A mechanical model for single-file transport of water through carbon nanotube membranes

Carbon nanotubes can be embedded into a polymer matrix to manufacture nanotube membranes generating rapid water transport. In particular, for nanotubes of small radii, the single-file transport of water diffusing rapidly and concertedly through densely filled carbon nanotubes has been reported. In this paper, we provide an additional methodology to investigate such problems by employing both applied mathematical modelling and classical phonon theory. Our approach has the merit of giving rise to rapid computational times in comparison to the molecular dynamics simulations approach. The total energy of a water molecule inside a carbon nanotube can be determined analytically using point-point interactions and the continuous approximation. In addition, we may use classical phonon theory for the collective motion of water molecules inside the nanotube to formulate the basic equations of motion for water diffusing through a carbon nanotube. Upon making a 'sufficiently long' hypothesis, the average water flow time can be deduced analytically. Furthermore, we incorporate external forces at the tube ends and show that water is virtually incompressible for external forces up to 3 pN. We also determine the variation of the water flow time under random fluctuations in the presence of the external forces and find that the random effect diminishes as the external force increases. This outcome could open up a precise engineering approach for using such nanotube membranes in numerous applications. (C) 2011 Elsevier B.V. All rights reserved.