Molecular self-diffusion in nanoscale cylindrical pores and classical Fick's law predictions

Molecular-dynamics calculations are carried out to study the self-diffusion of water molecules confined in cylindrical pores. It is found that the classical Fick's law description provides a surprisingly accurate prediction for the general behaviors of self-diffusion even for pore size of a few molecular diameters. The diffusion coefficient in the axial direction is reduced relative to bulk fluids for pore size less than about ten molecular diameters. In the radial direction, the mean-square displacement accurately follows Fick's law prediction, but with an average diffusion coefficient slightly lower than the bulk value. The origin of the diffusion behaviors is traced to the molecular motion in the restricted geometry of the cylindrical pores.