From normal to anomalous diffusion of water molecules in narrow carbon nanotubes with defects, gases, and salts

In this letter, we study the diffusion of water molecules inside narrow carbon nanotubes in the presence of nanotube defects, gas molecules and salt ions by using molecular dynamics simulations. Mean square displacement (MSD) with a power-law fitting parameter ${\alpha}$ , and the probability distribution function (PDF) with an ${\alpha}{\text{-stable}}$ distribution parameter a, of water molecules are calculated. It is found that within the diffusion time scale, water molecules exhibit a superdiffusion behavior with ${\alpha}>1$ inside a perfect nanotube and the superdiffusion is weakened in the presence of gas molecules and salt ions. Meanwhile, a normal diffusion behavior with ${\alpha} = 1$ is observed inside a defective nanotube, and it is replaced by a subdiffusion behavior with ${\alpha}<1$ when gas molecules and salt ions are involved. PDF of water molecules is found to be Gaussian-like with $a = 2$ subject to superdiffusion and normal diffusion, while it becomes a center-peaked and long-tailed Lévy distribution with a < 2 subject to subdiffusion. Furthermore, it is found that the diffusion behavior of water molecules approaches normal diffusion as the radius size of the nanotube increases. Our result implies anomalous transport behavior of water in nanochannels due to the common presence of defects, gases and salts in nanochannels