Modelling carbon nanocones for selective filter

This paper investigates the potential use of carbon nanocones as selective filtration devices. Using a continuum approach and the Lennard-Jones potential, we determine the energy of truncated carbon nanocones interacting with ions (Na+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{+}$$\end{document} and Cl-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{-}$$\end{document}) and water molecules. The Verlet algorithm is adopted to determine the dynamics of the ions and the water molecules as a result of the interaction with the nanocones. The acceptance energy is derived to determine the minimum and critical radii of the truncated nanocones that block the ions and allow only water molecules to pass through. Our results show that the channel with apex angle of 19.2∘\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$19.2^{\circ}$$\end{document} and opening radius in the range 3.368–3.528 Å gives highest suction energy.