The work is devoted to the study of gyroscopic phenomena in the interaction of a rotating fullerene molecule and a xenon atom incident on it. The methods of classical molecular physics are used: intermolecular potentials, Newton's equations for describing the motion of particles, and the Runge–Kutta numerical method of high order of accuracy. A mathematical model is constructed and implemented for the rotation frequencies of fullerene up to 1014 Hz and the speed of the incident xenon atom of the order of 103 m s−1. For such parameters of the problem, the de Broglie wavelength of the incident atom and the fullerene molecule become smaller than the diameter of the carbon atomic nucleus. This made it possible to apply the Newtonian approach without involving quantum mechanics. The aim of this work is the consistent application of the apparatus of classical mechanics to reveal the effect of the precession of rotating fullerene inside fullerite.
The present paper describes rotations of C60 fullerene molecules in the solid phase of a fullerite. The conducted studies show that these relatively large molecules rotate according to the same laws as macroscopic bodies, i.e., according to the laws of classical mechanics. The performed calculations confirm that fullerene rotations do not cause friction. We suggest a method for a strong increase in the internal energy of the material that does not lead to its destruction. It is theoretically shown that in standard fullerite, in the absence of electric and magnetic fields, fullerene rotations occur with an average angular frequency of 0.34·× 1012 rad·s−1, which is consistent with the experimental data obtained using nuclear magnetic resonance. By means of calculations, we found that alternating magnetic fields of a certain configuration wind fullerenes encapsulated by iron. In this case, two temperatures arise in the fullerite crystal: a high rotational temperature and a vibrational temperature close to normal. For the purpose of determining this velocity, as well as the nature of rotations, the present paper suggests a way of integrating the dynamic Euler equations for the projections of a molecule’s angular velocity vector onto the coordinate axes associated with the fullerene. The stages of computer simulation of fullerene movements, which was carried out without using previously developed packages of molecular-dynamic modelling, are consistently described.
A modification of the Lennard-Jones potential allowed us, via integration over the volume of the bodies of different shapes, to determine the integral action (potential energy barrier) generated by the distributed force centers. The body generating the potential barrier was a carbon plate and the test particles overcoming this barrier were atoms or molecules of a number of gases (hydrogen, helium and methane). When considering the transit of particles (gas atoms or molecules) over this barrier, use was made of the energy barrier wave theory and the potential of a continuous body was used as a barrier. In so doing, the Schrödinger equation was integrated numerically for the molecular density. This integration yielded the expected wave pattern of the process of transit and reflection of the molecules, so a phase averaging procedure had to be applied. By varying the parameters of the layer containing force centers -field sources, the dimensions and density of the carbon plate possessing high selectivity towards separation of gas mixture containing helium, hydrogen and methane were determined. The data obtained provide an interpretation of the sorption properties of barrier carbon systems capable of filtering or separating gases.
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