Ground state and thermal properties of a lattice gas on a cylindrical surface

TL;DR

This paper models adsorption of gases on cylindrical surfaces like nanotubes, analyzing ground state energies, structural transitions, and thermodynamic properties, revealing nonanalytic behaviors and similarities to the 1D Ising model.

Contribution

It introduces a model for lattice gas adsorption on cylindrical surfaces, calculating energies and structures, and explores temperature-dependent thermodynamics with novel insights into commensuration effects.

Findings

Structural transitions depend on cylinder radius R.

Energy and structure are nonanalytic functions of R.

Specific heat shows resemblance to 1D Ising model behavior.

Abstract

Adsorbed gases within, or outside of, carbon nanotubes may be analyzed with an approximate model of adsorption on lattice sites situated on a cylindrical surface. Using this model, the ground state energies of alternative lattice structures are calculated, assuming Lennard-Jones pair interactions between the particles. The resulting energy and equilibrium structure are nonanalytic functions of radius (R) because of commensuration effects associated with the cylindrical geometry. Specifically, as R varies, structural transitions occur between configurations differing in the "ring number", defined as the number of atoms located at a common value of the longitudinal coordinate (z). The thermodynamic behavior of this system is evaluated at finite temperatures, using a Hamiltonian with nearest-neighbor interactions. The resulting specific heat bears a qualitative resemblance to that of the one-dimensional Ising model.