Micromechanical analysis of ionic clustering in Nafion perfluorinated membrane

The cluster morphology in a water-swollen Nafion perfluorinated membrane is studied using a micromechanics approach. The cluster size is determined from the minimization of the free energy as a function of the equivalent weight of Nafion, the volume fraction of water, and the temperature, taking into account the electrostatic dipole interaction energy, the elastic polymer chain reorganization energy, and the cluster surface energy, leading to results which are in accord with experimental observations. By minimizing the sum of: (1) the electro-elastic interaction energy between an ionic cluster and the fluorocarbon matrix, and (2) the cluster surface energy, it is concluded that the eAective cluster shape is spherical in the absence of an electric field, and becoming an oblate spheroid when an electric field is applied. The eAect of cluster morphology on the eAective electro-elastic moduli and the eAective ionic conductivity is then studied by a micromechanical multi-inclusion model. The result seems to describe the available empirical relation when a spherical cluster shape is assumed. It correctly predicts the insulator-to-conductor transition which occurs in Nafion, as the water volume fraction is increased. ” 2000 Elsevier Science Ltd. All rights reserved.

[1]  Y. Benveniste,et al.  A new approach to the application of Mori-Tanaka's theory in composite materials , 1987 .

[2]  C. Heitner-Wirguin.  Recent advances in perfluorinated ionomer membranes : structure, properties and applications , 1996 .

[3]  Sia Nemat-Nasser,et al.  Electromechanical response of ionic polymer-metal composites , 2000 .

[4]  Toshio Mura,et al.  Micromechanics of defects in solids , 1982 .

[5]  Kenneth A. Mauritz,et al.  Review and Critical Analyses of Theories of Aggregation in Ionomers , 1988 .

[6]  S. Nemat-Nasser,et al.  Micromechanics: Overall Properties of Heterogeneous Materials , 1993 .

[7]  K. Osseo-Asare,et al.  Characterization of nafion® membranes by transmission electron microscopy , 1989 .

[8]  A. Hopfinger,et al.  Simple model for clustering and ionic transport in ionomer membranes , 1984 .

[9]  K. Tanaka,et al.  Average stress in matrix and average elastic energy of materials with misfitting inclusions , 1973 .

[10]  D. M. Barnett,et al.  Dislocations and line charges in anisotropic piezoelectric insulators , 1975 .

[11]  R. K. Thomas,et al.  Local and long-range structure of water in a perfluorinated ionomer membrane , 1992 .

[12]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[13]  W. Forsman.  Effect of segment-segment association on chain dimensions , 1982 .

[14]  W. Cheston.  Elementary theory of electric and magnetic fields , 1964 .

[15]  F. C. Wilson,et al.  The morphology in nafion† perfluorinated membrane products, as determined by wide- and small-angle x-ray studies , 1981 .

[16]  M. Shahinpoor.  Conceptual design, kinematics and dynamics of swimming robotic structures using ionic polymeric gel muscles , 1992 .

[17]  A. Eisenberg.  Clustering of Ions in Organic Polymers. A Theoretical Approach , 1970 .

[18]  M. Taya,et al.  Metal Matrix Composites: Thermomechanical Behavior , 1989 .

[19]  E. Kröner.  Berechnung der elastischen Konstanten des Vielkristalls aus den Konstanten des Einkristalls , 1958 .

[20]  P. Meakin,et al.  Ion Percolation and Insulator-to-Conductor Transition in Nafion Perfluorosulfonic Acid Membranes , 1980 .

[21]  Statistical Mechanics of Ion-Pair Association in Ionomers , 1987 .

[22]  J. D. Eshelby.  The determination of the elastic field of an ellipsoidal inclusion, and related problems , 1957, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[23]  T. Gierke,et al.  Elastic theory for ionic clustering in perfluorinated ionomers , 1982 .

[24]  B. Budiansky.  On the elastic moduli of some heterogeneous materials , 1965 .