Van der Waals interaction between microparticle and uniaxial crystal with application to hydrogen atoms and multiwall carbon nanotubes

Abstract

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.

Comparison of hydrodynamic and Dirac models of dispersion interaction between graphene and H,He∗, or Na atoms

“…As was shown in Refs. [16,29], for the calculation of dispersion forces, the polarizabilities can be represented with sufficient precision in the framework of single-oscillator model…”

“…The second-order perturbation theory was also used [28] to calculate line shifts of a two-level atom interacting with a nanotube. For the multiwalled carbon nanotubes with at least several walls, the concept of dielectric permittivity of graphite was shown to be applicable [29].…”

Thermal correction to the Casimir force, radiative heat transfer, and an experiment

“…(1) and (12) with reflection coefficients (27), (28) and the impedance function (31). Our aim is to find the asymptotic behavior of the free energy and entropy of a fluctuating field at low temperatures at separation distances between two similar plates of a few hundred nanometers, so that the characteristic frequency Ω c belongs to the region of infrared optics.…”

“…Later the main equations of this theory, including the famous Lifshitz formula, were rederived in different formalisms [4,5,6,7] and in particular on the basis of thermal quantum field theory in the Matsubara formulation [8]. The Lifshitz theory was recently used for the interpretation of many experiments on the measurement of the Casimir force [9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24], in the application of the Casimir and van der Waals forces in nanotechnology [25,26,27,28,29], in Bose-Einstein condensation [30,31] and also for the description of radiative heat transfer between two bodies at different temperatures through a vacuum gap [32,33].…”

How to modify the van der Waals and Casimir forces without change of the dielectric permittivity

“…The distance range of dispersion forces extends from several angströms to a few nanometers (the van der Waals regime where the relativistic retardation is not important) and from a few nanometers to a few micrometers (the Casimir regime where the retardation effects contribute more and more as the separation distance increases). The diverse applications of dispersion forces vary from the physics of surface and nanostructures [3,4,5,6,7,8,9,10] to obtaining constraints on the predictions of unification theories of fundamental interactions beyond the Standard Model [11,12,13].…”