TWO-LEVEL STATISTICAL DESCRIPTION OF THE STRUCTURE OF HOMOGENEOUS MACROSCOPIC SYSTEMS AND OF SPHERICAL CRYSTALLINE NANOPARTICLES

摘要

A two-level molecular-statistical approach is used to describe the structure and thermodynamic characteristics of equilibrium of homogeneous and heterogeneous systems. It is based on the joint application of Bogolyubov's method of correlative functions (BBGKI), Rott's method of conditional distributions, and of the method of thermodynamic potentials, which in the case of inhomogeneous systems are functionals of the medium field density. With successive implementation of the two-level approach, approximate analytical expressions are obtained for the average singleparticle potential of interaction of the selected condensed medium molecule with the remaining molecules statistically distributed in cells, whose centers form a corresponding crystalline lattice-a regular one for homogeneous and irregular for inhomogeneous macroscopic systems and systems of a small number of atoms or molecules (clusters), the representatives of which are nanoparticles. These potentials are used as convenient approximate expressions for the potentials of average forces of the two-level approach. As a result, the single-particle distribution functions of molecules of the homogeneous macroscopic crystal with a face-centered cubic (FCC) lattice, as well as for a nanoparticle consisting of 13 molecules in the form of an icosahedron and nanoparticles of different sizes with a FCC lattice.