Theoretical framework for confined ion transport in two-dimensional nanochannels

Quantitative understanding of ion transport mechanism is crucial for numerous applications of two-dimensional (2D) nanochannels, but is far from being resolved. Here, we formulated a theoretical framework for both self-diffusion and electromigration of hydrated monatomic ions in various 2D nanochannels (e.g. graphene, h-BN, g-C₃N₄, MoS₂), by molecular dynamics simulations. The self-diffusivity and mobility of ions in 2D nanochannels both increases linearly with ion-wall distance for small hydrated ions, yet keeps constant for large ones. The underlying mechanism reveals that when ions approach water-layers in nanochannels or possess large hydration shell, their hydration shells become severely distorted. This increases the free energy difference between hydration shell and the surrounding water-layers, water residence time in hydration shell and ion-water friction. Several involving quantitative relations were revealed, with Nernst-Einstein relation validated with both simulations and theoretical derivation. This work shows profound implications for various applications, including ion-sieving, nanodevices and nano-power generators, etc.