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Diffusional kurtosis is introduced to characterize the heterogeneity of the channel architecture for ionic transport in proton exchange membranes. Measuring the apparent kurtosis by a pulsed-fi eld-gradient NMR spectroscopy technique may yield additional information about membrane morphology not available to the conventional water-diffusion method. Water diffusional kurtosis and the apparent diffusion coeffi cient are investigated for perfl uorinated sulfonic acid (PFSA)/SiO 2 nanocomposites. Diffusional kurtosis is anisotropic revealing higher channel heterogeneity in-plane of solution-cast fi lms compared with the transverse direction. Diffusional kurtosis is related to the nonGaussian character of the averaged diffusion propagator. A universal relationship is proposed for the root-mean-squared displacement.