Packing configurations for methane storage in carbon nanotubes

In this paper we investigate methane packing in single-walled carbon nanotubes. We employ classical applied mathematical modelling using the basic principles of mechanics to exploit the Lennard-Jones potential function and the continuous approximation, which assumes that intermolecular interactions can be approximated by average atomic surface densities. We consider both zigzag and spiral configurations formed by packing methane molecules into (9, 5), (8, 8) and (10, 10) carbon nanotubes, and we derive analytical expressions for the interaction potential energy of these configurations. Our findings indicate that for the zigzag configuration for a (9, 5) tube, the potential energy of the system is minimized when the methane molecules simply form a linear chain along the tube axis, but genuine zigzag patterns are found as the tube size increases such as for the (8, 8) and (10, 10) tubes. For the spiral configuration, the potential energy of the system is minimized when the angular spacing is approximately equal to π for the (9, 5) and (8, 8) tubes, and π/2 for the (10, 10) tube. Overall, our results are in good agreement with molecular dynamics simulations in the literature and show that the most energetically efficient packing configuration of the three tubes studied, occurs for a (10, 10) tube with a zigzag packing, while a (10, 10) tube with a spiral packing configuration has the largest free-cavity volume for methane adsorption at higher temperatures.