  Ion transport in highly-confined space is important to various applications,
such as biosensing and seawater desalination with nanopores. All-atom molecular
dynamics simulations are conducted to investigate the transport of Na$^+$ and
Cl$^-$ ions through nanopores with the diameter below 6 nm. It is found that
the formation of the contact ion pair plays a critical role in reducing the ion
mobility inside a nanopore without surface charges. The mobility for both
cations and anions decreases with the reduced pore size because it is easier to
form the contact ion pairs inside the neutral nanopore with smaller diameter.
Inside a charged nanopores, besides the contact ion pair formation, the surface
charges also play a significant role in reducing the counterion mobility
through surface trapping. It is uncovered that the mobility of Na$^+$ ions
increases first and then decreases with the surface charge density, while
Cl$^-$ ions have the opposite trend. A modified first-passage time model is
proposed to take into account the ion pair formation and the trapped ions
inside a nanopore, which provides a clear picture in describing ion transport
through a nanopore.
