Skip to main content
SpringerLink
Log in

Inclusion of surface heterogeneity in bridging PEM fuel cell electrode contamination kinetics and transport via a competitive Langmuir-Freundlich isotherm

  • Original Paper
  • Published:
Journal of Solid State Electrochemistry Aims and scope Submit manuscript

Abstract

This paper reports the development of mathematical model that bridges PEMFC transport phenomena with surface reaction kinetics in rough and heterogeneous electrodes, in which specifically the anode is modeled under carbon monoxide contamination. The mathematical bridging is done by converting surface concentration of reactants and contaminant into surface coverage of relevant adsorbates using the Langmuir-Freundlich isotherm to statistically include heterogeneity in binding site energetics. Thermodynamically optimized kinetic rate and equilibrium constants are calculated using coverage-dependent activation energies and provided as input to the HOR, ORR, and a kinetic-based limiting current model developed to solve for the distribution of activation overpotential. A novel model for a closed-form calculation of activation overpotential is proposed to allow numerical investigation via a galvanostatic approach. The kinetic reaction models are highly coupled with three-dimensional transport equations and solved iteratively under single-phase and steady-state conditions. Comparison is done with respect to two sets of available literature data in order to test the kinetic model validity under variation of CO concentrations and cell operating temperatures, in which good agreement is found. The results confirm that a Langmuir-Freundlich isotherm could be a more suitable isotherm compared to the extensively used Langmuir-specific isotherm for rough heterogeneous surfaces physically found in PEMFC catalysts. Results from the model show that rate of HOR is higher under the ribs of the cell since most of the active sites under channel are blocked with CO, with the effect exacerbated at lower temperatures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Abbreviations

a :

Water activity

c :

Concentration, mol m−3

c p :

Specific heat, J kg−1 K−1 or J mol−1 K−1

A :

Area, m2

D :

Diffusion coefficient, m2 s−1

\( \widehat{D} \) :

Pseudo-diffusion coefficient, m2 s−1

E :

Electrode potential, V

\( {\tilde{E}}_{\mathrm{a}} \) :

Activation energy, J mol−1

F :

Faraday’s constant, 96,485 C mol−1

h :

Heterogeneity index

i :

Local current density based on geometric area, A m−2

\( \overline{i} \) :

Local current density based on Pt area, A m − 2Pt

j :

Volumetric local current density, A m−3

k :

Thermal conductivity, W m−1 K−1

k f :

Forward rate constant, first order, m3 mol−1 s−1, second order, m5 mol−2 s−1

k b :

Backward rate constant, first order, s−1, second order, m2 mol−1 s−1

K :

Equilibrium constant, H, CO, O, and H2O adsorption, kPa−1, H2O desorption, kPa

L Pt :

Catalyst loading, mgPt cm−2

K p :

Hydraulic permeability, m2

M :

Molecular weight, kg mol−1

P :

Pressure, Pa

r f :

Roughness factor

R :

Universal gas constant, 8.314 J mol−1 K−1

R ohmic :

Ohmic resistance, Ω m2

s 0 :

Sticking coefficient

S :

Source term

\( \widehat{S} \) :

Pseudo-source term

ΔS :

Entropy change, J mol−1 K−1

T :

Temperature, K

u :

Velocity, m s−1

X :

Mole fraction

\( \widehat{X} \) :

Pseudo-mole fraction

x, y, z :

Cartesian coordinates, m

Γ:

Site density, mol m−2

α :

Symmetry coefficient

β :

Temperature exponent, K

ε :

Porosity

η :

Overpotential, V

θ :

Surface coverage

λ :

Hydration

μ :

Dynamic viscosity, Pa s

ρ :

Density, kg m−3

τ :

Tortuosity

σ :

Conductivity, S m−1

φ :

Relative humidity, %

ϕ :

Local potential, V

0:

Standard

a:

Anode

c:

Cathode

eff:

Effective

geom:

geometric

i, j :

Species i or j

in:

Inlet

M:

Ionomer phase

r:

Reactive

rev:

reversible

s:

solid phase

References

  1. Li X (2006) Principles of fuel cells. Taylor & Francis, New York

    Google Scholar 

  2. Gottesfeld S, Pafford J (1988) J Electrochem Soc 135(10):2651–2652

    Article  CAS  Google Scholar 

  3. Somorjai GA (2010) Introduction to surface chemistry and catalysis. Wiley, New Jersey

    Google Scholar 

  4. Gilman S (1964) J Phys Chem 68(1):70–80

    Article  CAS  Google Scholar 

  5. Hasmady S, Hatakeyama T, Wacker MP, Fushinobu K, Okazaki K (2009) Therm Sci Eng 17:147–156

    CAS  Google Scholar 

  6. Springer TE, Rockward T, Zawodzinski TA, Gottesfeld S (2001) J Electrochem Soc 148(1):A11–A23

    Article  CAS  Google Scholar 

  7. Camara GA, Ticianelli EA, Mukerjee S, Lee SJ, McBreen J (2002) J Electrochem Soc 149(6):A748–A53

    Article  CAS  Google Scholar 

  8. Bhatia KK, Wang C-Y (2004) Electrochim Acta 49:2333–2341

    Article  CAS  Google Scholar 

  9. Baschuk JJ, Li X (2003) Int J Energy Res 27:1095–1116

    Article  CAS  Google Scholar 

  10. Zhou T, Liu H (2004) J Power Sources 138:101–110

    Article  CAS  Google Scholar 

  11. Ju H, Lee KS, Um S (2008) J Mech Sci Technol 22:991–998

    Article  Google Scholar 

  12. Siegel C (2008) Energy 33:1331–1352

    Article  CAS  Google Scholar 

  13. Shah AA, Luo KH, Ralph TR, Walsh FC (2011) Electrochim Acta 56:3731–3757

    Article  CAS  Google Scholar 

  14. Franco AA, Schott P, Jallut C, Maschke B (2006) J Electrochem Soc 153(6):A1053–A1061

    Article  CAS  Google Scholar 

  15. Wei ZD, Ran HB, Liu XA, Liu Y, Sun CX, Chan SH, Shen PK (2006) Electrochim Acta 51:3091–3096

    Article  CAS  Google Scholar 

  16. Hartnig C, Koper MTM (2002) J Electroanal Chem 532:165–170

    Article  CAS  Google Scholar 

  17. Mazumder S, Cole JV (2003) J Electrochem Soc 150(11):A1503–A1509

    Article  CAS  Google Scholar 

  18. Nguyen PT, Berning T, Djilali N (2004) J Power Sources 130:149–157

    Article  CAS  Google Scholar 

  19. Ju H, Meng H, Wang C-Y (2005) Int J Heat Mass Transfer 48:1303–1315

    Article  CAS  Google Scholar 

  20. Hwang JJ (2006) J Electrochem Soc 153(2):A216–A224

    Article  CAS  Google Scholar 

  21. Weber AZ, Newman J (2004) Chem Rev 104:4679–4726

    Article  CAS  Google Scholar 

  22. Wang C-Y (2004) Chem Rev 104:4727–4766

    Article  CAS  Google Scholar 

  23. Yi JS, Nguyen TV (1999) J Electrochem Soc 146(1):38–45

    Article  CAS  Google Scholar 

  24. Berning T, Djilali N (2003) J Electrochem Soc 150(12):A1589–A1598

    Article  CAS  Google Scholar 

  25. Lum KW, McGuirk JJ (2005) J Power Sources 143:103–124

    Article  CAS  Google Scholar 

  26. Khajeh-Hosseini-Dalasm N, Fushinobu K, Okazaki K (2010) J Electrochem Soc 157(10):B1358–B1369

    Article  CAS  Google Scholar 

  27. Oetjen HF, Schmidt VM, Stimming U, Trila F (1996) J Electrochem Soc 143(12):3838–3842

    Article  CAS  Google Scholar 

  28. Lee SJ, Mukerjee S, Ticianelli EA, McBreen J (1999) Electrochim Acta 44:3283–3293

    Article  CAS  Google Scholar 

  29. Reid RC, Sherwood TK (1958) The properties of gases and liquids. McGraw-Hill, New York

    Google Scholar 

  30. Hirschfielder JO, Curtis CF, Bird RB (1954) Molecular theory of gases and liquids. Wiley, New York

    Google Scholar 

  31. Bird RB, Stewart WE, Lightfoot EN (2002) Transport phenomena. Wiley, New York

    Google Scholar 

  32. Taylor R, Krishna R (1993) Multicomponent mass transfer. Wiley, New York

    Google Scholar 

  33. Springer TE, Zawodzinski TA, Gottesfeld S (1991) J Electrochem Soc 138(8):2334–2342

    Article  CAS  Google Scholar 

  34. Zamel N (2011) Transport properties of the gas diffusion layer of PEM fuel cells, PhD Thesis, University of Waterloo, Ontario, Canada

  35. Masuda M (2003) Hydrogen-based integrated energy system for building equipment, PhD Thesis (in Japanese), Tokyo Institute of Technology, Tokyo, Japan

  36. Japan Society of Mechanical Engineers (1986) JSME data book: heat transfer. Maruzen, Tokyo

    Google Scholar 

  37. Gasteiger HA, Gu W, Makharia R, Mathias MF, Sompalli B (2003) Handbook of fuel cells. In: Vielstich W, Lamm A, Gasteiger HA (eds) Fuel cell technology & applications, vol 3. Wiley, West Sussex, pp 593–610

    Google Scholar 

  38. Markovic NM, Grgur BN, Lucas CA, Ross PN (1999) J Phys Chem B 103:487–495

    Article  CAS  Google Scholar 

  39. Koper MTM, Jansen APJ, van Santen RA, Lukkien JJ, Hilbers PAJ (1998) J Chem Phys 109:6051–6062

    Article  CAS  Google Scholar 

  40. Breiter MW (2003) Handbook of fuel cells. In: Vielstich W, Lamm A, Gasteiger HA (eds) Electrocatalysis, vol 2. Wiley, West Sussex

    Google Scholar 

  41. Umpleby RJ, Baxter SC, Chen Y, Shah RN, Shimizu KD (2001) Anal Chem 73(19):4584–4591

    Article  CAS  Google Scholar 

  42. Sips R (1948) J Chem Phys 16(5):490–495

    Article  CAS  Google Scholar 

  43. de Becdelièvre AM, de Becdelièvre J, Clavilier J (1990) J Electroanal Chem 294:97–100

    Article  Google Scholar 

  44. Balasubramanian S, Lakshmanan B, Hetzke CE, Sethuraman VA, Weidner JW (2011) Electrochim Acta 58:723–728

    Article  CAS  Google Scholar 

  45. Hauptmann W, Votsmeiera M, Vogel H, Vlachos DG (2011) Appl Catal A Gen 397:174–182

    Article  CAS  Google Scholar 

  46. Kee RJ, Coltrin ME, Glarborg P (2003) Chemically reacting flow: theory & practice. Wiley, New Jersey

    Book  Google Scholar 

  47. Zhdanov VP, Kasemo B (2006) Electrochem Commun 8:1132–1136

    Article  CAS  Google Scholar 

  48. Gurau V, Liu H, Kakac S (1998) AIChE J 44(11):2410–2422

    Article  CAS  Google Scholar 

  49. Benziger J, Kimball E, Mejia-Ariza R, Kevrekidis I (2011) AIChE J 57(9):2505–2517

    Article  CAS  Google Scholar 

  50. Nitta I, Hottinen T, Himanen O, Mikkola M (2007) J Power Sources 171:26–36

    Article  CAS  Google Scholar 

  51. Gurau B, ELAT® Gas Diffusion Layers. http://fuelcellsetc.com/store/DS/ELAT-Property-Sheet.pdf. Accessed 26 November 2013

  52. Pasaogullari U, Mukherjee PP, Wang C-Y, Chen KS (2007) J Electrochem Soc 154(8):B823–B834

    Article  CAS  Google Scholar 

  53. Lampinen MJ, Fomino M (1993) J Electrochem Soc 140(12):3537–3546

    Article  CAS  Google Scholar 

  54. Ralph TR, Hogarth MP (2002) Platin Met Rev 46(3):117–135

    CAS  Google Scholar 

Download references

Acknowledgment

Part of this work was supported by the Grant-in-Aid for Scientific Research from MEXT/JSPS.

Author information

Authors and Affiliations

  1. Department of Mechanical and Control Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Japan, 152-8552

    Saiful Hasmady & Kazuyoshi Fushinobu

Authors
  1. Saiful Hasmady
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kazuyoshi Fushinobu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saiful Hasmady.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hasmady, S., Fushinobu, K. Inclusion of surface heterogeneity in bridging PEM fuel cell electrode contamination kinetics and transport via a competitive Langmuir-Freundlich isotherm. J Solid State Electrochem 18, 3387–3405 (2014). https://doi.org/10.1007/s10008-014-2521-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10008-014-2521-0

Keywords

Search

Navigation