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Transport in Proton Exchange Membranes for Fuel Cell Applications—A Systematic Non-Equilibrium Approach
Open accessAbstract
We hypothesize that the properties of proton-exchange membranes for fuel cell applications cannot be described unambiguously unless interface effects are taken into account. In order to prove this, we first develop a thermodynamically consistent description of the transport properties in the membranes, both for a homogeneous membrane and for a homogeneous membrane with two surface layers in contact with the electrodes or holder material. For each subsystem, homogeneous membrane, and the two surface layers, we limit ourselves to four parameters as the system as a whole is considered to be isothermal. We subsequently analyze the experimental results on some standard membranes that have appeared in the literature and analyze these using the two different descriptions. This analysis yields relatively well-defined values for the homogeneous membrane parameters and estimates for those of the surface layers and hence supports our hypothesis. As demonstrated, the method used here allows for a critical evaluation of the literature values. Moreover, it allows optimization of stacked transport systems such as proton-exchange membrane fuel cell units where interfacial layers, such as that between the catalyst and membrane, are taken into account systematically.
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![Figure 2 Nafion™ 117 conductivity value comparison. Springer et al. at 80 °C, in-plane, 2-probe (●) [30]; Zawodinski et al. at 30 °C, in-plane, 2-probe (○) [24]; Lee et al. at 60 °C, in-plane, 4-probe (▲) [12]; Lee et al. at 60 °C, in-plane, 2-probe (▽) [12]; Alberti et al., through-plane, 2-probe (♦) [25].](/paper-figures/90586859ef91438cac35794c248dfcaf/transport-in-proton-exchange-membranes-for-fuel-cell-applicationsa-systematic-figure-2.jpg)
![Figure 3 Effect of geometry: (a) Springer et al. [30] in-plane (●) vs. Alberti et al. [25] through-plane (○); (b) Lee et al. 2-probe (●) vs. 4-probe measurements (○) [12].](/paper-figures/8d65423bb11e4d6286333f3708150efa/transport-in-proton-exchange-membranes-for-fuel-cell-applicationsa-systematic-figure-3.jpg)
![Figure 4 Water permeability. Ise, Kreuer at 27 °C (●) [31]; Rivin et al. at 32 °C (◻) [1]; Zhao et al. at 70 °C (◊) [8]; Majztrik et al. at 80 °C (×) [9]; Zawodinski et al. at 30 °C (♦) [23]; Zhao et al. at 70 °C (◐) [8]; Edmondson et al. at room temperature (⧩) [22].](/paper-figures/b4f1679820bf44c085a7eba6e48d8175/transport-in-proton-exchange-membranes-for-fuel-cell-applicationsa-systematic-figure-4.jpg)

![Figure 6 Hydrogen permeability. Schalenbach at 80 °C (●) [35]; Broka et al. at 80 °C (◻) [38]; Sakai et al. at 80 °C (◻) [32]; Jiang et al. at 80 °C (extrapolated) (○) [34]; Dry membrane (▲) [35]; Wet membrane (△) [35].](/paper-figures/ff6ed6aed31b4d2c938ae8a95cfe7af5/transport-in-proton-exchange-membranes-for-fuel-cell-applicationsa-systematic-figure-6.jpg)

![Figure 8 Electro-osmotic drag data compilation. Ise, Kreuer at 27 °C (◼) [31]; Kreuer et al. at 27 °C (▽) [40]; Springer et al. at 80 °C (○) [30]; Onda et al. at 80 °C (×) [42]; Kreuer et al. at 80 °C (+) [2]; Zawodinski at 30 °C (⧩) [23].](/paper-figures/842a75f9bac049ef82ba6f5852522dff/transport-in-proton-exchange-membranes-for-fuel-cell-applicationsa-systematic-figure-8.jpg)
![Figure 9 K-drag—(a) at 30 °C (◻) Electrophoretic NMR [43]; (▼) Volumetric method [23]; (○) Electrolysis cell [42]; (b) at 80 °C (◻) ENMR [40]; (▽) Volumetric [30]; (◻) Electrolysis cell [42].](/paper-figures/d7b6e46718ae4ab9bd6f64368b45b851/transport-in-proton-exchange-membranes-for-fuel-cell-applicationsa-systematic-figure-9.jpg)

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“Rangel-Cárdenas and Koper included H2 permeation of the membrane in a non-equilibrium thermodynamic model, but without any further application of the equations derived thereby [120].”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [120]
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“Evidence for significant interfacial contributions to membrane conductivity measurements has also been presented by Rangel-Cárdenas and Koper [120].”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [120]
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Cites
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Zawodzinski, T. A., Neeman, M., Sillerud, L. O., & Gottesfeld, S. (1991) · The Journal of Physical Chemistry · doi:10.1021/j100168a060 · Cited by 987
Modeling and Experimental Diagnostics in Polymer Electrolyte Fuel Cells
Springer, T. E., Wilson, M. S., & Gottesfeld, S. (1993) · Journal of The Electrochemical Society · doi:10.1149/1.2221120 · Cited by 581
Effect of Interfacial Water Transport Resistance on Coupled Proton and Water Transport Across Nafion
Cheah, M. J., Kevrekidis, I. G., & Benziger, J. (2011) · The Journal of Physical Chemistry B · doi:10.1021/jp204785t · Cited by 68
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Cited by
Sorted by citations
Dickinson, E. J. F., & Smith, G. (2020) · Membranes · doi:10.3390/membranes10110310 · Cited by 109
Metadata
- Authors
- Rangel-Cárdenas, A., & Koper, G.
- Affiliations
- Delft University of Technology (NL)
- Corresponding author
- Koper, Ger
- Venue
- Materials
- Publisher
- MDPI AG
- Published
- 2017-05-25
- Volume
- 10
- Issue
- 6
- Pages
- 576
- ISSN
- 1996-1944 (ISSN-L)
- PMC
- PMC5552083
- OpenAlex
- W2618099852
- Cited by
- 33
- References
- 4
- Citations by year
- 2026: 1 · 2025: 3 · 2024: 2 · 2023: 5 · 2022: 3 · 2021: 5 · 2020: 7 · 2019: 1 · 2018: 5 · 2017: 1
- FWCI
- 1.59
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Licence
- Locations
- Materials (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
- 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 › Chemical Engineering › Filtration and Separation › Membrane-based Ion Separation Techniques
- Keywords
- proton exchange membranes, fuel cell membranes, membrane transport properties, interface effects, surface layer, thermodynamic consistency, nonequilibrium transport, membrane parameters
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