Noble gas encapsulation into carbon nanotubes: predictions from analytical model and DFT studies

The energetics for the interaction of the noble gas atoms with the carbon nanotubes (CNTs) are investigated using an analytical model and density functional theory calculations. Encapsulation of the noble gas atoms, He, Ne, Ar, Kr, and Xe into CNTs of various chiralities is studied in detail using an analytical model, developed earlier by Hill and co-workers. The constrained motion of the noble gas atoms along the axes of the CNTs as well as the off-axis motion are discussed. Analyses of the forces, interaction energies, acceptance and suction energies for the encapsulation enable us to predict the optimal CNTs that can encapsulate each of the noble gas atoms. We find that CNTs of radii 2.98 - 4.20 Å (chiral indices, (5,4), (6,4), (9,1), (6,6), and (9,3)) can efficiently encapsulate the He, Ne, Ar, Kr, and Xe atoms, respectively. Endohedral adsorption of all the noble gas atoms is preferred over exohedral adsorption on various CNTs. The results obtained using the analytical model are subsequently compared with the calculations performed with the dispersion-including density functional theory at the M06 - 2X level using a triple-zeta basis set and good qualitative agreement is found. The analytical model is however found to be computationally cheap as the equations can be numerically programmed and the results obtained in comparatively very less time.