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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]
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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]
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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]
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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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Self-citation
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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