Variational models of network formation and ion transport: Applications to perfluorosulfonate ionomer membranes

Polymers

Volumn 4, Issue 1, 2012, Pages 630-655

  Gavish, Nir ^a   Jones, Jaylan ^a   Xu, Zhengfu ^b   Christlieb, Andrew ^a   Promislow, Keith ^a  

^a MICHIGAN STATE UNIVERSITY   (United States)

^b MICHIGAN TECHNOLOGICAL UNIVERSITY   (United States)

Author keywords

Functionalized cahn hilliard; Ionic transport; Ionomer membrane; Network morphology

Indexed keywords

BI-LAYER; COUNTERIONS; ELECTROCHEMICAL POTENTIAL; ENDCAPS; ENTROPIC EFFECTS; FUNCTIONALIZED; FUNCTIONALIZED POLYMERS; GRADIENT FLOW; ION TRANSPORTS; IONIC TRANSPORTS; IONOMER MEMBRANES; MEMBRANE CASTING; NETWORK FORMATION; NETWORK MORPHOLOGY; NETWORK STRUCTURES; PERFLUOROSULFONATE IONOMERS; PINCHOFF; TOTAL FREE ENERGY; VARIATIONAL MODELS;

ENTROPY; FUNCTIONAL POLYMERS; IONIC CONDUCTION;

MORPHOLOGY;

EID: 84861778168     PISSN: None     EISSN: 20734360     Source Type: Journal    
DOI: 10.3390/polym4010630     Document Type: Article

References (61)

1. Ameduri, B. From Vinyidene Fluoride (VDF) to the applications of VDF-containing polymers and co-polymers: Recent developments and future trends. Chem. Rev. 2009, 109, 6632-6686.
2. Wetzel, E.; Beyer, F. Self-Assembling Nanomembranes through Electrostatic Melt Processing of Copolymer Films; ARL-TR-2800; Army Research Laboratory: Adelphi, MD, USA, 2002.
3. Wu, D.S.; Paddison, S.J.; Elliott, J.A. Effect of molecular weight on hydrated morphologies of the short-side-chain perfluorosulfonic acid membrane. Macromolecules 2009, 42, 3358-3367.
4. Eikerling, M.; Paddison, S.J.; Pratt, L.R.; Zawodzinski, T.A. Defect structure for proton transport in a triflic acid monohydrate solid. Chem. Phys. Lett. 2003, 368, 108-114.
5. Promislow, K.; Wetton, B. PEM fuel cells: A mathematical overview. SIAM J. Appl. Math. 2009, 70, 369-409.
6. Rubatat, L.; Gebel, G.; Diat, O. Fibriallar structure of Nafion: Matching Fourier and real space studies of corresponding films and solutions. Macromolecules 2004, 37, 7772-7783.
7. Lee, K.-M.; Hsu, C.-Y.; Chiu, W.-H.; Tsui, M.-C.; Tung, Y.-L.; Tsai, S.-Y.; Ho, K.-C. Dye-sensitized solar cells with mirco-porous TiO2 electrode and gel polymer electrolytes prepared by in situ cross-link reaction. Sol. Energy Mater. Sol. Cells 2009, 93, 2003-2007.
8. Peet, J.; Heeger, A.; Bazan, G. "Plastic" solar cells: Self-assembly of bulk hetrojunction nanomaterials by spontaneous phase separation. Acc. Chem. Res. 2009, 42, 1700-1708.
9. Crossland, E.; Kamperman, M.; Nedelcu, M.; Ducati, C.; Wiesner, U.; Smilgies, D.; Toombes, G.; Hillmyer, M.; Ludwigs, S.; Steiner, U.; Snaith, H. A Bicontinuous double gyroid hybrid solar cell. Nano Lett. 2009, 9, 2807-2812.
10. Arora, P.; Zhang, Z.M. Battery separators. Chem. Rev. 2004, 104, 4419-4462.
11. Ichikawa, T.; Yoshio, M.; Hamaskai, A.; Kagimoto, J.; Ohno, H.; Kato, T. 3D interconnected ionic nano-channels formed in polymer films: Self-organization and polymerization of thermotropic bicontinuous cubic liquid cyrstals. J. Am. Chem. Soc. 2011, 133, 2163-2169.
12. Caflisch, R.E. The fluid dynamic limit of the nonlinear Boltzmann equation. Commun. Pure Appl. Math. 1980, 33, 651-666.
13. Golse, F. Hydrodynamic Limits. In Proceedings of the European Congress of Mathematics, Stockholm, Sweden, 27 June-2 July 2004; European Mathematics Society: Zürich, Sweden, 2005; pp. 699-717.
14. Müller, M. Concurrent coupling between a particle simulation and a continuum description. Eur. Phys. J. Spec. Top. 2009, 177, 149-164.
15. Knox; C.; Voth, G.A. Probing selected morphological models of hydrated nafion using large-scale molecular dynamics simulations. J. Phys. Chem. B 2010, 144, 3205-3218.
16. Levine, B.G.; LeBard, D.N.; DeVane, R.; Shinoda, W.; Kohlmeyer, A.; Klein, M.L. Micellization studied by gpu-accelerated coarse-grained molecular dynamics. J. Chem. Theory Comput. 2011, 7, 4135-4145.
17. Zhang, Z.; Promislow, K.; Martin, J.; Wang, H.; Balcom, B. Bi-modal water transport behavior across a simple Nafion membrane. J. Power Sources 2011, 196, 8525-8530.
18. Weber, A.Z.; Newman, J. Modeling transport in polymer-electrolyte membranes. Chem. Rev. 2004, 104, 4679-4726.
19. Weber, A.Z.; Newman, J. Transport in polymer-electrolyte membranes-II. Mathematical model. J. Electrochem. Soc. 2004, 151, A311-A325.
20. Eikerling, E.; Berg, P. Poroelectrostatic theory of water sorption and swelling in polymer electrolyte membranes. Soft Matter 2011, 7, 5976-5990.
21. Mauritz, K.A.; Moore, R.B. State of understanding of nafion. Chem. Rev. 2004, 104, 4535-4585.
22. Doyle, M.; Rajendran, G. Perfluorinated membranes. In Handbook of Fuel Cells-Fundamentals, Technology and Applications; Vielstich, W., Lamm, A., Gasteiger, H.A., Eds.; John Wiley & Sons, Ltd.: Chichester, UK, 2003; Volume 3, pp. 351-395.
23. Hsu, W.; Gierke, T. Ion transport and clustering in Nafion perfluorinated membranes. J. Membr. Sci. 1983, 13, 307-326.
24. Cahn, J.W.; Hilliard, J.E. Free energy of a nonuniform system. I. Interfacial free energy. J. Chem. Phys. 1958, 28, 258-267.
25. Morgan, F. Geometric Measure Theory: A Beginners Guide; Academic Press: Waltham, MA, USA, 2000.
26. de Giorgi, E. Some remarks onΓ-Convergence and least squares methods. In Composite Media and Homogenization Theory; Dal Maso, G., Dell-Antonio, G.F., Eds.; Birkhäuser: Basel, Switzerland, 1991; pp. 135-142.
27. Promislow, K.; Zhang, H. Critical points of functionalized lagrangians. Discret. Contin. Dyn. Syst. Ser. A 2012, in press.
28. Canham, P. Minimum energy of bending as a possible explanation of biconcave shape of human red blood cell. J. Theor. Biol. 1970, 26, 61-81
29. Helfrich, W. Elastic properties of lipid bilayers-Theory and possible experiments. Z. Naturforsch. C 1973, 28, 693-703.
30. Kamien, R. The geometry of soft materials: A primer. Rev. Mod. Phys. 2002, 74, 953-971.
31. Liu, C.; Walkington, N. An eulerian description of fluids containing visco-elastic particles. Arch. Ration. Mech. 2001, 159, 229-252.
32. Gavish, N.; Hayrapetyan, G.; Promislow, K.; Yang, L. Curvature driven flow of bi-layer interfaces. Physica D 2011, 240, 675-693.
33. Freger, V. Hydration of ionomers and schroeder's paradox in nafion. J. Phys. Chem. B 2009, 113, 24-36.
34. Paddison, S.J. The modeling of molecular structure and ion transport in sulfonic acid based ionomer membranes. J. New. Mat. Electorchem. Syst. 2001, 4, 197-207.
35. Kreuer, K.D.; Paddison, S.J.; Spohr, E.; Schuster, M. Transport in proton conductors for fuel-cell applications: Simulations, elementary reactions, and phenomenology. Chem. Rev. 2004, 104, 4637-4678.
36. Paul, R.; Paddison, S.J. A statistical mechanical model for the calculation of the permittivity of water in hydrated polymer electrolyte membrane pores. J. Chem. Phys. 2001, 115, 7762-7771.
37. Paul, R.; Paddison, S.J. Structure and dielectric saturation of water in hydrated polymer electrolyte membranes: Inclusion of the internal field energy. J. Phys. Chem. B 2004, 108, 13231-13241.
38. Sumeet, J.; Bates, F. Consequences of nonergodicity in aqueous binary PEO-PB micellar dispersions. Macromolecules 2004, 37, 1511-1523.
39. Elliott, J.A.; Hanna, S.; Elliott, A.M.S.; Cooley, G.E. Interpretation of the small-angle X-ray scattering from swollen and oriented perfluorinated ionomer membranes. Macromolecules 2000, 33, 4161-4171.
40. Kim, H.-H.; Glinka, C.J.; Grot, S.A.; Grot, W.G. SANS study of the effects of water vapor sorption in the nanoscale structure of perfluorinated sulfonic acid (Nafion) membranes. Macromolecules 2006, 39, 4775-4787.
41. Phillips, K.A.; Moore, R.B. Mechanical and transport property modifications of perfluorosulfonate ionomer membranes prepared with mixed organic and inorganic counterions. J. Polym. Sci. Part B Polym. Phys. 2006, 44, 2267.
42. Starkweather, H.W. Crystallinity in perfluorosulfonic acid ionomers and related polymers. Macromolecules 1982, 15, 320-323.
43. Krivandin, A.V.; Solov'ena, A.B.; Glagolev, N.N.; Shatalova, O.V.; Kotova, S.L. Structure alterations of perfluorinated sulfocationic membranes under the actoni of ethylene glycol (SAXS and WAXS) studies. Polymer 2003, 44, 5789-5796.
44. Schmidt-Rohr, K.; Chen, Q. Parallel cylindrical water nanochannels in Nafion fuel-cell membranes. Nat. Mater. 2008, 7, 75-83.
45. Rubatat, L.; Rollet, A.L.; Gebel, G.; Diat, O. Evidence of elongated polymeric aggregates in Nafion. Macromolecules 2002, 35, 4050-4055.
46. Paddison, S.J.; Promislow, K.S. Device and Materials Modeling of Polymer Electrolyte Membrane Fuel Cells; Springer: New York, NY, USA, 2009.
47. Wu, D.S.; Paddison, S.J.; Elliott, J.A. A comparative study of hydrated morphologies of perfluorosulfonic acid fuel cell membranes with mescopic simulations. Energy Environ. Sci. 2008, 1, 284-293.
48. Litt, M.H. A reevaluation of nafion morphology. ACS Polym. Prepr. 1997, 38, 80-81.
49. Whang, G.S.; Kaviany, M.; Gostick, J.T.; Kientiz, B.;Weber, A.Z.; Kim, M.W. Role of water states on water uptake and proton transport in Nafion using molecular simulations and bimodal network. Polymer 2011, 52, 2584-2593.
50. Nemet-Nasser, S. Micromechanics of actuation of ionic polymer-metal composites. J. Appl. Phys. 2002, 92, 2899-2915.
51. Zawodzinski, T.A.; Derouin, C.; Radzinski, S.; Sherman, R.S.; Smith, V.T.; Springer, T.E.; Gottesfeld, S. Water uptake by and transport through Nafion 117 membranes. J. Electrochem. Soc. 1993, 140, 1041-1047.
52. Dogonadzem, R.R.; Kornyshev, A.A. Polar solvent structure in the theory of ionic solvation. J. Chem. Soc. Farad. Trans. 1974, 70, 1121-1132.
53. Kornyshev, A.A. Nonlocal screening of ions in a structured polar liquid-new aspects of solvent description in electrolyte theory. Electrochim. Acta 1981, 26, 1-20.
54. Kornyshev, A.A. Nonlocal electrostatics in solvations. In The Chemical Physics of Solvation, Part A; Dogonadze, R.R., Kalman, E., Kornyshev, A.A., Ulstrup, J., Eds.; Elsevier: Amsterdam, The Netherlands, 1985; pp. 77-118.
55. Rubinstein, A.; Sherman, S. Influence of the solvent structure on the electrostatic interactions in proteins. Biophys. J. 2004, 87, 1544-1557.
56. Bazant, M.Z.; Kilic, M.S.; Storey, B.D.; Ajdari, A. Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions. Adv. Colloid Interface Sci. 2009, 106, 104119:1-104119:83.
57. Zhang, H.; Hassanali, A.A.; Shin, Y.K.; Knight, C.; Singer, S.J. The water-amorphous silica interface: Analysis of the Stern layer and surface conduction. J. Chem. Phys. 2011, 134, 024705:1-024705:13
58. Promislow, K.; Ryham, R. The Conductive Polymer Membrane Equations; preprint
59. Moore, R.B.; Martin, C.R. Procedure for preparing solution-cast perfluorosulfonate ionomer films and membranes. Anal. Chem. 1986, 58, 2569-2570.
60. Moore, R.B.; Martin, C.R. Chemical and morphological properties of solution-cast perfluorosulfonate ionomers. Macromolecules 1988, 21, 1334-1339.
61. Maragliano, L.; Vanden-Eijnden, E. A temperature accelerated method for sampling free energy and determining reaction pathways in rare event simulations. Chem. Phys. Lett. 2006, 426, 168-175.