Interpretation of small-angle x-ray and neutron scattering data for perfluorosulfonated ionomer membranes
Article first published online: 11 MAR 2003
Copyright © 1986 John Wiley & Sons, Inc.
Journal of Polymer Science Part B: Polymer Physics
Volume 24, Issue 8, pages 1767–1782, August 1986
How to Cite
Kumar, S. and Pineri, M. (1986), Interpretation of small-angle x-ray and neutron scattering data for perfluorosulfonated ionomer membranes. J. Polym. Sci. B Polym. Phys., 24: 1767–1782. doi: 10.1002/polb.1986.090240812
- Issue published online: 11 MAR 2003
- Article first published online: 11 MAR 2003
- Manuscript Accepted: 17 JUN 1985
- Manuscript Received: 21 MAR 1983
In small-angle x-ray and neutron scattering studies of ion-containing polymers, it is observed that there is a maximum in the intensity and also an increase in the intensity at very low Q. Several ion clustering models have been proposed in the literature to explain the peak and the intensity increase. The SAXS data of Gierke et al. and the SANS data of Roche et al. are considered in this paper in order to elucidate the possible cluster morphology in perfluorosulfonated ionomer membranes. For these samples the occurrence of the SAXS peak is accounted for quantitatively; it is shown to arise from the interference between ionic aggregates (clusters), assuming them to be noninteracting hard spheres. In these calculations the volume fraction of the clusters (the cluster is assumed to be constituted of SO3−, a cation, and a swelling agent, which is water in the present case) is determined from water absorption values, equivalent weight, and from the density of the dry polymer. The size of the ionic clusters is chosen to match the calculated and observed peak positions. In these calculations it is assumed that all the ions are in clusters. The calculated peak value of the relative intensity invariant is found to be within ±15% of the experimentally observed intensity invariant for samples of different equivalent weight, and in different cationic form, soaked or boiled in water. Samples equilibrated at lower levels of humidity showed greater deviations. The deviations become smaller if either or both of two assumptions are made; that with a decrease in humidity (i) the percentage of clustering ions decreases, (ii) a fraction of the polymer chains is present in the clusters. This work gives credence to the thought that the small-angle scattering peak in ion-containing polymers is not a Bragg peak. This invalidates the conventional method of comparing the macroscopic and microscopic degrees of swelling. Previous SAXS work on dense groups of particles has neglected a term which is shown to be important at low angles. We found that this term is capable of qualitatively explaining the observed increase in intensity at low angles in perfluorosulfonated ionomers. The possibility of the presence of an intercluster potential, which can also contribute to the increase in intensity at these angles, is also discussed.