STATISTICAL RESEARCH OF MOLECULAR SYSTEM PHASE DIAGRAM FORM IN THE CRITICAL POINT NEIGHBOURHOOD

UDC 531.19;538.911

Narkevich Ivan Ivanovich − DSc (Physics and Mathematics), Professor, Professor, the Department of Physics. Belarusian State Technological University (13a Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: narkevich@belstu.by

Farafontova Elena Valer’yevna − PhD (Physics and Mathematics), Assistant Professor, the Department of Physics. Belarusian State Technological University (13a Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: farafontova @belstu.by

Narkevich Grigoriy Eduardovich – student. Moscow Institute of Physics and Technology (9 Institutsky lane, 1417016, Dolgoprudny, Moscow reg., Russia).

DOI: https://doi.org/ 10.52065/2520-6141-2025-290-5.

Key words: two-level statistical method, density fluctuation in nanoparticles, phase diagrams, critical point, critical indices.

For citation: Narkevich I. I., Farafontova E. V., Narkevich G. E. Statistical research of molecular system phase diagram form in the critical point neighbourhood. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2025, no. 1 (290), pp. 26–30 (In Russian). DOI: 10.52065/2520-6141-2025-290-5.

Abstract

Previously, the first steps were taken to practically implement the idea of the fundamental possibility of an abbreviated description of density field fluctuations using the introduced chain of correlative functions for an ensemble of interacting elementary density fluctuations (EDF). With a certain probability, they appear and disappear randomly against the background of a homogeneous macroscopic system with given thermodynamic parameters and therefore they can be considered as quasiparticles. Their correlative functions are introduced in the same way as was done for a system of real particles (atoms or molecules) in the well-known Bogolyubov – Born – Green – Kirkwood – Yvon (BBGKY) method. As potentials of interaction of EDFs with a homogeneous medium (without taking into account fluctuations) and among themselves, this work uses the formation energies of single and paired (binary) EDFs. Specific numerical calculations were performed for a simple molecular system with Lennard-Jones interparticle interaction, which is a spherical nanoparticle located in a thermostat with given thermodynamic parameters (temperature and chemical potential). That is why to statistically describe such a system, a large thermodynamic potential is used, which is a functional of the density field in the presence of an EDF in the volume of the system. As known, the contribution of thermal fluctuations to the thermodynamic characteristics of equilibrium systems appears significant near the phase transition lines. Moreover, these contributions are most significant in the vicinity of the liquid-gas critical point in molecular systems, which leads to power laws of the system characteristics described by critical indices. In particular, this is connected with the shape of the phase diagram in a close neighborhood of the critical point. In this connection, taking into account the extreme properties of the large thermodynamic potential, theoretical phase diagrams temperaturedensity and pressure-density in the entire interval of the liquid-gas phase transition have been built in this work with the help of the two-level statistical method. The calculations were performed with relative error no more than 2% to localize the critical point and determine the critical parameters: temperature, pressure, and density.

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References

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30.12.2024