Water–polymer interfacial area in Nafion: Comparison with structural models

The water–polymer interfacial area per volume, S/V, which is reflected in the Porod region of small-angle scattering data, is an important parameter of different models of the Nafion fuel cell membrane. Therefore, we have compared published experimental S/V data of Nafion over a wide range of hydration levels with various structural models featuring stiff polymer backbones, in particular the parallel water-channel and the polymer ribbon models. The S/V curve at intermediate hydration levels typical of fuel-cell conditions (ca. 20 vol% water) matches that of the parallel water-channel model with molecular corrugation. At higher hydration levels, i.e. for membranes soaked in water or autoclaved at elevated pressures, the polymer-ribbon model matches the decreasing S/V ratio with increasing water content, while the polymer-bundle model predicts a higher surface area. However, the ribbon or bundle models cannot apply at low hydration (<3 water molecules per Nafion side group), since we show that the interfacial area in this regime must increase strongly with hydration, being determined by the available surface area of the water molecules. The pronounced asymmetry of the plot of S/V vs. water volume fraction is explained in terms of the difference in the diameters of the water molecules and the polymer aggregates.