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A hydrophobic pore of subnanometer dimensions can appear impermeable to an ion even though its radius is still much wider than that of the ion. Pores of molecular dimensions can be found, for instance, in carbon nanotubes, zeolites, or ion channel proteins. We quantify this barrier to ion permeation by calculating the potential of mean force from umbrella-sampled molecular dynamics simulations and compare them to continuum-electrostatic Poisson-Boltzmann calculations. The latter fail to describe the ion barrier because they do not account for the properties of water in the pore. The barrier originates from the energetic cost to desolvate the ion. Even in wide pores, which could accommodate an ion and its hydration shell, a barrier of several kT remains because the liquid water phase is not stable in the hydrophobic pore. Thus, the properties of the solvent play a crucial role in determining permeation properties of ions in confinement at the molecular scale.

Original publication




Journal article


J Am Chem Soc

Publication Date





14694 - 14695