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In the present paper the Euler approach which is generalised for the case of interaction of bodies with deformation is used to describe motions of dimers and unbound fullerenes inside a carbon nanotube. Frequencies and amplitudes of longitudinal vibrations of fullerenes and their dimers inside a CNT are calculated. The conditions under which the energy of rotational motion of a dimer can be transformed into the energy of its translational displacements are determined. This effect has an important application in medicine, specifically, in the sphere of targeted delivery of drugs where a nanotube plays the role of a molecular container.

The research is devoted to the problem of designing materials with an adjustable property of permeability. The obtained tool for property regulation allows achieving hyper-selectivity in relation to separation of helium isotope mixtures, as well as some other gas mixtures. The reasearch is theoretical in nature; however, it suggests a clear direction of activity for experimenters. The result obtained is valid for ultrathin barriers of any form. As a result, a new exact solution of the Schrödinger equation of wave dynamics, which is valid for the case of two-barrier systems, is found. This solution allows for comprehensive consideration of the process of wave passage through a barrier and identification of the causes leading to super-permeability of individual components.

An analytical solution to the problem of wave transport of matter through composite hyper-fine barriers is constructed. It is shown that, for a composite membrane consisting of two identical ultra-thin layers, there are always distances between the layers at which the resonant passage of one of the components is realized. Resonance makes it possible to separate de Broiler waves of particles with the same properties, which differ only in masses. Broad bands of hyper-selective separation of a hydrogen isotope mixture are found at the temperature of 40 K.

In this paper, the question about the use of wave dynamics for solving problems of membrane separation of helium isotopes in the gas state at cryogenic temperatures is considered. The dimensionless form of the stationary Schrödinger differential equation is obtained. Following that, the integral representation form of the wave function is written. This form, which is equivalent to the classical equation, is similar to the integral equation with a degenerate core; however, it contains a modulus of the argument with a shift along the real axis. Using the shift operator, the existing exponential function in the Schrödinger integral equation can be split into a differential operator and an exponential function of the argument module which does not contain a shift. The Fourier identity allows reducing the exponent of the modulus of the argument to a regular exponent. Next, based on the general property of a differential operator acting on an exponent, it is possible to calculate the spectral functions of the problem and write down the distribution for the wave function. This distribution is ultimately expressed through the spectra of the potential barrier. Thereafter, the structure and the spectrum of the composite barrier are considered. With the expression determining the reflection coefficient, it is found that the double-barrier system can have a resonant passage of one of the components in the sequence of distances between the layers of the membrane.

The present paper deals with permeability of the low-temperature phase of a fullerite using molecular dynamics methods. A discrete model of the material based on “atom−atom” interactions between penetrating components and nodes of the fullerene crystal structure is considered. For the purpose of saving calculation time, when collecting statistical data on passage of molecules and atoms through the porous material under consideration, we found a centrally symmetric distribution of the fullerene action energy and constructed a model of the material based on “smoothed” fullerene particles. The calculations determined permeability of a fullerite membrane containing up to ten planar lattices of the crystal structure. The selectivity factor of the considered membrane, with respect to other components of natural gas is also determined.