Enhancement of the water flow velocity through carbon nanotubes resulting from the radius dependence of the friction due to electron excitations

Secchi et al. [Nature (London) 537, 210 (2016)] observed a large enhancement of the permeability and slip length in carbon nanotubes when the tube radius is of the order of 15 nm, but not in boron nitride nanotubes. It will be pointed out that none of the parameters that appear in the usual molecular dynamics treatments of water flow in carbon nanotubes have a length scale comparable to 15 nm, which could account for the observed flow velocity enhancement. It will be demonstrated here, however, that if the friction force between the water and the tube walls in carbon nanotubes is dominated by friction due to electron excitations in the tube walls, the enhanced flow can be accounted for by a reduction in the contribution to the friction due to electron excitations in the wall, resulting from the dependence of the electron energy band gap on the tube radius.

Figure 1

A plot of $L_s$ versus $R$ based on Eq. (9) with $L_{s0}$ chosen so that $L_s=300\mathrm{nm}$ when $R=15\mathrm{nm}$.

Figure 2

An illustration of the calculation in Eq. (A12).