Theory of the Radius Dependence of Water Flow through Carbon and Boron Nitride Nanotubes

Secchi, et. al. observed that the flow velocity of water in carbon nanotubes increases rapidly as the tube radius decreases below 50nm, but they observed that the same flow velocity enhancement with decreasing radius does not occur in boron nitride nanotubes, despite the fact that they have the same crystal structure. Scaling arguments show that in order for such large flow velocity enhancement to occur at such large tube radii compared to the interatomic spacing in the wall and the spacing between water molecules, the diffusion rate of water molecules near the wall would have to be much larger than that found by molecular dynamics for a flat carbon surface, which should be applicable to nanotubes of such large radii. It will be shown that the enhancement of the flow velocity when the radius drops from 50m to 15nm, observed by Secchi, et. al., that occurs in carbon, but not boron nitride, nanotubes can be accounted for (for semiconducting nanotubes) by a reduction in the contribution to the friction from electron excitations in the wall with decreasing radius, resulting from the fact that the electron energy band gap in carbon, but not boron nitride, nanotubes varies from less than to greater than the product of Boltzmann’s constant and the temperature over this radius range.