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Relations between the diffusion anomaly and cooperative rearranging regions in a hydrophobically nanoconfined water monolayer

We simulate liquid water between hydrophobic walls separated by 0.5 nm, to study how the diffusion constant D_\parallel parallel to the walls depends on the microscopic structure of water. At low temperature T, water diffusion can be associated with the number of defects in the hydrogen bonds network. However, the number of defects solely does not account for the peculiar diffusion of water, with maxima and minima along isotherms. Here, we calculate a relation that quantitatively reproduces the behavior of D_\parallel, focusing on the high-T regime. We clarify how the interplay between breaking of hydrogen bonds and cooperative rearranging regions of 1-nm size gives rise to the diffusion extrema, possibly relevant for both bulk and nanoconfined water.