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Cited by 3,528Fuel Cells and Related MaterialsAdvancements in Solid Oxide Fuel CellsMembrane-based Ion Separation Techniques

Polymer Electrolyte Fuel Cell Model

Open access
Springer, T. E., Zawodzinski, T. A., Gottesfeld, S.·1991·Journal of The Electrochemical Society
DOI 10.1149/1.2085971
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Abstract

We present here an isothermal, one‐dimensional, steady‐state model for a complete polymer electrolyte fuel cell (PEFC) with a 117 Nafion® membrane. In this model we employ water diffusion coefficients electro‐osmotic drag coefficients, water sorption isotherms, and membrane conductivities, all measured in our laboratory as functions of membrane water content. The model predicts a net‐water‐per‐proton flux ratio of 0.2 under typical operating conditions, which is much less than the measured electro‐osmotic drag coefficient for a fully hydrated membrane. It also predicts an increase in membrane resistance with increased current density and demonstrates the great advantage of a thinner membrane in alleviating this resistance problem. Both of these predictions were verified experimentally under certain conditions.

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Crossref · 10.1149/1.2085971

Cites

1 of 1 references verified0 citation errors · 0 not checkable

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  • A number of empirical sorption isotherms have been established experimentally based on measurements on Nafion 1100.

    “A number of empirical sorption isotherms have been established experimentally based on measurements on Nafion 1100 [39,51,52,53,54].”

    From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [39]

    The Mathematical Model section (page unavailable) reports an experimentally measured isopiestic curve and an empirical fit relating water content to water activity for Nafion 117. It supports the existence of an experimentally based sorption relationship, but does not establish that this paper presents a number of isotherms or identify the measured membrane as “Nafion 1100.” (LLM, conf=0.83)

    Experimental — accuracy not yet measured

  • The most commonly used sorption isotherm is an empirical polynomial relation due to Springer et al.

    “The most commonly used sorption isotherm is an empirical polynomial relation due to Springer et al. [39]:”

    From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [39]

    The Mathematical Model section (page not available) gives an empirical polynomial relating membrane water content to water activity, supporting the attribution of that relation to Springer et al. Our copy does not establish that it is the most commonly used sorption isotherm. (LLM, conf=0.88)

    Experimental — accuracy not yet measured

  • The original water diffusivity fit used by Springer et al. was reported incompletely and is now deprecated because it was later refined by Motupally et al.

    “The original fit used by Springer et al. was reported incompletely [39] and is now deprecated, since it was later refined by Motupally et al. [83]”

    From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [39]

    The Mathematical Model gives an explicit water-diffusivity fit only for water content above 4; for lower values, it says the model used tabular interpolation. That supports the narrower point that the published fit does not cover the full range, but the paper does not call its reporting incomplete. The later refinement and deprecation are attached to a different citation in the citing sentence and cannot be established from this source. (LLM, conf=0.78)

    Experimental — accuracy not yet measured

  • Models that focus on conditions of vapour equilibration, especially those based on the Springer model and its transient extension, may ignore pressure gradients altogether.

    “Models that focus on conditions of vapour equilibration, especially those based on the Springer model and its transient extension, may ignore pressure gradients altogether [39,124,145].”

    From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [39]

    The Mathematical Model section says the model assumes concentration gradients, not total-pressure gradients, across the electrodes, and the General Aspects section assumes water-vapour equilibrium at the electrode–membrane interface. But the paper expressly allows a pressure drop across the membrane when anode and cathode pressures differ, so “altogether” is too broad; it also does not describe the transient extension. (LLM, conf=0.87)

    Experimental — accuracy not yet measured

  • Experimental measurements of the inelastic expansion strain due to membrane swelling suggest a magnitude of the order of 0.01 per unit λ in unreinforced membranes.

    “Experimental measurements of the inelastic expansion strain due to membrane swelling suggest a magnitude of the order of 0.01 per unit λ in unreinforced membranes [1,39,150];”

    From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [39]

    The Mathematical Model section (page unavailable) uses a thickness expansion factor of (1 + sλ) and reports s = 0.0126 from measurements of dry and fully hydrated Nafion 117, supporting an expansion of order 0.01 per unit λ. It does not characterize that expansion as inelastic or establish the value for unreinforced membranes generally. (LLM, conf=0.82)

    Experimental — accuracy not yet measured

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Cites

Flagged first, then by citations

Research works printed but not linked: 14

  1. R. A. Lemons, J. Power Sources, 29, 251 (1990).
  2. M. Verbrugge and R. Hill, J. Phys. Chem., 92, 6778 (1988).
  3. M. Verbrugge, This Journal, 136, 417 (1989).
  4. R. Hill and M. Verbrugge, ibid., 137, 886 (1990).
  5. J. L. Fales, N. E. Vanderborgh, and P. Stroeve, in "Dia- phragms, Separators, and Ion-Exchange Mem- branes," J.W. van Zee, R. E. White, K. Kinoshita, and H.S. Burney, Editors, PV86-13, p. 179, The Electrochemical Society Softbound Proceedings Series, Pennington, NJ (1986).
  6. T. Fuller and J. Newman, in "Fuel Cells," R. E. White and A. J. Appleby, Editors, PV 89-14, p. 25, The Elec- trochemical Society Softbound Proceedings Series, Pennington, NJ (1984).
  7. J. C. Slattery and R. B. Bird, AtChE J., 4, 137 (1958).
  8. R. E. De La Rue and C. W. Tobias, This Journal, 106, 827 (1959).
  9. "Handbook of Chemistry and Physics," 62nd ed., CRC Press, Boca Raton, FL (1981).
  10. C. Derouin, J. Pafford, S. Radzinski, T. Springer, and S. Gottesfeld, Abstract 627, p. 903, The Electrochem- ical Society Extended Abstracts, Vol. 89-1, Los Angeles, CA, May 7-12, 1989.
  11. S. C. Yeo and A. Eisenberg, J. Appl. Polym. Sci., 21, 875 (1977).
  12. J. Crank, "The Mathematics of Diffusion," 2nd ed., Clarendon, Oxford (1975).
  13. T. Nguyen, J. C. Hedstrom, and N. Vanderborgh, in "Fuel Cells," R. White and A. Appleby, Editors, PV 89-14, p. 39, The Electrochemical Society, Soft- bound Proceedings Series, Pennington, NJ (1989).
  14. T.E. Springer and I. D. Raistrick, This Journal, 136, 1594 (1989).

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Related

Authors
Springer, T. E., Zawodzinski, T. A., & Gottesfeld, S.
Affiliations
Los Alamos National Laboratory (US)
ORCID
Venue
Journal of The Electrochemical Society
Publisher
The Electrochemical Society
Published
1991-08-01
Volume
138
Issue
8
Pages
2334-2342
ISSN
  • 0013-4651 (ISSN-L)
  • 1945-7111
DOI
10.1149/1.2085971
OpenAlex
W2044307855
Cited by
3,528
References
1
Citations by year
2026: 164 · 2025: 157 · 2024: 169 · 2023: 151 · 2022: 155 · 2021: 151 · 2020: 111 · 2019: 125 · 2018: 128 · 2017: 140 · 2016: 114 · 2015: 120 · 2014: 133 · 2013: 106 · 2012: 149
FWCI
5.10
Type
journal article
Language
en
Open access
Licence
Locations
Journal of The Electrochemical Society (publishedVersion)
Funders
U.S. Department of Energy
Topics
  • Physical Sciences › Engineering › Electrical and Electronic Engineering › Fuel Cells and Related Materials
  • Physical Sciences › Materials Science › Materials Chemistry › Advancements in Solid Oxide Fuel Cells
  • Physical Sciences › Engineering › Biomedical Engineering › Membrane-based Ion Separation Techniques
Keywords
proton exchange membrane fuel cells, Nafion membrane, one-dimensional steady-state model, water diffusion coefficient, moisture sorption isotherms, membrane conductivity, membrane hydration, membrane resistance, current density, membrane thickness

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