STATISTICAL DESCRIPTION OF ADSORPTION ON SPHERICAL NANOPARTICLES FROM THEIR DIMENSIONS AND TEMPERATURE

UDC 531.19;538.911

 

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 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

Yazenok Valeria Andreevna – student. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus).

 

DOI: https://doi.org/ 10.52065/2520-6141-2023-272-2-8 (In Russian).

 

Key words: two-level statistical method, nanoparticle, density field, variation method, heterogeneous system, adsorption on nanoparticles.

 

For citation: Farafontova E. V. Narkevich I. I., Yazenok V. A. Statistical description of adsorption on spherical nanoparticles from their dimensions and temperature. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2023, no. 2 (272), pp. 47–52. DOI: 10.52065/2520-6141-2023-272-2-8 (In Russian).

Abstract

For a statistical description of the of adsorption dependence from the gas phase on the temperature and dimensions of spherical nanoparticles, is used the previously obtained closed system of integral and algebraic equations, which describes the structural and thermodynamic characteristics of unhomogeneous (heterogeneous) molecular systems. It was obtained in with of a two-level statistical method, which is based on the joint use of the Bogolyubov – Born – Green – Kirkwood – Yvon (BBGKI) correlative functions method, the Rott conditional correlative functions method and the thermodynamic density functionals method. As a result, a relationship has been established between the macroscopic characteristics of crystalline nanoparticles and the microscopic parameters of a system of interacting particles (atoms or molecules) at temperatures below the triple point temperature. In the region of the “crystalline nanoparticle – gaseous medium” phase transition, the radial density profile is approximated using a three-parameter function containing a hyperbolic tangent. One parameter determines the occupation numbers for a homogeneous liquid or gaseous medium, which is in equilibrium with a crystalline spherical nanoparticle, and the other two are variational parameters in solving the variational problem of finding the large thermodynamic potential minimum of a heterogeneous system. The two-level statistical method made it possible to obtain an expression for a large thermodynamic potential, which is a functional of the desired density field. As a result of varying this potential, calculations were made for the amount of adsorbed substance from the gas phase on nanoparticles of different sizes, it was possible to follow the radial displacement of the fcc-lattice sites near their boundaries, and proceed to describe the dependence of adsorption from the gas phase on temperature.

 

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References

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20.04.2023