The Lifshitz theory of the van der Waals force is extended for the case of an atom (molecule) interacting with a plane surface of an uniaxial crystal or with a long solid cylinder or cylindrical shell made of isotropic material or uniaxial crystal. For a microparticle near a semispace or flat plate made of an uniaxial crystal the exact expressions for the free energy of the van der Waals and Casimir-Polder interaction are presented. An approximate expression for the free energy of microparticle-cylinder interaction is obtained which becomes precise for microparticle-cylinder separations much smaller than cylinder radius. The obtained expressions are used to investigate the van der Waals interaction between hydrogen atoms (molecules) and graphite plates or multiwall carbon nanotubes. To accomplish this the behavior of graphite dielectric permittivities along the imaginary frequency axis is found using the optical data for the complex refractive index of graphite for the ordinary and extraordinary rays. It is shown that the position of hydrogen atoms inside multiwall carbon nanotubes is energetically preferable compared with outside.
The Lifshitz-type formulas describing the free energy and the force of the van der Waals interaction between an atom ͑molecule͒ and a single-walled carbon nanotube are obtained. The single-walled nanotube is considered as a cylindrical sheet carrying a two-dimensional free-electron gas with appropriate boundary conditions on the electromagnetic field. The obtained formulas are used to calculate the van der Waals free energy and force between a hydrogen atom ͑molecule͒ and single-walled carbon nanotubes of different radii. Comparison studies of the van der Waals interaction of hydrogen atoms with single-walled and multiwalled carbon nanotubes show that depending on atom-nanotube separation distance, the idealization of graphite dielectric permittivity is already applicable to nanotubes with only two or three walls.
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.
The general perturbative expression for the lateral Casimir force between two plates covered by longitudinal corrugations of arbitrary shape is obtained. This expression is applicable for corrugation periods larger than the separation distance. The cases of asymmetric corrugations are considered, which allow to increase the maximum to minimum force ratio and affect the character of equilibrium points. This opens new opportunities to control the lateral Casimir forces for use in microelectromechanical devices based entirely on the vacuum fluctuation properties.
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