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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.

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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 work, mathematical modeling of relative dynamics of a bifullerene complex is carried out on the assumption that the inner shell does not form covalent bonds with an outer carbon skeleton. This fact enables free angular movements of the inner shell. In particular, the directed rotation of the inner fullerene can be provided. This, in turn, allows for accumulating of a significant fraction of kinetic energy at internal degrees of freedom of the complex under consideration. In this case, the direction of rotations is not related to temperature; the outer shell of the complex restrains the transfer of the stored energy into thermal vibrations. Therefore, calculations are performed to estimate the stability of the rotational motion of an encapsulated fullerene relative to translational displacements of the outer shell. The calculations are carried out using a separate description of the dynamics of closed carbon molecules in terms of translational and rotational displacements. Translational displacements are determined using the equations of motion for the centers of mass of molecules. Rotational displacements are found on the basis of the dynamic Euler equations. The power centers in the considered framework structures of the molecules are carbon atoms. Therefore, the strength characteristics of intermolecular interactions are obtained in accordance with an atom-atom approach. In this case, the interaction parameters of individual atoms correspond to the case when these atoms are located in a structure of the surface carbon crystal.