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Transport in Polymer-Electrolyte Membranes
Open accessAbstract
A mathematical model is developed that is based on our previous physical model. The governing equations are presented for both the vapor- and liquid-equilibrated transport modes as well as when they both occur. Thus, this model bridges the gap between the one-phase and two-phase macroscopic models currently used in the literature. In addition to being able to model such phenomena as Schroeder's paradox, the model incorporates other relatively novel features including the effect of temperature on water uptake by the membrane from water vapor, and its associated effects on transport properties. Just as in the physical model, the mathematical model uses the wealth of knowledge contained in the literature to examine and determine values for the relevant transport and membrane parameters. This also helps in corroborating the physical model. The mathematical model developed is further validated and its results examined in a subsequent paper where it is placed in a simple fuel-cell model. © 2004 The Electrochemical Society. All rights reserved.
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“From a thermodynamic standpoint, the inclusion of pressure as a local variable, in addition to electrolyte potential and water content, is almost certainly an overdetermination of the system except for the liquid-equilibrated case; it has not found general support [65,78].”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [65]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“The substantive difference between the transport equations used for the Weber–Newman model and the Springer model is the presence of a cross-term contribution to the current density expression due to water streaming current, which is non-zero wherever the water chemical potential is non-uniform through the membrane.”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [65]
Experimental — accuracy not yet measuredThe source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“This equation is unsuitable in the VE regime where the assumption of the presence of liquid water is not valid [65,96].”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [65]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“Weber and Newman have advocated the interpretation of the hydrated membrane as a system with three chemical components: water, protons, and fixed membrane structure [65].”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [65]
The cited source says what the claim attributes to it.
In the citing paper
“From a thermodynamic standpoint, the inclusion of pressure as a local variable, in addition to electrolyte potential and water content, is almost certainly an overdetermination of the system except for the liquid-equilibrated case; it has not found general support [65,78].”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [65]
The cited source says what the claim attributes to it.
In the citing paper
“Hence, the LE water flux becomes a hydraulic flow [65]:(103)Nw,L=−αw,L∇p+ξLFi”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [65]
The cited source says what the claim attributes to it.
In the citing paper
“In the Weber–Newman model, the liquid-equilibrated gradient of water chemical potential in (47) is expressed as [65]:(102)∇μw,L=V¯w∇p”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [65]
The cited source says what the claim attributes to it.
In the citing paper
“Weber and Newman compiled then-available experimental data to give the following expressions for H2 and O2 permeability under VE and LE conditions, with water content-dependence in the former case (coefficient data are tabulated in Table 9, and permeation coefficients are plotted against temperature in Figure 9) [65]:(117)ψi,V=(ψw,iϕw+ψV0,i)exp(EA,DV,iR(1T0−1T)) (118)ψi,L=ψL0,iexp(EA,DL,iR(1T0−1T)”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [65]
The cited source says what the claim attributes to it.
In the citing paper
“The proton conductivity and water diffusivity are generally agreed to obey Arrhenius equations in the range 50 °C < T < 80 °C [1,59,65].”
From Modelling the Proton-Conductive Membrane in Practical Polymer Electrolyte Membrane Fuel Cell (PEMFC) Simulation: A Review (2020) · cites this paper as [65]
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Carneiro, L. F., da Costa, E. F., Andrade, S. T. D. P., & Matencio, T. (2025) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2025.04.451 · Cited by 4
Krowne, C. M. (2024) · Journal of The Electrochemical Society · doi:10.1149/1945-7111/ad80d4 · Cited by 4
Ryu, J.-H., Lee, H.-J., & Sunwoo, M.-H. (2010) · Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering · doi:10.1243/09544070jauto1269 · Cited by 4
Test Procedure for the Prediction of Water Transport in Polymer Electrolyte Fuel Cells
Lübben, L., Kirsch, S., Kadyk, T., & Eikerling, M. H. (2022) · Journal of Power Sources · doi:10.1016/j.jpowsour.2022.232504 · Cited by 4
Electrochemical Materials for PEM Fuel Cells: Insights from Physical Theory and Simulation
Eikerling, M. H., & Malek, K. (2008) · Modern aspects of electrochemistry · doi:10.1007/978-0-387-49582-8_5 · Cited by 4
Song, Y., Wang, C., Wang, L., Wang, X., Jia, L., & Wang, Q. (2026) · eTransportation · doi:10.1016/j.etran.2026.100545 · Cited by 3
Evaluating the PEM fuel cell performance under accelerated creep of sealants
Kumar, P. V., & Koorata, P. K. (2025) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2025.01.024 · Cited by 3
Flores, D. F. F. R., Franceschini, E. A., Calderón, C. A., Acosta, R. H., & Velasco, M. I. (2025) · Journal of Membrane Science · doi:10.1016/j.memsci.2025.123958 · Cited by 3
Zanella, E., Longhi, M., Tondelli, G., Minguzzi, A., Comite, A., Vertova, A., & Pirola, C. (2025) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2025.04.014 · Cited by 3
Bechtel, S., Vidaković-Koch, T. R., Weber, A. Z., & Sundmacher, K. (2020) · Journal of The Electrochemical Society · doi:10.1149/1945-7111/ab6449 · Cited by 3
Self-citationThermodynamics of Interaction between Poly(perfluorosulfonic acid) Nafion and Water
Chernyuk, S. D., Сафронов, А. П., Adamova, L. V., & Бушкова, О. В. (2023) · Polymer Science Series A · doi:10.1134/s0965545x23700839 · Cited by 3
Fluid Physics Impacting Vanadium and Other Redox Flow Batteries
Krowne, C. M. (2024) · Journal of The Electrochemical Society · doi:10.1149/1945-7111/ad5252 · Cited by 3
Desai, A. N., Mohanty, S., Ramadesigan, V., & Singh, S. (2025) · Chemical Engineering Journal · doi:10.1016/j.cej.2025.165945 · Cited by 3
Rama, P., & Chen, R. (2010) · Journal of Fuel Cell Science and Technology · doi:10.1115/1.4001004 · Cited by 3
Yang, X. L., Yin, Y. S., Jia, B., & Du, Q. (2012) · Advanced materials research · doi:10.4028/www.scientific.net/amr.625.235 · Cited by 3
Effect of molecular structure of sulphonated polyimide membranes on water sorption
Li, Y., Nguyen, Q. T., Buquet, C. L., & Marais, S. (2014) · IET Nanobiotechnology · doi:10.1049/iet-nbt.2013.0036 · Cited by 3
Secanell, M., Jarauta, A., Kosakian, A., Sabharwal, M., & Zhou, J. (2017) · ERA: Education and Research Archive (University of Alberta) · doi:10.7939/r3-86yz-q927 · Cited by 4
Proton Conductivity and Methanol Permeability of Sulfonated Syndiotactic Polystyrene Membranes
Borriello, A., & Napolitano, T. (2011) · Soft Materials · doi:10.1080/1539445x.2011.552382 · Cited by 3
Modeling of Polymer Electrolyte Membrane Fuel‐Cell Components
Wang, Y., & Chen, K. S. (2012) · Wiley eBooks · doi:10.1002/9783527650248.ch30 · Cited by 3
Modeling Nanoscale Ohmics in Carbon Supports of Fuel Cell Cathodes
Wan, C. T., Darling, R. M., Chiang, Y., & Brushett, F. R. (2023) · Journal of The Electrochemical Society · doi:10.1149/1945-7111/acd4ef · Cited by 2
Built-In Open Circuit Reference Electrodes in a PEM Water Electrolysis Cell – A Proof of Concept
Franzetti, I., Dai, C., Metz, S., & Smolinka, T. (2025) · Journal of The Electrochemical Society · doi:10.1149/1945-7111/ae204e · Cited by 2
Modeling of hydrogen crossover in a pressurized PEM electrolyzer
Haque, S. M. A., Aziz, M., Amrite, A., & Prasad, A. K. (2026) · International Journal of Hydrogen Energy · doi:10.1016/j.ijhydene.2026.155571 · Cited by 2
Metadata
- Authors
- Weber, A. Z., & Newman, J.
- Affiliations
- University of California, Berkeley (US)
- Venue
- Journal of The Electrochemical Society
- Publisher
- The Electrochemical Society
- Published
- 2004
- Volume
- 151
- Issue
- 2
- Pages
- A311
- ISSN
- 0013-4651 (ISSN-L)
- OpenAlex
- W1903915324
- Cited by
- 462
- References
- 97
- Citations by year
- 2026: 26 · 2025: 29 · 2024: 29 · 2023: 30 · 2022: 27 · 2021: 16 · 2020: 17 · 2019: 22 · 2018: 18 · 2017: 14 · 2016: 15 · 2015: 16 · 2014: 20 · 2013: 15 · 2012: 23
- FWCI
- 16.60
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Journal of The Electrochemical Society (publishedVersion)
- Topics
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Fuel Cells and Related Materials
- Physical Sciences › Chemical Engineering › Filtration and Separation › Membrane Separation and Gas Transport
- Physical Sciences › Materials Science › Materials Chemistry › Advancements in Solid Oxide Fuel Cells
- Keywords
- polymer electrolyte membranes, water transport, two-phase transport, water absorption, temperature effects, fuel cells
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