STATISTICAL DESCRIPTION OF ADSORPTION FROM THE GAS PHASE ON SPHERICAL NANOPARTICLES TAKING INTO ACCOUNT THE SPATIAL RELAXATION OF THE CRYSTAL LATTICE
UDC 531.19; 538.911
Key words: two-level statistical method, variation method, potential of average forces, heterogeneous system, nanoparticle, density field.
For citation: Farafontova E. V. Narkevich I. I. Statistical description of adsorption from the gas phase on spherical nanoparticles taking into account the spatial relaxation of the crystal lattice. Proceedings of BSTU, issue 3, Physics and Mathematics. Informatics, 2022, no. 2 (260), pp. 55–59 (In Russian). DOI: https://doi.org/10.52065/2520-6141-2022-260-2-55-59.
Abstract
In this work, a previously developed method for the variational calculation of the density profile in the vicinity of a spherical crystalline nanoparticle in equilibrium with a gaseous medium is used. Within a two-level statistical method, which is based on the correlative functions Bogolyubov – Born – Green – Kirkwood – Yvon (BBGKI) method, the conditional correlative Rott functions method and the method of thermodynamic density functionals, an expression is obtained for grand thermodynamic potential as a functional of the field density. As a result, the interrelation has been established between the microscopic parameters of a system of interacting particles (atoms or molecules) and the macroscopic characteristics of crystalline nanoparticles in equilibrium with a gaseous environment at a temperature below the triple point temperature.
The radial density profile in the interfacial region is approximated by a three-parameter function containing a hyperbolic tangent. One of the parameters determines the filling numbers for a homogeneous liquid or gaseous medium in equilibrium with the crystalline spherical nanoparticle under study, and the other two are variational parameters in solving the variational problem to find the minimum of grand thermodynamic potential of a heterogeneous system.
The presence of a statistical expression for grand potential as a functional of the density field made it possible to carry out its variation, thus calculate the amount of adsorbed substance on nanoparticles of different sizes and to follow the radial displacement of the FCC lattice sites near their boundaries.
References
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