The self-diffusion of fluids in narrow pores is ubiquitous in many fields including material science, physics, chemistry, and biology^1-4. It is therefore of practical interest to understand the properties that govern the diffusion mechanisms (e.g., ballistic motion, Fickian (3-D) diffusion, or single-file diffusion) of molecules confined in carbon nanotubes (CNTs) ^5-7  Grand Canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations were used to compute adsorption isotherms, adsorption energies, and diffusivities of Lennard-Jones fluids and water confined in CNTs.  We focus on the crossover from Fickian (3-D) to single-file diffusion in various helices of CNTs.  We investigate the effects of fluid type, diameter, loading, and pressure.

We report that the transition between Fickian (3-D) and single-file diffusion strongly depends on the type of fluid, size of the CNT relative to the size of the fluid particle, and the loading of fluid in the CNT.  Our results show a sudden decrease in the loading near a specific reduced diameter of the tube (which we define as the transition diameter).  At diameters smaller than the transition diameter, the diffusion is purely single-file.  However, at the transition, a decrease in the loading is found and is due to the tube diameter being too small to accommodate a second layer of fluid molecules.  At diameters greater than the transition diameter, the particles start to pack into more than one layer, and the diffusion mechanism becomes Fickian (3-D).  Our results are in agreement with those of Mon and Percus who studied hard spheres in cylindrical pores with hard walls ⁸.

The chirality of the CNT can affect the diffusivity of confined fluids in CNTs.  For water at room temperature, the self-diffusion in zigzag CNTs is much slower than that in armchair CNTs at similar pore sizes. Calculation of PESs (potential energy surfaces) indicates that in armchair CNTs water diffuses in a spiral path along the axis of the tube.  However, in zigzag carbon nanotubes more diffusion occurs in the q direction of the tube, and the diffusion along the axis of the tube is slower in zigzag nanotubes compared to armchair nanotubes.  For Lennard-Jones fluids we only see an effect of chirality when the temperature is low enough such that the kinetic energy is not enough to overcome the fluid-wall interaction energy.    

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