Theory of friction for periodic water structures moving through a subnanometer carbon nanotube

In this paper, we provide a theoretical framework for understanding the friction of water flowing in carbon nanotubes with diameters of the order of a nanometer. Molecular dynamics simulations show that under such circumstances, water forms one-dimensional water wires or hollowed cylindrical periodic structures. Since these structures are likely incommensurate with the nanotube, they exhibit very low friction, analogous to "superlubricity" in solids. We calculate the sliding friction arising from phonon excitation in nanotubes and in water structures, and show that it scales linearly with the sliding velocity, and the interfacial friction coefficient is consistent with the results of the molecular simulations. Next, we consider the existence of defects in the water structures and show that they give rise to a nonviscous friction. Using a Langevin equation, we show how our model can account for the water flow measured in experiments for extremely narrow carbon nanotubes.