Transport of ions in hydrophobic nanotubes

Abstract

The theory of electrokinetic ion transport in cylindrical channels of a fixed surface charge density is revisited. Attention is focused on the impact of the hydrophobic slippage and mobility of adsorbed surface charges. We formulate generalized Onsager relations for a cylinder of an arbitrary radius and then derive exact expressions for the mean electro-osmotic mobility and conductivity. To employ these expressions, we perform additional electrostatic calculations with a special focus on the non-linear electrostatic effects. Our theory provides a simple explanation of a giant enhancement of the electrokinetic mobility and conductivity of hydrophobic nanotubes by highlighting the role of appropriate electrostatic and hydrodynamic length scales and their ratios. We also propose a novel interpretation of zeta potentials of cylindrical channels.