The Nanostructure of Nafion for Fuel-Cell Membranes from Small-Angle Scattering and NMR Analysis

We have investigated the long contentious nanometer-scale structure of the Nafion ionomer used in proton exchange membranes of H$_{2}$/O$_{2}$ fuel cells. Using a simple algorithm based on 3D numerical Fourier transformation, we have quantitatively simulated previously published small-angle scattering data of hydrated Nafion. The characteristic ''ionomer peak'' arises from long, parallel but otherwise randomly packed water channels surrounded by the partially hydrophilic sidebranches, forming inverted-micelle cylinders. The channels are stabilized by the considerable stiffness of the Nafion backbones, detected by $^{13}$C and $^{19}$F NMR. An upper limit of 300 nm to the persistence length of the water channels has been estimated from $^{2}$H NMR of $^{2}$H$_{2}$O in the channels. At 20 vol{\%} water, the water channels have diameters between 1.8 and 3.5 nm, with a 2.4-nm average. The hydration-induced changes in small-angle scattering patterns and in the surface-to-volume ratio have also been analyzed in quantitative detail. Nafion crystallites ($\sim $10 vol{\%}), which form physical crosslinks crucial for the mechanical properties of Nafion films, are elongated and parallel to the water channels, with cross sections of $\sim $(5 nm)$^{2}$. Simulations for a dozen other models of Nafion, including Gierke's cluster and the polymer-bundle model, do not match the scattering data. The water-channel model is the first without constrictions of $\sim $1.2 nm diameter; it can explain important features of Nafion, including fast diffusion of water and protons through Nafion and its persistence at low temperatures.