Electrostatic Screening in Nanotubes: A Tubular Response Function Framework

Abstract

The structure and transport of electrolytes in nanoscale channels are known to be affected by the electronic properties of the confining walls. This influence is particularly pronounced in quasi-one-dimensional nanotubes, where the high surface-to-volume ratio makes the wall the dominant source of electrostatic screening. For instance, ideal metallic tubes suppress long-range Coulomb interactions between ions exponentially. Yet, there exists no generic framework for evaluating electrostatic interactions in tubular confinement. Here, we introduce tubular response functions -- a generalisation of surface response functions that captures how nanotubes with arbitrary electronic properties screen Coulomb interactions. Using this framework, we evaluate the interaction potential of ions confined in a metallic carbon nanotube, treating its electronic properties exactly within a Luttinger liquid model. We demonstrate that the long-range exponential screening characteristic of ideal metals persists in realistic metallic nanotubes, regardless of their electron density. We trace the origin of this perfect screening property to the quantum confinement of electrons along the tube circumference. Our framework opens the way for quantitative descriptions of ionic correlations and charge storage in nanotube-based electrodes, and can be further extended to address confined ion dynamics.