(208c) Crossover from Fickian to Single-File Diffusion of Fluids Confined In Carbon Nanotubes

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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Srivastava, Phys. Rev. Lett. 91, 235901(2003).

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