Skip to main content
SpringerLink
Log in

A time and hydration dependent viscoplastic model for polyelectrolyte membranes in fuel cells

  • Published:
Mechanics of Time-Dependent Materials Aims and scope Submit manuscript

Abstract

Ionomers are co-polymers with ionic groups. One of the interesting applications of ionomer membranes is as electrolytes in proton exchange membrane (PEM) fuel cells. The most commonly used membranes in PEM fuel cells are perfluorosulfonic acid (PFSA) membranes, e.g., Nafion® from DuPontTM. Besides its dependency on temperature and hydration due to phase inversion and cluster formation, Nafion® as a polymer, exhibits strong time and rate effects. In this work, the stress–strain behavior of Nafion® at different strain rates has been obtained in an environmental chamber for various temperatures and hydrations. After a certain strain was reached in each test, stress relaxation was performed for an hour to observe the relaxation behavior of Nafion®. We attempted to use a nonlinear, time-dependent constitutive model to predict the hygro-thermomechanical behavior of Nafion®. Because a substantial component of the response is unrecoverable, a viscoplastic model was employed. The proposed two-layer viscoplasticity model consisted of an elastoplastic network that was in parallel with an elastic-viscous network (Maxwell model) which separates the rate-dependent and rate-independent behavior of the material. After obtaining the necessary parameters for different hydrations, this model showed reasonably accurate success in predicting the stress–strain behavior at different strain rates, and matched the relaxation test results. Finite element simulations based on the proposed two-layer viscoplasticity model were in good agreement with test results and can be used to study the stress–strain state of the ionomer membranes in fuel cell configurations.

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.

Similar content being viewed by others

References

  • ABAQUS Analysis User’s Manual, V 6.5. HKS (2005)

  • Banerjee, S., Curtin, D.E.: Nafion(R) perfluorinated membranes in fuel cells. J. Fluor. Chem.: Fluor. Altern. Energy Sources 125(8), 1211–1216 (2004)

    Google Scholar 

  • Bauer, F., Willert-Porada, S.D.M.: Influence of temperature and humidity on the mechanical properties of Nafion®117 polymer electrolyte membrane. J. Polym. Sci. B 43(7), 786–795 (2005)

    Article  Google Scholar 

  • Bauer, F., Denneler, S., Willert-Porada, M.: Influence of temperature and humidity on the mechanical properties of Nafion®117 polymer electrolyte membrane. J. Polym. Sci. B 43(7), 786–795 (2005)

    Article  Google Scholar 

  • Benziger, J., et al.: The dynamic response of PEM fuel cells to changes in load. Chem. Eng. Sci. 60(6), 1743–1759 (2005)

    Article  Google Scholar 

  • Bergstrom, J.S., Boyce, M.C.: Large strain time-dependent behavior of filled elastomers. Mech. Mater. 32(11), 627–644 (2000)

    Article  Google Scholar 

  • Bergstrom, J.S., Hilbert, Jr., L.B.: A constitutive model for predicting the large deformation thermomechanical behavior of fluoropolymers. Mech. Mater. 37(8), 899–913 (2005)

    Article  Google Scholar 

  • Boyce, M.C., Arruda, E.M.: Constitutive models of rubber elasticity: A review. Rubber Chem. Technol. 73(3), 504–523 (2000)

    Google Scholar 

  • Choi, P., Datta, R.: Sorption in proton-exchange membranes. An explanation of Schroeder’s paradox. J. Electrochem. Soc. 150(12) (2003)

  • Christensen, R.M.: Theory of Viscoelasticity: An Introduction, 2nd edn., p. 364. Academic, New York (1982)

    Google Scholar 

  • E.I. du Pont de Nemours & Company: Physical Properties for Nafion Membrane – Types NR and NRE (2003). http://www.dupont.com/fuelcells/pdf/dfc201.pdf

  • Gebel, G.: Structural evolution of water swollen perfluorosulfonated ionomers from dry membrane to solution. Polymer 41(15), 5829–5838 (2000)

    Article  Google Scholar 

  • Gierke, T.D., Munn, G.E., Wilson, F.C.: The morphology in nafion perfluorinated membrane products, as determined by wide- and small-angle X-ray studies. J. Polym. Sci. Part A-2 Polym. Phys. 19(11), 1687–1704 (1981)

    Google Scholar 

  • Hinatsu, J.T., Mizuhata, M., Takenaka, H.: Water uptake of perfluorosulfonic acid membranes from liquid water and water vapor. J. Electrochem. Soc. 141(6), 1493–1498 (1994)

    Article  Google Scholar 

  • Huang, X., et al.: Mechanical endurance of polymer electrolyte membrane and PEM fuel cell durability. J. Polym. Sci. B 44(16), 2346–2357 (2006)

    Article  Google Scholar 

  • Kawano, Y., et al.: Stress–strain curves of nafion membranes in acid and salt forms. Polímeros 12(2), 96–101 (2002)

    Article  Google Scholar 

  • Kichenin, J., Dang Van, K., Boytard, K.: Finite-element simulation of a new two-dissipative mechanisms model for bulk medium-density polyethylene. J. Mater. Sci. 31(6), 1653–1661 (1996)

    Article  Google Scholar 

  • Kletschkowski, T., Schomburg, U., Bertram, A.: Endochronic viscoplastic material models for filled PTFE. Mech. Mater. 34(12), 795–808 (2002)

    Article  Google Scholar 

  • Kletschkowski, T., Schomburg, U., Subramanian, S.: Experimental investigations on the plastic memory effect of PTFE compound. J. Mater. Process. Manuf. Sci. 9(2), 113–130 (2000)

    Article  Google Scholar 

  • Kundu, S., et al.: Mechanical properties of Nafion electrolyte membranes under hydrated conditions. Polymer 46(25), 11707–11715 (2005)

    Article  Google Scholar 

  • Kusoglu, A., et al.: Mechanical response of fuel cell membranes subjected to a hygro-thermal cycle. J. Power Sources 161(2), 987–996 (2006)

    Article  Google Scholar 

  • Kyu, T., Eisenberg, A.: Underwater Stress Relaxation Studies of Nafion (Perfluorosulfonate) Ionomer Membranes. In: Journal of Polymer Science, Polymer Symposia. Waco, TX, USA (1984)

  • Lai, Y.-H., et al.: Viscoelastic stress model and mechanical characterizaton of perfluorosulfonic acid (PFSA) polymer electrolyte membranes. In: Proceedings of the 3rd International Conference on Fuel Cell Science, Engineering, and Technology, 2005. Ypsilanti, MI (2005)

  • Liu, D., et al.: Tensile behavior of nafion and sulfonated poly(arylene ether sulfone) copolymer membranes and its morphological correlations. J. Polym. Sci. B 44(10), 1453–1465 (2006)

    Article  Google Scholar 

  • Mauritz, K.A., Moore, R.B.: State of understanding of Nafion. Chem. Rev. 104(10), 4535–4585 (2004)

    Article  Google Scholar 

  • Morris, D.R., Sun, X.: Water-sorption and transport properties of Nafion 117 H. J. Appl. Polym. Sci. 50(8), 1445–1452 (1993)

    Article  Google Scholar 

  • Nielsen, L.E., Landel, R.F.: Mechanical Properties of Polymers and Composites, 2nd edn. Marcel Dekker, New York (1994)

    Google Scholar 

  • Rollet, A.-L., Diat, O., Gebel, G.: A new insight into nafion structure. J. Phys. Chem. B 106(12), 3033–3036 (2002)

    Article  Google Scholar 

  • Satterfield, M.B., et al.: Mechanical properties of Nafion and titania/Nafion composite membranes for polymer electrolyte membrane fuel cells. J. Polym. Sci. B 44(16), 2327–2345 (2006)

    Article  Google Scholar 

  • Schapery, R.A.: Nonlinear viscoelastic and viscoplastic constitutive equations based on thermodynamics. Mech. Time-Depend. Mater. 1(2), 209–240 (1997)

    Article  Google Scholar 

  • Solasi, R., et al.: Mechanical response of 3-layered MEA during RH and temperature variation based on mechanical properties measured under controlled T and RH. In: Proceedings of 4th International ASME Conference on Fuel Cell Science, Engineering and Technology, FUELCELL2006 (2006)

  • Solasi, R., et al.: On mechanical behavior and in-plane modeling of constrained PEM fuel cell membranes subjected to hydration and temperature cycles. J. Power Sources 167(2), 366–377 (2007)

    Article  Google Scholar 

  • Springer, T.E., Zawodzinski, T.A., Gottesfeld, S.: Polymer electrolyte fuel cell model. J. Electrochem. Soc. 138(8), 2334–2342 (1991)

    Article  Google Scholar 

  • Tang, Y., et al.: Stresses in proton exchange membranes due to hydration-dehydration cycles. In: Proceedings of the 3rd International Conference on Fuel Cell Science, Engineering, and Technology, 2005, Ypsilanti, MI (2005)

  • Tang, Y., et al.: An experimental investigation of humidity and temperature effects on the mechanical properties of perfluorosulfonic acid membrane. Mater. Sci. Eng. A 425(1–2), 297–304 (2006)

    Google Scholar 

  • Tang, Y., et al.: Stresses in proton exchange membranes due to hygro-thermal loading. J. Fuel Cell Sci. Technol. 3(2), 119–124 (2006)

    Article  Google Scholar 

  • Weber, A.Z., Newman, J.: Transport in polymer-electrolyte membranes. I. Physical model. J. Electrochem. Soc. 150(7) (2003)

  • Weber, A.Z., Newman, J.: A theoretical study of membrane constraint in polymer-electrolyte fuel cells. AIChE J. 50(12), 3215–3226 (2004)

    Article  Google Scholar 

  • Yeo, S.C., Eisenberg, A.: Physical properties and supermolecular structure of perfluorinated ion-containing(nafion) polymers. J. Appl. Polym. Sci. 21(4), 875–898 (1977)

    Article  Google Scholar 

  • Zawodzinski, Jr., T.A., et al.: Determination of water diffusion coefficients in perfluorosulfonate ionomeric membranes. J. Phys. Chem. 95(15), 6040 (1991)

    Article  Google Scholar 

  • Zawodzinski, Jr., T.A., et al.: A comparative study of water uptake by and transport through ionomeric fuel cell membranes. J. Electrochem. Soc. 140(7), 1981–1985 (1993)

    Article  Google Scholar 

  • Zou, Y.: Hygrothermal Mechanical Properties and Durability of Ionomer Membranes. In: Mechanical Engineering Department. University of Connecticut: Storrs, CT (2007)

Download references

Author information

Authors and Affiliations

  1. Connecticut Global Fuel Cell Center, University of Connecticut, 44 Weaver Rd. Unit 5233, Storrs, CT, 06269, USA

    Roham Solasi, Yue Zou, Xinyu Huang & Kenneth Reifsnider

Authors
  1. Roham Solasi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yue Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinyu Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Kenneth Reifsnider
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Roham Solasi.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Solasi, R., Zou, Y., Huang, X. et al. A time and hydration dependent viscoplastic model for polyelectrolyte membranes in fuel cells. Mech Time-Depend Mater 12, 15–30 (2008). https://doi.org/10.1007/s11043-007-9040-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11043-007-9040-7

Keywords

Search

Navigation