V. M. Mostepanenko

Force dependences for the definition of the atomic force microscopy spatial resolution

Abstract An approximate method of calculation is suggested by means of which the force and the spatial AFM resolution are derived as a function of the distance between a sample and a top. The measurements of these values are carried out with the help of the AFM model and a good coincidence of the theory with experiments is demonstrated.

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

The Lifshitz theory of the van der Waals force is 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. For a microparticle near a semispace or flat plate made of a 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 the 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.

Measuring the Casimir force gradient from graphene on a SiO 2 substrate

The gradient of the Casimir force between a Si-SiO

The Casimir effect leads to new restrictions on long-range force constants

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Thermal Casimir effect in the interaction of graphene with dielectrics and metals

-graphene substrate and an Au-coated sphere is measured by means of a dynamic atomic force microscope operated in the frequency shift technique. It is shown that the presence of graphene leads to up to 9% increase in the force gradient at the shortest separation considered. This is in qualitative agreement with the predictions of an additive theory using the Dirac model of graphene.

van der Waals interaction between a microparticle and a single-walled carbon nanotube

Restrictions on constants of potentials of l/rn type resulting from measuring Casimir forces between a plane plate and a spherical lens are discussed. With n = 2, 3 these restrictions are shown to be much stronger than those resulting from other experiments. A new restriction on the electron-arion coupling constant xe < 60 has been obtained.

The Casimir force between plates with small deviations from plane parallel geometry

We investigate the thermal Casimir interaction of a suspended graphene described by the Dirac model with a plate made of dielectric or metallic materials. The reflection coefficients on graphene expressed in terms of a temperature-dependent polarization tensor are used. We demonstrate that for a graphene with nonzero mass gap parameter the Casimir free energy remains nearly constant (and the thermal correction negligibly small) over some temperature interval. For the interaction of graphene with metallic plate, the free energy is nearly the same, irrespective of whether the metal is nonmagnetic or magnetic and whether it is described using the Drude- or plasma-model approaches. The free energy computed using the Dirac model was compared with that computed using the hydrodynamic model of graphene and big differences accessible for experimental observation have been found. For dielectric and nonmagnetic metallic plates described by the Drude model these differences vanish with increasing temperature (separation). However, for nonmagnetic metals described by the plasma model and for magnetic metals, a severe dependence on the chosen theoretical description of graphene remains even at high temperature. In all cases the analytic asymptotic expressions for the free energy at high temperature are obtained and found in a very good agreement with the results of numerical computations.

Theory of the Casimir interaction from graphene-coated substrates using the polarization tensor and comparison with experiment

The Lifshitz-type formulas describing the free energy and the force of the van der Waals interaction between an atom (molecule) 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 (molecule) 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.

Corrections to the Casimir force between plates with stochastic surfaces

We present a general calculation of the corrections to the Casimir force between plates with small deviations from plane parallel geometry of the arbitrary type. These corrections are considered up to the fourth order with respect to the relative amplitudes of the deviations. The developed formalism is applied to the cases of nonparallel plates and of large scale as well as short scale deformations of the surfaces of different types. A number of particular examples are explicitly calculated. The method used is the previously developed method of additive summation of the Casimir force potentials with a subsequent renormalization. The results obtained by this method are tested by comparison with the results from the Green function method. A special investigation is performed into the role of mixed terms in the expansion with respect to the deviation amplitudes resulting from different plates. It is shown that such contributions are present already in the first nonvanishing correction to the Casimir force, so that this correction is nonadditive.

On the strengthening of restrictions on hypothetical Yukawa-type forces with extremely small range of action

We propose a theory of the thermal Casimir interaction for multilayered test bodies coated with a graphene sheet. The reflection coefficients on such structures are expressed in terms of the components of the polarization tensor and the dielectric permittivities of material layers. The developed theory is applied to calculate the gradient of the Casimir force between an Au-coated sphere and a graphene sheet deposited on a SiO