Casimir-Polder interaction between an atom and a cylinder with application to nanosystems

Recently the Lifshitz theory of dispersion forces was extended for the case of an atom (molecule) interacting with a plane surface of a uniaxial crystal or with a long solid cylinder or cylindrical shell made of isotropic material or uniaxial crystal. The obtained results are applicable to nanosystems. In particular, we investigate the Casimir-Polder interaction between hydrogen atoms (molecules) and multi-wall carbon nanotubes. It is demonstrated that the hydrogen atoms located inside multiwall carbon nanotubes have a lower free energy compared to those located outside. We also perform comparison studies of the interaction of hydrogen atoms between themselves and with multi-wall carbon nanotube. The obtained results are important for the problem of hydrogen storage. PACS numbers: 73.22.-f, 12.20.Ds, 34.50.Dy, 34.20.Cf In the last few years, carbon nanotubes and other nanostructures attracted much attention in connection with the problem of hydrogen storage (see Refs. [1, 2] for a review). Many important properties of carbon nanotubes are determined by the van der Waals and Casimir-Polder interactions. In particular, the Casimir-Polder forces acting between hydrogen atoms or molecules and carbon nanotubes play the main role in absorption phenomena. However, for a long time they were practically unexplored. Recently, modern methods using density functional theory, quantum molecular dynamics and Monte Carlo simulations were applied to investigate the interaction of hydrogen atoms and molecules with single-wall nanotubes [3–6] and fullerenes [7, 8]. Multi-wall carbon nanotubes with sufficiently many layers can be modeled by a graphite cylindrical shell of some length L, external radius R ≪ L, and thickness d < R. In this case the crystal optical axis z is perpendicular to the surface of the shell formed by the hexagonal layers of a graphite lattice and the material of the shell is described by the dielectric permittivities εx(ω) = εy(ω) and εz(ω). In Ref. [9] the Lifshitz formula for the Casimir-Polder interaction between an atom and a semispace made of isotropic material [10, 11] was generalized for the cases when a semispace is replaced by a plate of finite thickness made of a uniaxial crystal or by Casimir-Polder interaction between an atom and a cylinder 2 a cylindrical shell made of the same material. In this paper we apply the obtained Lifshitz-type formulas to describe the Casimir-Polder interaction of hydrogen atoms and molecules with multi-wall carbon nanotubes. In the case of atom or molecule with a dynamic polarizability α(ω) at separation a from a plane surface of a plate made of a uniaxial crystal at temperature T at thermal equilibrium, the free energy of the Casimir-Polder interaction is given by [9] F(a, T ) = −B 8a {