Unraveling concentration gradient-driven ion transport in nanopores with classical Nernst–Planck equation

The diffusion of ions in nanopores plays a pivotal role in numerous industrial applications, including water desalination, energy conversion, and biological systems. However, when the diameter of the nanopore approaches to that of the ion's hydration shell, the uncertainty associated with the diffusion coefficient of ions in nanopores leads to deviations in the prediction of diffusion flux from classical Nernst–Planck (N–P) equation. In this study, we employ molecular dynamics simulations to investigate the concentration-driven migration of ions in nanopores. Our findings indicate that the N–P equation retains its predictive accuracy for ion permeability when the nanopore diffusion coefficient is accurately determined. In order to accurately calculate the diffusion coefficient within nanopores, we propose a novel method by selectively analyzing ions transport within regions adjacent to both sides of the nanopore, enabling accurate calculation of the ion diffusion coefficient along the direction of concentration gradients. This research enhances our comprehension of ion transport phenomena in nanoscale and boosts the related theoretical modeling.