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A Three-Scale Model of Basic Mechanical Properties of Nafion

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Mechanics of Composite Materials Aims and scope

The mechanical properties of Nafion are explained and modeled on the basis of Kafka’s general mesomechanical model and confronted with experimental results. In this approach, Nafion is looked upon as a composite consisting of three constituents: a crystalline Nafion, amorphous Nafion, and water. Taking into account the degree of hydration, its elastic, elastic-plastic, and hysteretic properties are discussed and modeled. It is shown how the interaction between the three constituents manifests itself on the macroscale.

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Abbreviations

σ ij :

stress tensor

δ ij σ :

isotropic part of σ ij (σ = σ ii /3)

s ij :

deviatoric part of σ ij (σ ij − δ ij σ)

ε ij :

strain tensor

δ ij ε :

isotropic part of ε ij (ε = ε ii /3)

e ij :

deviatoric part of ε ij (ε ij − δ ij ε)

δ ij :

Kronecker’s delta

E :

Young’s modulus

ν:

Poisson’s ratio

μ = (1+ν)/E :

deviatoric elastic compliance

ρ = (1 − 2ν) / E :

isotropic elastic compliance.

\( \overline{\Big|} \) :

overbar that relates the symbol | to its macroscopic value — the average in the representative volume element RVE

|ω or | ω :

index that relates the symbol | to the ω -constituent — the average in the subvolume of RVE that is filled in by the ω -constituent

ω = e :

elastic constituent in the general two-phase model

ω = n :

inelastic constituent in the general two-phase model

ω = a :

amorphous constituent in Nafion

ω = c :

crystalline constituent in Nafion

ω = w :

water comprised in Nafion

ω = wa :

aggregate of two constituents in Nafion: of the amorphous Nafion with water

| ij :

Einstein’s notation

\( {\varepsilon}_{ij}^{\prime }={\varepsilon}_{ij}-{\overline{\varepsilon}}_{ij}; \)

δ ij ε′:

isotropic part of ε ′ ij

e ′ ij :

deviatoric part of ε ′ ij

σ ′ ij :

stress related to ε ′ ij similarly as σ ij is related to ε ij

δ ij σ′:

isotropic part of σ ′ ij

s ′ ij :

deviatoric part of σ ′ ij

ν e {ν n }:

volume fraction of the elastic {inelastic} constituent in the general two-phase model

ν a {ν w }:

volume fraction of the amorphous Nafion {of water} in the aggregate of amorphous Nafion with water

V ω :

volume fraction of the ω - constituent in the total Nafion (ω = a, c, w, wa);

\( {R}_a^c=\frac{V_c}{V_a}; \)

c a :

elastic limit of s a11 in the a -constituent

C wa :

elastic limit of s wa11 in the wa -constituent

n ω :

structural parameter (ω = a, c, w, wa)

|Ω :

superscript that relates the symbol | to the respective Ω -specimen of Nafion

Ω = H :

hydrated specimen

Ω = D :

dry specimen

p = V H c η c μ c  + V H wa η wa μ H wa

\( q=\frac{\mu_c}{V_c^H}\left(p\left|+{\eta}_c{\eta}_{wa}{\mu}_{wa}^H\right.\right) \).

\( \overset{\cdot }{h} \) :

formal variable equal to 0 in elasticity and to \( \overset{\cdot }{\lambda } \) in plasticity

| L :

value of | at the elastic limit.

References

  1. K. Schmidt-Rohr and Q. Chen, “Parallel cylindrical water nanochannels in Nafion fuel-cell membranes,” Nature Mater., 7, 75-83 (2008).

    Article  Google Scholar 

  2. R. Knake, P. Jacquinot, A. W. E. Hodgson, and P. C. Hauser, “Amperometric sensing in the gas phase,” Analytica Chimica Acta, 549, 1-9, (2005).

    Article  Google Scholar 

  3. F. Opekar and K. Stulik, “Electrochemical sensors with polymer electrolytes,” Analytica Chimica Acta, 385, 151-162, (1999).

    Article  Google Scholar 

  4. V. Mehta and J. S. Cooper, “Review and analysis of PEM fuel cell design and manufacturing,” J. of Power Sources, 114, 32-53, (2003).

    Article  Google Scholar 

  5. V. Antonuccia, A. Di Blasi, V. Baglioa, R. Ornelasb, F. Matteuccib, J. Ledesma-Garciac, L. G. Arriagac, and A. S. Arico, “High-temperature operation of a composite membrane-based solid polymer electrolyte water electrolyser,” Electrochimica Acta, 53, 7350-7356, (2008).

    Article  Google Scholar 

  6. A. A. Gronowski and H. L. Yeager, “Factors which affect the permselectivity of Nafion membranes in chloralkali electrolysis,” J. of the Electrochemical Soc., 138, 2690-2697, (1991).

    Article  Google Scholar 

  7. M. Shahinpoor, Y. Bar-Cohen, J. O. Simpson, and J. Smith, “Ionic polymer-metal composites (IPMCs) as biomimetic sensors, actuators and artificial muscles — a review,” Smart Mater. Struct., 7, R15-R30, (1998).

    Article  Google Scholar 

  8. J. Brufau-Penella, M. Puig-Vidal, P. Giannone, S. Graziani, and S. Strazzeri, “Characterization of the harvesting capabilities of an ionic polymer metal composite device,” Smart Mater. Struc., 17, 015009, (2008).

    Article  Google Scholar 

  9. Y. Tang, A. M. Karlsson, M. H. Santare, M. Gilbert, S. Cleghorn, and W. B. Johnson, “An experimental investigation of humidity and temperature effects on the mechanical properties of perfluorosulfonic acid membrane,” Mater. Sci. Eng., A, 425, 297-304, (2006).

    Article  Google Scholar 

  10. M. B. Satterfield, P. W. Majsztrik, H. Ota, J. B. Benziger, and A. B. Bocarsly, “Mechanical properties of Nafion and titania/Nafion composite membranes for polymer electrolyte membrane fuel cells,” J. Polym. Sci., Part B, Polymer Physics, 44, 2327-2345, (2006).

    Article  Google Scholar 

  11. M. N. Silberstein and M. C. Boyce, “Constitutive modeling of the rate-, temperature-, and hydration-dependent deformation response of Nafion to monotonic and cyclic loading,” J. of Power Sources, 195, 5692-5706, (2010).

    Article  Google Scholar 

  12. G. Gebel, “Structural evolution of water-swollen perfluorosulfonated ionomers from dry membrane to solution,” Polymer, 41, 5829-5838, (2000).

    Article  Google Scholar 

  13. D. Liu, S. Kyriakides, S. W. Case, J. J. Lesko, Y. Li, and J. E. McGrath, “Tensile behavior of Nafion and sulfonated poly(arylene ether sulfone) copolymer membranes and its morphological correlations,” J. Polym. Sci., Part B, Polymer Physics, 44, 1453-1465, (2006).

    Article  Google Scholar 

  14. A. Kusoglu, A. M. Karlsson, and M. H. Santare, “Structure–property relationship in ionomer membranes,” Polymer, 51, 1457-1464, (2010).

    Article  Google Scholar 

  15. Y. Qi and Y. H. Lai, “Mesoscale modeling of the influence of morphology on the mechanical properties of proton exchange membranes,” Polymer, 52, 201-210, (2011).

    Article  Google Scholar 

  16. V. Freger, “Hydration of ionomers and Schroeder’s paradox in Nafion,” J. Phys Chem. B, 113, 24-36, (2009).

    Article  Google Scholar 

  17. M. N. Silberstein, P. V. Pillai, and M. C. Boyce, “Biaxial elastic-viscoplastic behavior of Nafion membranes,” Polymer 52, 529-539, (2010).

    Article  Google Scholar 

  18. M. N. Silberstein and M. C. Boyce, “Hygro-thermal mechanical behavior of Nafion during constrained swelling,” J. of Power Sources, 196, 3452-3460, (2011).

    Article  Google Scholar 

  19. K. J. Kim and M. Shahinpoor, “Ionic polymer-metal composites: II. Manufacturing techniques,” Smart Mater. Struct., 12, 65-79, (2003).

    Article  Google Scholar 

  20. R. Tiwari and K. J. Kim, “Disc-shaped ionic polymer metal composites for use in mechano-electrical applications,” Smart Mater. Struct., 19, 065016, (2010).

    Article  Google Scholar 

  21. D. Pugal, K. J. Kim, A. Punning, H. Kasemagi, M. Kruusmaa, and A. Aabloo, “A self-oscillating ionic polymer-metal composite bending actuator,” J. of Appl. Phys., 103, 084908, (2008).

    Article  Google Scholar 

  22. S. Nemat-Nasser, “Micromechanics of actuation of ionic polymer-metal composites”, J. of Applied Physics, 92, 2899-2915, (2002).

    Article  Google Scholar 

  23. S. Nemat–Nasser and S. Zamani, “Modeling of electrochemomechanical response of ionic polymer-metal composites with various solvents,” J. of Appl. Phys., 100, 064310, (2006).

    Article  Google Scholar 

  24. G. Alberti, R. Narducci, and M. Sganappa, “Effects of hydrothermal/thermal treatments on the water-uptake of Nafion membranes and relations with changes of conformation, counter-elastic force and tensile modulus of the matrix,” J. of Power Sources, 178, 575-583, (2008).

    Article  Google Scholar 

  25. V. Kafka, Mesomechanical Constitutive Modeling, World Scientific, Singapore (2001).

    Google Scholar 

  26. A. Eisenberg and J. S. Kim, Introduction to Ionomers, Wiley, New York (1998).

    Google Scholar 

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Acknowledgements

This work was supported by the Czech Science Foundation within projects P108/10/1296 and 103/09/2101. Acknowledged is also the support through the Institutional Project RVO: 68378297. D. Vokoun would like to thank Dr. M. Paidar for fruitful discussions.

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Authors and Affiliations

  1. Institute of Theoretical and Applied Mechanics ASCR, v.v.i., Prosecka 76, 19000, Prague, Czech Republic

    V. Kafka

  2. Institute of Physics ASCR, v.v.i., Na Slovance 2, 18221, Prague, Czech Republic

    D. Vokoun

Authors
  1. V. Kafka
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  2. D. Vokoun
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Corresponding author

Correspondence to D. Vokoun.

Additional information

Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 50, No. 6, pp. 1065-1082 , November-December, 2014.

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Kafka, V., Vokoun, D. A Three-Scale Model of Basic Mechanical Properties of Nafion. Mech Compos Mater 50, 763–776 (2015). https://doi.org/10.1007/s11029-015-9466-y

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  • DOI: https://doi.org/10.1007/s11029-015-9466-y

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