The figure on the right shows a snapshot from the simulation of O₂ transport through an opened, hydrogen-terminated, (10,0) single-walled nanotube. Graphite sheets are set up at the right and left ends of the gas reservoir. The graphite sheet at the interface of the gas reservoir and the nanotube is open.

      Periodic boundary conditions are applied to the directions perpendicular to the nanotube axis.

      It is found from the figure on the left that the rate of transport of the O₂ molecules entering the nanotube from the gas reservoir does not depend on the helical symmetry of the nanotube, but does strongly depend on its pore size. Up to 50 ps, the molecular densities in the various nanotubes increase at almost the same rate.

      In this study, the transport of the gas molecules down nanotubes that are about 100 Å for 400 ps can be classified into 3 stages.

      In the first stage, gas molecules enter the nanotube and move down its axis. To enter the nanotube, a molecule must have a larger net repulsive force between the gas molecule and the other gas molecules in the gas reservoir than a net repulsive force between the gas molecule and nanotube tip atoms, or have enough kinetic energy to allow decelerated molecules to keep moving into the nanotube. This stage is dominated by non-equilibrium transport.

      When the molecule reaches the nanotube end closest to posterior region, the molecule is affected by strong attractive van der Waals interactions with the nanotube atoms. As the diameter of the nanotube decreases, this attractive interaction increases because more nanotube tip atoms can get close to the molecule. The gas molecule that cannot overcome the attractive force changes its direction of motion and moves backwards into the nanotube.

      The second stage of transport is dominated by chaotic flow, as some molecules in the nanotubes move towards the posterior region, and some molecules move towards the gas reservoir. The molecules moving forward and backward disturb the movements of the molecules that are just entering the nanotube by colliding with them, which initiates molecular "bouncing" motions inside the nanotube.

      As the simulation progresses, molecules continuously enter the nanotube from the gas reservoir moving towards the posterior region. The buildup of molecular density in the nanotube overcomes the molecular attraction with the nanotube and forces molecules that are within the nanotube and near the posterior region to exit. This is the third stage, which is characterized by near steady-state transport of molecules from the gas reservoir, into the nanotube, and out to the posterior region. In this stage there is still some molecular motion in the opposite direction, but it is much less dominant than it was in the second stage and the molecular motion is consequently significantly less chaotic. The movie on the right shows the change from the first to third stage.

      An equilibrium-state system consists of an opened, hydrogen-terminated nanotube in a self-contained, three-dimensional "box" that is filled with oxygen molecules.

      Figures on the right are projection views of equilibrium transport systems consisting of a 107 Å long (10,0), (14,0), and (17,0) opened CNTs at 500 ps. O₂ molecules are separated from the nanotube by about 3.5 Å both inside and outside the (10,0) nanotube. The projection view for a (14,0) nanotube shows O₂ molecules in the nanotube form a ring. Although the molecules in the (14,0) nanotube occupy more space as the nanotube diameter is increased by 1.6 Å, the wall-O₂ distance is slightly decreased by 0.2 Å, and standard deviation is still small. For a larger (17,0) nanotube, the spatial distribution of O₂ molecules changes to a different pattern. Some O₂ molecules are located at the center of the nanotube, and they look separated from the other molecules that still form a layer apart from the wall.

      If the molecular structure is spherical, molecular transport behavior can be clearly distinguished as either normal-mode or single-file mode in time scales of about 100 ps. For methane, no changes in diffusion mode and minimal changes in diffusion coefficient are predicted as a function of the helical symmetry of the nanotube.

      If the molecular shape is asymmetrical, transition-mode diffusion occurs when molecules are able to pass each other if they are perfectly aligned parallel to the nanotube axis, but are not able to pass each other if they have undergone small-angle rotational motion during transport. In this case, molecules can pass each other some of the time but not at other times. For ethane and ethylene, molecular transport is predicted to follow a spiral path around the circumference of the nanotube that matches the helical symmetry of the system. This only occurs for nanotubes with diameters between 16 and 22 Å at very low molecular concentrations. The driving force is the strong interaction energy between C-C molecular and nanotube wall bonds; nanotubes try to continue this alignment as the molecules move through the nanotube.