Modeling on ion rejection using membranes comprising ultra-small radii carbon nanotubes

In this paper, we investigate the complete ion rejection using carbon nanotube membranes comprising ultra-small radii nanotubes. Three acceptance radii for a water molecule, a sodium ion and a chloride ion are determined assuming the continuous approximation. Given the acceptance radii, we may confine the scope of the nanotube radius so that only water molecules can pass through but the heavier sodium and chloride ions are repulsed from the nanotube ends. We assume that the collective motion of water molecules inside a sufficiently long nanotube is driven by atomic vibrations so that classical phonon theory might be used to deduce the average water transit time inside the nanotube for ion rejection. We predict that for carbon nanotube membranes comprising nanotubes of radii lying between 3.4 and 3.9 angstrom, only water molecules will pass through, and sodium and chloride ions will not, which together using phonon theory, we deduce that the smaller the nanotube radius, the lower the average water transit time and the higher the efficiency of the membrane for ion rejection purposes. The present theoretical approach has the merit of rapid computational times and indicates those nanotube radii where future experimental work might be focussed.