Proton transport (PT) in solutions of small amphiphiles in water has previously been shown to be subdiffusive for long times. The present study analyzes simulations of hydrated perfluorosulfonic acid (PFSA) membranes in order to determine whether PT is also subdiffusive in these important amphiphilic systems. We show that PT is indeed subdiffusive for several hundred picoseconds for all hydration levels examined, and the subdiffusive behavior is highly dependent on water concentration. We also investigate the caging of the excess proton using a recently developed technique and show that the excess proton exhibits caging effects up to at least 1 ns in PFSA systems. In order to fully characterize the long-time behavior of PT in PFSAs, these results demonstrate that multiple nanosecond trajectories are needed, well beyond the current capabilities of ab initio molecular dynamics.
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