article  Google Scholar 

  136. Abdul Rasheed RK, Ehteshami SMM, Chan SH (2014) Analytical modelling of boiling phase change phenomenon in high-temperature proton exchange membrane fuel cells during warm-up process. Int J Hydrogen Energy 39:2246–2260

    Article  Google Scholar 

  137. Singdeo D, Dey T, Ghosh PC (2014) Contact resistance between bipolar plate and gas diffusion layer in high temperature polymer electrolyte fuel cells. Int J Hydrogen Energy 39:987–995

    Article  Google Scholar 

  138. Kazdal TJ, Lang S, Kühl F et al (2014) Modelling of the vapour-liquid equilibrium of water and the in situ concentration of H3PO4 in a high temperature proton exchange membrane fuel cell. J Power Sources 249:446–456

    Article  Google Scholar 

  139. Yin Y, Wang J, Yang X et al (2014) Modeling of high temperature proton exchange membrane fuel cells with novel sulfonated polybenzimidazole membranes. Int J Hydrogen Energy 39:13671–13680

    Article  Google Scholar 

  140. Kim M, Kang T, Kim J et al (2014) One-dimensional modeling and analysis for performance degradation of high temperature proton exchange membrane fuel cell using PA doped PBI membrane. Solid State Ion 262:319–323

    Article  Google Scholar 

  141. Oh K, Jeong G, Cho E et al (2014) A CO poisoning model for high-temperature proton exchange membrane fuel cells comprising phosphoric acid-doped polybenzimidazole membranes. Int J Hydrogen Energy 39(36):21915–21926. http://dx.doi.org/10.1016/j.ijhydene.2014.06.101

    Article  Google Scholar 

  142. Bockris O’MJ, Reddy AKN (1970) Modern electrochemistry. Plenum, New York

    Book  Google Scholar 

  143. Bird RB, Stewart WE, Lightfoot EN (2007) Transport phenomena, revised 2nd edn. Wiley, New York

    Google Scholar 

  144. Newman JS (1990) Electrochemical systems, 2nd edn. Prentice Hall, Englewood Cliffs

    Google Scholar 

  145. COMSOL Multiphysics 5.0 (2014) Batteries & fuel cells module—user manual

    Google Scholar 

  146. Björnbom P (1987) Modelling of a double-layered PTFE-bonded oxygen electrode. Electrochim Acta 32:115–119

    Article  Google Scholar 

  147. COMSOL Multiphysics 5.0 (2014) CFD module manual—user manual

    Google Scholar 

  148. Korte C (2012) Phosphoric acid, an electrolyte for fuel cells—temperature and composition dependence of vapour pressure and proton conductivity. In: Stolten D, Emonts B (eds) Fuel cell science and engineering—materials, processes, systems and technology. Wiley-VCH, Weinheim, pp 335–359

    Chapter  Google Scholar 

  149. Schrödter K, Bettermann G, Staffel T, Wahl F, Klein T, Hofmann T (2008) Phosphoric acid and phosphates. In: Ullmann’s encyclopedia of industrial chemistry. Wiley-VCH, Weinheim, pp 1–48

    Google Scholar 

  150. Zemaitis JF Jr, Clark DM, Rafal M et al (1986) Handbook of aqueous electrolyte thermodynamics: theory & application. Wiley, New York

    Book  Google Scholar 

  151. Platonov VA (2000) Properties of polyphosphoric acid. Fibre Chem 32:325–329

    Google Scholar 

  152. Othmer K (2007) Kirk-Othmer encyclopedia of chemical technology, 5th edn. Wiley, Hoboken

    Google Scholar 

  153. Archie GE (1941) Electrical resistivity log as an aid in determining some reservoir characteristics. Soc Petrol Eng J 146:54–62

    Google Scholar 

  154. Bouchet R, Siebert E (1999) Proton conduction in acid doped polybenzimidazole. Solid State Ion 118:287–299

    Article  Google Scholar 

  155. Ma YL, Wainright JS, Litt MH et al (2004) Conductivity of PBI membranes for high-temperature polymer electrolyte fuel cells. J Electrochem Soc 151:A8–A16

    Article  Google Scholar 

  156. Daletou MK, Kallitsis JK, Voyiatzis G et al (2009) The interaction of water vapors with H3PO4 imbibed electrolyte based on PBI/polysulfone copolymer blends. J Membr Sci 326:76–83

    Article  Google Scholar 

  157. Bandlamudi G (2011) Systematic characterization of HT PEMFCs containing PBI/H3PO4 systems. Dissertation, Logos Verlag, Berlin

    Google Scholar 

  158. Pitzer KS (ed) (1991) Activity coefficients in electrolyte solutions, 2nd edn. CRC, Boca Raton

    Google Scholar 

  159. Rafal M, Berthold JW, Scrivner NC et al (1994) Models for electrolyte solutions. In: Sandler SI (ed) Models for thermodynamic and phase equilibria calculations. Marcel Dekker, New York, pp 601–669

    Google Scholar 

  160. Loehe JR, Donohue MD (1997) Recent advances in modeling thermodynamic properties of aqueous strong electrolyte systems. AIChE J 43:180–195

    Article  Google Scholar 

  161. Anderko A, Wang P, Rafal M (2002) Electrolyte solutions: from thermodynamic and transport property models to the simulation of industrial processes. Fluid Phase Equilib 194–197:123–142

    Article  Google Scholar 

  162. Pohl HA, Chartoff RP (1964) Carriers and unpaired spins in some organic semiconductors. J Polym Sci Part A 2:2787–2806

    Google Scholar 

  163. Chin D, Chang H (1989) On the conductivity of phosphoric acid electrolyte. J Appl Electrochem 19:95–99

    Article  Google Scholar 

  164. Mason CM, Culvern JB (1949) Electrical conductivity of orthophosphoric acid and of sodium and potassium dihydrogen phosphates at 25°C. J Am Chem Soc 71:2387–2393

    Article  Google Scholar 

  165. Greenwood NN, Thompson A (1959) The mechanism of electrical conduction in fused phosphoric and trideuterophosphoric acids. J Chem Soc 3485–3492

    Google Scholar 

  166. MacDonald DI, Boyack JR (1969) Density, electrical conductivity, and vapor pressure of concentrated phosphoric acid. J Chem Eng Data 14:380–384

    Article  Google Scholar 

  167. Xiao L, Zhang H, Scanlon E et al (2005) High-temperature polybenzimidazole fuel cell membranes via a sol–gel process. Chem Mater 17:5328–5333

    Article  Google Scholar 

  168. Lang S, Kazdal TJ, Kühl F et al (2014) Diffusion coefficients and VLE data of aqueous phosphoric acid. J Chem Thermodyn 68:75–81

    Article  Google Scholar 

  169. Christensen JH, Reed RB (1955) Design and analysis data—density of aqueous solutions of phosphoric acid measurements at 25°C. Ind Eng Chem 47:1277–1280

    Article  Google Scholar 

  170. Kunz H, Gruver G (1978) The effect of electrolyte concentration on the catalytic activity of platinum for electrochemical oxygen reduction in phosphoric acid. Electrochim Acta 23:219–222

    Article  Google Scholar 

  171. Klinedinst K, Bett J, Macdonald J, Stonehart P (1974) Oxygen solubility and diffusivity in hot concentrated H3PO4. J Electroanal Chem Interfacial Electrochem 57:281–289

    Article  Google Scholar 

  172. Scharifker BR, Zelenay P, Bockris O (1987) The kinetics of oxygen reduction in molten phosphoric acid at high temperatures. J Electrochem Soc 134:2714–2725

    Article  Google Scholar 

  173. Brown EH, Whitt CD (1952) Vapor pressure of phosphoric acids. Ind Eng Chem 44:615–618

    Article  Google Scholar 

  174. Wartenberg V (1937) The thermochemistry of the chemical substances. Russel Bichowsky RR, Rossini DF. Book Department Reinhold Publishing Corporation, New York. Z Elektrochem Angew Phys Chem 43:72

    Google Scholar 

  175. Gubbins KE, Walker RD (1965) The solubility and diffusivity of oxygen in electrolytic solutions. J Electrochem Soc 112:469–471

    Article  Google Scholar 

  176. Yatskovskii F (1969) Solubility and diffusion of hydrogen in solution of potassium hydroxide and phosphoric acid. Russ J Phys Chem 43:575–776

    Google Scholar 

  177. Wakefield ZT, Luff BB, Reed RB (1972) Heat capacity and enthalpy of phosphoric acid. J Chem Eng Data 17:420–423

    Article  Google Scholar 

  178. Turnbull AG (1965) Thermal conductivity of phosphoric acid. J Chem Eng Data 10:118–119

    Article  Google Scholar 

  179. Walters HV (1983) Corrosion of a borosilicate glass by orthophosphoric acid. J Am Ceram Soc 66:572–574

    Article  Google Scholar 

  180. Kreysa G, Schütze M (eds) (2008) Corrosion handbook—corrosive agents and their interaction with materials. Wiley-VCH, Weinheim

    Google Scholar 

  181. Li Q, Gang X, Hjuler HA et al (1994) Limiting current of oxygen reduction on gas-diffusion electrodes for phosphoric acid fuel cells. J Electrochem Soc 141:3114–3119

    Article  Google Scholar 

  182. Galbiati S, Baricci A, Casalegno A et al (2012) Experimental study of water transport in a polybenzimidazole-based high temperature PEMFC. Int J Hydrogen Energy 37:2462–2469

    Article  Google Scholar 

  183. Hirschberg HG (1999) Handbuch Verfahrenstechnik und Anlagenbau. Chemie, Technik und Wirtschaftlichkeit. Springer, Berlin

    Google Scholar 

  184. Schmalz EO (1969) Bestimmung der Dampfdruckkurven von Wasser über Phosphorsäuren. Z Phys Chem Leipzig 245:344–350

    Google Scholar 

  185. Kablukov IA, Zagwosdkin KI (1935) Die Dampfspannungen der Phosphorsäurelösungen. Z Anorg Allg Chem 224:315–321

    Article  Google Scholar 

  186. Fontana BJ (1951) The vapor pressure of water over phosphoric acids. J Am Chem Soc 73:3348–3350

    Article  Google Scholar 

  187. Elmore KL, Mason CM, Christensen JH (1946) Activity of orthophosphoric acid in aqueous solution at 25°C from vapor pressure measurements. J Am Chem Soc 68:2528–2532

    Article  Google Scholar 

  188. Jiang C (1996) Thermodynamics of aqueous phosphoric acid solution at 25°C. Chem Eng Sci 51:689–693

    Article  Google Scholar 

  189. Elmore KL, Hatfield JD, Dunn RL et al (1965) Dissociation of phosphoric acid solutions at 25°C. J Phys Chem 69:3520–3525

    Article  Google Scholar 

  190. Mesmer RE, Baes CF (1974) Phosphoric acid dissociation equilibria in aqueous solutions to 300°C. J Solution Chem 3:307–322

    Article  Google Scholar 

  191. Preston CM, Adams WA (1979) A laser Raman spectroscopic study of aqueous orthophosphate salts. J Phys Chem 83:814–821

    Article  Google Scholar 

  192. Cherif M, Mgaidi A, Ammar N et al (2000) A new investigation of aqueous orthophosphoric acid speciation using raman spectroscopy. J Solution Chem 29:255–269

    Article  Google Scholar 

  193. Marshall WL, Begun GM (1989) Raman spectroscopy of aqueous phosphate solutions at temperatures up to 450°C. Two liquid phases, supercritical fluids, and pyro- to ortho-phosphate conversions. J Chem Soc, Faraday Trans 2(85):1963–1978

    Article  Google Scholar 

  194. Higgins CE, Baldwin WH (1955) Dehydration of orthophosphoric acid. Anal Chem 27:1780–1783

    Article  Google Scholar 

  195. Jameson RF (1959) The composition of the strong phosphoric acids. J Chem Soc: 752–759

    Google Scholar 

  196. Huhti AL, Gartaganis PA (1956) The composition of the strong phosphoric acids. Can J Chem 34:785–797

    Article  Google Scholar 

  197. Nelson AK (1964) Hydrolysis rates of solutions of pyrophosphoric acid. J Chem Eng Data 9:357

    Article  Google Scholar 

  198. Bunton CA, Chaimovich H (1965) The acid-catalyzed hydrolysis of pyrophosphoric acid. Inorg Chem 4:1763–1766

    Article  Google Scholar 

  199. Nuri B (2011) Das Dampf-flüssig-Gleichgewicht Phosphorsäure-Wasser bei Anwesenheit von Polybenzimidazol. Diplomarbeit, Technische Universität Darmstadt

    Google Scholar 

  200. Squires RG, Reklaitis GV (eds) (1980) Computer applications to chemical engineering. Computation of phase and chemical equilibrium: a review. ACS symposium series. American Chemical Society, Washington, DC, pp 115–134

    Google Scholar 

  201. Smith WR (1980) The computation of chemical equilibria in complex systems. Ind Eng Chem Fund 19:1–10

    Article  Google Scholar 

  202. Greiner H (1988) Computing complex chemical equilibria by generalized linear programming. Math Comput Model 10:529–550

    Article  MathSciNet  MATH  Google Scholar 

  203. Debye P, Hückel E (1923) Zur Theorie der Elektrolyte. I. Gefrierpunktserniedrigung und verwandte Erscheinungen. The theory of electrolytes. I. Lowering of freezing point and related phenomena. Physik Z 24:185–206

    MATH  Google Scholar 

  204. Waisman E, Lebowitz JL (1970) Exact solution of an integral equation for the structure of a primitive model of electrolytes. J Chem Phys 52:4307–4309

    Article  Google Scholar 

  205. Poling BE, Prausnitz JM, O’Connell JP (2001) The properties of gases and liquids, 5th edn. McGraw-Hill, New York

    Google Scholar 

  206. Wang P, Springer RD, Anderko A et al (2004) Modeling phase equilibria and speciation in mixed-solvent electrolyte systems. Fluid Phase Equilib 222–223:11–17

    Article  Google Scholar 

  207. Messnaoui B, Bounahmidi T (2005) Modeling of excess properties and vapour-liquid equilibrium of the system H3PO4–H2O. Fluid Phase Equilib 237:77–85

    Article  Google Scholar 

  208. Pitzer K, Silvester L (1976) Thermodynamics of electrolytes. VI. Weak electrolytes including H3PO4. J Solution Chem 5:269–278

    Article  Google Scholar 

  209. Cherif M, Mgaidi A, Ammar MN et al (2000) Modelling of the equilibrium properties of the system H3PO4-H2O: Representation of VLE and liquid phase composition. Fluid Phase Equilib 175:197–212

    Article  Google Scholar 

  210. Cherif M, Mgaidi A, Ammar MN et al (2002) Representation of VLE and liquid phase composition with an electrolyte model: application to H3PO4-H2O and H2SO4-H2O. Fluid Phase Equilib 194–197:729–738

    Article  Google Scholar 

  211. Rumpf B, Maurer G (1994) Solubility of ammonia in aqueous solutions of phosphoric acid: model development and application. J Solution Chem 23:37–51

    Article  Google Scholar 

  212. Barker JA (1967) Perturbation theory and equation of state for fluids: the square-well potential. J Chem Phys 47:2856–2861

    Article  Google Scholar 

  213. Barker JA (1967) Perturbation theory and equation of state for fluids. II. A successful theory of liquids. J Chem Phys 47:4714–4721

    Article  Google Scholar 

  214. Gross J, Sadowski G (2001) Perturbed-chain SAFT: an equation of state based on a perturbation theory for chain molecules. Ind Eng Chem Res 40:1244–1260

    Article  Google Scholar 

  215. van Nhu N, Singh M, Leonhard K (2008) Quantum mechanically based estimation of perturbed-chain polar statistical associating fluid theory parameters for analyzing their physical significance and predicting properties. J Phys Chem B 112:5693–5701

    Article  Google Scholar 

  216. Cameretti LF, Sadowski G, Mollerup JM (2005) Modeling of aqueous electrolyte solutions with perturbed-chain statistical associated fluid theory. Ind Eng Chem Res 44:3355–3362

    Article  Google Scholar 

  217. Held C, Reschke T, Mohammad S, Luza A, Sadowski G (2014) ePC-SAFT revised. Chem Eng Res Des. http://dx.doi.org/10.1016/j.cherd.2014.05.017

  218. Naeem S, Sadowski G (2010) pePC-SAFT: modeling of polyelectrolyte systems. Fluid Phase Equilib 299:84–93

    Article  Google Scholar 

  219. Lewis WK, Whitman WG (1924) Principles of gas absorption. Ind Eng Chem 16:1215–1220

    Article  Google Scholar 

  220. Toor HL, Marchello JM (1958) Film-penetration model for mass and heat transfer. AIChE J 4:97–101

    Article  Google Scholar 

  221. Higbie R (1935) The rate of absorption of a pure gas into still liquid during short periods of exposure. Trans Am Inst Chem Eng 35:36–60

    Google Scholar 

  222. Danckwerts PV (1951) Significance of liquid-film coefficients in gas absorption. Ind Eng Chem 43:1460–1467

    Article  Google Scholar 

  223. Hertz H (1882) Ueber die Verdunstung der Flüssigkeiten, insbesondere des Quecksilbers, im luftleeren Raume. Ann Phys 253:177–193

    Article  Google Scholar 

  224. Knudsen M (1915) Die maximale Verdampfungsgeschwindigkeit des Quecksilbers. Ann Phys 352:697–708

    Article  Google Scholar 

  225. Prüger W (1940) Die Verdampfungsgeschwindigkeit der Flüssigkeiten. Z Phys 115:202–244

    Article  Google Scholar 

  226. Eames IW, Marr NJ, Sabir H (1997) The evaporation coefficient of water: a review. Int J Heat Mass Transfer 40:2963–2973

    Article  MATH  Google Scholar 

  227. Matsumoto M (1998) Molecular dynamics of fluid phase change. Fluid Phase Equilib 144:307–314

    Article  Google Scholar 

  228. Meland R, Frezzotti A, Ytrehus T et al (2004) Nonequilibrium molecular-dynamics simulation of net evaporation and net condensation, and evaluation of the gas-kinetic boundary condition at the interphase. Phys Fluids 16:223–243

    Article  MATH  Google Scholar 

  229. Marek R, Straub J (2001) Analysis of the evaporation coefficient and the condensation coefficient of water. Int J Heat Mass Transfer 44:39–53

    Article  MATH  Google Scholar 

  230. Schrage RW (1953) A theoretical study of interphase mass transfer. Columbia University Press, New York

    Google Scholar 

  231. Nabavian K, Bromley LA (1963) Condensation coefficient of water. Chem Eng Sci 18:651–660

    Article  Google Scholar 

  232. Kwon K, Park JO, Yoo DY et al (2009) Phosphoric acid distribution in the membrane electrode assembly of high temperature proton exchange membrane fuel cells. Electrochim Acta 54:6570–6575

    Article  Google Scholar 

  233. Chen C, Lai W (2010) Effects of temperature and humidity on the cell performance and resistance of a phosphoric acid doped polybenzimidazole fuel cell. J Power Sources 195:7152–7159

    Article  Google Scholar 

  234. Matar S, Higier A, Liu H (2010) The effects of excess phosphoric acid in a polybenzimidazole-based high temperature proton exchange membrane fuel cell. J Power Sources 195:181–184

    Article  Google Scholar 

  235. Kaserer S, Caldwell KM, Ramaker DE, Roth C (2013) Analyzing the influence of H3PO4 as catalyst poison in high temperature PEM fuel cells using in-operando X-ray absorption spectroscopy. J Phys Chem C 117:6210–6217

    Article  Google Scholar 

  236. Sui Y, Ding H, Spelt PD (2014) Numerical simulations of flows with moving contact lines. Annu Rev Fluid Mech 46:97–119

    Article  MathSciNet  MATH  Google Scholar 

  237. Lee MS, Aute V, Riaz A, Radermacher R (2012) A review on direct two-phase. Phase change flow simulation methods and their applications. In: International refrigeration and air conditioning conference, Purdue University Purdue e-Pubs, Paper 1289. http://docs.lib.purdue.edu/iracc/1289

  238. Mukherjee PP, Kang Q, Wang C (2011) Pore-scale modeling of two-phase transport in polymer electrolyte fuel cells—progress and perspective. Energy Environ Sci 4:346–369

    Article  Google Scholar 

  239. Garnett JCM (1904) Colours in metal glasses and in metallic films. Philos Trans R Soc A 203:385–420

    Article  MATH  Google Scholar 

  240. Das PK, Li X, Liu Z (2010) Effective transport coefficients in PEM fuel cell catalyst and gas diffusion layers: beyond Bruggeman approximation. Appl Energy 87:2785–2796

    Article  Google Scholar 

  241. Huang JC (1979) Oxygen reduction on platinum in 85% orthophosphoric acid. J Electrochem Soc 126:786–792

    Article  Google Scholar 

  242. Kunz HR, Gruver G (1975) The catalytic activity of platinum supported on carbon for electrochemical oxygen reduction in phosphoric acid. J Electrochem Soc 122:1279–1287

    Article  Google Scholar 

  243. Neyerlin K, Singh A, Chu D (2008) Kinetic characterization of a Pt-Ni/C catalyst with a phosphoric acid doped PBI membrane in a proton exchange membrane fuel cell. J Power Sources 176:112–117

    Article  Google Scholar 

  244. Liu Z, Wainright JS, Litt MH, Savinell RF (2006) Study of the oxygen reduction reaction (ORR) at Pt interfaced with phosphoric acid doped polybenzimidazole at elevated temperature and low relative humidity. Electrochim Acta 51:3914–3923

    Article  Google Scholar 

  245. Li Q, Gang X, Hjuler HA, Bjerrum NJ (1995) Oxygen reduction on gas-diffusion electrodes for phosphoric acid fuel cells by a potential decay method. J Electrochem Soc 142:3250–3256

    Article  Google Scholar 

  246. Peters R, Scharf F (2012) Computational fluid dynamic simulation using supercomputer calculation capacity. In: Stolten D, Emonts B (eds) Fuel cell science and engineering—materials, processes, systems and technology. Wiley-VCH, Weinheim, pp 703–732

    Chapter  Google Scholar 

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Siegel, C., Lang, S., Fontes, E., Beckhaus, P. (2016). Approaches for the Modeling of PBI/H3PO4 Based HT-PEM Fuel Cells. In: Li, Q., Aili, D., Hjuler, H., Jensen, J. (eds) High Temperature Polymer Electrolyte Membrane Fuel Cells. Springer, Cham. https://doi.org/10.1007/978-3-319-17082-4_18

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