Quasielastic Neutron Scattering Study of Water Dynamics in Hydrated Nafion Membranes

We report a QENS study of the molecular motions in a perfluorinated ionomer membrane, Nafion, under increasing hydration levels from almost dry to fully saturated. Combined experiments performed on time-of-flight and backscattering spectrometers have been used to investigate the picosecond to the nanosecond dynamic behavior of water. The experimental spectra have been simulated over the whole Q range from 0.34 to 2.25 Å -1 by a single theoretical model taking into account the localized motions within confining domains, the microscopic features of the elementary jump process, and the long-range diffusion mechanism. The diffusion in a restricted geometry with ill-defined boundaries has been described by Gaussian statistics, contrary to the popular diffusion inside an impermeable sphere model where the boundaries are well defined. Evaluation of the spectra reveals the existence of two populations of protons in Nafion at all hydrations that are nonexchangeable on the nanosecond time-scale. A first population of three protons per ionic group is involved in a slow jump mechanism on characteristic length-scales of 2 to 4 Å and typical times ranging from 500 to 150 ps when increasing the water content in the membrane. This slow population, already present in the dried state, is presumably composed of the protons of the hydronium ions. The second fast population is composed of the additional hydrating water molecule protons. Between low hydration (3 H 2 O/SO 3 - ) and saturation (17.5 H 2 O/SO 3 - ), these protons are involved in a faster localized motion on roughly the same length scale, i.e., in the same water droplet as the hydronium ion. Long-range diffusion of these protons between neighboring domains of restricted motions is observed, even at very low hydration. As the number of water molecules in the membrane increases, a general finding is that the characteristic sizes increase and the characteristic times decrease, approaching asymptotic values at saturation. This is further reflected by the behavior of the local diffusion coefficient (inside a droplet) and the long-range diffusion coefficient (from one droplet to another) that vary, respectively, from 0.45 to 2 (10 -5 cm 2 /s), and 0.1 to 0.58 (10 -5 cm 2 /s), for λ ∼ 3 to 17.5. Overall, a molecular scenario for the proton motions among the different hydration steps has been proposed on the basis of the quantification of the dynamics on different length scales and time scales: below 10 H 2 O/SO 3 - the hydration protons diffuse faster and faster in ionic clusters of growing size. Above this first hydration regime, the asymptotic upper limit with increased hydration is reached: the water molecules locally display a bulk-like behavior within the hydrophilic domains. The long-range diffusion appears to be correlated to the enhancement of hydronium mobility with water loading. These findings, that qualitatively confirm the results of a previous similar study, bring a significant improvement to the description of the experimental data and new quantitative information concerning the nature of the molecular motions in hydrated Nafion.